**TCAS II CHANGE PROPOSAL (CP)**

  ----------- ---- --- ---- --- ---- ------------------------------------- ---------
  **DATE:**   03   /   29   /   99   **No.:**                              **98**

  ----------- ---- --- ---- --- ---- ------------------------------------- ---------

  ------------------- ----------------- ---- -------------------- --------
  **TCAS II           **DO-185A (v7)**  X    **Other (Specify)**  
  Version:**                                                      

  ------------------- ----------------- ---- -------------------- --------

  ---------------------- ------------------ ---- -------------- ---- --------- ----
  **MOPS Function        **Surveillance**        **Display           **CRS**   X
  Area:**                                        Req'ts**                      

  ---------------------- ------------------ ---- -------------- ---- --------- ----

  ---------------------- ----------------- ---- ----------- ---- ----------- ----
                         **CAS             X    **Test           **Other**   
                         Pseudocode**           Suites**                     

  ---------------------- ----------------- ---- ----------- ---- ----------- ----

  --------------- ------------- ----- --------------- ----- -------------- -----
  **Priority:**   **URGENT**    X     **Necessary**         **Optional**   

  --------------- ------------- ----- --------------- ----- -------------- -----

  ------------ ----------- ---- ----------------- ---- -------------------- ----
  **CP Type:** **ERROR**   X    **Enhancement**        **Evaluation         
                                                       Request**            

  ------------ ----------- ---- ----------------- ---- -------------------- ----

  ------------ --------- ---- ------------------ ---- ----------------- ----
                              **Editorial             **Editorial       
                              (Logic)**               (Text)**          

  ------------ --------- ---- ------------------ ---- ----------------- ----

**Description of Problem/Issue:**

During TCAS flight testing nuisance failures of the barometric altitude
credibility monitor have been observed. They have occurred during
vertical rate maneuvers approaching 1g in acceleration. This is in
excess of the standard RA maneuver that Air Transport category aircraft
are likely perform. However, it is not unlikely that business jets and
military aircraft with TCAS would perform maneuvers such as this on a
regular basis.

Discussion with Mitre indicates that the baro altitude credibility
monitor was designed to handle approximately ½ g accelerations maximum.

It is believed that if not corrected this monitor design will result in
regular occurrences of TCAS system failures during climbout and during
resolution advisories where the pilot responds aggressively.

**Proposed Resolution:**

Intruder altitude tracking was affected similarly.

Constants only changed in Pcode and CRS. Changes attached.

Three new tests, EN04TS49.dat, EN03TS79.dat, and EN03TS80.dat, were
produced to cover the CRS transitions 3.92-C2, 3.98-C2, and 3.57-C1,
respectively. The RWG verified that the tests do, in fact, cover these
transitions. TSIM was updated with the constant modifications and used
to produce an updated set of expected outputs and transition files for
all existing tests. The updated expected outputs were successfully
compared to the outputs generated by several of the TCAS manufacturer's
implementations.

  --------------------- -------------------------------------------------
  **Requester:**        Aaron Reinholz

  --------------------- -------------------------------------------------

  --------------------- -------------------------------------------------
  **Organization:**     Rockwell Collins

  --------------------- -------------------------------------------------

**DISPOSITION OF CHANGE PROPOSAL (Per RWG):**

  ------------------------------------- ----- --- ---------- ---- ----------
  **DATE OF DISPOSITION**               8     /   Apr        /    1999

  ------------------------------------- ----- --- ---------- ---- ----------

  -------------- ----- --- -------------- ----- --- --------------- --- --- --- --- --- --------
  **Rejected**             **Deferred**             **\[Review          /       /       **\]**
                                                    Date:**                             

  -------------- ----- --- -------------- ----- --- --------------- --- --- --- --- --- --------

  -------------- ------- --- -------------- ------ --- --------------- ------
  **Accepted**   X           **Modified**              **Withdrawn**   

  -------------- ------- --- -------------- ------ --- --------------- ------

**DISPOSITION OF CHANGE:**

  -------- --- --------------- --- ------------- --- ---------- --- ------------- --- --- --- --- --- --------
  **On         **Designing**       **Testing**       **Done**   X   **\[Date:**       /       /       **\]**
  Hold**                                                                                              

  -------- --- --------------- --- ------------- --- ---------- --- ------------- --- --- --- --- --- --------

**Final Approval of Changes:**

  ------------------ --------- --- ------- --- -------- ---------------------
  **Signature:**     Kathryn                            
                     W.                                 
                     Ybarra,                            
                     RWG Chair                          

  **Date:**          21        /   Apr     /   1999     
  ------------------ --------- --- ------- --- -------- ---------------------

CRS Changes For Altitude Credibility Modifications

Page 149 -- From Addendum: State Switch_Own_Tracker, Abbreviation
CREDIBLE_INIT_CHECK.

> In line 3, change 35.0 ft to 65.0 ft (CREDZADC) and change 10 to 5
> (MAXSOFT).

Page 151 -- State Own_Tracker_Softness, Figure 2-27 and Description.

> Remove states 2, 6, 7, 8, 9, and 10. Add arrow for default entry state
> to state 5. Remove arrow showing the 4 to 5 transition. Reverse
> direction of arrow from state 5 to the bar connector so that it points
> from the bar connector to state 5 (thus indicating the ANY to 5
> transition as well as the 4 to 5 transition). In line 7 of
> [Note]{.underline}: Description, change "value of 2" to "value of 3".

Page 152 -- State Own_Tracker_Softness, Transition 1.

> Change the state transition from ANY → 10 to ANY → 5.

Page 153 -- State Own_Tracker_Softness, Transition 2.

> Remove the state transitions for 2 → 3, 5 → 6, 6 → 7, 7 → 8, 8 → 9,
> and 9 → 10.

Page 154 -- State Own_Tracker_Softness, Transition 3.

> Remove the state transitions for 3 → 2, 6 → 5, 7 → 6, 8 → 7, 9 → 8,
> and 10 → 9.

Page 409 -- Macro Own_Altitude_Coast.

> In line 1 of Definition, change 35.0 ft to 65.0 ft (CREDZADC). In
> Abbreviation SOFTNESS_FACTOR, remove lines for softness factors 2, and
> 6 through 10 which coorespond to Own_Tracker_Softness states 2, 6, 7,
> 8, 9, and 10.

Page 448 -- Macro VT_Credible_Report(T,DZM,TSTART,TDAT,ZD,QUANT).

> In line 4 of Definition, change 20 ft/s to 30 ft/s and change 8
> ft/s^2^ to 20 ft/s^2^.

Page 654 -- APPENDIX A, CONSTANT DEFINITIONS.

> Change the value of CREDACCDIV from 8.0 ft/s^2^ to 20 ft/s^2^.
>
> Change the value of CREDZADC from 35.0 ft to 65.0 ft.
>
> Change the value of CREDZDERR from 20 ft/s to 30 ft/s.

Page 656 -- From Addendum --APPENDIX A, CONSTANT DEFINITIONS.

> Change the value of MAXSOFT from 10 to 5.

![](media/image1.jpeg){width="6.476388888888889in" height="8.4in"}

![](media/image2.jpeg){width="6.631944444444445in"
height="8.740277777777777in"}

![](media/image3.jpeg){width="6.7131944444444445in" height="8.6in"}

![](media/image4.jpeg){width="6.54375in" height="8.5in"}

![](media/image5.jpeg){width="6.4743055555555555in" height="8.4in"}

![](media/image6.jpeg){width="6.143055555555556in" height="8.0in"}

![](media/image7.jpeg){width="6.550694444444445in" height="8.5in"}

![](media/image8.jpeg){width="6.336805555555555in" height="8.3in"}

![](media/image9.jpeg){width="6.188888888888889in" height="8.0in"}

CONSIDER_INCREASE 6 RESVAR.select_advisory

CONSIDER_REVERSE 8 MACVAR.multiaircraft

CONT_REVERSE 8 MACVAR.multiaircraft

CONVERGE_SEP 8 MACVAR.multiaircraft

CORRECTIVE_CLM 2 G.display

CORRECTIVE_DES 2 G.display

COSB 4 TRACKVAR.horizontal

COV(2,2) 2 ITF.mdf

COV(2,2) 4 TRACKVAR.horizontal

CREDACCDIV2 2 PN.credibility 8 ft/s2

CREDINIT 2 PN.credibility 200 ft/s

CREDMINDT 2 PN.credibility 5.5 s

CREDZADC 2 P.track 35 ft

CREDZDERR 2 PN.credibility 20 ft/s

CREFNO 2 ITF.identity

CREFPTR(100) 2 G.cross_reference

CROSSING 2 TO_DISP_AURL.additional_aural

CROSSING_RA 2 G.broadcast

CROSSTHR 2 P.general 100 ft

CROSSTHRL 2 P.general 100 ft

CUR_SENSE 6 RESVAR.modeling

CURRENT_SENSE 8 MACVAR.multiaircraft

CVC 2 INTENT_TO_THREAT.RA_intent

CVC 3 RCV_VAR.message

DBINS 4 TRACKVAR.vertical

DELAY 6 RESVAR.modeling

DELT 4 TRACKVAR.vertical

DELZ 4 TRACKVAR.vertical

DELZDT 2 PN.no_transition 4 s

MAXSOFT 2 P.track 10

MAXZDINT 2 P.detect 10000 ft/min

MAXZDTIME 2 PN.transition 17 s

MDF_HIT_COUNT 2 ITF.mdf

MEDHISCORE 2 P.traffic 500

MEDLOSCORE 2 P.traffic 300

MEDSCORE 2 P.traffic 400

MID 2 INTENT_TO_THREAT.RA_intent

MID 3 RCV_VAR.message

MIN_NOM_SEP 8 MACVAR.multiaircraft

MIN_PTS_FOR_SWITCH 2 P.track 3

MIN_REV_SEP 8 MACVAR.multiaircraft

MIN_RI_TIME 2 P.model 4 s

MINBINS 2 PN.alpha_beta_tracker 3

MINDRATE 2 P.seladv -- 4400 ft/min

MINFIRM 2 P.eval 2

MININITHFIRM 2 P.mdf 3

MINRVSTIME 2 P.model 10 s

MINSOFT 2 P.track 2

MINTATIME 2 P.traffic 8 s

MINTAU 2 P.delay 0 s

MNSIGDPX 2 P.mdf 0.7

MNVR_SHTDWN_TM 2 P.mdf 10

MODC 2 S.identity

MODC 2 ITF.capability

MODEC_FLAG 4 TRACKVAR.vertical

MODEL_T 2 P.model 9 s

MODEL_ZD 2 P.model 2500 ft/min

MTB 2 INTENT_TO_THREAT.RA_intent

CONSIDER_INCREASE 6 RESVAR.select_advisory

CONSIDER_REVERSE 8 MACVAR.multiaircraft

CONT_REVERSE 8 MACVAR.multiaircraft

CONVERGE_SEP 8 MACVAR.multiaircraft

CORRECTIVE_CLM 2 G.display

CORRECTIVE_DES 2 G.display

COSB 4 TRACKVAR.horizontal

COV(2,2) 2 ITF.mdf

COV(2,2) 4 TRACKVAR.horizontal

CREDACCDIV2 2 PN.credibility 20 ft/s2

CREDINIT 2 PN.credibility 200 ft/s

CREDMINDT 2 PN.credibility 5.5 s

CREDZADC 2 P.track 65 ft

CREDZDERR 2 PN.credibility 30 ft/s

CREFNO 2 ITF.identity

CREFPTR(100) 2 G.cross_reference

CROSSING 2 TO_DISP_AURL.additional_aural

CROSSING_RA 2 G.broadcast

CROSSTHR 2 P.general 100 ft

CROSSTHRL 2 P.general 100 ft

CUR_SENSE 6 RESVAR.modeling

CURRENT_SENSE 8 MACVAR.multiaircraft

CVC 2 INTENT_TO_THREAT.RA_intent

CVC 3 RCV_VAR.message

DBINS 4 TRACKVAR.vertical

DELAY 6 RESVAR.modeling

DELT 4 TRACKVAR.vertical

DELZ 4 TRACKVAR.vertical

DELZDT 2 PN.no_transition 4 s

MAXSOFT 2 P.track 5

MAXZDINT 2 P.detect 10000 ft/min

MAXZDTIME 2 PN.transition 17 s

MDF_HIT_COUNT 2 ITF.mdf

MEDHISCORE 2 P.traffic 500

MEDLOSCORE 2 P.traffic 300

MEDSCORE 2 P.traffic 400

MID 2 INTENT_TO_THREAT.RA_intent

MID 3 RCV_VAR.message

MIN_NOM_SEP 8 MACVAR.multiaircraft

MIN_PTS_FOR_SWITCH 2 P.track 3

MIN_REV_SEP 8 MACVAR.multiaircraft

MIN_RI_TIME 2 P.model 4 s

MINBINS 2 PN.alpha_beta_tracker 3

MINDRATE 2 P.seladv -- 4400 ft/min

MINFIRM 2 P.eval 2

MININITHFIRM 2 P.mdf 3

MINRVSTIME 2 P.model 10 s

MINSOFT 2 P.track 3

MINTATIME 2 P.traffic 8 s

MINTAU 2 P.delay 0 s

MNSIGDPX 2 P.mdf 0.7

MNVR_SHTDWN_TM 2 P.mdf 10

MODC 2 S.identity

MODC 2 ITF.capability

MODEC_FLAG 4 TRACKVAR.vertical

MODEL_T 2 P.model 9 s

MODEL_ZD 2 P.model 2500 ft/min

MTB 2 INTENT_TO_THREAT.RA_intent

Roland Lejeune

31 March 1999

## Proposed Change to the Airdata-Tracker Credibility Window

Rockwell-Collins recently identified an issue with the altitude tracker
used in TCAS II Version 7 to track own aircraft altitude when finely
quantized altitude measurements are available. This tracker is referred
to as the airdata-tracker in the Version 7 pseudocode.

# Issue

During a flight test in which the pilot responded very aggressively to a
Climb RA (post-flight data analysis showed that the vertical
acceleration reached 1.0g for a very short time), the airdata-tracker
declared the altitude measurements "not credible" during the
acceleration. The track was then coasted. The track continued to coast
until the altitudes measurements were re-captured by the credibility
window 19 seconds later.

The MOPS require that TCAS be taken down by the System Performance
Monitor when the own aircraft track is coasted for 5 seconds. Thus, if a
similarly aggressive maneuver was executed by a pilot during an
operational flight, the TCAS function would be terminated. This would
not only result in a serious nuisance, since a TCAS unit taken down by
the System Performance Monitor needs to be pulled off the airplane and
sent to maintenance, but could also raise a safety issue, if the TCAS
function was terminated during an RA.

# Background

Originally, the CAS logic did not include a specific credibility check
for own aircraft altitude. A comment in the pseudocode simply stated
that the credibility of the altitude measurements should be checked
before being passed to the tracker, presumably by the System Performance
Monitoring function. In May 1996, the Requirements Working Group decided
that the credibility check of altitude measurements supplied by the
airdata computer (or other source of finely quantized altitude
measurements) should be performed by the logic itself (altitude tracker)
rather than by the System Performance Monitor. CRF257 was generated to
address this new requirement. However, the specific requirements to
which the credibility check should be designed were left wide open.

A first credibility check intended to capture altitude measurements
corresponding to a vertical acceleration of up to 0.35g was implemented
in the logic. (The largest acceleration assumed by the logic when a
pilot responds to an RA is 0.35g.) Shortly thereafter, the value of one
credibility check parameter (CREDZADC) was slightly increased to improve
the ability of the airdata-tracker to maintain track during short
vertical accelerations of up to 0.5g.

The purpose of the credibility check is to ensure that bad altitude
measurements (i.e., measurements having a measurement error much larger
than that anticipated in the tracker design) will not be passed to the
tracker. Altitude tracks recorded during the TCAS Transition Program and
analyzed by the FAA Technical Center were found to have a few, rare bad
measurements characterized by very larger errors (3,000 to 5,000 ft).
However, comments made by one avionics manufacturer indicated that a
measurement error as small as 300 ft was seen on at least one occasion.
In the absence of further characterization of bad altitude measurements,
the design of the credibility window should thus be aimed at rejecting
bad measurements characterized by measurement errors as small as 300 ft.

# Discussion

A few simulations were performed with the currently specified
credibility window (parameters: CREDZDAC = 35 ft; MINSOFT = 2; MAXSOFT =
10). They confirmed that, with the current credibility window, the
airdata-tracker was capable of maintaining track during accelerations
reaching 0.5g for a short duration (change in vertical rate no greater
than 3,000 fpm) when none of the altitude measurements are bad. However,
the airdata-tracker starts failing to properly maintain track when the
acceleration increases beyond 0.5g, or even when a maximum acceleration
of 0.5g is maintained for more than about 2 seconds (resulting in a
change in the vertical rate larger than 3,000 fpm). Also, the ability of
the current credibility window to capture a good measurement following a
bad one is relatively poor when the bad measurement happens to occur in
the middle of a moderate to large acceleration. In short, these new
performance simulations confirmed that a further widening of the
credibility window was necessary to raise the probability that the track
for own aircraft will be maintained during an aggressive maneuver.

# Analysis

The attached spreadsheet contains a quick analysis of the sizing of the
credibility window. The analysis is based on a worst-case scenario.

In this worst-case scenario, own aircraft initially descends at 6,000
fpm, then, after a short time, reverses its vertical rate with an
acceleration that builds up at the high rate of 8 ft/s^3^ (jerk) to a
maximum acceleration of 40 ft/s^2^ (1.25g). The first 4 columns of the
spreadsheet show the time, acceleration, vertical rate, and altitude for
every second of this short scenario.

The next four columns show the response of an alpha-beta tracker similar
to that specified for the airdata-tracker. Note that in this simple
spreadsheet model, the measurements, which are the same as the true
altitudes, do not include a measurement error.

The column entitled \"residual\" shows the build up of the tracker lag
during the acceleration. The maximum residual (difference between the
measured altitude and the predicted altitude) is 130 ft. To maintain
track during this scenario, the credibility window should thus be sized
so as to accommodate a residual of at least 130 ft. In fact, the
credibility window should be somewhat larger than that in order to
simultaneously accommodate an adequate amount of random measurement
error (or noise). Assuming a worst random measurement error standard
deviation (sigma) of 10 ft and aiming at a 3-sigma margin leads to a
credibility window with a half-width of at least 160 ft.

A credibility window with a half-width of 160 ft will in fact not be
quite sufficient. Indeed, the error in the predicted altitude, which is
one component of the residual, is the result of not only the tracker lag
accumulated during the acceleration but also of the random error in the
tracked vertical rate (which itself is caused by the random measurement
errors on the previous cycles). Increasing the window half-width by
another 20 to 30 ft should accommodate the latter source of error. This
leads to a credibility window with a half-width of about 180 ft to 190
ft.

Note that a credibility window with a half-width of about 180 ft will
accommodate an even large acceleration (\>1.25g) when the standard
deviation of the measurement random error is less than the assumed 10
ft. However, a scenario with an acceleration that is worse than the one
assumed in this analysis is hard to imagine for the simple reason that,
in the physical world, the acceleration itself cannot increase
instantaneously, but needs to be gradually built up (jerk).

In the above scenario, a constant jerk of 0.25g/s has been assumed. Even
with such a large jerk, it takes 5 seconds to reach an acceleration of
1.25g. By the time this acceleration is reached, the accumulated change
in the vertical rate (since the beginning of the acceleration) is
already 4,800 fpm. Keeping the 1.25g acceleration for 1.0 second, then
reducing the acceleration back down to zero with the same 0.25g/s jerk,
results in a total change in the vertical rate of 12,000 fpm. A scenario
worse than that would probably not be credible. In fact, this worst-case
scenario may very well already be somewhat beyond the envelope of what
would be considered an "aggressive" aircraft maneuver in a civilian
airspace.

The next issue to be considered in designing the credibility window is
its ability to capture a good measurement following a bad one. The worst
time for a bad measurement to occur is on the cycle where the residual
would normally be the largest (if the measurement was good). This
happens at time 12 seconds in the worst-case scenario. When the bad
measurement is rejected, the track is coasted (i.e., the vertical rate
estimate is not updated), which causes the tracker lag to increase even
further. In the worst-case scenario, a rejected measurement at time 12
seconds results in a residual equal to 228 ft on the next cycle. Thus,
to ensure with a high probability that a good measurement on that cycle
will be captured by the credibility window, the window half-width should
be at least 228 ft. In reality, a window half-width of about 260 to 270
ft will probably be necessary to accommodate the two sources of
additional random errors discussed above.

Finally, the question of how large the window should be at track
initialization needs to be examined. For this purpose, the following
worst-case scenario is defined. The aircraft has a maximum climb rate of
9,000 fpm when the track is initialized and the second measurement is a
bad one. How wide should the window be to capture the third measurement?
The altitude displacement over 2 seconds at that vertical rate is 300
ft. This suggests that the credibility window half-width should be of
the order of 300 + 1.41\*30 = 340 ft to accommodate the random
measurement errors in the first and third measurements.

How should the current credibility window in the Version 7 pseudocode be
modified? To summarize the above considerations, the credibility window
should have a half-width of about 180 to 190 ft when track softness
(inverse of track firmness) is at its minimum, a half-width of about 260
to 270 ft following one track coast, and a half width of about 340 ft
when softness is at its maximum. These three requirements can be met
with the following credibility window parameters: CREDZADC = 65 ft,
MINSOFT = 3, and MAXSOFT = 5. This combination of parameters results in
a credibility window with a half-width of 195 ft when softness is
minimum, 325 ft when softness is maximum, and 260 ft in-between.

# Testing Requirements

The operation of the airdata-tracker is, for all practical purposes,
independent of the remainder of the CAS logic. The interface between the
airdata-tracker and the remainder of the logic is simple and
straight-forward. The airdata-tracker receives altitude inputs from some
barometric altitude measuring device (airdata computer or gyro),
estimates the altitude and vertical rate of own aircraft on each
tracking cycle, and passes these two estimates to the remainder of the
logic. The airdata-tracker does not receive any input or feedback from
the logic; it does not have multiple modes of operations that depend on
the states of the logic. Thus, a comprehensive type of end-to-end
testing of the proposed change that would involve the entire CAS logic
is not absolutely necessary.

New Safety Study simulations and new Operational Evaluation simulations
are similarly not absolutely necessary in this case. Neither the
scenarios used in the Safety Study simulations nor those used in the
Operational Evaluation simulations have aircraft maneuvering with
accelerations larger than 0.5g. The current airdata-tracker with the
current credibility window tracks such maneuvers without problem.
Therefore, the proposed credibility window change would not affect the
result of these simulations.

Given the above considerations, the following testing was performed.
Simulation-based testing was performed at the module level using the
airdata-tracker (with the proposed credibility window) and a driver
capable of generating quantized altitude measurements that include an
adequate amount of random measurement error (maximum quantization level
= 10 ft; maximum error sigma = 10 ft). Altitude profiles with maximum
accelerations between 0.5g and 1.25g (0.5g, 0.75g, 1.0g, and 1.25g) were
simulated. Simulated accelerations were built up gradually (maximum jerk
= 0.25g/s). For each profile, three cases were simulated. In the first
case, all measurements were good; in the second case, an isolated bad
measurement was introduced at the worst possible time; and in the third
case, two successive bad measurements were introduced starting on a
cycle randomly selected in an interval beginning 8 cycles (seconds)
before the beginning of the acceleration and ending 8 cycles (seconds)
after the end of the acceleration. (Note that this interval is centered
on the period of acceleration and includes the worst possible cycle for
a bad measurement to occur.)

Simulations were performed both for the worst-case scenario used in the
analysis and for a less extreme scenario in which the aircraft is
initially in level flight. Simulations were also performed to test the
initialization performance of the proposed credibility window. The
results of all these simulations are summarized in an attached
spreadsheet. They show that, for the worst-case scenario simulated, the
proposed design was able to maintain track 100% of the time for all
maximum accelerations up to 1.25g when none of the altitude measurements
were bad. They also show that the ability of the tracker to maintain
track when one isolated bad measurement occurs at the worst possible
time or when two successive bad measurements occur at a random time
remains very good for accelerations of less than 1.0g and fairly good
for accelerations of 1.0g or more.

[Note:]{.underline} In this analysis, a track is considered "maintained"
when fewer than 5 successive altitude measurements are rejected by the
credibility window. When testing the ability of the window to capture a
good measurement following two successive bad ones, the first bad
measurement is generated at least 8 cycles prior to the end of the
simulated track to allow sufficient time for determining whether the
track has been maintained or not. The geometry of the simulated
scenarios is such that, when the credibility window rejects the first
good measurement following one or more bad ones, it continues to reject
the following good measurements as well.

The ability of the credibility window to reject bad measurements was
examined as follows. In a first set of simulation runs, bad measurements
were simulated by adding 1,000 ft to the true altitude. Given the size
of the credibility window such bad measurements are always rejected.
Then, the amount of error defining a bad measurement was progressively
reduced and the percentages of tracks maintained throughout were
compared to those obtained when the error defining a bad measurement was
1,000 ft. Identical performance was taken to indicate that all bad
measurements were correctly rejected. Identical performance was obtained
for all acceleration scenarios with the following error magnitudes:

-   one isolated bad measurement: +200 ft and --400 ft,

-   two successive bad measurements: +600 ft and --600ft.

Identical performance was obtained for all initialization scenarios with
the following error magnitudes:

-   one isolated bad measurement: +400 ft and --600 ft,

-   two successive bad measurements: +400 ft and --600ft.

Note that the tracker lag causes the rejection performance of the
credibility window to depend on the sign of the error when one isolated
bad measurement is generated at the worst possible time.

Under much more common operating conditions, when the vertical rate of
own aircraft is constant or when a mild vertical acceleration is taking
place (0.25g or less), the credibility window, which has a half-width of
195 ft when softness is at its minimum and 260 ft after one cycle of
coasting, would reject all isolated bad measurements and all pairs of
successive bad measurements characterized by a positive or negative
error of 300 ft or more. (The maximum tracker lag accumulated during a
sustained 0.25g acceleration is equal to 17 ft.)

<table>
<colgroup>
<col style="width: 4%" />
<col style="width: 2%" />
<col style="width: 3%" />
<col style="width: 1%" />
<col style="width: 2%" />
<col style="width: 6%" />
<col style="width: 0%" />
<col style="width: 2%" />
<col style="width: 0%" />
<col style="width: 6%" />
<col style="width: 0%" />
<col style="width: 0%" />
<col style="width: 2%" />
<col style="width: 7%" />
<col style="width: 0%" />
<col style="width: 0%" />
<col style="width: 1%" />
<col style="width: 1%" />
<col style="width: 6%" />
<col style="width: 0%" />
<col style="width: 1%" />
<col style="width: 2%" />
<col style="width: 0%" />
<col style="width: 2%" />
<col style="width: 4%" />
<col style="width: 0%" />
<col style="width: 0%" />
<col style="width: 2%" />
<col style="width: 0%" />
<col style="width: 2%" />
<col style="width: 4%" />
<col style="width: 0%" />
<col style="width: 0%" />
<col style="width: 2%" />
<col style="width: 1%" />
<col style="width: 2%" />
<col style="width: 4%" />
<col style="width: 0%" />
<col style="width: 3%" />
<col style="width: 10%" />
</colgroup>
<tbody>
<tr class="odd">
<td colspan="18"><strong>Credibility Window Analysis</strong></td>
<td colspan="4"></td>
<td colspan="7"></td>
<td colspan="6"></td>
<td colspan="4"></td>
<td></td>
</tr>
<tr class="even">
<td colspan="3"></td>
<td colspan="3"></td>
<td colspan="5"></td>
<td colspan="5"></td>
<td colspan="4"></td>
<td colspan="6"></td>
<td colspan="7"></td>
<td colspan="5"></td>
<td colspan="2"></td>
</tr>
<tr class="odd">
<td colspan="3"></td>
<td colspan="3"></td>
<td colspan="5"></td>
<td colspan="5"></td>
<td colspan="4"></td>
<td colspan="6"></td>
<td colspan="7"></td>
<td colspan="5"></td>
<td colspan="2"></td>
</tr>
<tr class="even">
<td colspan="9">initial altitude (ft) =</td>
<td>10000</td>
<td colspan="5"></td>
<td colspan="4">alpha =</td>
<td colspan="5">0.58</td>
<td colspan="6"></td>
<td colspan="6"></td>
<td colspan="4"></td>
</tr>
<tr class="odd">
<td colspan="9">initial vertical rate (fpm) =</td>
<td>-6000</td>
<td colspan="5"></td>
<td colspan="4">beta =</td>
<td colspan="5">0.25</td>
<td colspan="6"></td>
<td colspan="6"></td>
<td colspan="4"></td>
</tr>
<tr class="even">
<td colspan="9">max. acceleration (ft/s2) =</td>
<td>40</td>
<td colspan="5"></td>
<td colspan="4"></td>
<td colspan="6"></td>
<td colspan="7"></td>
<td colspan="5"></td>
<td colspan="3"></td>
</tr>
<tr class="odd">
<td colspan="9">max. jerk (ft/s3) =</td>
<td>8</td>
<td colspan="5"></td>
<td colspan="4"></td>
<td colspan="6"></td>
<td colspan="7"></td>
<td colspan="5"></td>
<td colspan="3"></td>
</tr>
<tr class="even">
<td colspan="9">final vertical rate (fpm) =</td>
<td>6000</td>
<td colspan="5"></td>
<td colspan="4"></td>
<td colspan="6"></td>
<td colspan="7"></td>
<td colspan="5"></td>
<td colspan="3"></td>
</tr>
<tr class="odd">
<td colspan="3"></td>
<td colspan="3"></td>
<td colspan="5"></td>
<td colspan="5"></td>
<td colspan="4"></td>
<td colspan="6"></td>
<td colspan="7"></td>
<td colspan="5"></td>
<td colspan="2"></td>
</tr>
<tr class="even">
<td colspan="3"></td>
<td colspan="3"></td>
<td colspan="5"></td>
<td colspan="5"></td>
<td colspan="4"></td>
<td colspan="6"></td>
<td colspan="7"></td>
<td colspan="5"></td>
<td colspan="2"></td>
</tr>
<tr class="odd">
<td colspan="2">time<br />
(s)</td>
<td colspan="3">accel (ft/s2)</td>
<td colspan="3"><p>rate</p>
<p>(ft/s)</p></td>
<td colspan="5"><p>altitude</p>
<p>(ft)</p></td>
<td colspan="4">Residual<br />
(m)</td>
<td colspan="6">z_track<br />
(ft)</td>
<td colspan="5">zd_track<br />
(ft/s)</td>
<td colspan="6">z_predict<br />
(ft)</td>
<td colspan="6"></td>
</tr>
<tr class="even">
<td>0</td>
<td colspan="3">0</td>
<td colspan="3">-100</td>
<td colspan="5">10000</td>
<td colspan="2"></td>
<td colspan="7">10000</td>
<td colspan="6">0</td>
<td colspan="4">10000</td>
<td colspan="9"></td>
</tr>
<tr class="odd">
<td>1</td>
<td colspan="3">0</td>
<td colspan="3">-100</td>
<td colspan="5">9900</td>
<td colspan="2">-100</td>
<td colspan="7">9900</td>
<td colspan="6">-100</td>
<td colspan="4">9800</td>
<td colspan="9"></td>
</tr>
<tr class="even">
<td>2</td>
<td colspan="3">0</td>
<td colspan="3">-100</td>
<td colspan="5">9800</td>
<td colspan="2">0</td>
<td colspan="7">9800</td>
<td colspan="6">-100</td>
<td colspan="4">9700</td>
<td colspan="9"></td>
</tr>
<tr class="odd">
<td>3</td>
<td colspan="3">0</td>
<td colspan="3">-100</td>
<td colspan="5">9700</td>
<td colspan="2">0</td>
<td colspan="7">9700</td>
<td colspan="6">-100</td>
<td colspan="4">9600</td>
<td colspan="9"></td>
</tr>
<tr class="even">
<td>4</td>
<td colspan="3">0</td>
<td colspan="3">-100</td>
<td colspan="5">9600</td>
<td colspan="2">0</td>
<td colspan="7">9600</td>
<td colspan="6">-100</td>
<td colspan="4">9500</td>
<td colspan="9"></td>
</tr>
<tr class="odd">
<td>5</td>
<td colspan="3">0</td>
<td colspan="3">-100</td>
<td colspan="5">9500</td>
<td colspan="2">0</td>
<td colspan="7">9500</td>
<td colspan="6">-100</td>
<td colspan="4">9400</td>
<td colspan="9"></td>
</tr>
<tr class="even">
<td>6</td>
<td colspan="3">0</td>
<td colspan="3">-100</td>
<td colspan="5">9404</td>
<td colspan="2">4</td>
<td colspan="7">9402</td>
<td colspan="6">-99</td>
<td colspan="4">9303</td>
<td colspan="9"></td>
</tr>
<tr class="odd">
<td>7</td>
<td colspan="3">8</td>
<td colspan="3">-92</td>
<td colspan="5">9320</td>
<td colspan="2">17</td>
<td colspan="7">9313</td>
<td colspan="6">-95</td>
<td colspan="4">9218</td>
<td colspan="9"></td>
</tr>
<tr class="even">
<td>8</td>
<td colspan="3">16</td>
<td colspan="3">-76</td>
<td colspan="5">9256</td>
<td colspan="2">38</td>
<td colspan="7">9240</td>
<td colspan="6">-85</td>
<td colspan="4">9155</td>
<td colspan="9"></td>
</tr>
<tr class="odd">
<td>9</td>
<td colspan="3">24</td>
<td colspan="3">-52</td>
<td colspan="5">9220</td>
<td colspan="2">65</td>
<td colspan="7">9193</td>
<td colspan="6">-69</td>
<td colspan="4">9124</td>
<td colspan="9"></td>
</tr>
<tr class="even">
<td>10</td>
<td colspan="3">32</td>
<td colspan="3">-20</td>
<td colspan="5">9220</td>
<td colspan="2">96</td>
<td colspan="7">9179</td>
<td colspan="6">-45</td>
<td colspan="4">9135</td>
<td colspan="9"></td>
</tr>
<tr class="odd">
<td>11</td>
<td colspan="3">40</td>
<td colspan="3">20</td>
<td colspan="5">9256</td>
<td colspan="2">121</td>
<td colspan="7">9205</td>
<td colspan="6">-15</td>
<td colspan="4">9190</td>
<td colspan="9"></td>
</tr>
<tr class="even">
<td>12</td>
<td colspan="3">32</td>
<td colspan="3">52</td>
<td colspan="5">9320</td>
<td colspan="2">130</td>
<td colspan="7">9266</td>
<td colspan="6">18</td>
<td colspan="4">9283</td>
<td colspan="9"></td>
</tr>
<tr class="odd">
<td>13</td>
<td colspan="3">24</td>
<td colspan="3">76</td>
<td colspan="5">9404</td>
<td colspan="2">121</td>
<td colspan="7">9353</td>
<td colspan="6">48</td>
<td colspan="4">9401</td>
<td colspan="9"></td>
</tr>
<tr class="even">
<td>14</td>
<td colspan="3">16</td>
<td colspan="3">92</td>
<td colspan="5">9500</td>
<td colspan="2">99</td>
<td colspan="7">9459</td>
<td colspan="6">73</td>
<td colspan="4">9531</td>
<td colspan="9"></td>
</tr>
<tr class="odd">
<td>15</td>
<td colspan="3">8</td>
<td colspan="3">100</td>
<td colspan="5">9600</td>
<td colspan="2">69</td>
<td colspan="7">9571</td>
<td colspan="6">90</td>
<td colspan="4">9661</td>
<td colspan="9"></td>
</tr>
<tr class="even">
<td>16</td>
<td colspan="3">0</td>
<td colspan="3">100</td>
<td colspan="5">9700</td>
<td colspan="2">39</td>
<td colspan="7">9684</td>
<td colspan="6">100</td>
<td colspan="4">9783</td>
<td colspan="9"></td>
</tr>
<tr class="odd">
<td>17</td>
<td colspan="3">0</td>
<td colspan="3">100</td>
<td colspan="5">9800</td>
<td colspan="2">17</td>
<td colspan="7">9793</td>
<td colspan="6">104</td>
<td colspan="4">9897</td>
<td colspan="9"></td>
</tr>
<tr class="even">
<td>18</td>
<td colspan="3">0</td>
<td colspan="3">100</td>
<td colspan="5">9900</td>
<td colspan="2">3</td>
<td colspan="7">9899</td>
<td colspan="6">105</td>
<td colspan="4">10003</td>
<td colspan="9"></td>
</tr>
<tr class="odd">
<td>19</td>
<td colspan="3">0</td>
<td colspan="3">100</td>
<td colspan="5">10000</td>
<td colspan="2">-3</td>
<td colspan="7">10001</td>
<td colspan="6">104</td>
<td colspan="4">10105</td>
<td colspan="9"></td>
</tr>
<tr class="even">
<td>20</td>
<td colspan="3">0</td>
<td colspan="3">100</td>
<td colspan="5">10100</td>
<td colspan="2">-5</td>
<td colspan="7">10102</td>
<td colspan="6">103</td>
<td colspan="4">10205</td>
<td colspan="9"></td>
</tr>
<tr class="odd">
<td>21</td>
<td colspan="3">0</td>
<td colspan="3">100</td>
<td colspan="5">10200</td>
<td colspan="2">-5</td>
<td colspan="7">10202</td>
<td colspan="6">101</td>
<td colspan="4">10303</td>
<td colspan="9"></td>
</tr>
<tr class="even">
<td>22</td>
<td colspan="3">0</td>
<td colspan="3">100</td>
<td colspan="5">10300</td>
<td colspan="2">-3</td>
<td colspan="7">10301</td>
<td colspan="6">101</td>
<td colspan="4">10402</td>
<td colspan="9"></td>
</tr>
<tr class="odd">
<td>23</td>
<td colspan="3">0</td>
<td colspan="3">100</td>
<td colspan="5">10400</td>
<td colspan="2">-2</td>
<td colspan="7">10401</td>
<td colspan="6">100</td>
<td colspan="4">10501</td>
<td colspan="9"></td>
</tr>
<tr class="even">
<td>24</td>
<td colspan="3">0</td>
<td colspan="3">100</td>
<td colspan="5">10500</td>
<td colspan="2">-1</td>
<td colspan="7">10500</td>
<td colspan="6">100</td>
<td colspan="4">10600</td>
<td colspan="9"></td>
</tr>
<tr class="odd">
<td>25</td>
<td colspan="3">0</td>
<td colspan="3">100</td>
<td colspan="5">10600</td>
<td colspan="2">0</td>
<td colspan="7">10600</td>
<td colspan="6">100</td>
<td colspan="4">10700</td>
<td colspan="9"></td>
</tr>
</tbody>
</table>

  --------------- -------------- ------------- -------------- -------- -------- ---------- --------- -- ---------- -- -------------- -- ---------- -- -- -- -- -- -- -- ---- ---- ----
  **Performance                                                                                                                                                                   
  Results for the                                                                                                                                                                 
  Proposed                                                                                                                                                                        
  Credibility                                                                                                                                                                     
  Window (I)**                                                                                                                                                                    

                                                                                                                                                                                  

  **Window                                     **CREDZADC**   65                                                                                                                  
  parameters:**                                                                                                                                                                   

                                 **MINSOFT**   3                                                                                                                                  

                                 **MAXSOFT**   5                                                                                                                                  

                                                                                                                                                                                  

  **1. Worst-case                                                                                                                                                                 
  Scenario                                                                                                                                                                        
  (Vertical Rate                                                                                                                                                                  
  Changed from                                                                                                                                                                    
  -6,000 to 6,000                                                                                                                                                                 
  fpm)**                                                                                                                                                                          

                                                                                                                                                                                  

  **Test**        **Test                                                                                              **Maximum                                                   
                  Conditions**                                                                                        Acceleration                                                
                                                                                                                      (g)**                                                       

  **Case**        **Jerk (g/s)** **Sigma       **Quant.       **1 Bad  **2 Bad  **0.25**   **0.5**      **0.75**      **1.00**          **1.25**                                  
                                 (ft)**        (ft)**         Meas**   Meas**                                                                                                     

  1               0.25           2             1              no       no       100        100          100           100               100                                       

  2               0.25           2             1              yes      no       100        100          100           100               100                                       

  3               0.25           2             1              no       yes      100        100          100           92                83                                        

  4               0.25           5             1              no       no       100        100          100           100               100                                       

  5               0.25           5             1              yes      no       100        100          100           100               82                                        

  6               0.25           5             1              no       yes      100        100          100           90                77                                        

  7               0.25           10            1              no       no       100        100          100           100               100                                       

  8               0.25           10            1              yes      no       100        100          100           88                63                                        

  9               0.25           10            1              no       yes      100        100          97            89                80                                        

  10              0.25           2             10             no       no       100        100          100           100               100                                       

  11              0.25           2             10             yes      no       100        100          100           100               81                                        

  12              0.25           2             10             no       yes      100        100          100           92                85                                        

  13              0.25           5             10             no       no       100        100          100           100               100                                       

  14              0.25           5             10             yes      no       100        100          100           98                83                                        

  15              0.25           5             10             no       yes      100        100          100           93                76                                        

  16              0.25           10            10             no       no       100        100          100           100               100                                       

  17              0.25           10            10             yes      no       100        100          100           85                55                                        

  18              0.25           10            10             no       yes      100        100          97            89                85                                        

  19              0.125          10            1              yes      no       100        100          100           100               N/A                                       

  20              0.125          10            1              no       yes      100        100          100           99                N/A                                       

  21              0.125          5             10             yes      no       100        100          100           100               N/A                                       

  22              0.125          5             10             no       yes      100        100          100           100               N/A                                       

  23              0.125          10            10             yes      no       100        100          100           100               N/A                                       

  24              0.125          10            10             no       yes      100        100          100           100               N/A                                       

                                                                                                                                                                                  

                                                                                                                                                                                  

  Note 1: The                                                                                                                                                                     
  numbers in the                                                                                                                                                                  
  last five                                                                                                                                                                       
  columns are the                                                                                                                                                                 
  percentages of                                                                                                                                                                  
  tracks that                                                                                                                                                                     
  were maintained                                                                                                                                                                 
  throughout the                                                                                                                                                                  
  scenario                                                                                                                                                                        

  Note 2: N/A                                                                                                                                                                     
  indicates that                                                                                                                                                                  
  the specified                                                                                                                                                                   
  maximum                                                                                                                                                                         
  acceleration                                                                                                                                                                    
  cannot be                                                                                                                                                                       
  reached in the                                                                                                                                                                  
  scenario                                                                                                                                                                        
  --------------- -------------- ------------- -------------- -------- -------- ---------- --------- -- ---------- -- -------------- -- ---------- -- -- -- -- -- -- -- ---- ---- ----

**Performance Results for the Proposed Credibility Window (II)**

  ---------------- -------------- ------------- -- -------------- -- -------- -- -------- -- ----------- -- ----------- -- -- -------------- -- -- ----------- -- -- ------------ -- -- -- -- ---
                                                                                                                                                                                              

  **Window                                         **CREDZADC**      65                                                                                                                       
  parameters:**                                                                                                                                                                               

                                  **MINSOFT**      3                                                                                                                                          

                                  **MAXSOFT**      5                                                                                                                                          

                                                                                                                                                                                              

  **2. Less                                                                                                                                                                                   
  Extreme Scenario                                                                                                                                                                            
  (Vertical Rate                                                                                                                                                                              
  Changed from 0                                                                                                                                                                              
  to 6,000 fpm)**                                                                                                                                                                             

                                                                                                                                                                                              

  **Test**         **Test                                                                                                     **Maximum                                                       
                   Conditions**                                                                                               Acceleration                                                    
                                                                                                                              (g)**                                                           

  **Case**         **Jerk (g/s)** **Sigma          **Quant.          **1 Bad     **2 Bad     **0.25**       **0.5**           **0.75**             **1.00**          **1.25**                 
                                  (ft)**           (ft)**            Meas**      Meas**                                                                                                       

  1                0.25           5                1                 yes         no          100            100               100                  100               N/A                      

  2                0.25           5                1                 no          yes         100            100               100                  100               N/A                      

  3                0.25           10               1                 yes         no          100            100               100                  100               N/A                      

  4                0.25           10               1                 no          yes         100            100               100                  100               N/A                      

  5                0.25           5                10                yes         no          100            100               100                  100               N/A                      

  6                0.25           5                10                no          yes         100            100               100                  100               N/A                      

  7                0.25           10               10                yes         no          100            100               100                  100               N/A                      

  8                0.25           10               10                no          yes         100            100               100                  100               N/A                      

                                                                                                                                                                                              

  Note 1: The                                                                                                                                                                                 
  numbers in the                                                                                                                                                                              
  last five                                                                                                                                                                                   
  columns are the                                                                                                                                                                             
  percentages of                                                                                                                                                                              
  tracks that were                                                                                                                                                                            
  maintained                                                                                                                                                                                  
  throughout the                                                                                                                                                                              
  scenario                                                                                                                                                                                    

  Note 2: N/A                                                                                                                                                                                 
  indicates that                                                                                                                                                                              
  the specified                                                                                                                                                                               
  maximum                                                                                                                                                                                     
  acceleration                                                                                                                                                                                
  cannot be                                                                                                                                                                                   
  reached in the                                                                                                                                                                              
  scenario                                                                                                                                                                                    

                                                                                                                                                                                              

  **3.                                                                                                                                                                                        
  Initialization                                                                                                                                                                              
  Scenario**                                                                                                                                                                                  

                                                                                                                                                                                              

  **Test**         **Test                                                                                                     **Vertical                                                      
                   Conditions**                                                                                               Rate (fpm)**                                                    

  **Case**         **Jerk (g/s)** **Sigma          **Quant.          **1 Bad     **2 Bad     **6,000**      **7,000**         **8,000**            **9,000**         **10,000**               
                                  (ft)**           (ft)**            Meas**      Meas**                                                                                                       

  1                N/A            5                1                 yes         no          100            100               100                  100               75                       

  2                N/A            5                1                 no          yes         100            90                78                   81                73                       

  3                N/A            10               1                 yes         no          100            100               100                  100               63                       

  4                N/A            10               1                 no          yes         100            90                79                   81                72                       

  5                N/A            5                10                yes         no          100            100               100                  100               61                       

  6                N/A            5                10                no          yes         100            93                79                   81                72                       

  7                N/A            10               10                yes         no          100            100               100                  100               54                       

  8                N/A            10               10                no          yes         100            90                79                   81                77                       

                                                                                                                                                                                              

                                                                                                                                                                                              

  Note 1: The                                                                                                                                                                                 
  numbers in the                                                                                                                                                                              
  last five                                                                                                                                                                                   
  columns are the                                                                                                                                                                             
  percentages of                                                                                                                                                                              
  tracks that were                                                                                                                                                                            
  maintained                                                                                                                                                                                  
  throughout the                                                                                                                                                                              
  scenario                                                                                                                                                                                    
  ---------------- -------------- ------------- -- -------------- -- -------- -- -------- -- ----------- -- ----------- -- -- -------------- -- -- ----------- -- -- ------------ -- -- -- -- ---

Roland Lejeune

4 April 1999

# Proposed Change to the 100-ft and 25-ft Altitude Tracker Credibility Window

The proposed change widens the credibility window used by both the
100-ft and the 25-ft altitude trackers. Its purpose is to ensure that
altitude reports generated during a vertical accelerations of up to
1.25g will be accepted, and thus, that track will be maintained on
aircraft performing such maneuvers.

## Background

The Requirements Working Group (RWG) agreed in March 1999 to widen the
credibility window of the alpha-beta tracker used to track own aircraft
altitude (airdata-tracker) to ensure that the tracker would be able to
maintain track on own aircraft during a 1.25g vertical acceleration (see
Change Proposal to the Airdata-Tracker Credibility Window). This change
prompted a re-examination the credibility window used by the 100-ft and
25-ft altitude trackers. Two considerations motivated the additional
effort. First, since the 100-ft tracker is used in some TCAS
installations to track own aircraft altitude (when the only source of
altitude information available is the altitude encoder of the Mode A/C
transponder), the same track maintenance requirements driving the design
of the airdata-tracker should also drive the design of the 100-ft
tracker. Second, since high performance aircraft are not limited to
playing role of own aircraft, but can also act as intruders to other
TCAS-equipped aircraft, the capabilities of the altitude trackers used
to track intruders should match those of the altitude tracker used for
own aircraft.

New simulations performed with both the 100-ft and the 25-ft altitude
trackers using the same worst-case scenario used to verify the track
maintenance performance of the airdata-tracker (see Change Proposal to
the Airdata-Tracker Credibility Window and below) revealed that neither
tracker was able to maintain track on an aircraft maneuvering with a
sustained acceleration greater than 0.5g. In light of these results, the
RWG agreed that a change to the credibility check of the 100-ft and
25-ft altitude trackers was necessary.

## Test Conditions

The worst-case scenario used to verify the track maintenance performance
of the altitude trackers is as follows. The tracked aircraft initially
descends at 6,000 fpm, then, after a short time, reverses its vertical
rate with an acceleration that builds up at the high rate of 8 ft/s^3^
(jerk) to a maximum acceleration of 40 ft/s^2^ (1.25g).

Since the function of associating successive altitude reports with
intruders is performed by the surveillance subsystem of TCAS and the
function of the 100-ft and 25-ft altitude trackers is limited to
estimating altitude and altitude rate, the notion of track maintenance
is vague when applied to these trackers. However, it is clear that
neither tracker would fulfill its function of providing accurate
altitude and altitude rate estimates if the credibility check was to
reject many successive valid altitude reports. In the absence of a
precise set of requirements, it seemed reasonable to adopt the same
track maintenance criterion that was used in the analysis of the
airdata-tracker. Specifically, a track is considered "maintained" when
fewer than 5 successive altitude measurements are rejected by the
credibility window.

The purpose of the credibility check is to ensure that bad altitude
reports (i.e., reports containing an erroneous altitude measurement or
reports mis-correlated by the surveillance function) will not be passed
to the tracker. Statistics characterizing bad reports are not available;
however, it is generally agreed that the credibility check should be
designed to reject isolated bad reports with an altitude error of 300 ft
or more whenever possible.

## Analysis

The width of credibility window used by the 100-ft and 25-ft altitude
trackers once the track has been initialized (i.e., after the first 5
seconds of the track's live) is controlled by two parameters, CREDZDERR,
which characterizes the largest credible error in the altitude rate
estimate, and CREDACCDIV2, which characterizes the largest credible
instantaneous acceleration. The current values of these two parameters
are CREDZDERR = 20 ft/s and CREDACCDIV2 = 8 ft/s^2^. Note that
CREDACCDIV2 in fact corresponds to one-half of the largest credible
acceleration during which the tracker is required to maintain track.

The new requirement for maintaining track during an acceleration of up
to 1.25g strongly suggests that the value of CREDACCDIV2 should be
changed to 20 ft/s^2^. It also suggests that the value of CREDZDERR may
also have to be increased. A first set of simulations were performed
after changing the value of CREDACCDIV2 as indicated, but without
changing the value of CREDZDERR. They showed that the ability of the
100-ft tracker to maintain track during accelerations peaking at 1.25g
was still weak (of the order of 70%). As a result, an increase to the
value of CREDZDERR seemed desirable.

Thus, the proposed change is to increase the values of CREDZDERR and
CREDACCDIV2 as follows: CREDZDERR = 30 ft/s and CREDACCDIV2 = 20
ft/s^2^.

Plots of the current and proposed windows as a function of the number of
successive coasts are shown in Figure 1. A plot of the credibility
window used in Version 6.04A is also shown. A "coast" is here defined as
a tracking cycle during which the track is coasted (i.e., the altitude
rate estimate is not updated) because either no altitude report was
received or the received altitude report was deemed not credible and
therefore rejected. Since all credibility windows are symmetric with
respect to zero, it is sufficient and convenient to plot their
half-widths instead of their total widths.

As the plot indicates, the ability of the credibility window to reject
bad altitude reports with an altitude error of 300 ft is limited to two
successive bad reports, or one bad report following one missing report.
Following the second coast, the half-width of the credibility window
becomes larger than 300 ft. However, the latter fact was also true with
the credibility window used in Version 6.04A.

![](media/image10.wmf){width="5.444444444444445in"
height="3.8333333333333335in"}

Figure 1. Current and Proposed Credibility Windows

## Simulation Results

The simulation results obtained with the proposed credibility window
using the worst-case scenario and various accelerations are shown in the
attached spreadsheet. Simulation results were also obtained for a less
extreme scenario in which the aircraft is initially level, then
accelerates to a vertical rate of 6,000 fpm.

As for the testing of the airdata-tracker (see Change Proposal to the
Airdata-Tracker Credibility Window for further details), the track
maintenance performance of the 100-ft and 25-ft trackers were examined
under three different conditions: (1) no bad altitude report, (2) one
bad altitude report at the worst possible time, and (3) two successive
bad altitude reports starting on a cycle randomly selected in an
interval beginning 8 cycles (seconds) before the beginning of the
acceleration and ending 8 cycles (seconds) after the end of the
acceleration. (In these simulations, a bad altitude report was a report
with a 5,000 ft error.)

  --------------- -------------- --------------- ------------ ---- -------- -- ------------- -- ---------- -- --------- -- -- -------------- -- -- ---------- -- -- ---------- -- -- -- -- -- -- -- ---- ---- ---- ----
  **Performance                                                                                                                                                                                                    
  Results:                                                                                                                                                                                                         
  Proposed 100 ft                                                                                                                                                                                                  
  Tracker                                                                                                                                                                                                          
  Credibility                                                                                                                                                                                                      
  Window (I)**                                                                                                                                                                                                     

                                                                                                                                                                                                                   

  **Window                                       **CREDINIT        200         (unchanged)                                                                                                                         
  Parameters**                                   =**                                                                                                                                                               

                                 **CREDZDERR =**              30                                                                                                                                                   

                                 **CREDACCDIV2                20                                                                                                                                                   
                                 =**                                                                                                                                                                               

                                                                                                                                                                                                                   

                                                                                                                                                                                                                   

  **1. Worst-case                                                                                                                                                                                                  
  Scenario                                                                                                                                                                                                         
  (Vertical Rate                                                                                                                                                                                                   
  Changed from                                                                                                                                                                                                     
  -6,000 to 6,000                                                                                                                                                                                                  
  fpm)**                                                                                                                                                                                                           

                                                                                                                                                                                                                   

                                                                                                                                                                                                                   

  **Test**        **Test                                                                                                      **Maximum                                                                            
                  Conditions**                                                                                                Acceleration                                                                         
                                                                                                                              (g)**                                                                                

  **Case**        **Jerk (g/s)** **Sigma\        **Quant.          **1 Bad     **2 Bad          **0.25**      **0.5**         **0.75**             **1.00**         **1.25**                                       
                                 (ft)**          (ft)**            Meas**      Meas**                                                                                                                              

  1               0.25           2               100               no          no               100           100             100                  100              100                                            

  2               0.25           2               100               yes         no               100           100             100                  100              100                                            

  3               0.25           2               100               no          yes              100           100             100                  100              100                                            

  4               0.25           5               100               no          no               100           100             100                  100              100                                            

  5               0.25           5               100               yes         no               100           100             100                  100              100                                            

  6               0.25           5               100               no          yes              100           100             100                  99               99                                             

  7               0.25           10              100               no          no               100           100             100                  100              100                                            

  8               0.25           10              100               yes         no               100           100             100                  100              100                                            

  9               0.25           10              100               no          yes              100           100             100                  99               96                                             

  10              0.125          2               100               yes         no               100           100             100                  100              N/A                                            

  11              0.125          2               100               no          yes              100           100             100                  100              N/A                                            

  12              0.125          5               100               yes         no               100           100             100                  100              N/A                                            

  13              0.125          5               100               no          yes              100           100             100                  100              N/A                                            

  14              0.125          10              100               yes         no               100           100             100                  100              N/A                                            

  15              0.125          10              100               no          yes              100           100             99                   98               N/A                                            

                                                                                                                                                                                                                   

                                                                                                                                                                                                                   

  Note 1: The                                                                                                                                                                                                      
  numbers in the                                                                                                                                                                                                   
  last five                                                                                                                                                                                                        
  columns are the                                                                                                                                                                                                  
  percentages of                                                                                                                                                                                                   
  tracks that                                                                                                                                                                                                      
  were maintained                                                                                                                                                                                                  
  throughout the                                                                                                                                                                                                   
  scenario                                                                                                                                                                                                         

  Note 2: N/A                                                                                                                                                                                                      
  indicates that                                                                                                                                                                                                   
  the specified                                                                                                                                                                                                    
  maximum                                                                                                                                                                                                          
  acceleration                                                                                                                                                                                                     
  cannot be                                                                                                                                                                                                        
  reached in the                                                                                                                                                                                                   
  scenario                                                                                                                                                                                                         
  --------------- -------------- --------------- ------------ ---- -------- -- ------------- -- ---------- -- --------- -- -- -------------- -- -- ---------- -- -- ---------- -- -- -- -- -- -- -- ---- ---- ---- ----

  ---------------- -------------- --------------- ------------ -- ---- -------- -- ------------- -- ----------- -- ----------- -- -------------- -- ----------- -- ------------ -- -- --- -- --- ---- ---- ---- ----
  **Performance                                                                                                                                                                                                 
  Results:                                                                                                                                                                                                      
  Proposed 100 ft                                                                                                                                                                                               
  Tracker                                                                                                                                                                                                       
  Credibility                                                                                                                                                                                                   
  Window (II)**                                                                                                                                                                                                 

                                                                                                                                                                                                                

  **Window                                        **CREDINIT           200         (unchanged)                                                                                                                  
  Parameters**                                    =**                                                                                                                                                           

                                  **CREDZDERR =**                 30                                                                                                                                            

                                  **CREDACCDIV2                   20                                                                                                                                            
                                  =**                                                                                                                                                                           

                                                                                                                                                                                                                

  **2. Less                                                                                                                                                                                                     
  Extreme Scenario                                                                                                                                                                                              
  (Vertical Rate                                                                                                                                                                                                
  Changed from 0                                                                                                                                                                                                
  to 6,000 fpm)**                                                                                                                                                                                               

                                                                                                                                                                                                                

  **Test**         **Test                                                                                                         **Maximum                                                                     
                   Conditions**                                                                                                   Acceleration                                                                  
                                                                                                                                  (g)**                                                                         

  **Case**         **Jerk (g/s)** **Sigma\        **Quant.             **1 Bad     **2 Bad          **0.25**       **0.5**        **0.75**          **1.00**       **1.25**                                     
                                  (ft)**          (ft)**               Meas**      Meas**                                                                                                                       

  1                0.25           2               100                  no          no               100            100            100               100            N/A                                          

  2                0.25           2               100                  yes         no               100            100            100               100            N/A                                          

  3                0.25           2               100                  no          yes              100            100            100               100            N/A                                          

  4                0.25           5               100                  no          no               100            100            100               100            N/A                                          

  5                0.25           5               100                  yes         no               100            100            100               100            N/A                                          

  6                0.25           5               100                  no          yes              100            100            100               100            N/A                                          

  7                0.25           10              100                  no          no               100            100            100               100            N/A                                          

  8                0.25           10              100                  yes         no               100            100            100               100            N/A                                          

  9                0.25           10              100                  no          yes              100            100            100               100            N/A                                          

                                                                                                                                                                                                                

                                                                                                                                                                                                                

  Note 1: The                                                                                                                                                                                                   
  numbers in the                                                                                                                                                                                                
  last five                                                                                                                                                                                                     
  columns are the                                                                                                                                                                                               
  percentages of                                                                                                                                                                                                
  tracks that were                                                                                                                                                                                              
  maintained                                                                                                                                                                                                    
  throughout the                                                                                                                                                                                                
  scenario                                                                                                                                                                                                      

  Note 2: N/A                                                                                                                                                                                                   
  indicates that                                                                                                                                                                                                
  the specified                                                                                                                                                                                                 
  maximum                                                                                                                                                                                                       
  acceleration                                                                                                                                                                                                  
  cannot be                                                                                                                                                                                                     
  reached in the                                                                                                                                                                                                
  scenario                                                                                                                                                                                                      

                                                                                                                                                                                                                

  **3.                                                                                                                                                                                                          
  Initialization                                                                                                                                                                                                
  Scenario**                                                                                                                                                                                                    

                                                                                                                                                                                                                

  **Test**         **Test                                                                                                         **Vertical                                                                    
                   Conditions**                                                                                                   Rate (fpm)**                                                                  

  **Case**         **Jerk (g/s)** **Sigma (ft)**  **Quant.             **1 Bad     **2 Bad          **6,000**      **7,000**      **8,000**         **9,000**      **10,000**                                   
                                                  (ft)**               Meas**      Meas**                                                                                                                       

  1                N/A            2               100                  yes         no               100            100            100               100            100                                          

  2                N/A            2               100                  no          yes              100            100            100               100            100                                          

  3                N/A            5               100                  yes         no               100            100            100               100            100                                          

  4                N/A            5               100                  no          yes              100            100            100               100            100                                          

  5                N/A            10              100                  yes         no               100            100            100               100            100                                          

  6                N/A            10              100                  no          yes              100            100            100               100            100                                          

                                                                                                                                                                                                                

                                                                                                                                                                                                                

  Note 1: The                                                                                                                                                                                                   
  numbers in the                                                                                                                                                                                                
  last five                                                                                                                                                                                                     
  columns are the                                                                                                                                                                                               
  percentages of                                                                                                                                                                                                
  tracks that were                                                                                                                                                                                              
  maintained                                                                                                                                                                                                    
  throughout the                                                                                                                                                                                                
  scenario                                                                                                                                                                                                      
  ---------------- -------------- --------------- ------------ -- ---- -------- -- ------------- -- ----------- -- ----------- -- -------------- -- ----------- -- ------------ -- -- --- -- --- ---- ---- ---- ----

  --------------- -------------- --------------- ------------ ---- -------- -- ------------- -- ---------- -- --------- -- -------------- -- ---------- -- ---------- -- -- -- -- -- -- ---- ---- ----
  **Performance                                                                                                                                                                                   
  Results:                                                                                                                                                                                        
  Proposed 25 ft                                                                                                                                                                                  
  Tracker                                                                                                                                                                                         
  Credibility                                                                                                                                                                                     
  Window (I)**                                                                                                                                                                                    

                                                                                                                                                                                                  

  **Window                                       **CREDINIT        200         (unchanged)                                                                                                        
  Parameters**                                   =**                                                                                                                                              

                                 **CREDZDERR =**              30                                                                                                                                  

                                 **CREDACCDIV2                20                                                                                                                                  
                                 =**                                                                                                                                                              

                                                                                                                                                                                                  

                                                                                                                                                                                                  

  **1. Worst-case                                                                                                                                                                                 
  Scenario                                                                                                                                                                                        
  (Vertical Rate                                                                                                                                                                                  
  Changed from                                                                                                                                                                                    
  -6,000 to 6,000                                                                                                                                                                                 
  fpm)**                                                                                                                                                                                          

                                                                                                                                                                                                  

                                                                                                                                                                                                  

  **Test**        **Test                                                                                                   **Maximum                                                              
                  Conditions**                                                                                             Acceleration                                                           
                                                                                                                           (g)**                                                                  

  **Case**        **Jerk (g/s)** **Sigma\        **Quant.          **1 Bad     **2 Bad          **0.25**      **0.5**      **0.75**          **1.00**      **1.25**                               
                                 (ft)**          (ft)**            Meas**      Meas**                                                                                                             

  1               0.25           2               25                no          no               100           100          100               100           100                                    

  2               0.25           2               25                yes         no               100           100          100               100           100                                    

  3               0.25           2               25                no          yes              100           100          100               100           100                                    

  4               0.25           5               25                no          no               100           100          100               100           99                                     

  5               0.25           5               25                yes         no               100           100          100               100           99                                     

  6               0.25           5               25                no          yes              100           100          100               100           99                                     

  7               0.25           10              25                no          no               100           100          100               93            87                                     

  8               0.25           10              25                yes         no               100           100          100               93            87                                     

  9               0.25           10              25                no          yes              100           100          97                94            92                                     

  10              0.125          2               25                yes         no               100           100          100               100           N/A                                    

  11              0.125          2               25                no          yes              100           100          100               100           N/A                                    

  12              0.125          5               25                yes         no               100           100          100               100           N/A                                    

  13              0.125          5               25                no          yes              100           100          100               100           N/A                                    

  14              0.125          10              25                yes         no               100           100          100               100           N/A                                    

  15              0.125          10              25                no          yes              100           100          99                98            N/A                                    

                                                                                                                                                                                                  

                                                                                                                                                                                                  

  Note 1: The                                                                                                                                                                                     
  numbers in the                                                                                                                                                                                  
  last five                                                                                                                                                                                       
  columns are the                                                                                                                                                                                 
  percentages of                                                                                                                                                                                  
  tracks that                                                                                                                                                                                     
  were maintained                                                                                                                                                                                 
  throughout the                                                                                                                                                                                  
  scenario                                                                                                                                                                                        

  Note 2: N/A                                                                                                                                                                                     
  indicates that                                                                                                                                                                                  
  the specified                                                                                                                                                                                   
  maximum                                                                                                                                                                                         
  acceleration                                                                                                                                                                                    
  cannot be                                                                                                                                                                                       
  reached in the                                                                                                                                                                                  
  scenario                                                                                                                                                                                        
  --------------- -------------- --------------- ------------ ---- -------- -- ------------- -- ---------- -- --------- -- -------------- -- ---------- -- ---------- -- -- -- -- -- -- ---- ---- ----

  ---------------- -------------- --------------- ------------ -- ---- -------- --- ------------- --- ----------- --- ----------- --- -------------- --- ----------- --- ------------ --- --
  **Performance                                                                                                                                                                           
  Results:                                                                                                                                                                                
  Proposed 25 ft                                                                                                                                                                          
  Tracker                                                                                                                                                                                 
  Credibility                                                                                                                                                                             
  Window (II)**                                                                                                                                                                           

                                                                                                                                                                                          

  **Window                                        **CREDINIT           200          (unchanged)                                                                                           
  Parameters**                                    =**                                                                                                                                     

                                  **CREDZDERR =**                 30                                                                                                                      

                                  **CREDACCDIV2                   20                                                                                                                      
                                  =**                                                                                                                                                     

                                                                                                                                                                                          

  **2. Less                                                                                                                                                                               
  Extreme Scenario                                                                                                                                                                        
  (Vertical Rate                                                                                                                                                                          
  Changed from 0                                                                                                                                                                          
  to 6,000 fpm)**                                                                                                                                                                         

                                                                                                                                                                                          

  **Test**         **Test                                                                                                             **Maximum                                           
                   Conditions**                                                                                                       Acceleration                                        
                                                                                                                                      (g)**                                               

  **Case**         **Jerk (g/s)** **Sigma\        **Quant.             **1 Bad      **2 Bad           **0.25**        **0.5**         **0.75**           **1.00**        **1.25**         
                                  (ft)**          (ft)**               Meas**       Meas**                                                                                                

  1                0.25           2               25                   no           no                100             100             100                100             N/A              

  2                0.25           2               25                   yes          no                100             100             100                100             N/A              

  3                0.25           2               25                   no           yes               100             100             100                97              N/A              

  4                0.25           5               25                   no           no                100             100             100                100             N/A              

  5                0.25           5               25                   yes          no                100             100             100                100             N/A              

  6                0.25           5               25                   no           yes               100             100             100                97              N/A              

  7                0.25           10              25                   no           no                100             100             100                100             N/A              

  8                0.25           10              25                   yes          no                100             100             100                100             N/A              

  9                0.25           10              25                   no           yes               100             100             98                 98              N/A              

                                                                                                                                                                                          

                                                                                                                                                                                          

  Note 1: The                                                                                                                                                                             
  numbers in the                                                                                                                                                                          
  last five                                                                                                                                                                               
  columns are the                                                                                                                                                                         
  percentages of                                                                                                                                                                          
  tracks that were                                                                                                                                                                        
  maintained                                                                                                                                                                              
  throughout the                                                                                                                                                                          
  scenario                                                                                                                                                                                

  Note 2: N/A                                                                                                                                                                             
  indicates that                                                                                                                                                                          
  the specified                                                                                                                                                                           
  maximum                                                                                                                                                                                 
  acceleration                                                                                                                                                                            
  cannot be                                                                                                                                                                               
  reached in the                                                                                                                                                                          
  scenario                                                                                                                                                                                

                                                                                                                                                                                          

  **3.                                                                                                                                                                                    
  Initialization                                                                                                                                                                          
  Scenario**                                                                                                                                                                              

                                                                                                                                                                                          

  **Test**         **Test                                                                                                             **Vertical                                          
                   Conditions**                                                                                                       Rate (fpm)**                                        

  **Case**         **Jerk (g/s)** **Sigma\        **Quant.             **1 Bad      **2 Bad           **6,000**       **7,000**       **8,000**          **9,000**       **10,000**       
                                  (ft)**          (ft)**               Meas**       Meas**                                                                                                

  1                N/A            2               25                   yes          no                100             100             100                100             100              

  2                N/A            2               25                   no           yes               100             100             100                100             100              

  3                N/A            5               25                   yes          no                100             100             100                100             100              

  4                N/A            5               25                   no           yes               100             100             100                100             100              

  5                N/A            10              25                   yes          no                100             100             100                100             100              

  6                N/A            10              25                   no           yes               100             100             100                100             100              

                                                                                                                                                                                          

                                                                                                                                                                                          

  Note 1: The                                                                                                                                                                             
  numbers in the                                                                                                                                                                          
  last five                                                                                                                                                                               
  columns are the                                                                                                                                                                         
  percentages of                                                                                                                                                                          
  tracks that were                                                                                                                                                                        
  maintained                                                                                                                                                                              
  throughout the                                                                                                                                                                          
  scenario                                                                                                                                                                                
  ---------------- -------------- --------------- ------------ -- ---- -------- --- ------------- --- ----------- --- ----------- --- -------------- --- ----------- --- ------------ --- --