Clock-aided satellite navigation receiver system for enhanced position estimation and integrity monitoring

A satellite navigation receiver system for determining an accurate three dimensional position estimate of a movable object and initiating correction of the location of the movable object in response to the three dimensional estimate, utilizing a receiver for receiving range measurement signals from a satellite navigation system, a clock having a constant frequency drift rate for at least a predetermined period of time, and a processing scheme capable of computing clock bias estimates over a predetermined period of time including an instantaneous time, using the clock bias estimates in a quadratic function to adaptively derive a smoothed clock bias estimates over the predetermined period of time including the instantaneous time, computing a three dimensional position estimate of the movable object's position using the smoothed clock bias estimate at the instantaneous time, and determining if the three dimensional position estimates are of sufficient quality for a user's intended purpose, whereby depending on the computed three dimensional position estimates, alone or in conjunction with the determination as to whether such estimates are of sufficient quality, the movable object is moved in response thereto.

FIELD OF THE INVENTION 
This invention relates to a clock-aided satellite navigation receiver 
system for determining position estimates of a movable object, as well as 
providing a measure of the accuracy of the position estimates. 
BACKGROUND OF THE INVENTION 
Global navigation satellite systems GPS and GLONASS, now being deployed in 
the United States and Russia, represent a revolutionary change in 
navigation and positioning technology. Other such systems will likely 
follow, which will be applicable to all forms of travel. One of the areas 
affected profoundly by the availability of satellite based navigation 
(SatNav) is civil aviation, where these systems show an enormous promise 
for enhancing economy as well as safety. Airports of the future will 
likely be equipped with local-area differential GPS, as well as wide-area 
differential GPS, particularly Wide Area Augmentations System (WAAS). 
Planning is underway in the U.S. to switch to GPS-based navigation and 
surveillance in all phases of flight including precision approaches. 
Precision approaches, carried out under poor visibility conditions, require 
navigational guidance both horizontally and vertically, and place 
stringent requirements on the accuracy of position estimates. Vertical 
guidance, in particular is of critical importance. Currently, precision 
approaches require local instrumentation, such as Instrument Landing 
System (ILS), and the Microwave Landing System (MLS), installed at each 
runway to provide navigational guidance to suitably equipped aircraft. The 
ILS and MLS are expected to be phased out in favor of satellite 
navigation. In the future, precision approaches using satellite navigation 
will use GPS in either differential mode, local mode, or wide area mode. 
The latter of such may be Wide Area Augmentation System (WAAS), which is 
planned to provide such capability over conterminous U.S. by the year 
2000. Satellite navigation systems however, are thought to offer 
significantly better horizontal than vertical position estimates. Thus, an 
important challenge in the industry is to provide systems with enhanced 
vertical position accuracy. 
Precision approaches under a Category I standard used internationally 
require horizontal and vertical navigational guidance down to an altitude 
(or "decision height") of 200 feet above the touchdown area. If the runway 
is in view when the plane reaches a decision height the pilot may land 
using the visual references for navigation. The decision heights for 
Category II and Category III standards are significantly lower. 
The deviation from a pre-defined flight path allowed an aircraft while 
being guided by a navigation system for a precision approach is strictly 
limited. As expected, the permissible deviation, called an alarm limit, 
changes with aircraft altitude. Thus, the closer the aircraft gets to 
touchdown, the less deviation allowed. Alarm limits are specified for both 
horizontal and vertical errors at each altitude. If at any point during an 
approach the aircraft deviation from the prescribed flight path exceeds 
the alarm limit, the pilot is warned promptly and the approach is aborted. 
Insofar as the aircraft position can only be estimated using satellite 
navigation, there will be some uncertainty associated with it. In order to 
ensure that the aircraft doesn't violate an alarm limit, the navigation 
system must be required to deliver position estimates of assured accuracy. 
The lower the aircraft altitude, the lower the deviation alarm limit, and 
the lower the error tolerable in the position estimate. If a position 
estimate cannot be assured by the navigation system to meet the current 
requirement on its accuracy, the pilot is warned. This function of 
ensuring that the quality of a position estimate is acceptable is referred 
to as integrity monitoring. 
Conventional methods of integrity monitoring have operated under the 
premise that, if assured of system integrity each user could count on 
obtaining a position estimate of a certain quality. This premise, however, 
does not hold for satellite navigation in general. For example, different 
users of a satellite navigation system may obtain position estimates of 
significantly different qualities. Thus, in adopting satellite navigation 
for civil aviation, an important issue to be resolved is providing the 
user (e.g., the pilot of an aircraft in this scenario) with a system 
capable of recognizing if a position estimate is good enough for a 
precision approach. This is even more important in the industry 
considering that conventional receivers often provide poor vertical 
position estimates. 
Generally, the quality of position estimates obtained by different users of 
a satellite navigation system vary greatly. Conventional receivers 
operating with satellite navigation systems measure the transit time of 
the signal and decipher the data to determine the satellite position. 
Given that the distance from a satellite to the receiver is determined by 
the speed of light multiplied by the signal travel time, it is important 
that time measurement be characterized accurately. For example, if the 
satellite clock and the receiver clock were out of sync by even 0.001 
second, the measurement of distance from the satellite to the receiver 
would be off by 1,860 miles. If receiver clocks were perfectly 
synchronized with the satellite clocks, only three measurements (x,y,z) of 
range to satellites would be needed to allow a user to compute a 
three-dimensional position. This process is known as mulitlateration. 
However, given the expense in providing a receiver clock whose time is 
exactly synchronized, a way to account for receiver clock bias has been to 
compute a measurement from a fourth satellite. This is done by a processor 
in the receiver which correlates the ranges measured from each satellite 
to where they intersect. If a series of measurements do not intersect, the 
processor either subtracts or adds time from all of the measurements, 
continuing to do so until it reaches a three-dimensional position estimate 
where all range estimates intersect. This is carried out by the use of 
basic trigonometry, usually four equations with four unknowns x,y,z,b. The 
amount b, by which the processor has added or subtracted time to achieve 
this intersection, is the bias between the receiver clock and the 
satellite clock. 
Having measurements obtained from four satellites in view, however, does 
not assure a good position estimate. The biased range measurements are 
called pseudoranges. Estimation of the four unknowns, x, y, z, b where b 
is the clock bias estimate, are referred to as 4-D estimations. The 
quality of a position estimate depends upon two factors: (1) the number of 
satellites in view and their spatial distribution relative to the user, 
and (2) the quality of the "pseudorange measurements". Satellite geometry 
is characterized by a parameter called "Dilution of Precision" (DOP). This 
parameter, DOP, can be thought of as roughly inversely proportional to the 
volume of a polyhedron with the receiver being at the apex and the 
satellite positions defining the base. The pseudorange measurements are 
range measurements which contain errors, thus the quality of pseudorange 
measurements is characterized by their rms error. There are several 
sources of error which affect range measurements including errors in the 
predicted ephemeris of the satellites, instabilities in the satellite and 
receiver clocks, ionospheric and tropospheric propagation delays, 
multipath, and receiver noise. Further errors in position estimates may be 
the result of the effects of an undetected or an unannounced system 
malfunction. The collective effect of these errors is referred to as the 
User Range Error (URE) and its rms value is .alpha.URE. The position error 
is thus expressed in terms of these two factors: RMS position 
error=(DOP)(.alpha.URE). In order for satellite navigation to be used 
globally, all users must have in view at least four satellites 
geometrically positioned for accuracy as well as a URE such that the 
resulting position estimate meets the user's requirement. As stated above, 
Category I approaches determine a range within which an aircraft must stay 
when performing a precision approach. 
Known systems generally cannot provide each user with the ability to 
accurately determine on the basis of satellite measurements when a 
position estimate meets accuracy requirements, and when it does not. 
Characterization of the accuracy of a position estimate in terms of the 
measurements themselves is referred to as receiver autonomous integrity 
monitoring. Currently, however, methods of integrity monitoring rely on 
inaccurate vertical position estimates obtained by conventional receivers. 
Some work in the area of developing methods of receiver autonomous 
integrity monitoring has dealt with guarding against measurement anomalies 
due to satellite malfunctions only, which is a factor responsible for 
introducing large errors in position estimates. Unfortunately, these 
methods require redundant measurements and can deal effectively only with 
one anomalous measurement. If multiple anomalies arose, these methods of 
integrity monitoring would fail to detect the problem and provide such 
detection to the user. 
The instant invention overcomes the problems of obtaining accurate vertical 
position estimates, and providing the user with an indication as to the 
accuracy of the vertical position measurement for an intended purpose, 
notwithstanding the degree of error or the number of anomalies effecting 
the error. 
SUMMARY OF THE INVENTION 
It is an object of the invention to provide a clock-aided satellite 
navigation receiver system for producing accurate position estimates of an 
object. 
It is an object of the invention to utilize a stable receiver clock to 
improve position estimates during satellite navigation. 
It is another object of the invention to increase the accuracy of vertical 
position estimates available from a satellite navigation system. 
It is yet another object of the invention to determine if a position 
estimate obtained from a satellite navigation system is reliable for an 
intended purpose. 
It is still another object of the invention to discern the error bound 
associated with a vertical position estimate. 
It is yet another object of the invention to provide an improved 
clock-aided satellite navigation system for aviation. 
It is still another object of the invention to provide an aircraft with the 
ability to monitor its position accurately during a precision approach 
using satellite navigation. 
It is a final object of the invention to provide a method for obtaining 
reliable position estimates during satellite navigation. 
These and other objects of the invention are provided by a navigation 
receiver system, and a related method, for determining and initiating 
correction of location in real time. The system can include a receiver and 
a processor. The receiver receives signals representative of range 
measurements from a plurality of satellites in a satellite navigation 
system, and it includes a stable clock having a constant frequency drift 
rate for at least a predetermined period of time. The processor utilizes 
the constant frequency drift rate and the signals from the satellites to 
determine a three-dimensional estimate of the position of the receiver. 
Also, according to the invention, a navigation receiver system for 
determining and initiating correction of location in real time is 
provided. The system includes a movable object moving along a path. A 
receiver receives signals representative of range measurements from a 
satellite navigation system. A clock in the receiver has a constant 
frequency drift rate for at least a predetermined period of time. A 
processor determines clock bias estimates over the predetermined period of 
time based on the satellite signals. The processor also determines a 
smoothed clock bias estimate over the predetermined period of time based 
on the clock bias estimates, and determines a three-dimensional position 
estimate of the movable object using the smoothed clock bias estimate at 
an instantaneous time. The processor compares the smoothed clock bias 
estimate at the instantaneous time with a clock bias estimate at the 
instantaneous time and generates a degree of error therebetween. It 
determines an error associated with the three-dimensional position 
estimate using the degree of error, and compares the error associated with 
the three-dimensional position estimate with a predetermined error range 
associated with the path of the movable object. The processor also 
determines whether the error associated with the three-dimensional 
position estimate is within the predetermined error range. The 
determination of whether the error associated with the three-dimensional 
position estimate is within the predetermined error range is then provided 
to the movable object. The location of the movable object is then changed, 
if necessary, based on this determination. 
Satellites in a satellite navigation system such as the Global Positioning 
System (GPS) transmit signals from which the receiver of the instant 
invention obtains snapshots of range measurements to the satellites. From 
such snapshots, the receiver is capable of computing estimates of the 
corresponding three coordinates of the receiver position, as well as the 
instantaneous receiver clock bias. The quality of such estimates depends 
upon the number and the geometry of satellites in view, and the degree of 
error of the measurements. When navigating with the system of the instant 
invention, the position of the receiver will change over time. The present 
receiver clock, instead of changing with time as do clocks in known 
systems, is predictable. It employs a stable clock. The predictability of 
the clock is based on improved stability characteristics of the clock. 
In the system of the instant invention, position estimates of a movable 
object are obtained by a receiver within or coupled with the movable 
object. The receiver clock is stable over at least a predetermined period, 
as its frequency drift rate is constant. Due to such stability, the bias 
relative to the satellite system time can be estimated in real time. This 
estimation is carried out by a quadratic function which estimates, over 
time, the clock bias with respect to the satellite navigation system. The 
user obtains a `smoothed` bias estimate from the quadratic function, 
enabling the user to use this smoothed clock bias estimate as a predictor 
of the clock bias for some time ahead. Using the smoothed clock bias 
estimate, the receiver processing scheme computes the three-dimensional 
position estimates from the snapshots of range measurements. The 
processing scheme thus only solves for three variables, thereby reducing 
the error in the position estimates obtained, particularly the error in 
the vertical position estimates. 
The processing scheme of the instant invention is also used for receiver 
autonomous integrity monitoring to allow the user of the movable object to 
determine whether the position estimate is accurate enough for an intended 
purpose. The smoothed clock bias estimate obtained above, is further 
compared with the clock bias at an instantaneous time to determine the 
amount of error associated with the current estimate. By obtaining the 
size of the error in the clock bias estimate, the processing scheme of the 
instant invention determines the degree of the error in the vertical 
position estimate as well as a high-confidence upper bound on the vertical 
position error. Knowing the degree of error, the system corrects for it 
either by allowing the movable object to maintain its position along a 
current path or by causing the movable object to abort its approach. 
The system of the instant invention in providing enhanced position 
estimates, relies on its ability to monitor the receiver clock behavior 
accurately over time using the GPS measurements. The basic system 
requirement is that there be no significant, unpredictable change in the 
clock frequency for a predetermined period; that is, the frequency drift 
rate is constant for a sufficient amount of time to allow for the clock 
parameters to be estimated from the GPS measurements. The accuracy of the 
vertical position estimate obtained from using GPS in a differential mode, 
local or wide-area, through the use of the short-term stability of the 
clock, provides a significant decrease in the rms error in the vertical 
position as compared to known systems. 
The system of the instant invention can be adapted for use with the Wide 
Area Augmentation System (WAAS), however, the invention is not to be 
limited thereto. Under WAAS, an added assurance on system operation is in 
the form of an integrity broadcast message indicating that the GPS signals 
as monitored at a number of geographically distributed reference stations 
are consistent with a specified model. The broadcast would include 
corrections to be applied to the measurements by a user in order to 
compensate in part for the measurement errors. The size of the remaining 
errors in a user's measurements then depends upon `age` of the 
corrections, local interference or multipath at the user and/or the 
reference station, local atmospheric anomalies, and any avionics errors. 
Furthermore, the system of the instant invention executes a receiver 
autonomous integrity monitoring scheme to provide the user with 
information to ensure that an aircraft stays within the prescribed 
airspace, a vital safety concern in civil aviation. The system of the 
instant invention presents a process for clock-aided integrity monitoring 
which offers several advantages over current methods as it yields tighter 
measures of the position integrity. The process is seen as meeting the 
integrity monitoring requirements of Category I precision approaches 
executed under differential GPS, local or wide-area, with near-100% 
availability. 
The instant invention overcomes the problems associated with conventional 
receiver systems, particularly the inaccurate vertical position estimates 
obtained by such receivers from satellite measurements, by providing a 
system yielding an improved position estimate as well as a reliable 
determination using clock aided integrity monitoring to tell the user 
whether this estimate is good enough for the user's purpose. 
The foregoing and other objects, aspects, features, and advantages of the 
invention will become more apparent from the following descriptions and 
from the claims.

DESCRIPTION 
The invention described herein utilizes the following definitions for 
purposes of clarity: a clock is defined as any mechanism which records, 
tracks, displays, or in any other manner, accounts for the passage of 
time, clock bias is defined as the amount by which a clock is recording, 
tracking, displaying or accounting for time, in relation to another clock, 
particularly such amount by which one clock is faster than or slower than 
another clock, frequency drift rate is defined as the rate by which a 
clock increases or decreases its speed in recording, tracking, displaying 
or accounting for the passage of time. 
The instant invention utilizes clock-aided navigation based on the premise 
that in estimation of the position and the receiver clock bias from a 
snapshot of satellite range measurements provided by a satellite 
navigation system, the errors in the estimates of vertical position and 
clock bias are highly correlated. If the clock bias estimate has a large 
error, so does the vertical position estimate, and vice-versa. This 
premise is exemplified in FIGS. 1A and 1B, which show scatter plots of the 
errors in the horizontal and vertical position estimates, respectively, 
versus the error in the corresponding clock bias estimates computed from 
the GPS measurements snapshots taken 10 seconds apart over a day. 
Note, however, in FIG. 1A that there exists no apparent correlation between 
horizontal error and receiver clock bias error. When the horizontal 
position error is +50 meters, the clock bias error can be -50 meters. By 
contrast, FIG. 1B, shows a strong linear correlation between clock bias 
error and vertical position error. Note that when the error in the clock 
bias is at a value, such as +50 meters, the error in the vertical position 
estimate is at roughly the same value of +50 meters. The instant invention 
utilizes this correlation, as the error in the clock bias estimate from a 
snapshot of range measurements is a reliable predictor of the error in the 
corresponding vertical position estimate. 
FIG. 2A shows a movable object 10, the position of which is determined with 
range measurements provided by a satellite navigation system 12. Within 
the movable object is the receiver system of the FIG. 2B. It is not 
essential to the invention that the receiver be within the movable object, 
as it could be remotely coupled to the movable object if the user desired. 
FIG. 2B shows the receiver's 14 system requirements of the instant 
invention. The receiver 14, preferably comprises an antenna 16, and an rf 
unit 18 through which the signals received from the antenna pass, a 
digital processing unit 20 (e.g., an analog-to-digital converter) which 
creates digital signals representing psuedorange measurements. Also 
connected to the digital processing unit 20 is the stable receiver clock 
22 which has a constant frequency drift rate over at least a predetermined 
period of time. The receiver clock 22 can be represented by a temperature 
compensated crystal oscillator (TCXO), an oven controlled crystal 
oscillator (OCXO), or any clock having a constant frequency drift rate 
over a period of time. After creating signals representing the pseudorange 
measurements, as well as the clock bias, these signals are sent to a 
computer 24 where the processing scheme of FIG. 7, to be discussed below, 
provides the user with enhanced vertical position estimate data as well as 
a data indicating whether such estimates are of sufficient quality for the 
user's purpose. The computer 24 typically includes at least a 
microprocessor, and it generally includes the elements of a central 
processing unit (CPU). The computer 24 then outputs such data which can be 
used to change the position of the object 10. 
The position of the object 10 can be altered by a movement actuator 26. The 
actuator 26 can be, for example, a mechanical or electromechanical 
actuator on an airplane. The computer 24 can directly cause the actuator 
26 to move, or alternatively an operator of the movable object 10 can be 
apprised of the position estimate and the operator can then make an 
independent determination whether a positional or course change is 
appropriate. 
For example, if the system is used in an aircraft, the knowledge of the 
three-dimensional position estimate could be used to provide the operator 
with the ability to know with increased accuracy his position with respect 
to a flight path. Particularly useful is enhanced vertical position 
estimate obtained with the system of the instant invention. Provided with 
such an enhanced position estimate, a pilot could change altitude in 
response thereto. For example, if during a precision approach, the pilot 
realizes that he should be at an altitude greater or less than the 
estimated position, he can either increase or decrease his altitude. 
Alternatively, if the aircraft was using autopilot, the enhanced vertical 
position estimate would cause the aircraft to either increase or decrease 
its altitude automatically. 
The correlation between clock bias estimates and vertical position 
estimates has been found to be true even if one or more of the position 
range measurements had arbitrary biases. This is further exemplified in 
FIGS. 3A-3D. 
FIG. 3A shows a scatter plot of vertical position error versus clock bias 
error in 4-D estimates from snapshots of actual GPS range measurements 
taken one minute apart over a week while `selective availability` (SA) 
error was active. `Selective availability` pertains to the signal 
degradation introduced by the government to discourage unauthorized use of 
the satellite navigation system. FIG. 2B shows the corresponding results 
where a bias has been added to a randomly chosen pseudorange measurement 
in each snapshot to simulate a satellite anomaly. The bias has been drawn 
from a zero-mean Gaussian distribution with standard deviation of 100 m. 
FIGS. 3C and 3D show the results where the similarly drawn biases have 
been added to two and three measurements per snapshot, to simulate 
multiple anomalies. Note that as the range measurement biases are 
increased, the error in the clock bias estimate grows, and the error in 
the vertical position estimate grows roughly proportionally. Based on 
these figures the instant invention utilizes a finding that the quality of 
the vertical position estimate can be obtained in general from the error 
in the estimate of the receiver clock bias. Moreover, this holds true when 
no external information is available as to satellite operating conditions, 
or the presence of anomalies due to system malfunction. 
The flow chart of FIG. 4 describes the processing scheme executed by the 
computer 24 to provide an improved vertical position estimate based on the 
above-noted correlation between error in the clock bias estimate and that 
in the vertical position estimate. Initially, as given in step 30, the 
receiver antenna receives range measurements from time t.sub.0 to time t. 
Time t.sub.0 is a time before the instantaneous time t. This is relevant 
in that the processing scheme provides improved position estimates at time 
t and beyond, using times t.sub.0 through t, to aid in fitting a clock 
bias model; a discussion of which is relevant to step 36. Looking however, 
at step 32, the processing scheme computes the user position estimates in 
three coordinates x,y,z at time t, and at 34, computes the instantaneous 
receiver clock bias estimate b at time t, by solving for x, y, z, and b in 
the equations to follow. Given n satellites in view and the position of 
the ith satellite at time t denoted by x.sub.i, y.sub.i, z.sub.i, where 
i=1,2,3 . . . n. The measured ranges to the ith satellite is r.sub.i. 
Thus, using the following equation for as many satellites as are in view, 
eg. up to the ith satellite, the system solves for unknowns x, y, z, and 
b: 
##EQU1## 
The processor solves this equation by solving for the x, y, z and b at 
time t, for as many satellites as are in view, that is, up to the ith 
satellite. Given that satellites are constantly moving to and out of view, 
the number of satellites providing range measurements are a plurality, 
preferably greater than three. Note that t is the time interval during 
which clock bias is modeled for use in determining the three-dimensional 
position estimates. It is also important to note that the stability of the 
clock is relevant to determining how long the interval t.sub.0 to t should 
be. Hypothetically, if the clock used has a constant frequency drift rate 
for a maximum of one hour, the interval t.sub.0 to t should be less than 
or equal to one hour. 
Once the instantaneous receiver clock bias b(t) is known, the processing 
scheme models the receiver clock bias over time from t.sub.0 to t, in step 
36, so that smoothed estimates of clock bias can be obtained for that time 
period, thereby eliminating the need to later solve for clock bias, 
reducing the equation above to only three unknowns x, y, and z. To explain 
this step in greater detail, the system of the invention utilizes the 
premise that the rms error in the clock bias estimate based upon a single 
snapshot of the pseudorange measurements is given by: 
EQU .sigma..sub.b =.sigma..sub.URE .multidot.TDOP. 
where .sigma..sub.URE', is the rms error in the GPS range measurements, 
and TDOP is the time dilution of precision parameter reflecting the 
satellite geometry. In the presence of selective availability (SA), 
.sigma..sub.URE', has remained at about 25 m over the past two years. For 
the constellations of interest, TDOP typically ranges between 0.75 and 
1.25. 
Taking a typical value of 1 for TDOP in our simple calculations below, the 
rms error in clock bias estimated from a single snapshot of the range 
measurements is given by: 
EQU .sigma..sub.b .apprxeq..sigma..sub.URE .multidot..apprxeq.25 m. 
The system of the instant invention obtains GPS measurements over a time 
period (t.sub.0, t) during which the receiver clock is known to be stable, 
and models the clock bias at time t simply, as the quadratic function 
which appears at 36; 
EQU b(t)=b.sub.0 +b.sub.1 (t-t.sub.0)+b.sub.2 (t-t.sub.0).sup.2, 
and estimates parameters b.sub.0,b.sub.1, and b.sub.2 from the available 
measurements. Given k statistically independent measurement snapshots, the 
rms error in the clock bias estimate will be .sigma..sub.b 
.apprxeq..sigma..sub.URE /.sqroot.k. The number of independent measurement 
snapshots obtained from GPS in an hour depends upon the correlation time 
of the measurements. 
In differential mode, the effects of both selective availability (SA) and 
the ionosphere are substantially undone, the system of the instant 
invention implements the processing scheme whereby the number of 
independent measurements increases due to reduced correlation time (say, 1 
minute). The differential corrections improve the quality of the range 
measurements. Denoting the residual error as the user differential range 
error (UDRE), .sigma..sub.UDRE .apprxeq.3 m is realistic TDOP is 
unchanged. As above, the rms error in clock bias estimated from a single 
snapshot of the differentially-corrected range measurements, 
.sigma..sub.UDRE .apprxeq.3 m. Given, say, 1-minute measurement samples 
over an hour, this is provided by: .sigma..sub.b .apprxeq..sigma..sub.URE 
/.sqroot.k., which, based on the above calculations appears as; 
.apprxeq.3/.sqroot.60.apprxeq.0.4 m. Note, however that the clock model 
parameters can be estimated both more accurately and more quickly in 
differential mode. 
The system's provision for clock modeling can thus accommodate a 
shorter-term stability in differential mode than in the mode where no 
differential corrections are available. At the conclusion of this step, 
the processing scheme adaptively derives clock bias estimates in a 
quadratic function. The quadratic function, yielding a least square fit of 
b(T) where T is greater than or equal to t0, and less than or equal to t, 
is used to define b'(t) which is a more accurate estimate of the clock 
bias, at time t, to be further discussed in step 40. After obtaining a 
least square fit, step 38 verifies the stability of the clock over the 
predetermined interval in which the GPS measurements were provided. This 
is carried out by examining the rms residual error in the model obtained 
in step 36. If this condition is met, a more precise estimate of the user 
position can be recomputed in step 40 from a snapshot of the GPS range 
measurements via 3-D estimation. 
At step 40, a true clock bias is given by b'(t) and solved for 
instantaneous time t, by taking the smoothed clock bias estimate from the 
values provided by the least square fit, which is the true instantaneous 
clock bias. Position estimates x'(t), y'(t), z'(t) are now recomputed with 
this more accurate clock bias estimate z'(t), as a given, to provide 
improved position estimates. This estimation is a 3-D estimation, as now 
there are only three unknowns, now that the clock bias estimate is given 
from the least square fit. 
Once these estimates are recomputed, they are transmitted to a user, as 
shown in step 42, or to the movement actuator 26, as indicated in step 44. 
Similarly, a user can transmit these enhanced position estimates to a 
movable object after first obtaining the knowledge indicated in step 42. 
The above processing scheme carries out receiver clock aided navigation to 
provide improved three-dimensional position estimate, the effects of the 
improvement particularly shown in the degree of error associated with the 
vertical position estimate. 
FIG. 5 provides a graphical representation of the vertical position 
estimates obtained from GPS measurements using the clock aided navigation 
of the instant invention, versus the vertical position estimates obtained 
from GPS measurements without it. This figure shows the vertical position 
estimates obtained from the GPS measurements over a six-hour period. The 
error in vertical position estimates obtained from 4-D estimation snapshot 
by snapshot are shown as `original` and demonstrate a high degree of 
error. These are to be compared with the vertical position estimate 
obtained from 3-D estimation shown as `clock-aided` carried out by the 
instant invention where we have used the estimates of clock bias derived 
adaptively from the measurements over an hour. As shown, obtaining 
position estimates using the receiver clock bias offers a distinct 
improvement, as the clock-aided navigation in 3-D avoids the peak errors 
obtained with 4-D estimation alone. Note that the rms error is cut nearly 
in half, noted by 38 m versus 22-m. Although this figure shows an original 
and clock-aided waveform as being similar waveforms in about the first 
half-hour, note that this is due to a cold receiver start-up. The initial 
transients in clock-aided position estimates last about 30 minutes while 
the clock model parameters b.sub.0,b.sub.1, and b.sub.2 are not estimated 
well enough to offer any improvement in performance. 
FIGS. 6A and 6B show the cumulative distribution functions of position 
errors in snapshot-by-snapshot and the clock-aided estimation from 
3-minute samples of GPS measurements over a week. As shown in these 
figures clock aiding offers a sharp improvement in the vertical position 
estimates, but relatively little change in the horizontal position 
estimates. Note that in FIG. 6A, 99% of the users of conventional receiver 
navigation systems will obtain an position error of 150 meters. However, 
99% of the users of the clock aided system of the instant invention 
sampled over a week period, obtained a position error of 80 meters. Thus 
it is evident that the vertical position estimates are greatly improved 
both in terms of the rms error and the curtailment of the tails. The 
improvement in the probability of obtaining more accurate vertical 
position measurements is particularly important in view of the fact that 
the accuracy requirements in civil aviation are generally stated in terms 
of the tails of the error distributions. With respect to the horizontal 
position estimates, there is slight improvement, with 99% of the users of 
conventional receiver navigation systems obtaining a position error of 90 
meters, as opposed to the 99% of users of the clock-aided system of the 
instant invention obtaining a position error of 80 meters. 
From the above discussion it is evident that the clock aided navigation 
system of the instant invention enhances the likelihood of the user having 
more exact knowledge of the vertical position of the movable object. 
FIG. 7 exhibits the vertical position estimates computed snapshot by 
snapshot obtained by the system using the differential mode as discussed 
above, with and without clock aiding to demonstrate the improvement in 
position estimates. The measurements consist of 12-second samples of 
pseudorange snapshots. Again, clock aiding with the instant invention is 
seen to offer a distinct improvement in the quality of the vertical 
position estimates. Note also in this figure the initial transients 
resulting from a cold start of the receiver. The duration of the 
transients are much shorter than the transients of FIG. 7, as they last 
only about 15 minutes. This figure further evidences the fact that the 
clock parameters are learned by the processing scheme in step 36, in the 
differential mode, using the quality of the measurements and shorter 
correlation times. 
Turning now to the implementation of the invention to civil aviation, the 
accuracy requirements mandated for certain flight approaches are very 
stringent. For example, the accuracy requirements for Category I 
approaches can be stated as follows: 
(i) P(vertical position error&lt;10 m)&gt;0.95 
(ii) P (vertical position error&gt;20 m and Receiver Autonomous Integrity 
Monitoring fails to detect&lt;10.sup.7 
These requirements specify the quality of vertical position estimates at 
the decision height of 200 feet. The first relates to the accuracy 
provided by the receiver in general and the second deals specifically with 
each position estimate accepted for navigation. We will refer to these as 
the accuracy requirement and the integrity monitoring requirement, 
respectively. The integrity monitoring requirement will be discussed in 
greater detail in FIG. 8. Note, however that the clock-aided vertical 
position estimates in FIG. 7 satisfy the accuracy requirement cited above 
for Category 1 standards, as discussed above. 
The above discussion has focused on the system of the instant invention and 
its applicability for clock aided navigation. Now we will discuss the 
system of the instant invention and its further applicability for receiver 
autonomous integrity monitoring. As mentioned briefly this requirement is 
to assure, through integrity monitoring that an aircraft stays within the 
prescribed airspace. The focus in our discussion thus shifts from a point 
estimate of the position, as discussed above, to a region within which the 
aircraft is sure to be. As expected, the prescribed airspace gets 
increasingly tighter as the aircraft approaches the runway. As the system 
enhances the quality of vertical position estimates, our discussion will 
be limited to vertical position, or altitude. Through integrity 
monitoring, the system of the instant invention determines an interval 
which includes the user altitude by estimating such an interval via the 
correlation structure of the 4-D estimates. If the altitude or vertical 
position, estimate falls within this interval, and the length of the 
interval is consistent with the position uncertainty allowed under the 
receiver autonomous integrity monitoring requirements, the approach can 
proceed. If it is concluded that the requirement is not met, the approach 
is to be aborted. 
Looking to the flow chart of FIG. 8, note that the processing scheme picks 
up from step 40 of FIG. 4. Thus, given that the receiver clock is stable 
over a predetermined interval t0-t, b is obtained by adaptive estimation 
of the clock parameters over time, as discussed in step 36, and position 
estimates at instantaneous time t can be recomputed in step 40. As shown 
in FIG. 8, step 46 takes the smoothed clock bias value at time t and 
determines any discrepancy between this value and the value estimated from 
the current snapshot obtained from the satellite navigation system. The 
discrepancy reflects the error in the clock bias estimate, which is likely 
due to current satellite geometry, measurement errors, and any other 
anomalies. 
As applicant's have determined the strong correlation between the clock 
bias error and the vertical position error, this discrepancy is related to 
the error in the snapshot-based vertical position estimate. Thus, the 
determination of the clock bias error can be used to define a high 
confidence bound for the-vertical position error. Next at step 48, the 
processing scheme defines an error boundary on the vertical position error 
in the values of x'(t), y'(t) and z'(t) as obtained in step 40 of FIG. 4, 
or in x(t), y(t), z(t) as obtained in step 32. 
This boundary is the Integrity Level (IL) associated with the vertical 
position estimate, and is defined by: 
EQU IL=.alpha.+.beta..vertline..DELTA.b(t).vertline. meters 
where IL is the computed Integrity Level with the actual position error and 
.alpha. and .beta. are parameters whose values depend upon the number of 
satellites, the geographical position of such satellites and the rms range 
of error in the measurements are computed for a particular GPS 
constellation. These values are obtained either by simulating or obtaining 
actual range measurements which are used to generate the correlation 
structure between the receiver clock bias error and the position 
estimates, particularly as shown in FIGS. 1A and 1B. For example, using a 
24 GPS satellite constellation, these parameters for WAAS are defined as 
.alpha.=10 meters and .beta.=1.4 meters. 
With respect to .vertline..DELTA.b(t).vertline., this represents the 
absolute value of an accurate estimate of the instantaneous clock bias 
error. If the integrity level is greater than the alarm limit, as in step 
50 then the user and/or the movable object is notified to abort the 
approach as given by step 52 due to the deviation of the movable object 
from the permissible boundaries which define the alarm limit. The movable 
object particularly if on autopilot, would receive such information 
regarding the deviation and in turn, change its course of direction 
automatically in response thereto, simply by moving out of, or away from 
the path in which it is traveling. Alternatively, in the event that the 
integrity level is less than the alarm limit, the object may continue to 
maintain its position on the path as given in step 54. 
Referring to FIG. 9, the system can be implemented to provide receiver 
autonomous integrity monitoring for a category I approach. In accordance 
with the concept of Required Navigation Performance (RNP), the overall 
performance requirements for each phase of flight would be specified in 
terms of two surfaces or, tunnels, 50, 52, defined around the flight path 
60 constructed by joining the waypoints known to the airborne system. For 
purposes of example only, this discussion focuses on Category I 
approaches. 
As stated above, RNP mandates the use of an imaginary inner tunnel to 
define a region around the approach path where the navigation center of 
the aircraft must be 95% of the time. A caution may be required if the 
estimated position of the center of navigation of the aircraft violates 
the inner tunnel dimensions. The outer tunnel represent a containment 
surface that no part of the aircraft may breach without a warning being 
provided to the pilot. 
The dimensions of tunnels 50, 52 vary with the altitude, thus the tunnels 
become narrower as the aircraft approaches the runway 62. Category I 
approaches currently require navigational guidance down to a decision 
height (DH) of 200 feet. The proposed dimensions of the inner and the 
outer tunnels corresponding to this decision height, are the tightest to 
be encountered during a Cat I approach. As integrity monitoring carried 
out by the system protects against undetected violation of the containment 
surface, with receiver autonomous integrity monitoring, an alarm is to be 
made on the basis of an estimate of the total system error (TSE), defined 
as deviation of the aircraft from the defined flight path. The dimensions 
associated with the outer tunnel as the TSE alarm limits. 
For an aircraft not to breach the containment tunnel: 
EQU Total system error (TSE)=flight technical error (FTE)+navigation sensor 
error (NSE), 
EQU .ltoreq.outer tunnel dimension-aircraft dimension. 
An aircraft with a smaller FTE can tolerate a larger navigation error, and 
vice versa. This trade off is cited as an important benefit of the RNP 
concept, as RNP allows for an aircraft to adapt to the requirements of the 
airspace in terms of equipage and pilot skills, rather than the airspace 
to be adapted to the least-capable aircraft. For an aircraft with a 
semi-span of 110' and height of 20', the TSE alarm limits at the DH of 
200' roughly are 96 m laterally and 27 m vertically. Obviously, an 
aircraft indicated by the navigation sensor to be following the predefined 
flight path exactly can tolerate an NSE of 96 m laterally and 27 m 
vertically without fear of violating the containment surface. On the other 
hand, for another aircraft, indicated to be barely within the inner 
tunnel, the permissible margin of navigation error will be smaller: 62 m 
laterally and 17 in vertically. An aircraft indicated to be flying outside 
the inner tunnel will have a smaller margin of tolerable error yet. The 
maximum permissible error in a position estimate is known as the user's 
NSE alarm limit. The system of the instant invention is thus capable of 
proving applications for integrity monitoring of the NSE alarm limit, 
given the FTE and the tunnel dimension, to ensures that the position error 
does not exceed this limit. If it does, the approach is to be aborted. 
Under the RNP concept, the NSE alarm limit varies from aircraft to 
aircraft, pilot to pilot, and situation to situation. As noted earlier, 
the tunnels are at their narrowest at the DH, and the NSE alarm limits at 
its most stringent, and at earlier instants during the approach, both TSE 
and NSE alarm limits are larger. As noted earlier, the requirement on 
probability of undetected violations of the containment tunnel is 
specified on a `per approach` basis. This probability will be allocated 
appropriately along the approach path to obtain the probability of 
undetected violation on a `per sample` basis. With navigational guidance 
from WAAS, a pilot following the flight path closely could be virtually 
assured of meeting the integrity requirements of Category 1. However, a 
pilot with a significant FTE if the aircraft is on the edge of the inner 
tunnel may have to abort the approach, execute a go-around, and try again 
with better control of the airplane. 
Variations, modifications, and other implementations of what is described 
herein will occur to those of ordinary skill in the art without departing 
from the spirit and scope of the invention as claimed. Accordingly, the 
invention is to be defined not by the preceding illustrative description 
but instead by the following claims.