**THE TWENTY-NINTH MEETING OF THE**

**INFORMAL PACIFIC ATC CO-ORDINATING GROUP**

**(IPACG/29)**

(Fukuoka, Japan, 29-31 October 2008)

Agenda Item 5: Air Traffic Management (ATM) Issues

**The Effect of Strategic Lateral Offset Procedures (SLOP) on Operations
in Airspace with 30 NM Lateral and 30 NM Longitudinal Separation
Standards in Place**

(Presented by the Federal Aviation Administration)

**[SUMMARY]{.underline}**

This paper provides an illustration of the effect of SLOP on the lateral
overlap probability used for the 30 nautical mile (NM) longitudinal and
30 NM lateral separation standards. An increased use of SLOP allows for
an overall decrease in the lateral overlap probability for use in 30 NM
longitudinal collision risk estimate. The use of SLOP has a very small
effect on the lateral overlap probability for the 30 NM lateral
collision risk model for same direction aircraft. A slight overall
increase in the lateral overlap probability for use in the 30 NM lateral
collision risk estimate where the opposite direction is on each pilot's
right side is observed. The resulting decrease in the lateral overlap
probability value from the use of SLOP for use in the vertical and
longitudinal collision risk models more than compensates for the slight
increase in the lateral overlap probability value resulting from the use
of SLOP used in the lateral collision risk model. This result, of
course, assumes the lateral offset procedure is used in accordance with
the recommended practice.

1.  **Introduction**

    1.  At the Twenty-Eighth Meeting of the Informal Pacific ATC
        Coordinating Group (IPACG/28), the Federal Aviation
        Administration (FAA) presented information on the increased use
        of, and safety benefits gained from, the use of Strategic
        Lateral Offset Procedures (SLOP) in oceanic and remote airspace
        (reference 1). This information briefly explained the importance
        of SLOP as it reduces the risk of collision in the vertical
        dimension, particularly for route systems with an alternate
        Flight Level Orientation Scheme (FLOS). Random distribution of
        aircraft on and to the right of the centerline is key to
        compensating for the extremely accurate navigation capabilities
        of modern aircraft based on Global Positioning System (GPS)
        navigation. By randomly offsetting either zero (0), one (1) or
        two (2) NM right of the center line, SLOP significantly reduces
        vertical risk and also incorporates wake turbulence avoidance
        procedures.

    2.  The use of SLOP in airspace also affects the estimate of
        collision risk in the lateral and longitudinal dimensions. The
        purpose of this paper is to illustrate this effect in airspace
        with the 30 NM lateral and 30 NM longitudinal separation
        standards in place.

2.  **Discussion**

    1.  The FAA has made significant contributions to the work which
        assessed the effect of the use of SLOP on collision risk.
        Reference 2 derives formulas and presents results for estimating
        the probability that airplanes assigned to adjacent parallel
        routes will have laterally overlapping positions. An important
        parameter in the collision risk model is the lateral overlap
        probability.

    2.  The definitions for the lateral overlap probability for the
        longitudinal and lateral collision risk models are provided in
        Table 1. We consider the effect of SLOP on airspace operations
        which utilize the 30 NM lateral and 30 NM longitudinal
        separation standards separately.

  ------------------------ ----------------------------------------------
  **Longitudinal Collision Lateral overlap probability is the probability
  Risk Model**             that airplanes assigned to the same route have
                           laterally overlapping positions.

  **Lateral Collision Risk Lateral overlap probability is the probability
  Model**                  that airplanes assigned to adjacent parallel
                           routes have laterally overlapping positions
  ------------------------ ----------------------------------------------

**Table 1.** Definitions of Lateral Overlap Probability for the
Longitudinal and Lateral Collision Risk Model

3.  *Effect of SLOP on Airspace Operations Utilizing the 30 NM
    Longitudinal Separation Standard*

    1.  The use of SLOP in airspace affects the risk of collision due to
        the loss of planned longitudinal separation in a similar manner
        as the use of SLOP affects the risk of collision in the vertical
        dimension. When the longitudinal separation standard is applied,
        the pair of airplanes are operating on the same track and flight
        level. The planned lateral separation between the pair of
        airplanes is equal to 0 NM. Both of the airplanes in the pair
        have the option to initiate SLOP and can elect to operate on one
        of the two available offset paths: the path 1 NM to the right of
        the center line or the path 2 NM to the right of center line.

    2.  The lateral navigation performance for the Required Navigation
        Performance (RNP) 4 airplanes eligible for the 30 NM
        longitudinal separation standards is modeled by a double double
        exponential (DDE) density function:

$f\left( x;\alpha,\lambda_{1},\lambda_{2} \right) = \frac{1 - \alpha}{2\lambda_{1}}e^{\frac{- |x|}{\lambda_{1}}} + \frac{\alpha}{2\lambda_{2}}e^{\frac{- |x|}{\lambda_{2}}}$
where 0 \< α \< 1, and 0 \< λ~1~ \< λ~2~ (1)

3.  The DDE density function, *f(x;α,λ~1~, λ~2~),* is a weighted sum of
    two double exponential densities, a "core" density with parameter
    λ~1~, and a "tail" density with parameter λ~2~. The weights are 1-α
    and α; the core density,
    $\frac{1}{2\lambda_{1}}e^{\frac{- |x|}{\lambda_{1}}}$, describes
    typical lateral deviations from the centerline of the aircraft's
    intended route; and the tail density,
    $\frac{1}{2\lambda_{2}}e^{\frac{- |x|}{\lambda_{2}}}$, describes
    atypical lateral deviations from the centerline of the intended
    route. The shape parameters, *λ~1~* and *λ~2~*, are respectively
    $\frac{\sqrt{2}}{2}$ times the standard deviations of typical
    lateral errors and atypical errors (reference 2). It is assumed that
    aircraft eligible for the 30 NM longitudinal separation standard
    meet level 4 of required navigation performance (RNP 4). The
    requirement for RNP 4 implies that 95 percent of typical deviations
    lie within 4 NM of the route center line. However, data observations
    of RNP 4 aircraft, or aircraft equipped with GPS, show the lateral
    navigation performance is much better than the 4 NM requirement for
    containment (reference 3). Therefore, to represent the actual
    lateral navigation performance of these aircraft more accurately, we
    assume that 95 percent of typical deviations lie within 0.15 NM of
    the route center line. Therefore, *λ~1~*, the parameter implied by
    the 95 percent containment requirement is equal to
    $- \frac{0\text{.}\text{15}}{\text{ln}(0\text{.}\text{05})}$. Then,
    *λ~2~* is the lateral distance between the routes, 30 NM, a
    conservative value which maximizes the probability of lateral
    overlap.

4.  FANS 1/A airplanes eligible for the 30 NM longitudinal separation
    standard utilize GPS as the navigation system. Therefore, the
    lateral deviations of both airplanes in the aircraft pair follow the
    same DDE density. Figure 1 provides an illustration of the possible
    positions of the airplanes which are following the same route
    utilizing SLOP when longitudinal separation is applied. The shaded
    grey airplanes in Figure 1 represent the possible offset locations
    from the route center line.

![](media/image1.wmf){width="2.298611111111111in" height="3.90625in"}

**Figure 1.** Illustration of the Possible SLOP Offsets for Airplanes
Following the Same Track and Flight Level in Longitudinal Separation

5.  The resulting probability of lateral overlap depends on the
    probability that a randomly chosen aircraft elects to fly an offset.
    The observed ADS-C data from Oakland Oceanic Center show a very
    small proportion of operations utilize SLOP.

6.  It is assumed that all airplanes eligible for the 30 NM longitudinal
    separation standard are capable of flying offsets. We also assume
    that any randomly chosen airplane has met the RNP 4, i.e. all
    airplanes are eligible for the reduced longitudinal separation
    standard. We do not consider the proportion of GPS and non-GPS
    operations. For illustration purposes, various proportions of
    operations choosing to elect an offset are examined.

7.  The DDE density function in equation (1) is used to model the
    lateral overlap probability. The lateral overlap probability for
    airplanes that operate with GPS navigation systems are assumed to
    perform at a level equivalent to RNP 0.15 as noted in reference 2.
    Reference 2 (paragraph 5.4) also provides the value for α in
    equation (1) for GPS airplanes as 4.8 x 10^-5^. Table 2 and Figure 2
    present these results.

8.  The unmodified lateral overlap probability provided in Table 2
    corresponds to the lateral displacement of 0 NM (e.g. flying on
    route center line), and offsets to the right of center line of
    either 1 or 2 NM. The probability of lateral displacement shown in
    Table 2 represents the proportion of airplanes that elect to fly on
    center line and those choosing an offset. There are many possible
    values for the probability that an individual aircraft chooses to
    fly an offset. One possible combination is shown in Table 2; this
    combination represents an even mix amongst the three possible
    choices for applying SLOP. In Table 2, the proportion of airplanes
    electing to fly on route center line is shown as 34 percent, and the
    proportions of airplanes electing to fly offsets of 1 NM and 2 NM
    are both 33 percent. Figure 2 shows the overall lateral overlap
    probability result for the possible lateral displacement
    combinations. The data shown in Figure 2 begins with 100 percent of
    the airplanes flying on route center line and ends with the even mix
    proportion shown in Table 2 where 34 percent of the airplanes fly on
    route centerline.

  ---------------- ------------------ ---------------- ---------------------
  RNP Equivalent   0.15                                
  (for GPS                                             
  Airplanes)                                           

  α                4.08E-05                            

  λ~1~             0.0500712                           

  λ~2~             30                                  

  λ~y~             0.0321                              

                                                       

  **Lateral        **Unmodified       **Probability of **Resulting
  Displacement**   Lateral Overlap    Lateral          Probability of
                   Probability        Displacement**   Lateral Overlap**
                   (P~y~(S))**                         

  0                3.205E-01          0.34             0.1090

  1                9.870E-08          0.33             3.257E-08

  2                8.168E-08          0.33             2.695E-08

                                                       0.10898
  ---------------- ------------------ ---------------- ---------------------

**Table 2.** The Effect of SLOP on the Lateral Overlap Probabilities for
the 30 NM Longitudinal Separation Standard

![](media/image2.wmf){width="5.284722222222222in"
height="2.998611111111111in"}

**Figure 2.** Probability of Lateral Overlap with an Increasing
Proportion of Operations Applying SLOP for the 30 NM Longitudinal
Separation Standard

9.  The results provided in Table 2 and Figure 2 show that an increased
    use of SLOP relates to a lower lateral overlap probability in
    airspace where GPS airplanes operate. These results show that in the
    event a longitudinal overtake occurs, the chance that the airplanes
    are in lateral overlap decreases with the use of SLOP. The overall
    percent decrease in the lateral overlap probability ranges from 10
    to 66 percent of the lateral overlap probability associated with all
    aircraft flying on route center line.

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4.  *Effect of SLOP on Airspace Operations Utilizing the 30 NM Lateral
    Separation Standard for Same Direction Routes*

    1.  When utilizing SLOP, the actual lateral separations between
        airplanes operating on same direction routes separated laterally
        by 30 NM ranges from 28 NM through 32 NM. The direction of the
        lateral displacement from route center line is to the pilot's
        right side, either 1 NM or 2 NM off route center line. The
        smallest lateral separation occurs when the airplane operating
        on the route located on the left side elects an offset 2 NM from
        route center line and the airplane operating on the route
        located on the right side chooses not to offset and operates on
        route center line. Figure 3 shows the possible lateral
        separation between aircraft for same direction routes with 30 NM
        lateral spacing. The shaded grey airplanes in Figure 3 represent
        the possible offsets locations from route center line.

![](media/image3.wmf){width="4.581944444444445in"
height="2.582638888888889in"}

**Figure 3.** Illustration of the Possible SLOP Offsets for Airplanes
Traveling on Same Direction Adjacent Routes Separated by 30 NM

2.  It is assumed that all airplanes eligible for the 30 NM lateral
    separation standard are capable of flying offsets. We also assume
    that any randomly chosen airplane has met the RNP 4, i.e. all
    airplanes are eligible for the reduced lateral separation standard.
    It is assumed the airplanes on these routes all use GPS for
    navigation. We do not consider the proportion of GPS and non-GPS
    operations. For illustration purposes, various proportions of
    operations choosing to elect an offset are examined.

3.  The DDE density function in equation (1) is used to model the
    lateral overlap probability. The lateral overlap probability for
    airplanes that operate with GPS navigation systems are assumed to
    perform at a level equivalent to RNP 0.15 as noted in reference 2.
    Reference 2 (paragraph 5.4) also provides the value for α in
    equation (1) for GPS airplanes as 4.8 x 10^-5^.

4.  The probability of each possible lateral separation distance between
    a pair of airplanes under SLOP depends on the likelihood that a
    pilot elects to fly an offset. Under SLOP, the possible lateral
    separation distances are *S~y~*, *S~y~*+1, *S~y~*+2, *S~y~*-1, and
    *S~y~*-2, where *S~y~* is the nominal lateral separation between the
    routes, in the case of the 30 NM lateral separation standard, *S~y~*
    is equal to 30 NM.

5.  Consistent with the same notation found in reference 2, we imagine
    that from our viewpoint the traffic on the two parallel adjacent
    routes is moving away from us, so that it makes sense to refer to a
    "left" route and a "right" route. Let L be the intended offset of
    the airplane chosen from the left route, and R be the intended
    offset of the airplane chosen from the right route. To compute the
    probability that the intended separation between a randomly chosen
    pair of airplanes is 30 NM, both airplanes would have chosen to fly
    the route center line or the same lateral offset, e.g. the
    individual lateral displacement from route center line would be the
    same for both airplanes, P(L=0, R=0) + P(L=1, R=1) + P(L=2, R=2).

6.  In addition, the probability that the lateral separation between a
    randomly chosen pair of airplanes is equal to 28 NM is equal to
    P(L=2,R=0). Table 3 contains a complete list of all possible
    combinations for the system of two parallel routes carrying same
    direction traffic.

  -------------------------------- --------------------------------------
  **Lateral Separation Distance    **Corresponding Probability**
  with the Application of SLOP     
  (NM)**                           

  28                               P(L=2, R=0)

  29                               P(L=1, R=0) + P(L=2, R=1)

  30                               P(L=0, R=0) + P(L=1, R=1) + P(L=2,
                                   R=2)

  31                               P(L=0, R=1) + P(L=1, R=2)

  32                               P(L=0, R=2)
  -------------------------------- --------------------------------------

**Table 3.** Lateral Separation Distances and the Corresponding
Probabilities with the Use of SLOP for Same Direction Routes with 30 NM
Lateral Spacing

7.  Table 4 and Figure 4 present the results showing the effect of SLOP
    on the 30 NM lateral separation standard for same direction routes.
    There are many possible values for the probability that a randomly
    chosen airplane elects an offset. For illustration purposes we show
    a range of possible values in Figure 4. One possible combination is
    shown in Table 4; this combination represents an even mix amongst
    the three possible choices for applying SLOP. In Table 4, the
    proportion of airplanes electing to fly on route center line is
    shown as 34 percent, and the proportions of airplanes electing to
    fly offsets of 1 NM and 2 NM are both 33 percent. Figure 4 shows the
    overall lateral overlap probability result for the possible lateral
    displacement combinations. The data shown in Figure 4 begins with
    100 percent of the airplanes flying on route center line and ends
    with the even mix of airplanes applying offsets where 34 percent of
    the airplanes operate on route centerline.

  ----------------- -------------------- ---------------- ------------- ------------- -------
  RNP Equivalent    0.15                                                              
  (for GPS                                                                            
  Airplanes)                                                                          

  α                 4.08E-05                              P(offset=0)                 0.34

  λ~1~              0.0500712                             P(offset=1)                 0.33

  λ~2~              30                                    P(offset=2)                 0.33

  λ~y~              0.0321                                                            

                                                                                      

  **Lateral         **Unmodified Lateral **Probability of               **Resulting   
  Displacement**    Overlap Probability  Lateral                        Probability   
                    (P~y~(S))**          Displacement**                 of Lateral    
                                                                        Overlap**     

  28                3.433E-08            0.1122                         3.852E-09     

  29                3.321E-08            0.2211                         7.342E-09     

  30                3.212E-08            0.3334                         1.071E-08     

  31                3.107E-08            0.2211                         6.869E-09     

  32                3.005E-08            0.1122                         3.371E-09     

                                                                        3.214E-08     
  ----------------- -------------------- ---------------- ------------- ------------- -------

**Table 4.** The Effect of SLOP on the Lateral Overlap Probabilities for
Routes with Same Direction Traffic for the 30 NM Lateral Separation
Standard

![](media/image4.wmf){width="5.531944444444444in"
height="3.3027777777777776in"}

**Figure 4.** Probability of Lateral Overlap for the 30 NM Lateral
Separation Standard for Routes with Same Direction Traffic with an
Increasing Proportion of Operations Applying SLOP

8.  The results provided in Table 4 and Figure 4 show that an increased
    use of SLOP on routes with same direction traffic relates to a very
    small increase in lateral overlap probability in airspace where GPS
    airplanes operate. The overall percent increase in the lateral
    overlap probability ranges from 0.03 to 0.07 percent of the lateral
    overlap probability associated with all aircraft flying on route
    center line. One reason for the minimum impact on the lateral
    overlap probability for the 30 NM lateral separation standard for
    routes with same direction traffic is under SLOP the chance that the
    pair of airplanes are actually separated by 30 NM is higher than all
    other possible lateral separations.

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5.  *Effect of SLOP on Airspace Operations Utilizing the 30 NM Lateral
    Separation Standard for Routes with Opposite Direction Traffic on
    Each Pilot's Right*

    1.  When applying SLOP, the actual lateral separations between
        airplanes operating on routes separated by 30 NM with the
        opposite direction route on each pilot's right, ranges from 26
        NM through 30 NM. The direction of the lateral displacement is
        to the pilot's right side, either 1 NM or 2 NM from route center
        line. The smallest lateral separation occurs when the airplane
        operating on the route located on the left side elects an offset
        2 NM from route center line and the airplane operating on the
        route located on the right side also elects an offset 2 NM to
        the right of route center line. Figure 6 shows the possible
        lateral separation between aircraft on parallel routes where the
        opposite direction is on each pilot's right side. The shaded
        grey airplanes in Figure 6 represent the possible offset
        positions from route center line.

![](media/image5.wmf){width="5.186111111111111in"
height="3.0729166666666665in"}

**Figure 6.** Illustration of the Possible SLOP Offsets for Airplanes
Traveling in Opposite Directions on Routes Separated by 30 NM (Where the
Opposite Direction Route is on Each Pilot's Right)

2.  Again, it is assumed that all airplanes eligible for the 30 NM
    lateral separation standard are capable of flying offsets. We also
    assume that any randomly chosen airplane has met the RNP 4, e.g. all
    airplanes are eligible for the reduced lateral separation standard.
    It is assumed the airplanes on these routes all use GPS for
    navigation. We do not consider the proportion of GPS and non-GPS
    operations. For illustration purposes, various proportions of
    operations choosing to elect an offset are examined.

3.  The DDE density function in equation (1) is used to model the
    lateral overlap probability. The lateral overlap probability for
    airplanes that operate with GPS navigation systems are assumed to
    perform at a level equivalent to RNP 0.15 as in reference 2.
    Reference 2 (paragraph 5.4) also provides the value for α in
    equation (1) for GPS airplanes as 4.8 x 10^-5^.

4.  The probability of each possible lateral separation distance between
    a pair of airplanes depends on the likelihood that a pilot elects to
    fly an offset. Under SLOP, the possible lateral separation distances
    are *S~y~*, *S~y~*-1, *S~y~*-2, *S~y~*-3, and *S~y~*-4, where *S~y~*
    is the nominal lateral separation between the routes, in the case of
    the 30 NM lateral separation standard, *S~y~* is equal to 30 NM.

5.  Consistent with the same notation found in reference 2, we imagine
    that from our viewpoint the traffic on the left route is moving away
    from us, and the traffic on the right route is moving toward us.
    Again we let L be the intended offset of the airplane chosen from
    the left route, and R be the intended offset of the airplane chosen
    from the right route. To compute the probability that the intended
    separation between a randomly chosen pair of airplanes is 30 NM,
    both airplanes would have chosen to fly the route center line,
    P(L=0, R=0).

6.  In addition, the probability that the lateral separation between a
    randomly chosen pair of airplanes is equal to 26 NM is equal to
    P(L=2, R=2). Table 5 contains a complete list of all possible
    combinations for the system of two parallel routes carrying opposite
    direction traffic where the opposite direction route is on each
    pilot's right.

  -------------------------------- --------------------------------------
  **Lateral Separation Distance    **Corresponding Probability**
  with the Application of SLOP     
  (NM)**                           

  26                               P(L=2, R=2)

  27                               P(L=1, R=2) + P(L=2, R=1)

  28                               P(L=0, R=2) + P(L=2, R=0) + P(L=1,
                                   R=1)

  29                               P(L=0, R=1) + P(L=1, R=0)

  30                               P(L=0, R=0)
  -------------------------------- --------------------------------------

**Table 5.** Lateral Separation Distances and the Corresponding
Probabilities with the Use of SLOP for Opposite Direction Routes with 30
NM Lateral Spacing and the Opposite Direction Traffic is on Each Pilot's
Right

7.  Table 6 and Figure 6 present the results showing the effect of SLOP
    on the 30 NM lateral separation standard where the opposite
    direction traffic is on each pilot's right. There are many possible
    values for the probability that a randomly chosen airplane elects an
    offset. For illustration purposes we show a range of possible
    values. One possible combination is shown in Table 6; this
    combination represents an even mix amongst the three possible
    choices for applying SLOP. In Table 6, the proportion of airplanes
    electing to fly on route center line is shown as 34 percent, and the
    proportions of airplanes electing to fly offsets of 1 NM and 2 NM
    are both 33 percent. Figure 6 shows the overall lateral overlap
    probability result for the possible lateral displacement
    combinations. The data shown in Figure 6 begins with 100 percent of
    the airplanes flying on route center line and ends with the even mix
    of airplanes applying offsets where 34 percent of the airplanes
    operate on route centerline.

  ---------------- -------------- --- ---------------- ------------- ------------- --------------
  RNP Equivalent   0.15                                P(offset=0)                 0.34
  (for GPS                                                                         
  Airplanes)                                                                       

  α                4.08E-05                            P(offset=1)                 0.33

  λ~1~             0.0500712                           P(offset=2)                 0.33

  λ~2~             30                                                              

  λ~y~             0.0321                                                          

                                                                                   

  **Lateral        **Unmodified       **Displacement                 **Resulting   
  Displacement**   Lateral            Probability**                  Probability   
                   Overlap                                           of Lateral    
                   Probability                                       Overlap**     
                   (P~y~(S))**                                                     

  26               3.670E-08          0.1089                         3.997E-09     

  27               3.550E-08          0.2178                         7.731E-09     

  28               3.433E-08          0.3333                         1.144E-08     

  29               3.321E-08          0.2244                         7.452E-09     

  30               3.212E-08          0.1156                         3.713E-09     

                                                                     3.434E-08     
  ---------------- -------------- --- ---------------- ------------- ------------- --------------

**Table 6.** The Effect of SLOP on the Lateral Overlap Probabilities for
Routes with Opposite Direction Traffic Where the Opposite Direction
Traffic is on Each Pilot's Right

![](media/image6.wmf){width="5.461111111111111in"
height="3.2604166666666665in"}

**Figure 6.** Probability of Lateral Overlap for the 30 NM Lateral
Separation Standard for Routes with Opposite Direction Traffic on Each
Pilot's Right with an Increasing Proportion of Operations Applying SLOP

8.  The results provided in Table 6 and Figure 6 show that an increased
    use of SLOP relates to a slightly elevated lateral overlap
    probability for routes with the opposite direction route on each
    pilot's right side. The overall percent increase in the lateral
    overlap probability ranges from 1.03 to 6.90 percent of the lateral
    overlap probability associated with all aircraft flying on route
    center line.

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6.  The resulting decrease in the lateral overlap probability value from
    the use of SLOP for use in the vertical and longitudinal collision
    risk models more than compensates for the slight increase in the
    lateral overlap probability value resulting from the use of SLOP
    used in the lateral collision risk model. This result, of course,
    assumes the lateral offset procedure is used in accordance with the
    recommended practice.

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3.  **Recommendation**

    1.  The meeting is invited to note the information provided.

**[References]{.underline}**

1.  "Summary of Discussions Twenty-Eighth Meeting of the Informal
    Pacific Air Traffic Control Coordinating Group (IPACG/28)", 12-16
    May 2008 Las Vegas, Nevada USA.

2.  Flax, Bennett, "Lateral Overlap Probabilities in Route Systems Where
    Lateral Offsets are Applied", WP/5, ICAO Separation and Airspace
    Safety Panel (SASP), First Meeting of the Working Group of the Whole
    (WG/WHL/1), Canberra, Australia, May 2002.

3.  Gerhardt-Falk, C., Martin, L., Ellis, S., "Correlation of Airborne
    Position Estimates to Ground Based Independent Estimates and
    Deviations from Flight-Planned Tracks," American Institute of
    Aeronautics and Astronautics (AIAA) Guidance, Navigation, and
    Control Conference, Hilton Head, South Carolina, USA, August 20-23,
    2007 (AIAA 2007-6520 - Invited Session).