Location of a moving target with round trip time vectors using an airborne platform
A method and devices are disclosed that locate a target station moving at a constant velocity. A method and devices are disclosed for producing an RTT vector that is based upon the changes in position of the airborne measuring station position and the relative change in position of the target station. In one embodiment, the target station is an access point or station conforming to the IEEE 802.11 Standard and the airborne measuring station may also be a device that conforms to the IEEE 802.11 Standard.
1. A method in an airborne station for determining a location of a moving ground-based wireless device (WD), the method comprising:
at each of a plurality of positions of the airborne station, at times t n−q for q=0 to q:
determining the longitude X n−q and latitude, Y n−q of the airborne station;
determining a round trip time RTT between the airborne station and the WD;
determining a distance, Rn, of the WD from the airborne station based at least in part on the determined longitude, latitude and RTT;
determining differences between earlier and later determinations of the latitude and longitude and differences (ΔRTTs) between earlier and later determinations of RTT;
scaling the RTTs to account for horizontal distance and altitude of the airborne station;
minimizing residuals between the determined ΔRTTs and a model ΔRTT, the model ΔRTT being based at least in part on parameters α, v N , and v E of the model, α being an angle between Rn and a reference axis, v N being a velocity of the WD in a first direction and v E being a velocity of the WD in a second direction perpendicular to the first direction; and
determining a location of the WD based at least in part on a value for a that minimizes the residuals and based at least in part on the distance Rn, the WD location being boxed by α±Δα, and by R±ΔR, ΔR being related to an uncertainty in short interface spacing (SIFS) time and where α and Δα are derived from a correlation matrix based on the model.
2. The method of claim 1 , wherein the model ΔRTT is based at least in part on:
Δ
R
T
T
=
(
2
R
n
C
)
{
(
1
+
d
n
‐
q
para
R
n
)
2
+
(
d
n
‐
q
perp
R
n
)
2
-
1
}
where d n−q para =COS(α) Δr N +SIN(α) Δr E +[COS(α) v N +SIN(α) v E ]*(t n −t n−q );
|d n−q perp |=|−SIN(α) Δr N +COS(α) Δr E +[−SIN(α) v N +COS(α) v E ]*(t n −t n−q )|
Δr N is a change in latitude of the WD; Δr E is a change in longitude of the WD and C is a speed of light.
3. The method of claim 1 , wherein values of v N and v E that minimize the residuals are used to predict an average velocity v=√{square root over (v N 2 +v E 2 )} of WD and a future location of the WD.
4. The method of claim 1 , wherein the RTTs are scaled by a factor given by
F
=
R
n
2
-
Alt
n
2
R
n
;
where Alt n is an altitude of the airborne station.
5. The method of claim 1 , wherein the residuals are minimized based at least in part on minimizing a sum of squared residuals.
6. The method of claim 1 , wherein a measure of a final value of an RTT is based at least in part on an average of a number predetermined RTTs.
7. The method of claim 1 , wherein Rn is determined based at least in part on a delay that is determined when the WD is stationary.
8. The method of claim 1 , wherein the residuals are based at least in part on a horizontal distance between the WD and the airborne station.
9. An airborne station for determining a location of a moving ground-based wireless device (WD), the airborne station comprising processing circuitry configured to:
at each of a plurality of positions of the airborne station, at times t n−q for q=0 to q:
determine the longitude X n−q and latitude, Y n−q of the airborne station;
determine a round trip time RTT between the airborne station and the WD;
determine a distance, R n , of the WD from the airborne station based at least in part on the determined longitude, latitude and RTT;
determine differences between earlier and later determinations of the latitude and longitude and differences (ΔRTTs) between earlier and later determinations of RTT;
scale the RTTs to account for horizontal distance and altitude of the airborne station;
minimize residuals between the determined ΔRTTs and a model ΔRTT, the model ΔRTT being based at least in part on parameters α, v N , and v E of the model, a being an angle between R n and a reference axis, v N being a velocity of the WD in a first direction and v E being a velocity of the WD in a second direction perpendicular to the first direction; and
determine a location of the WD based at least in part on a value for a that minimizes the residuals and based at least in part on the distance Rn, the WD location being boxed by α±Δα, and by R±ΔR, ΔR being related to an uncertainty in short interface spacing (SIFS) time and where α and Δα are derived from a correlation matrix based on the model.
10. The airborne station of claim 9 , wherein the model ΔRTT is based at least in part on:
Δ
R
T
T
=
(
2
R
n
C
)
{
(
1
+
d
n
‐
q
para
R
n
)
2
+
(
d
n
‐
q
perp
R
n
)
2
-
1
}
where d n−q para =COS(α)Δ r N +SIN(α)Δ r E +[COS(α) v N +SIN(α) v E ]*( t n −t n−q );
| d n−q perp |=|−SIN(α) Δ r N +COS(α) Δ r E +[−SIN(α) v N +COS(α) v E ]*( t n −t n−q )|
Δr N is a change in latitude of the WD; Δr E is a change in longitude of the WD and C is a speed of light.
11. The airborne station of claim 9 , wherein values of v N and v E that minimize the residuals are used to predict an average velocity v=√{square root over (v N 2 +v E 2 )} of WD and a future location of the WD.
12. The airborne station of claim 9 , wherein the RTTs are scaled by a factor given by
F
=
R
n
2
-
Alt
n
2
R
n
;
where Alt n is an altitude of the airborne station.
13. The airborne station of claim 9 , wherein the residuals are minimized based at least in part on minimizing a sum of squared residuals.
14. The airborne station of claim 9 , wherein a measure of a final value of an RTT is based at least in part on an average of a number predetermined RTTs.
15. The airborne station of claim 9 , wherein Rn is determined based at least in part on a delay that is determined when the WD is stationary.
16. The airborne station of claim 9 , wherein the residuals are based at least in part on a horizontal distance between the WD and the airborne station.