Geo-locating moving wireless devices

1. A method in a wireless device (WD) for determining a best-fit geo-location of a target station using a plurality of round-trip times (RTTs), each RTT being a time elapsed between a transmission of a ranging packet by the WD and a reception of a response packet by the WD, the target station being movable, the method comprising:

assigning values to current target station parameters, the current target station parameters including a current location for the target station and movement parameters;

determining a plurality of square residuals based at least in part on the current target station parameters, each square residual of the plurality of square residuals corresponding to one RTT, determining the plurality of square residuals including:

determining a first group of residuals based on stationary parameters and a second group of residuals based on the movement parameters;

for each of the first group and the second group of residuals:

determining a model fit probability based at least in part on one of the determined first group of residuals and the determined second group of residuals;

determining a sum of squared residuals (SSR);

performing non-linear fitting based at least on the determined SSR;

determining new parameters based at least on the non-linear fitting;

determining new residuals based at least in part on the determined new parameters;

determining a minimum of the SSR based at least on the plurality of square residuals;

determining best-fit parameters based at least in part on the determined minimum of the SSR;

performing an F-test to determine whether the non-linear fitting corresponding to moving parameters is a better fit than the non-linear fitting corresponding to the stationary parameters;

if the non-linear fitting corresponding to the moving parameters is the better fit, using the non-linear fitting corresponding to the moving parameters to determine the best-fit geo-location; and

if the non-linear fitting corresponding to the moving parameters is not the better fit and one of a first condition is met and a second condition is met, using the non-linear fitting corresponding to the stationary parameters to determine the best-fit geo-location, the first condition being met when a first difference between the SSR and a subsequent SSR is less than a predetermined minimum, the second condition being met when an absolute value of a second difference between a target station parameter and a subsequent target station parameter is less than the predetermined minimum; and

determining the best-fit geo-location of the target station based at least on the best-fit parameters.

2. The method of claim 1 , wherein performing non-linear fitting and determining new parameters are further based on a Levenberg-Marquardt process.

3. The method of claim 1 , wherein the first group of residuals is defined by:

⁢

f

⁡

(

x

i

,

α

)

=

α

OFF

+

(

2

c

)

*

d

⁡

(

x

i

,

α

)

.

⁢

Where

⁢

⁢

d

⁡

(

x

i

,

α

)

=

[

(

x

i

LAT

-

α

LAT

)

2

+

(

(

x

i

L

⁢

⁢

0

⁢

N

-

α

LON

)

*

cos

⁡

(

x

i

LAT

)

)

2

+

(

x

i

ALT

-

α

ALT

CONVERSION

)

2

]

1

2

;

and

the second group of residuals is defined by:

⁢

f

⁡

(

x

i

,

α

)

=

α

OFF

+

(

2

c

)

*

d

⁡

(

x

i

,

α

)

,

⁢

Where

⁢

⁢

d

⁢

(

x

i

,

α

)

=

[

(

x

i

LAT

-

(

α

LAT

+

α

VelNorth

*

x

i

TD

)

)

2

+

(

(

x

i

LON

-

(

α

LON

+

α

VelEast

*

x

i

TD

)

)

*

cos

⁡

(

x

i

LAT

)

)

2

+

(

x

i

ALT

-

α

ALT

CONVERSION

)

2

]

1

2

,

x i represents WD location parameters,

α represents location parameters of the target station,

x i TD is a negative time span of the corresponding RTT and a current time,

α VelEast is in degrees latitude per time and is converted to a spherical coordinate by multiplying by cos(x i LAT ) before converting units, and

CONVERSION refers to conversion of altitude units to geographic distance units where speed of light is in units of geographic distance divided by units of RTT.

4. The method of claim 1 , wherein the target station is moving, and the movement parameters include a first velocity vector in a first direction and a second velocity vector in a second direction.

5. The method of claim 1 , the method further including:

measuring the plurality of RTTs;

appending WD location parameters to each RTT of the plurality of RTTs, the WD location parameters being associated with a location of the WD at a time of the reception of the response packet and being determined based in part on Global Positioning System (GPS) information;

storing appended WD location parameters as records in a database; and

when a preset period of time has elapsed and a number of stored records in a dataset exceeds a predetermined number, retrieving the stored records from the database to determine the plurality of square residuals.

6. The method of claim 1 , the method further including:

determining a target location ellipse for the target station based on the determined best-fit parameters; and

performing the determination of the best-fit geo location of the target station further based on the determined target location ellipse.

7. The method of claim 6 , the method further including:

determining at least one of a Jacobian matrix, a Hessian sum, and a correlation matrix to determine the target location ellipse.

8. A wireless device (WD) for determining a geo-location of a target station using round-trip times (RTTs) of a plurality of signals transmitted by the WD to the target station, and response signals received from the target station corresponding to the transmitted signals, the WD comprising processing circuitry configured to:

assign values to current target station parameters, the current target station parameters including a current location for the target station and movement parameters;

determine a plurality of square residuals based at least in part on the current target station parameters, each square residual of the plurality of square residuals corresponding to one RTT, determining the plurality of square residuals including:

determining a first group of residuals based on stationary parameters and a second group of residuals based on the movement parameters;

for each of the first group and the second group of residuals:

determining a model fit probability based at least in part on one of the determined first group of residuals and the determined second group of residuals;

determining a sum of squared residuals (SSR);

performing non-linear fitting based at least on the determined SSR;

determining new parameters based at least on the non-linear fitting;

determining new residuals based at least in part on the determined new parameters;

determine a minimum of the SSR based at least on the plurality of square residuals;

determine best-fit parameters based at least in part on the determined minimum of the SSR;

perform an F-test to determine whether the non-linear fitting corresponding to moving parameters is a better fit than the non-linear fitting corresponding to the stationary parameters;

if the non-linear fitting corresponding to the moving parameters is the better fit, use the non-linear fitting corresponding to the moving parameters to determine the best-fit geo-location; and

if the non-linear fitting corresponding to the moving parameters is not the better fit and one of a first condition is met and a second condition is met, use the non-linear fitting corresponding to the stationary parameters to determine the best-fit geo-location, the first condition being met when a first difference between the SSR and a subsequent SSR is less than a predetermined minimum, the second condition being met when an absolute value of a second difference between a target station parameter and a subsequent target station parameter is less than the predetermined minimum; and

determine the best-fit geo-location of the target station based at least on the best-fit parameters.

9. The WD of claim 8 , wherein performing non-linear fitting and determining new parameters are further based on a Levenberg-Marquardt process.

10. The WD of claim 8 , wherein the first group of residuals is defined by:

⁢

f

⁡

(

x

i

,

α

)

=

α

OFF

+

(

2

c

)

*

d

⁡

(

x

i

,

α

)

.

⁢

Where

⁢

⁢

d

⁡

(

x

i

,

α

)

=

[

(

x

i

LAT

-

α

LAT

)

2

+

(

(

x

i

L

⁢

⁢

0

⁢

N

-

α

LON

)

*

cos

⁡

(

x

i

LAT

)

)

2

+

(

x

i

ALT

-

α

ALT

CONVERSION

)

2

]

1

2

;

and

the second group of residuals is defined by:

⁢

f

⁡

(

x

i

,

α

)

=

α

OFF

+

(

2

c

)

*

d

⁡

(

x

i

,

α

)

,

⁢

Where

⁢

⁢

d

⁢

(

x

i

,

α

)

=

[

(

x

i

LAT

-

(

α

LAT

+

α

VelNorth

*

x

i

TD

)

)

2

+

(

(

x

i

LON

-

(

α

LON

+

α

VelEast

*

x

i

TD

)

)

*

cos

⁡

(

x

i

LAT

)

)

2

+

(

x

i

ALT

-

α

ALT

CONVERSION

)

2

]

1

2

,

x i represents WD location parameters,

α represents location parameters of the target station,

x i TD is a negative time span of the corresponding RTT and a current time,

α VelEast is in degrees latitude per time and is converted to a spherical coordinate by multiplying by cos(x i LAT ) before converting units, and

CONVERSION refers to conversion of altitude units to geographic distance units where speed of light is in units of geographic distance divided by units of RTT.

11. The WD of claim 8 , wherein the target station is moving, and the movement parameters include a first velocity vector in a first direction and a second velocity vector in a second direction.

12. The WD of claim 8 , wherein the WD further comprises a transmitter receiver in communication with the processing circuitry, the transmitter receiver being configured to:

measure the plurality of RTTs;

the processing circuitry being further configured to:

append WD location parameters to each RTT of the plurality of RTTs, the WD location parameters being associated with a location of the WD at a time of the reception of the response packet and being determined based in part on Global Positioning System (GPS) information;

store appended WD location parameters as records in a database; and

when a preset period of time has elapsed and a number of stored records in a dataset exceeds a predetermined number, retrieve the stored records from the database to determine the plurality of square residuals.

13. The WD of claim 8 , wherein the processing circuitry is further configured to:

determine a target location ellipse for the target station based on the determined best-fit parameters; and

perform the determination of the best-fit geo location of the target station further based on the determined target location ellipse.

14. The WD of claim 13 , wherein the processing circuitry is further configured to:

determine at least one of a Jacobian matrix, a Hessian sum, and a correlation matrix to determine the target location ellipse.

15. A measuring station for determining a best-fit geo-location of a target station using a plurality of round-trip times (RTTs), each RTT being a time elapsed between a transmission of a ranging packet by the measuring station and a reception of a response packet by the measuring station, the measuring station comprising:

a wireless device comprising:

a transmitter receiver configured to:

measure the plurality of RTTs; and

processing circuitry in communication with the transmitter receiver, the processing circuitry being configured to:

assign values to current target station parameters, the current target station parameters including a current location for the target station and movement parameters;

determine a plurality of square residuals based at least in part on the current target station parameters, each square residual of the plurality of square residuals corresponding to one RTT, determining the plurality of square residuals including:

determining a first group of residuals based on stationary parameters and a second group of residuals based on the movement parameters;

for each of the first group and the second group of residuals:

 determining a model fit probability based at least in part on one of the determined first group of residuals and the determined second group of residuals;

 determining the SSR;

 performing non-linear fitting based at least on the determined SSR;

 determining new parameters based at least on the non-linear fitting; and

 determining new residuals based at least in part on the determined new parameters;

determine a minimum of a sum of squared residuals (SSR) based at least on the plurality of square residuals;

determine best-fit parameters based at least in part on the determined minimum of the SSR;

perform an F-test to determine whether the non-linear fitting corresponding to moving parameters is a better fit than the non-linear fitting corresponding to the stationary parameters;

if the non-linear fitting corresponding to the moving parameters is the better fit, use the non-linear fitting corresponding to the moving parameters to determine the best-fit geo-location; and

if the non-linear fitting corresponding to the moving parameters is not the better fit and one of a first condition is met and a second condition is met, use the non-linear fitting corresponding to the stationary parameters to determine the best-fit geo-location, the first condition being met when a first difference between an SSR and a subsequent SSR is less than a predetermined minimum, the second condition being met when an absolute value of a second difference between a target station parameter and a subsequent target station parameter is less than the predetermined minimum; and

determine the best-fit geo-location of the target station based at least on the best-fit parameters.