Methods and apparatus for N-lateration with noisy data measurements

1. A method for determining the position of a device, the method comprising:

receiving at a receiver a set of N measurements from signals transmitted by a respective set of N references devices, where N is an integer greater than two, the N measurements being suitable for determining a position of the device using N-lateration;

generating, via a processor, respective reliability metrics for the N measurements based on information about uncertainty of individual measurements; and

iteratively refining, via a processor, an estimate of the position of the device using N-lateration, wherein each iteration includes adjusting the estimate of the position of the device based on a least squares function that is weighted in accordance with the reliability metrics for the N measurements, wherein the least squares function implements Newton's iterative method for minimizing the sum of squares of errors.

2. The method of claim 1 , wherein the least squares function further comprises a Hessian matrix of second order partial derivates of the sum of squares of errors.

3. A method for determining the position of a device, the method comprising:

receiving at a receiver a set of N measurements from signals transmitted by a respective set of N references devices, where N is an integer greater than two, the N measurements being suitable for determining a position of the device using N-lateration;

generating, via a processor, respective reliability metrics for the N measurements based on information about uncertainty of individual measurements; and

iteratively refining, via a processor, an estimate of the position of the device using N-lateration, wherein each iteration includes adjusting the estimate of the position of the device based on a least squares function that is weighted in accordance with the reliability metrics for the N measurements, wherein:

each iteration includes computing an N×1 error vector whose N components are the respective errors between the N measurements and distances between the estimate of the position of the device and the N reference devices; and

the least squares function comprises an N×N matrix computed from the Jacobian matrix of the error vector, wherein the least squares function implements Newton's iterative method for minimizing the sum of squares of errors.

4. The method of claim 3 , wherein the N×N matrix is biased towards steepest decent by weighting mixed partial derivatives less than self partial derivatives of the Jacobian matrix.

5. The method of claim 3 , wherein the N×N matrix is computed using a weighting matrix that respectively weights the N components of the error vector in accordance with the reliability metrics for the N measurements.

6. The method of claim 5 , wherein diagonal elements of the weighting matrix comprise inverse variances indicating reliabilities associated with respective components of the error vector.

7. The method of claim 5 , wherein the method is repeated for successive sets of N measurements, wherein the weighting matrix is adaptive from one set of N measurements to the next based on information about uncertainty of individual measurements.

8. The method of claim 1 , wherein the method is repeated for successive sets of N measurements, wherein the reliability metrics are adaptive from one set of N measurements to the next based on information about uncertainty of individual measurements.

9. The method of claim 1 , wherein the method is repeated for successive sets of N measurements, wherein the value of N is permitted to vary from one set of measurements to a next set of measurements.

10. The method of claim 1 , wherein N is greater than three.

11. A method for determining the position of a device, the method comprising:

receiving at a receiver a set of N measurements from signals transmitted by a respective set of N references devices, where N is an integer greater than two three, the N measurements being suitable for determining a position of the device using N-lateration; and

iteratively refining, via a processor, an estimate of the position of the device using N-lateration, wherein each iteration includes adjusting the estimate of the position of the device based on a least squares function,

wherein each iteration includes computing an N×1 error vector whose N elements are the respective errors between the N measurements and distances between the estimate of the position of the device and the N reference devices, and wherein the least squares function comprises an N×N matrix computed from the Jacobian matrix of the error vector, the least squares function implementing Newton's iterative method for minimizing the sum of squares of errors.

12. An apparatus for determining the position of a mobile device, the apparatus comprising:

a receiver configured to generate a set of N measurements based on signals transmitted by a respective set of N references devices, where N is an integer greater than two, the N measurements being suitable for determining a position of the mobile device using N-lateration;

a reliability assessment module configured to generate respective reliability metrics for the N measurements based on information about uncertainty of individual measurements; and

an N-lateration module configured to iteratively refine an estimate of the position of the mobile device using N-lateration, wherein the N-lateration module iteratively adjusts the estimate of the position of the mobile device based on a least squares function that implements Newton's iterative method for minimizing the sum of squares of errors, and wherein the N-lateration module weights the least squares function in accordance with the reliability metrics for the N measurements.

13. The apparatus of claim 12 , wherein:

for each iteration, the N-lateration module computes an N×1 error vector whose N components are the respective errors between the N measurements and distances between the estimate of the position of the device and the N reference sources; and

the least squares function comprises an N×N matrix computed from the Jacobian matrix of the error vector.

14. The apparatus of claim 13 , wherein the N×N matrix is biased towards steepest decent by weighting mixed partial derivatives less than self partial derivatives of the Jacobian matrix.

15. The apparatus of claim 13 , wherein the N-lateration module computes the N×N matrix using a weighting matrix that respectively weights the N components of the error vector in accordance with the reliability metrics for the N measurements.

16. The apparatus of claim 15 , wherein diagonal elements of the weighting matrix comprise inverse variances indicating reliabilities associated with respective components of the error vector.

17. The apparatus of claim 12 , wherein the N-lateration module repeatedly uses N-lateration to determine the position of the mobile device from successive sets of N measurements, wherein the reliability metrics are adaptive from one set of N measurements to the next based on information about uncertainty of individual measurements.

18. The apparatus of claim 12 , wherein the N-lateration module repeatedly uses N-lateration to determine the position of the mobile device from successive sets of N measurements, wherein the value of N is permitted to vary from one set of measurements to a next set of measurements.

19. The apparatus of claim 12 , wherein the apparatus comprises at least a portion of the mobile device.

20. The apparatus of claim 12 , wherein the apparatus is a separate device from the mobile device.

21. A computer readable medium storing instructions, that when executed by a computer, cause the computer to perform functions of:

generating a set of N measurements from signals transmitted by a respective set of N references devices, where N is an integer greater than two, the N measurements being suitable for determining a position of the device using N-lateration;

generating respective reliability metrics for the N measurements based on information about uncertainty of individual measurements; and

iteratively refining an estimate of the position of the device using N-lateration, wherein each iteration includes adjusting the estimate of the position of the device based on a least squares function that minimizes a sum of squares of errors that implements Newton's iterative method for minimizing the sum of squares of errors, wherein the least squares function is weighted in accordance with the reliability metrics for the N measurements.

22. The method of claim 1 , wherein the least squares function minimizes a sum of squares of errors between the N measurements and distances between the estimate of the position of the device and the N reference devices.

23. The method of claim 3 , wherein the least squares function minimizes a sum of squares of errors between the N measurements and distances between the estimate of the position of the device and the N reference devices.

24. The method of claim 11 , wherein the least squares function minimizes a sum of squares of errors between the N measurements and distances between the estimate of the position of the device and the N reference devices.

25. The apparatus of claim 12 , wherein the least squares function minimizes a sum of squares of errors between the N measurements and distances between the estimate of the position of the device and the N reference devices.

26. The apparatus of claim 12 , wherein the least squares function further comprises a Hessian matrix of second order partial derivates of the sum of squares of errors.

27. The computer readable medium of claim 21 , wherein the least squares function minimizes a sum of squares of errors between the N measurements and distances between the estimate of the position of the device and the N reference devices.

28. The computer readable medium of claim 21 , wherein the least squares function further comprises a Hessian matrix of second order partial derivates of the sum of squares of errors.

29. The computer readable medium of claim 21 , wherein:

each iteration includes computing an N×1 error vector whose N components are the respective errors between the N measurements and distances between the estimate of the position of the device and the N reference devices; and

the least squares function comprises an N×N matrix computed from the Jacobian matrix of the error vector.