Alternative Algorithms for Least Square Solution of Pseudo-range Measurements

Samsung Lim

Abstract:	The GPS pseudo-range equation is squared to lessen its non-linearity. Then, the position becomes a function the receiver clock bias. Utilizing the position and the receiver clock bias as unknown variables, we can linearize and solve the squared equation. This method applied to a ten minute long C/A code pseudo-range data that has a large amount of receiver clock bias. The result shows the meter level accuracy, compared to the standard linear least square method. The direct method presented in this paper is very useful for the situation where no initial position is available. To improve the accuracy, another linear iterative algorithm is formulated by employing the squared pseudo-range equation. The same C/A code pseudo-range data is used to prove that the difference of this solution from the standard linear least square solution is sub-millimeter level. This algorithm does not involve any quadratic polynomials for selecting an appropriate solution. The linear iterative method based on the fixed point theorem and it converges to the solution even though a sufficiently accurate initial approximation is not provided.
Published in:	Proceedings of the 55th Annual Meeting of The Institute of Navigation (1999) June 27 - 30, 1999 Royal Sonesta Hotel Cambridge, MA
Pages:	677 - 681
Cite this article:	Lim, Samsung, "Alternative Algorithms for Least Square Solution of Pseudo-range Measurements," Proceedings of the 55th Annual Meeting of The Institute of Navigation (1999), Cambridge, MA, June 1999, pp. 677-681.
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