Application and computation of Huber's M-estimator in the Global Positioning System.

摘要

In the Global Positioning System (GPS), the accuracy of position estimates, which are usually computed by the least squares (LS) method, could be impaired due to some unreliable measurements. Robust estimators aim to reduce the influence of measurements with large errors, thus improve the estimate accuracy. This thesis applies Huber's M-estimator, one of the most important robust estimators, to two GPS relative positioning models, one based on the code measurements only and the other based on the code and carrier phase measurements.;Two numerical methods, the iteratively reweighted least squares (IRLS) method and Newton's method, are used to compute Huber's M-estimates. In Newton's method, the singularity problem, the line search strategy and the updating/downdating techniques are discussed in details. For the code based model, our simulation results show that Newton's method can be much faster than the IRLS method. For the code and carrier phase based model, a modified Newton's method was proposed to reduce the computation cost and required memory. The simulation results show that Huber's M-estimator can greatly suppress the measurement outliers and yield more accurate position estimates for both models than LS method.