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Issues of Different Estimation Models for Epoch-by-Epoch Double-Difference GPS Observation Equations: A Comparative Study
Abstract and Figures
In short-timespan processing of GPS observations the combination of code and carrier phase observations has the shortcoming that the normal matrix is often ill-conditioned and giving unstable computation. The regularized least-squares (RLS) and the iterative least-squares (ILS) methods are often proposed as alternatives to the conventional least-squares (CLS) method. The RLS are claimed to give better reliability of GPS ambiguity solving for short-period observations and to improve the quality of the normal equation, also reducing the condition number of the normal matrix. The regularization parameter is determined by minimizing the trace of the mean square error matrix. However, the regularization induces a biased estimation and its benefits are difficult to be confirmed. On the other hand, the ILS do not improve the estimate results and their stochastic properties, apart from stabilizing the normal matrix and reducing its condition number: this, however, depends on the given initial estimate vector. In this work we investigate the performance of RLS and ILS as compared to CLS when applied to single-frequency epoch-by-epoch processing with ambiguity solving by LAMBDA method. Results show that, while the investigated methods do not produce significant differences in terms of estimated baseline precision, improvements are instead observed in the condition number of the normal matrix, with ILS producing the best results when using estimated initial values from CLS. On the other hand, the RLS method fails to improve the condition number for epoch-by-epoch strategy. All methods also give practically equal reliability for ambiguity resolution, where the evaluation is taken in terms of success rate.
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