On BIQUE Procedures Applied to GPS Pseudorange Measurements

Abstract

Best-Invariant-Quadratic-Unbiased-Estimation (BIQUE) of the variance factors is used in this work to evaluate the adequacy, or goodness, of different stochastic models affecting GPS pseudorange measurements (assumed uncorrelated), using the linear Gauss-Markov functional model. Four different stochastic models of the observations are tested, verifying that incorrect results of the BIQUE estimates (i.e. negative variance components) imply large inaccuracies of GPS-derived user positions. Results on real measurement campaigns show that the SNR (Signal to Noise Ratio) is effective in reducing the GPS position errors, by using models with SNR and SNR squared. BIQUE estimations with negative variance components allowed us to reject one of the four chosen stochastic models. No significant differences have been noted using slightly different (high) values of the redundancy r of the observations (r = 20 and r = 28). We use formulas in which the BIQUE methodology does not require the evaluation of least-squares (LS) residuals. Therefore, the BIQUE of the variance and covariance components could be performed in pre-adjustment, without the necessity of cumbersome LS adjustments during each iteration.