A New Stochastic Model to Improve Positioning Accuracy of the Recursive Least Squares Method

In determining position using GPS, due to local effects, pseudo-range errors cannot be mitigated by methods such as the use of reference stations or mathematical models; however, by using precise carrier phase observations and deploying a statistically optimal filter such as Phase-Adjusted Pseudo-range (PAPR) algorithm, the error can be significantly reduced. Additionally, the correlation between observations is a factor affecting positioning accuracy. In this paper, by using both pseudo-range and carrier phase observations and taking into account the effect of spatial correlation between observations to determine the variance-covariance matrix, the accuracy of position determination using the recursive Least Squares method is increased. For this purpose, the PAPR algorithm was implemented to reduce error. Next, a non-diagonal variance-covariance matrix was introduced to estimate the variance of the observations based on their spatial correlations. Experimental results on real data show that the proposed method improves positioning accuracy by at least 10% compared to previous methods. To evaluate the complexity of the proposed models, we employed an ARM STM32H743 processor. The findings indicate a modest increase in the proposed model complexity compared to earlier models, along with a substantial improvement in positioning accuracy.