Modified leaky LMS algorithms applied to satellite positioning

Abstract

With the recent advances in the theory of fractional Brownian motion (fBm), this model is used to describe the position coordinate estimates of Global Navigation Satellite System (GNSS) receivers that have long-range dependencies. The Modified Leaky Least Mean Squares (ML-LMS) algorithms are proposed to filter the long time series of the position coordinate estimates, which uses the Hurst parameter estimates to update the filter tap weights. Simulation results using field measurements demonstrate that these proposed modified leaky least mean squares algorithms can outperform the classical LMS filter considerably in terms of accuracy (mean squared error) and convergence. We also deal with the case study where our proposed algorithms outperform the leaky LMS. The algorithms are tested on simulated and real measurements.