Leaky LMS Algorithm and Fractional Brownian Motion Model for GNSS Receiver Position Estimation

This paper presents a new approach for smoothing long time series of position estimates of ground GNSS (global navigation satellite system) receivers. The fractional Brownian motion (fBm) model is employed to describe the position coordinate estimates that have long-range dependencies. A new and low-complexity method is proposed to estimate the Hurst parameter and the simulation results show that the new method achieves good accuracy and low complexity. A modified leaky least mean squares (ML-LMS) estimator is 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 demonstrate that this ML-LMS estimator outperforms the classic LMS estimator considerably in terms of both accuracy and convergence.