Evaluating Process and Measurement Noise in Extended Kalman Filter for GNSS Position Accuracy

Extended Kalman filter (EKF) is widely used in the dynamic systems under the assumption that the process and measurement noises are Gaussian distributed. It is well known that the covariance matrixes of process noise and measurement noise have a significant impact on the EKF's performance. To evaluate its impact on the estimation of user position, this paper proposes two models. The first model depends on the power spectral densities of speed noise, clock bias noise and frequency drift noise to estimate covariance matrix of process noise. The second model is an exponential model that depends on the satellite elevation angle to estimate covariance matrix of measurement noise.

I. Introduction

GNSS (Global Navigation Satellite System) has been widely used in various situations thanks to its convenience and usefulness. In particular, it allows user position estimation based on nonlinear equations. For solving these nonlinear position equations, two techniques are widely discussed and applied in the literature: nonlinear least squares [1]-[4] and the Extended Kalman filter (EKF) [5]-[9]. This paper emphasizes the EKF for determination of GNSS receiver position.