Estimation of noise covariance matrices for a linear time-varying stochastic process
Automatica (Journal of IFAC)
A new autocovariance least-squares method for estimating noise covariances
Automatica (Journal of IFAC)
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In this paper, the problem of estimating the measurements' noise statistics of the Global Positioning System (GPS) is addressed. First, a model matching technique is used to estimate the GPS measurements' noise statistics. Then, the formulation of the measurements and process noise estimation using the Autocovariance Least Squares technique will be derived for the time-varying GPS/IMU system. It is assumed that the process noise covariance matrix is known or determined a priori through off-line calibration. The Autocovariance Least Squares method improves on the assumptions of the model matching technique by considering the time-correlation in the measurements' residual sequence due to the a priori unknown GPS measurements' noise covariance matrix. Both methods make use of statistical sampling theory in the estimation filter. Simulation results for both methods will be presented at the end of the paper. The results are compared and the improvement gained when using the Autocovariance Least Squares method in comparison to the model matching technique will be shown.