Recursive maximum likelihood estimation with [formula omitted]-distribution noise model

Abstract

In this paper, a recursive t-distribution noise model based maximum likelihood estimation algorithm for discrete-time dynamic state estimation is proposed. The proposed estimator is robust to outliers because the “thick tail” of the t-distribution reduces the effect of large errors in the likelihood function. A computationally efficient recursive algorithm is derived using the influence function. As the t-distribution reduces to the Gaussian distribution when its degree of freedom tends to infinity, the proposed estimator reduces to the Kalman filter. The mean squared error is used to evaluate the performance of the proposed estimator. Compared with the Kalman filter, the proposed estimator is more robust to outliers in the process and measurement noise. Simulations show that for the particle filter to give a better mean squared error, its computational time is two orders of magnitude slower than the proposed estimator.