A comparison of iteratively reweighted least squares and Kalman Filter with EM in measurement error covariance estimation

An unknown measurement error covariance in a stochastic dynamical system is to be estimated from measurements. A least squares approach is implemented by extending the iteratively reweighted least squares (IRLS) technique to handle system dynamics over a time window. The performance of this method, in terms of convergence rate and error, is compared to the standard Kalman Filter Expectation-Maximization (KFEM) approach via simulations of a single moving target with known stochastic dynamics tracked by two sensor measurements. We demonstrate that the extended IRLS outperforms KFEM in estimation accuracy. It also has a slightly better convergence rate at most epochs under any of a more uncertain, less uncertain, or re-estimated prior for the KFEM method.