A Fix-Up for the EKF Parameter Estimator

Abstract

We have reduced recursive parameter estimation to Kalman filtering, with a few added fixes. By incorporating projections in the parameter gain updates and parameter variance estimates, the recursive maximum likelihood method asymptotically becomes a reformulation and fix-up of the extended Kalman filter used as a parameter estimator (EKFPE), except that an additional n x n linear symmetric matrix must also be updated for each parameter estimate. Estimates for both the process and measurement noise variances, as well as for structural parameters, have been proven globally convergent to a local maximum of the likelihood function. This obviates the usual guesswork in finding noise variances when fitting data using the EKFPE, and assures the existence of the innovations representation for the recursive maximum likelihood method. Slightly non-linear and also slightly unstable linear, as well as drastically time-varying stable linear, system parameters can be estimated even in severe noise environments On average, the rate of convergence of parameter estimates appears to be faster than other methods if no projection limit is hit.