Gaussian deterministic recursive estimator with online tuning capabilities

A tuning algorithm is presented allowing the optimal estimation of an unknown deterministic state vector observed through noisy measurements. The estimation technique named the fading Gaussian deterministic filter is based on a KF-like set of recursive equations and is considered to be optimal because the gain matrix is an algebraic consequence of a formal minimization of a cost function, with no other assumption. This fading behavior allows the algorithm to work despite other unknowns in the problem that are not measurement noise. A numerical example was provided where angular rate estimation is performed from magnetometer readings of a tumbling satellite. Results were obtained by searching offline for the best configuration over a filter bank, sharing the same structure and simulated measurements, but using different fading factors. The tuning procedure proved to work satisfactorily under large. modeling errors, with remarkable performance in the estimation of the angular rates from noisy readings. In fact, in the tuned condition only, the algorithm was able to estimate both the actual covariance of the measurement noise and the true error covariance related to the state vector estimate with satisfactory accuracy.