Non-stationary noise estimation with adaptive filters

Non-linear flight-path reconstruction is basically a state estimation problem that can be solved with adaptive filtering techniques, as it involves the estimation of flight trajectories and unknown parameters such as biases, scale factors, and noise statistical uncertainties of flight instrumentation systems, The Modified Recursive Maximum Likelihood (MRML) method, developed at the Delft University of Technology (DUT), is a new scheme in adaptive filtering for non-linear state-parameter estimation problems, It has been successfully applied in cases that the system and observation noises are stationary. In this paper it is shown that the MRML adaptive filter can be applied to estimate non-stationary noise intensities as well, Because of the fact that for the MRML adaptive filter the effect of the parameter estimator is included in the prediction error computation, the possibility exists to introduce time-varying noise statistical uncertainties as additional stochastic variables instead of constant parameters. The research of the application of the MRML adaptive filter in order to estimate non-stationary noise intensities has been carried out by numerical simulations for a simple non-linear model containing non-stationary noises, The model is based on the reconstruction of the attitude angles of a spacecraft For the numerical simulations the software package MATLAB(TM) has been used. From the numerical experiments it could be seen that the original MRML adaptive filter is not able to give a satisfactory estimation of non-stationary noise statistical parameters, After introduction of noise statistical uncertainties as random walks instead of constant parameters, the MRML adaptive filter is capable of tracking the time-varying noise intensity.