Abstract
An adaptive scheme is proposed for obtaining the steady-state optimal filter gain matrix for a linear time-invariant discrete-time system when it is assumed that the observations are contaminated with unknown coloured noise. An autoregressive vector moving-average model is proposed for the coloured observation noise and the parameters of this model are estimated by using a recent multivariate linear least-squares estimation technique. This is followed by an algorithm for tracking the gain matrix and correcting it for optimality. Results of simulation of an inert ial navigation system are included.
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