Cramér–Rao lower bound in nonlinear filtering problems under noises and measurement errors dependent on estimated parameters

Abstract

This paper derives recurrent expressions for the maximum attainable estimation accuracy calculated using the Cramér–Rao inequality (Cramér–Rao lower bound) in the discretetime nonlinear filtering problem under conditions when generating noises in the state vector and measurement error equations depend on estimated parameters and the state vector incorporates a constant subvector. We establish a connection to similar expressions in the case of no such dependence. An example illustrates application of the obtained algorithms to lowerbound accuracy calculation in a parameter estimation problem often arising in navigation data processing within a model described by the sum of a Wiener sequence and discrete-time white noise of an unknown variance.