AN INVESTIGATION OF EXTENDED KALMAN FILTERING IN THE ERRORS-IN-VARIABLES FRAMEWORK - A Joint State and Parameter Estimation Approach

Abstract

The paper addresses the problem of errors-in-variables filtering, i.e. the optimal estimation of inputs and outputs from noisy observations. While the optimal solution is known for linear time-varying systems of known parameterisation, this paper considers a suboptimal approach where only an approximated set of parameters is available. The proposed filter is derived by the means of joint state and parameter estimation using the extended Kalman filter approach which, in turn, leads to a coupled state-parameter estimation procedure. However, the resulting parameter estimates appear to be biased in the presence of input noise. The novel filter is compared with a previously proposed suboptimal filter.