Performance analysis and filter choice for an errors-in-variables method

An errors-in-variables problem where the system as well as the white measurement noises are in continuous-time is considered. Due to the intrinsic nature of the measurement noises, a strategy of lowpass filtering followed by instantaneous sampling is used for obtaining data from the system. A previously developed covariance function based parameter estimation method is first slightly improved. Thereafter, it is analyzed by evaluating the covariance matrix of the estimated parameter vector. Three different expressions for a generic element of an intermediate matrix in the expression for the covariance matrix are derived. One exact but computationally demanding, one approximate valid for small sampling intervals, and one exact for the case when the sampling interval tends to zero. The covariance matrix can be used for studying the influence of some user parameters, including the choice of the lowpass filter, on the quality of the estimated parameter vector.