Optimal initialization of linear recursive filters

Based on a combination of the Bayesian viewpoint and the classical (non-Bayesian) weighted least squares (WLS) method, an optimal estimator. for a linear stochastic system particularly suitable for I ecm sive filter initialization is presented. It accounts for the fact that the data set for initialization in practice consists of the measurements of the time-varying state of the dynamic system, which is random in filtering problems and thus the initialization problem cannot be properly handled either by a Bayesian approach ol in the classical WLS formulation. The results ale given for both continuous- and discrete-time models of a dynamic system with discrete-time measurements. The proposed estimator is compared with the popular two-point differencing technique for initialization, which is a special form of the classical WLS method. Simulation results are provided to support the theoretical results.