A comparison of indirect and direct filter designs from data for LTI systems: the effect of unknown noise covariance matrices

Existing literature on model-based filter design for stochastic LTI systems assumes complete correspondence between the system and its model. When the system is not completely known, the standard indirect model-based (two-steps) filtering solution consists of: (i) identify a model of the system from measured input/output data; (ii) design a Kalman filter based on the estimated model. The performance of this indirect approach are limited by the model and noise covariance matrices accuracy. To overcome such limitations, this paper investigates a direct (one-step) solution to the filtering problem for SISO LTI systems in the Prediction Error Method (PEM) identification framework. Simulation results indicate the effectiveness of the direct filtering approach, especially when the noise covariance matrices are misspecified.