Finite Horizon Estimation for Linear Systems with Noisy Measurements

This article focuses on the estimation of linear time independent systems with the additive noise at the output. Estimation is done on a finite batch of noisy measurements. Finite horizon estimation performs better than the standard Kalman filter, once the complete information about the noise statistics is not known. The direct form and the iterative forms are derived to implement the filter, without any knowledge of noise characteristics. The convergence of the proposed scheme is also presented. The effectiveness is verified through simulation examples.