Paper Title
Kalman Assimakis Lainiotis Filter

Abstract
Linear estimation is associated with linear state space systems describing the relation between the n dimensional state and the m dimensional measurement as well as the relation between two successive states. The traditional Kalman filter computes iteratively the state prediction and estimation taking into account the previous time measurement; in each iteration the computation of the inversion of a m×m dimensional square matrix is required and the Kalman filter gain is derived. On the other hand, the traditional Lainiotis filter computes iteratively the state estimation; in each iteration the computation of the inversion of a n×n dimensional square matrix is required. A combination of Kalman and Lainiotis filters for time invariant systems is introduced in this paper. The derived Kalman Assimakis Lainiotis filter computes the state prediction and estimation using the Kalman filter gain, the computation of which requires the inversion of a n×n dimensional square matrix in everyiteration. The proposed Kalman Assimakis Lainiotis filter may be faster than the traditional Kalman filter, depending on the state and measurement dimensions. Keywords - Linear Estimation, Kalman Filter, Lainiotis Filter.