A new generalized recursion for the fast computation of the Kalman gain to solve the covariance equations

This paper introduces a sequential fast scheme of the Kalman type to solve the covariance equations of linear prediction. The new algorithm constitutes a generalization of the scheme introduced recently by D. Falconer and L. Ljung, and applies to a more general situation. The algo rithm is characterized by conceptual simplicity and efficiency. Although it is based on matrix partitioning concepts and shifting properties of the signal vector, it does not have the restriction of prewindowing as it is the case with the previously mentioned algorithm, thus it can be used to model small frames of signals as well as to model signals generated by an AR model, giving in this case the exact solution. Finally it must be noted that the algorithm is strictly time recursive and leads to O(13p) multiplications per recursion only. Thus, this new scheme is the fastest existing method for the sequential solution of the general covariance equations when prewindowing is not desirable.