Statistically optimal null filters: Kalman equivalence

A new approach in the enhancement/suppression of narrowband signals, based on the combination of the maximum output SNR and the least-squares optimizing criteria, has been presented previously. The resulting statistically-optimal null filters (SONFs) have also been presented as recursive filters. Because of their time-varying nature, optimality under the MSE criterion and the similarity to the RLS method, it is anticipated that the SONFs may be related to the well known Kalman filter. In this paper, we show the SONFs to be an alternate implementation of the Kalman filter. For the first order case we show this analytically. Due to mathematical intractability, for the higher order case we set up the mathematical formulations and use simulations for verification