This paper presents a novel partial update algorithm for FIR adaptive filters based on a Kalman background engine. In the proposed system, a Kalman filter is setup with the coefficients of the full adaptive filter as the states to be estimated. The observation of the Kalman filter is the subset of the coefficients of the adaptive FIR filter being updated. It is shown that this setup allows for an improved estimation of the full set of filter coefficients despite the partial update. We propose two methods for postmortem improvements on an ordinary M-Tap periodic update LMS. We also propose a Kalman feedback method, in conjunction with a 1-Tap periodic update TMS, which has a similar performance to a full length LMS, for non-stationary system identification.