Discrete Kalman filtering using a generalized companion form
Zijian Luo, Thomas E. Bullock · IEEE Transactions on Automatic Control · 1975
For annth-order constant system withpoutputs, this short paper shows that the Kalman filter gain can be described bynp -p(p - 1)/ 2difference equations instead of the usualn(n + 1)/2difference equations. This is the minimum number of difference equations required for the solution of the Kalman filter gain. For the special case of stationary processes, this short paper further shows that onlynp-p(p - 1)/2combinations of the system noise covariance enter into determination of the Kalman filter gain. The results have application in filtering and in the quadratic regulator problems.