On digital implementation of the fast kalman algorithms

The roundoff noise in a finite-precision digital implementation of the fast Kalman algorithm presented in [1]-[3] is known to adversely affect the algorithm's performance. By experience, we found that such performance degradation is closely related to an abnormal behavior of a quantity in this algorithm. More explicitly, this quantity can be interpreted as a ratio between two autocorrelations, and hence should always be positive. However, in a finite-precision implementation, its computed value can go negative. The algorithm performance is found to degrade noticeably near where this computed value becomes negative for the first time. As a remedy, we consider a special method of reinitializing the algorithm periodically. For this, a "covariance fast Kalman algorithm" is derived. This algorithm does not assume a zero input signal prior to the start of computation as the original fast Kalman algorithm does.