Error propagation properties of recursive least-squares adaptation algorithms

-The numerical properties of implementations of the cessing/systolic arrays and/or VLSI chiprecursive least-squares identification algorithm are of grea t implementation. importance for their continuous use in various adaptive schemes. Here we investigate how an error that is introduced at an (d) Programming investment required. arbitrary point in the algorithm propagates. It is shown that (e) Resilience to bad or abnormal data (such as conventional LS algorithms, including Bierman's UDpoorly exciting input). factorization algorithm are exponentially stable with respect to such errors, i.e. the effect of the error decays exponentially. The i f) Error propagation properties. base of the decay is equal to the forgetting factor. The same is true (g) Effect and amplification of round-off noise. for fast lattice algorithms. The fast least-squares algorithm, Which aspects are the most imporW.nt ones in a sometimes known as the 'fast Kalman algorithm' is however shown to be unstable with respect to such errors, given case depends on the application. A lot of attention has recently been given to (a) and (b). Socalled fast algorithms have been developed that