The fast recursive least squares (RLS) algorithms have wide applications in signal processing and control. They are computationally efficient. Thus their stability is of major concern. In this paper, we investigate the error propagation and stability of some typical fast RLS algorithms. Through a random example, we show that a typical conventional fast RLS algorithm is weakly unstable in computing both the residuals and the gain vectors and a QR based algorithm is expected to be weakly stable in computing the residuals but weakly unstable in computing the gain vectors. We propose an error correction scheme for computing the gain vectors.
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