Convergence analysis of the binormalized data-reusing LMS algorithm

3235 but with m = l = 12, only 8% of the number of flops were required for STAN 1 and about 7% for EIV-PAST. From Fig. 1, we conclude that all considered algorithms offer similar tracking accuracy. Example 2: As previously stated, one of the main advantages with STAN, compared with, for example EIV-PAST, is that estimates of the signal singular values are available. In Fig. 2, the estimated signal singular values and the singular values of ^ R R R x (t) are shown in a scenario where the number of signals is time varying. The STAN 3 algorithm is run with the hypothesis that n = 2. We note that the estimates obtained from STAN3 allow us to detect changes in n. Example 3: This example considers the stationary accuracy of the proposed algorithms. In this scenario, two planar wavefronts arrive from DOA's [0 20 ]. Further, the estimates of the first 300 samples are discarded so that the effects of the initial conditions are negligible. The results in Fig. 3 are based on 200 independent realizations, and = 0:97. The first conclusion is that STAN1 performs as well as EIV-PAST and the SVD approach. The second conclusion is that STAN 3 performs as wel as EIV-PAST and the SVD approach, only for " medium to high " values of the SNR. V. CONCLUSIONS In this correspondenec, we have proposed an O((m + l)n 2) class of perturbation-based low-rank tracking algorithms, which are referred to as STAN. The low complexity of STAN is achieved by applying a novel approximation of a residual matrix. For the AC case with exponential forgetting, none of the STAN algorithms are new. However, the analysis that led to the different variants is useful. It was, for example, shown that Karasalo's algorithm and the algorithm F2 in [1] are closely related. Only the approximation of the residual matrix differs. Furthermore , the introduced perturbation-based framework allowed us to propose a novel sliding window algorithm for the AC case, and attractive algorithms for the CC case were found. REFERENCES [1] P. Comon and G. H. Golub, " Tracking a few extreme singular values and vectors in signal processing, " Array processing in correlated noise fields based on instrumental variables and subspace fitting, " IEEE Abstract—Normalized least mean squares algorithms for FIR adaptive filtering with or without the reuse of past information are known to …