A general efficient method for chaotic signal estimation

and SNLMS is obvious from Fig. 1. Note that the performance of the proposed algorithm is quite comparable with the NLMS algorithm. The slow convergence speed of the SBNLMS and SNLMS algorithms relative to the NLMS algorithm in Fig. 1 is not surprising since the convergence of the SBNLMS and SNLMS algorithms is expected to be eight times slower than the NLMS algorithm. On the other hand, the strategy of adapting the set of coefficients to be updated has minimized the loss in performance compared with the full-update case. This example is repeated for lower SNR using a disturbance noise of 0.1 variance (SNR ' 21 dB). Fig. 2 illustrates that the proposed algorithm maintains its superior performance under low SNR conditions. The choice of M is generally limited by the allowable complexity. However, the algorithm can be expanded to maintain a predetermined performance, irrespective of the input signal condition. We define the instantaneous performance measure PM(n) = M j=1 x (n0i +1) X (n)X(n) and require that M be selected at each instant n such that PM(n) PM0, where 0 < PM0 1, and x(n 0 ij + 1); j = 1;. .. ; M are the largest M values. Accordingly, (1 0 PM(n)) 2 (1 0 PM 0) 2 , and the reduction in the a posteriori error ep(n) after adaptation relative to that of e(n) previous is kept approximately constant at each iteration. Note that PM NLMS (n) = 1, and therefore, PM 0 can be indicative of the relative performance of the modified algorithm compared with the NLMS. The modified algorithm is used in the above example (SNR ' 51 dB) with = 1 and PM 0 = 0:5, and the ensemble average of M is plotted in Fig. 3. Fig. 3 indicates that for this particular distribution, EfPM(n)g is a constant that depends only on the value of M. In the second example, we compare the performance of the proposed M-Max NLMS algorithm for M = 1 with the Max-NLMS algorithm described in [5] and [6]. Both algorithms will pick identical coefficients to update (coefficient with maximum x(n 0 i + 1)). However, the update term is slightly different (compare [5, Eq. (5)] for the Max NLMS and (1) for the proposed algorithm). It is shown in [5] and [6] that the Max NLMS algorithm diverges for some input signals with certain nonsymmetric distribution for …