A Stochastic Total Least Squares Solution of Adaptive Filtering Problem

An efficient and computationally linear algorithm is derived for total least squares solution of adaptive filtering problem, when both input and output signals are contaminated by noise. The proposed total least mean squares (TLMS) algorithm is designed by recursively computing an optimal solution of adaptive TLS problem by minimizing instantaneous value of weighted cost function. Convergence analysis of the algorithm is given to show the global convergence of the proposed algorithm, provided that the stepsize parameter is appropriately chosen. The TLMS algorithm is computationally simpler than the other TLS algorithms and demonstrates a better performance as compared with the least mean square (LMS) and normalized least mean square (NLMS) algorithms. It provides minimum mean square deviation by exhibiting better convergence in misalignment for unknown system identification under noisy inputs

Fuzzy Recursive Least-Squares Approach in Speech System Identification: A Transformed Domain LPC Model

In speech system identification, linear predictive coding (LPC) model is often employed due to its simple yet powerful representation of speech production model. However, the accuracy of LPC model often depends on the number and quality of past speech samples that are fed into the model; and it becomes a problem when past speech samples are not widely available or corrupted by noise. In this paper, fuzzy system is integrated into the LPC model using the recursive least-squares approach, where the fuzzy parameters are used to characterize the given speech samples. This transformed domain LPC model is called the FRLS-LPC model, in which its performance depends on the fuzzy rules and membership functions defined by the user. Based on the simulations, the FRLS-LPC model with this special property is shown to outperform the LPC model. Under the condition of limited past speech samples, simulation result shows that the synthetic speech produced by the FRLS-LPC model is better than those produced by the LPC model in terms of prediction error. Furthermore with corrupted past speech samples, the FRLS-LPC model is able to provide better reconstructed speech while the LPC model is failed to do so