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One reason that recursive least-squares (RLS) algorithms are not used as widely as LMS algorithms is an instability problem resulting from finite precision errors in the calculations; leaky LMS algorithms that are numerically stable have been proposed in the LMS literature. In this paper, we offer a new RLS criterion that includes a strong parameter energy factor. Experiments show that adaptive algorithms that meet this criterion are numerically more stable than conventional RLS algorithms. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(4): 26–37, 1999 [ABSTRACT FROM AUTHOR]

This paper presents some conditions to determine decimation ratio in subband adaptive identification ofa time-varying system. It has been reported in some experiments that a large decimation ratio is not suitable for subband identification of a time-varying system. However, theoretical conditions for a maximally decimated ratio in a time-varying system have not to date been reported. A short-time invariant mode! is the starting point for this research. The relation between a forgetting factor used in the recursive weighted least-squares (RWLS) algorithm and a time variation of the time-varying system are derived. Then, new forgetting factors are derived for the multirate processing case. Using a convergence property provided by these forgetting factors, theoretical conditions are obtained having parameters estimated from decimated signals that are as accurate as those from all observed signals. The propriety of these conditions is demonstrated using simulations. [ABSTRACT FROM AUTHOR]

The recursive least-squares method (RLS) is often employed in the identification of the linear discrete-time system, in which the parameters are time-varying. This paper aims at producing the output which is an estimation of the system parameters, and derives a new algorithm which minimizes the RLS criterion with (time-variable) forgetting factor. A parallel architecture is proposed which executes the algorithm. The derived algorithm is composed of two-step processes, which are the Agee-turner PD factorization update theorem and the forward-substitution for salving linear triangular systems. The proposed parallel architecture is composed of a large number of processing elements (PE) connected in a regular way. The communication is performed only between adjacent PE, and the architecture can easily be implemented by VLSI. It can be considered as a systolic array composed of FE with a queue (FIFO memory). By introducing PE with a queue, the two-step processes can be executed in parallel for the first time. It is shown that by employing the proposed parallel architecture composed of (N² + 5N - 2)/2 PE in the real-time processing, the estimated parameters for any time can be produced as the output, in a processing time independent of the number of parameters of the estimation, even though the computational complexity is of the order of square of the number of estimated parameters. [ABSTRACT FROM AUTHOR]

In this paper it shown that covariant data of a synthesized signal corresponds to the covariant data of a real signal. This occurs when an ARMA lattice synthesis filter is used and the minimum mean square value of the estimation error is zero. Hence, a new terminal condition of the ARMA lattice filter is derived so that the covariant date of the synthesized signal will always correspond to the covariant data of a real signal. To this end, a design method for the normalized ARMA lattice filter is presented in this paper, and normalized estimation error are derived. Finally, the starting condition and design for the normalized ARMA lattice filter is given. [ABSTRACT FROM AUTHOR]

In spectrum estimation of nonstationary signals, the modeling of time-varying characteristics and the parameter estimation of the model are important. Several adaptive estimation methods such as the recursive least-squares (RLS) method are often used for parameter estimation of time-varying models. However, the RLS method becomes less efficient for rapidly time-varying models because this method assumes short-time stationarity. This paper proposes an adaptive estimation method of time-varying parameters modeled as linear combinations of a set of basis functions. In this method, linear exponential time functions are employed as basis functions. This algorithm is realized by the RLS algorithm with a rectangular window and a procedure that shifts basis functions. In some experiments, the performance of the proposed method is compared with that of the conventional method with short-time stationary assume. [ABSTRACT FROM AUTHOR]