Numerically robust least-squares lattice-ladder algorithms with direct updating of the reflection coefficients (original) (raw)
Related papers
A generalized multichannel least squares lattice algorithm based on sequential processing stages
IEEE Transactions on Acoustics, Speech, and Signal Processing, 1984
A generalized multichannel least squares (LS) lattice algorithm which is appropriate for multichannel adaptive filtering and estimation is presented in this paper. It is shown that a muitichannel LS estimation algorithm with a different number of parameters to be estimated in each channel can be implemented by cascading lattice stages of nondescending dimension to form a generalized lattice structure. A
IEEE Transactions on Signal Processing, 2001
Several algorithms for adaptive IIR filters parameterized in lattice form can be found in the literature. The salient feature of these structures when compared with the direct form is that ensuring stability is extremely easy. On the other hand, while computing the gradient signals that drive the direct form update algorithms is straightforward, it is not so for the lattice algorithms. This has led to simplified lattice algorithms using gradient approximations. Although, in general, these simplified schemes present the same stationary points as the original algorithms, whether this is also true for convergent points has remained an open problem. This also applies to nongradient-based lattice algorithms such as hyperstability based and the Steiglitz-McBride algorithms. Here, we answer this question in the negative, by showing that for several adaptive lattice algorithms, there exist settings in which the stationary point corresponding to identification of the unknown system is not convergent. In addition, new lattice algorithms with improved convergence properties are derived. They are based in the cascade lattice structure, which allows the derivation of sufficient conditions for local stability.
The numerical stability of the lattice algorithm for least squares linear prediction problems
BIT, 1984
The numerical stability of the lattice algorithm for least-squares linear prediction problems is analysed. The lattice algorithm is an orthogonalization method for solving such problems and as such is in principle to be preferred to normal equations approaches. By performing a first-order analysis of the method and comparing the results with perturbation bounds available for leastsquares problems, it is argued that the lattice algorithm is stable and in fact comparable in accuracy to other l~nown stable but less efficient methods for least-squares problems.
Rounding error analysis of the triangular lattice and escalator algorithms
Electronics and Communications in Japan (Part I: Communications), 1988
This paper deals with the Triangular lattice (TL) and Escalator (ES) algorithms for recursive least squares filtering problems. First, systolic array implementations of these algorithms are compared. analysis of fixed point errors for the normalized TL and ES algorithms are performed and the expressions for the steady state biases in the estimated coefficients are derived. Finally, the total effects of finite wordlength arithmetics on both algorithms are compared through a numerical example. Next,. . On the ... 2 , t ' ' xd,t' alization of x~,~, 2 other hand, as shown below, the TL algorithm is easily derived from the Circular Lattice (CL) algorithm that is originally proposed for a multivariate autoregressive modeling [ 5 ]. The CL algorithm can be regarded as a multivariate version of the recursive least square ladder estimation algorithm for scalar case. A distinguished feature of this algorithm is that it involves only scalar calculations, and is suitable for parallel processing. Before these algorithms were published, Ahmed and Youn had proposed an adap-tive gradient type escalator algorithm [ 6 ] , and Sharman and Durrani, an adaptive gradient type triangular lattice algorithm for spatial signal processing [ 7 ]. However, they are suboptimal, and a faster convergence has not been obtained.
Acoustical Science and Technology, 2007
In this paper, we propose a method of estimating the reflection coefficients of an adaptive lattice filter. In this method, conventional adaptive algorithms, for example, the normalized least mean square (NLMS) algorithm, are used for the estimation. In general, the reflection coefficients are estimated as cross-correlation coefficients between forward and backward prediction errors in each stage of the adaptive lattice filter. Accordingly, two divisions in each stage, and effectively doubling the number of stages, are required. A problem is that the processing cost of division is higher than that of multiplication, especially in cheap digital signal processors (DSPs). Hence, the reduction of the number of divisions is strongly desired in practical use. The proposed technique can decrease the number of divisions to one, provided that the NLMS algorithm is used. Moreover, in the application of the adaptive lattice filter, system identification is also important. In this paper, we present a technique for the application. The technique is derived from the proposed method.
Convergence properties of an adaptive digital lattice filter
IEEE Transactions on Acoustics, Speech, and Signal Processing, 1981
Convergence properties of a continuously adaptive digital lattice filter. used as a linear predictor are investigated for both an unnormalized and a normalized gradient adaptation algorithm. The PARCOR coefficient mean values and the output mean-square error (MSE) are approximated and a simple model is described which approximates these quantities as functions of time. Calculated curves using this model are compared with simulation results. Results obtained for a two-stage lattice are then compared with the two-stage least mean-square (LMS) transversal filter algorithm, demonstrating that it is possible but unlikely for the transversal filter to converge faster than the analogous lattice filter. I.
Least-squares adaptive lattice and transversal filters: A unified geometric theory
IEEE Transactions on Information Theory, 1984
Ah.vtracf--A unified theory is presented to characterize least-squares adaptive filters, in either lattice or transversal-filter form, for nonstationary processes. The derivations are based upon a geometric formulation of least-squares estimation and on the concept of displacement ...
This paper presents a performance analysis of three categories of adaptive filtering algorithms in the application of linear prediction. The classes of algorithms considered are Least-Mean-Square (LMS) based, Recursive Least-Squares (RLS) based and Lattice based adaptive filtering algorithms. The performances of the algorithms in each class are compared in terms of convergence behavior, execution time and filter length. The analysis determines the best converging algorithm from each class. Finally the best performing algorithm for adaptive linear prediction is selected.