Showing papers on "Recursive least squares filter published in 1991"

Numerically stable fast transversal filters for recursive least squares adaptive filtering

Abstract: A solution is proposed to the long-standing problem of the numerical instability of fast recursive least squares transversal filter (FTF) algorithms with exponential weighting, an important class of algorithms for adaptive filtering. A framework for the analysis of the error propagation in FTF algorithms is first developed; within this framework, it is shown that the computationally most efficient 7N form is exponentially unstable. However, by introducing redundancy into this algorithm, feedback of numerical errors becomes possible; a judicious choice of the feedback gains then leads to a numerically stable FTF algorithm with a complexity of 8N multiplications and additions per time recursion. The results are presented for the complex multichannel joint-process filtering problem. >

Fast adaptive schemes for tracking voltage phasor and local frequency in power transmission and distribution systems

Abstract: Devices specifically dedicated to highly accurate measurement of frequency have been described for specific applications like power system stabilizers. However, in most situations the digital estimate of the frequency deviation is needed concurrently with other decision quantities. Therefore, its value is usually obtained as a by-product of a more general-purpose algorithm, based, for instance, on the extended Kalman filtering or the recursive least error squares techniques. Unfortunately, a common problem with these Kalman filters is the high computational requirements, due to transcendental functions evaluation in real-time. Therefore, the need still exists for more clever implementations of the various real-time algorithms, which could alleviate the computational burden and enhance the adaptation speed during transients. To fulfil this need to some extent, two new methods suitable for fast adaptive estimation of voltage phasor and frequency deviation are outlined. >

A recursive least error squares algorithm for power system relaying and measurement applications

Abstract: A recursive algorithm suitable for microprocessor-based power system relaying and measurement applications is described. The algorithm is designed using the least error squares (LES) curve fitting technique. The mathematical background for the nonrecursive least error squares algorithm is extended to form a recursive algorithm. A method for including decaying DC and harmonic frequencies in the algorithm is described. Sample studies are presented to demonstrate the performance of the developed algorithm. The recursive LES (RLES) algorithm is shown to be computationally efficient and does not require the time constant of decaying DC and statistical information concerning the signal. It is shown that a 12-RLES algorithm can be used for implementing transformer differential protection. >

Estimation of time-varying respiratory mechanical parameters by recursive least squares.

Abstract: Continuous estimation of time-varying respiratory mechanical parameters is required to fully characterize the time course of bronchoconstriction. To achieve such estimation, we developed an estimat...

Adaptive recovery of a chirped sinusoid in noise. II. Performance of the LMS algorithm

Abstract: The authors study the ability of the exponentially weighted recursive least square (RLS) algorithm to track a complex chirped exponential signal buried in additive white Gaussian noise (power P/sub n/). The signal is a sinusoid whose frequency is drifting at a constant rate Psi . lt is recovered using an M-tap adaptive predictor. Five principal aspects of the study are presented: the methodology of the analysis; proof of the quasi-deterministic nature of the data-covariance estimate R(k); a new analysis of RLS for an inverse system modeling problem; a new analysis of RLS for a deterministic time-varying model for the optimum filter; and an evaluation of the residual output mean-square error (MSE) resulting from the nonoptimality of the adaptive predictor (the misadjustment) in terms of the forgetting rate ( beta ) of the RLS algorithm. It is shown that the misadjustment is dominated by a lag term of order beta /sup -2/ and a noise term of order beta . Thus, a value beta /sub opt/ exists which yields a minimum misadjustment. It is proved that beta /sub opt/=((M+1) rho Psi /sup 2/)/sup 1/3/, and the minimum misadjustment is equal to (3/4)P/sub n/(M+1) beta /sub opt/, where rho is the input signal-to-noise ratio (SNR). >

Givens rotation based least squares lattice and related algorithms

Abstract: The author presents a general and systematic approach for deriving new LS (least squares) estimation algorithms that are based solely on Givens rotations. In particular, this approach is used to derive efficient Givens-rotation-based LS lattice algorithms-the Givens-lattice algorithms. By exploiting the relationship between the Givens algorithms and the recursive modified Gram-Schmidt algorithm, it is shown that the time and order update of any order-recursive LS estimation algorithm can be realized by employing only Givens rotations. Applying this general conclusion to LS estimation of time-series signals results in the Givens-lattice algorithms. Two Givens-lattice algorithms, one with square roots and the other without, are presented. It is shown that the Givens-lattice algorithms are computationally more efficient than the fast QR algorithm of Cioffi (1987). The derivation of other Givens rotation-based LS estimation algorithms and their systolic array implementations are discussed. >

Adaptive MLSE-VA receiver for digital cellular radio

Abstract: A TDMA RF received signal is demodulated by first being filtered with a fixed transversal filter having a characteristic selected for matching a fixed square root raised cosine pulse characteristic of the received signal. The filtered signal is then adaptively filtered for compensating for a time varying impulse response of the channel. The adaptive filtering is performed initially during a synchronizing portion (preamble) of the filtered signal in accordance with a fast recursive least squares algorithm. Subsequent filter adaptation to a data portion of the filtered signal is accomplished in accordance with a computationally less expensive normalized least mean square procedure. The adaptive filter repetitively applies a modified Viterbi algorithm to blocks of 2D symbols, such that D symbols are released for adapting the adaptive filter means during the data portion of the filtered signal and the signal. The released symbols are also employed for adapting elements required in computing a metric for the modified Viterbi algorithm and the reconstructed signal used to form an error signal that drives the adaptation algorithms.

Fast tracking RLS algorithm using novel variable forgetting factor with unity zone

Abstract: A new fast tracking recursive least squares (RLS) algorithm for time-varying systems is presented. The new algorithm is based on an innovative variable forgetting factor with a unity zone and its extra computational burden is trivial compared with the standard RLS algorithm. Fast tracking and low parametric error variance properties are verified via computer simulations.

Fast adaptive equalizers for narrow-band TDMA mobile radio

Abstract: It is pointed out that the future European cellular digital mobile radio system in the 900 MHz band adopts a narrowband time division multiple access (TDMA) scheme with Gaussian minimum-shift keying (GMSK) modulation and burst type transmission. Consequently, very fast adaptation methods are necessary to cope with the time- and frequency-selective distortions produced by Rayleigh and multipath fading. The authors examine a few theoretical aspects of the application of recursive least squares (RLS) adaptation algorithms to the narrowband TDMA mobile radio system and give the relevant performance results for the fast Kalman algorithm, which turns out to be suitable for the considered application. In particular, signature curves, bit error rate, speed of convergence, steady-state behavior, numerical stability, required accuracy, and hardware complexity are discussed. Linear transversal and nonlinear decision-feedback equalizers are considered. >

Variable length stochastic gradient algorithm

Abstract: The transversal variable-length stochastic gradient algorithm is described. It is a modification of the stochastic gradient algorithm that allows dynamic allocation of coefficients of an adaptive filter. The order of the filter and the adaptation step size are changed automatically when an appropriate level of performance is reached during the course of the adaptation process. In this way, the algorithm results in fast convergence, typical of low-order filters, and good steady-state performance, typical of high-order filters. >

Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms

Abstract: Numerical linear algebra, digital signal processing, and parallel algorithms are three disciplines with a great deal of activity in the last few years. The interaction between them has been growing to a level that merits an Advanced Study Institute dedicated to the three areas together. This volume gives an account of the main results in this interdisciplinary field. The following topics emerged as major themes of the meeting: - Singular value and eigenvalue decompositions, including applications, - Toeplitz matrices, including special algorithms and architectures, - Recursive least squares in linear algebra, digital signal processing and control, - Updating and downdating techniques in linear algebra and signal processing, - Stability and sensitivity analysis of special recursive least squares problems, - Special architectures for linear algebra and signal processing. This book contains tutorials on these topics given by leading scientists in each of the three areas. A consider- able number of new research results are presented in contributed papers. The tutorials and papers will be of value to anyone interested in the three disciplines.

Recursive least squares based estimation schemes for self‐tuning control

Abstract: Recursive Least Squares (RLS) is the most popular parametric identification method used for on-line process model estimation and self-tuning control. The basic least squares scheme is outlined in this paper and its lack of ability to track changing process parameters is illustrated and explained. Several variants of the basic algorithm which have appeared elsewhere in the literature are discussed. Some of these algorithms contain different modifications to the basic scheme which are intended to prevent this loss of alertness to changing process parameters. Other variations of the least squares algorithm are presented which attempt to deal with parameter estimation in the presence of disturbances and unmodelled process dynamics.

Channel-estimation-based adaptive DFE for fading multipath radio channels

Abstract: The performance of an adaptive decision feedback equaliser (DFE) over an HF channel when its taps are derived from an estimate of the sampled channel impulse response is examined. The conventional approach to adaptation is to adjust the equaliser taps directly to minimise a least squares error cost function. It is shown that the channel estimate approach not only yields superior performance, but also involves fewer computations than the conventional square-root-Kalman approach. The problem of channel estimation is mathematically analysed for both the steepest descent and recursive least squares algorithms, and theoretical results are compared with simulation. It is also shown how simple theoretical predictions of the performance of the DFE can be made when using this alternative method of implementation.

A novel approach for stabilizing recursive least squares filters

Abstract: A novel approach for stabilizing recursive least squares (RLS) filters is presented. The approach relies on a detailed fixed point analysis, which provides two important benefits. The analysis reveals a bias in the error propagation mechanism, providing an analytical basis for instability problems. The analysis then indicates which specific roundoff errors are causing instability. These roundoff errors are then biased in such a way that the overall filter is biased towards stable performance. Experimental results indicate that stability can be achieved with negligible loss in least squares performance. >

Computationally efficient QR decomposition approach to least squares adaptive filtering

Abstract: The least squares lattice algorithm for adaptive filtering based on the technique of QR decomposition (QRD) is derived from first principles. In common with other lattice algorithms for adaptive filtering, this algorithm only requires O(p) operations for the solution of a pth order problem. The algorithm has as its root the QRDbased recursive least squares minimisation algorithm and hence is expected to have superior numerical properties when compared with other fast algorithms. This algorithm contains within it the QRD-based lattice algorithm for solving the least squares linear prediction problem. The algorithm is presented in two forms: one that involves taking square-roots and one that does not. The relationship between the QRD-based lattice algorithm and other least squares lattice algorithms is briefly discussed. The results of some computer simulations of a channel equaliser, using finiteprecision floating-point arithmetic, are presented.

Adaptive filters based on order statistics

Abstract: An adaptive filter structure which is based on linear combinations of order statistics is proposed. An efficient method to update the filter coefficients is presented, which is based on the minimal mean-square error criterion and which is similar to the Widrow algorithm for the linear adaptive filters. Another method for coefficient update is presented, which is similar to the recursive least squares (RLS) algorithm and which has faster convergence properties. The proposed-filter can adapt well to a variety of noise probability distributions, including impulsive noise. It also performs well in the case of nonstationary signals and, therefore, it is suitable for image-processing applications. >

Time-varying spectral estimation using AR models with variable forgetting factors

Abstract: A method of estimating time-varying spectra of nonstationary signals using recursive least squares (RLS) with variable forgetting factors (VFFs) is described. The VFF is adapted to a nonstationary signal by an extended prediction error criterion which accounts for the nonstationarity of the signal. This method has better adaptability than the conventional algorithm with high fixed forgetting factor (FFF) in the nonstationary situation, and has lower variance than the conventional one with low FFF in the stationary situation. The extra computation time for the forgetting adaptation is almost negligible. >

Adaptive control of linear stochastic evolution systems

Abstract: An adaptive control problem for some linear stochastic evolution systems in Hilbert spaces is formulated and solved in this paper. The solution includes showing the strong consistency of a family of least squares estimates of the unknown parameters and the convergence of the average quadratic costs with a control based on these estimates to the optimal average cost. The unknown parameters in the model appear affinely in the infinitesimal generator of the C 0 semigroup that defines the evolution system. A recursive equation is given for a family of least squares estimates and the bounded linear operator solution of the stationary Riccati equation is shown to be a continuous function of the unknown parameters in the uniform operator topology

The equivalence of the total least squares and minimum norm methods (signal processing)

Abstract: It is shown that the minimum norm solution is equivalent to the total least squares solution. It is noted that two versions of the total least squares solution exist, one based on the signal subspace and another based on the noise subspace. >

Adaptive equalization with RLS-MLSE for frequency-selective fast fading mobile radio channels

Abstract: The authors propose a novel adaptive equalization scheme which is a combination of the recursive least squares adaptive algorithm and maximum likelihood sequence estimation (RLS-MLSE). The performance of the scheme is demonstrated in frequency-selective fast fading mobile radio channels. RLS-MLSE employs a parallel estimation scheme in which the state of the channel is estimated by the Viterbi algorithm and the parameters of the channel impulse response are estimated by RLS. A simplified RLS algorithm and an extension to the diversity reception scheme are discussed. Computer simulations show that RLS-MLSE is suitable for 40-kb/s QPSK (quadrature phase shift keying) transmission in 900-MHz-band mobile radio systems, and that equalization with two-branch diversity operates up to a maximum Doppler frequency of 160 Hz. >

New forms of Levinson and Schur algorithms

Abstract: The Levinson and Schur solutions to the adaptive filtering and parameter estimation problem of recursive least squares processing are described. Unnormalized versions of a newly developed Schur RLS adaptive filter are presented. A systolic array of the Schur RL adaptive filter is devised and its performance is illustrated with a typical example. The classical Levinson and Schur algorithms drop out as special cases of the more general Levinson and Schur RLS adaptive filtering algorithms. The recently introduced split Levinson and Schur algorithms, which are obtained by exploiting the symmetry in the Toeplitz-structured extended normal equations, are reviewed. >

Linearized least-squares training of multilayer feedforward neural networks

Abstract: The authors develop a linearized least-squares formulation for estimating the weight coefficients of a neural network. Linearization of the nonlinear network about the most recent weight estimates leads to a conditional least-squares criterion which may be solved recursively in time. The resulting coefficient update equations resemble those of the recursive least-squares solution in adaptive filtering, much as the update equations for linearized stochastic gradient descent (backpropagation) resemble those of the least mean squares solution in adaptive filtering. Simulations on small logic mapping problems indicate a three- to tenfold increase in training efficiency for this technique as compared to gradient descent. >

Recursive identification and adaptive prediction in linear stochastic systems

Abstract: By making use of extended stochastic Lyapunov functions and martingale limit theorems, established herein are certain basic properties of adaptive d-step ahead predictors associated with the extended least squares, stochastic gradient (without interlacing), and monitored recursive maximum likelihood algorithms for recursive identification of an ARMAX system. Both the direct (or implicit) and indirect (or explicit) approaches to adaptive prediction are considered within a unified framework involving stochastic regression models. Applications to adaptive control of ARMAX systems are also discussed.

Some issues on the practical use of recursive least squares identification in self-tuning control

Abstract: System identification plays an extremely important role in the self-tuning controller. As the recursive least squares (RLS)identification technique has the advantages of simple calculation and good convergence properties, it is the preferred technique for use in the design of the self-tuning controllers. However, use of RLS identification in a real-time environment does raise some problems such as the speed of parameter convergence, identification going to ‘sleep’, covariance matrix ‘blow up’, biased identification, etc. This paper deals with the problems which may arise in the practical use of the RLS identification technique. These issues are the summary of several years' experience of designing self-tuning controllers with RLS identification technique for power system applications. Although some of these issues are difficult to analyse, they are quite effective in dealing with the practical problems.

Dynamic range, stability, and fault-tolerant capability of finite-precision RLS systolic array based on Givens rotations

Abstract: The QR decomposition recursive least-squares (QRD RLS) algorithm for mapping onto a systolic array for signal processing and communication applications is considered. Detailed analysis is presented to show that the rotation parameters of the RLS algorithm based on the Givens rotation method will eventually reach the quasi-steady-state if the forgetting factor lambda is very close to 1. With this model, the dynamic range of each processing cell can be derived, and from this a proper wordlength can be chosen to ensure correct operation of the algorithm. The proposed solutions are simple and effective. Simulations have demonstrated that the wordlengths chosen by the proposed dynamic range work well. The stability of the QRD RLS algorithm is demonstrated under a finite-precision implementation with this observation. Finally, the missing error detection and false alarm problems are considered based on the results obtained from the model. The wordlength is overflow-free without missing error detection and false alarm problems. The results in this study are of practical importance. Not only can a finite-precision QRD RLS systolic array be designed with a minimum wordlength that ensures correct operations, but also a fault-tolerant system that can detect a given error size and is false-alarm-free under the quantization effect can be provided. >

Some asymptotic results in recursive identification using laguerre models

Abstract: This paper deals with recursive identification of time-varying systems using Laguerre models. Laguerre models generalize finite impulse response (FIR) models by using a priori information about the dominating time constants of the system to be identified. Three recursive algorithms are considered: the stochastic gradient algorithm, the recursive least squares algorithm and a Kalman-filter-like recursive identification algorithm. Simple and explicit expressions for the model quality are derived under the assumptions that the system varies slowly, that the model is updated slowly and that the model order is high. The derived expressions show how the use of Laguerre models affects the model quality with respect to tracking capability and disturbance rejection.

New Forms of

Abstract: This paper describes the Levinson and Schur solutions to the adaptive _filtering and parameter estimation problem of recursive least squares @US) processing. Unnormalized and normalized versions of a newly developed Schur RLS adaptive filter are presented. A systolic array of the Schur RLS adaptivejllter is devised and its performance is illustrated with a typical example. The classical Levinson, and Schur algorithms drop out as special cases of the more general Levinson and Schur RLS adaptivejlltering algorithms. In the _final section, we review the recently introduced split Levinson and Schur algorithms which are obtained by a clever exploitation of the symmetry in the Toeplitz-structured extended Normal Equations. ANY adaptive signal processing tasks involve the solution of sysM tems of linear equations where the system matrix has special properties. In the theory of linear prediction of stationary random sequences, it is well known that the determination of the optimal predictor coefficients involves the solution of a linear system of equations with a system matrix having Toeplitz structure. An order

Surface approximation using weighted splines

Abstract: The surface reconstruction problem is formulated as a two-stage reconstruction procedure. The first stage is a robust local fit to the data in a multiresolution scheme and the second is a regularized least squares fit, with the addition of an adaptive mechanism in the smoothness functional in order to make the solution well behaved. The authors present the details of the second stage in which they use the weighted bicubic spline as a surface representation in a regularization framework, with a Tikhonov stabilizer, as the smoothness norm. It is shown how the adaptive weights, in the stabilizer help the surface bend across discontinuities by varying the energy of the surface. >