Showing papers on "Adaptive algorithm published in 1986"

The CM array: An adaptive beamformer for constant modulus signals

Abstract: This paper introduces a new adaptive beam-forming algorithm called the CM Array. Unlike existing adaptive beamformers, the adaptive CM Array exploits the constant modulus (cm) property of the signal of interest (soi) to steer a beam in the direction of the soi while steering nulls in the directions of interference.

Adaptive interpolation of discrete-time signals that can be modeled as autoregressive processes

Abstract: This paper presents an adaptive algorithm for the restoration of lost sample values in discrete-time signals that can locally be described by means of autoregressive processes. The only restrictions are that the positions of the unknown samples should be known and that they should be embedded in a sufficiently large neighborhood of known samples. The estimates of the unknown samples are obtained by minimizing the sum of squares of the residual errors that involve estimates of the autoregressive parameters. A statistical analysis shows that, for a burst of lost samples, the expected quadratic interpolation error per sample converges to the signal variance when the burst length tends to infinity. The method is in fact the first step of an iterative algorithm, in which in each iteration step the current estimates of the missing samples are used to compute the new estimates. Furthermore, the feasibility of implementation in hardware for real-time use is established. The method has been tested on artificially generated auto-regressive processes as well as on digitized music and speech signals.

The h , p and h-p versions of the finite element methods in 1 dimension . Part III. The adaptive h-p version.

Abstract: : The paper is the third and final part in the series of three devoted to the detailed analysis of the three basic versions of the finite element method in one dimension. The first part analyzed the p-version, and the second part concentrated on the h and h-p version. This paper analyzes a theoretical frame of the adaptive h-p version and based on it the authors provide concrete algorithm for the one dimensional problem. It is proven that in the case that the solution has x sub alpha-type singularity, the adaptive algorithm give an exponential rate of convergence, very close to the optimal one analyzed in the second part of the paper. Additional keyword: Error analysis.

On the optimum data nonlinearity in LMS adaptation

Abstract: The effect of an arbitrary nonlinear operation on the data input to the weight update equation in the LMS adaptive algorithm is investigated for a Gaussian data model. Exact difference equations are derived for the weight first and second moments that include the effects of an arbitrary nonlinear operation on the data sequence. The difference equations are used to obtain expressions for the transient behavior of the mean-square error. The mean-square error is minimized over the choice of nonlinearity for a fixed transient behavior. The best choice of nonlinearity is shown exactly to be of the form (x/1 + bx2) when the input data are white. For an arbitrary data covariance matrix, the optimum nonlinearity is shown to be linear when the product of the algorithm step size and input power is much less than unity.

The block-processing FTF adaptive algorithm

Abstract: A new block-type adaptive-filtering algorithm is presented. This new block adaptive filter differs from the frequency-domain block adaptive filters of Ferrara (1980), and of Clark, Mitra, and Parker (1980), in that the new method applies a deterministic time-domain least-squares criteria within each of the data blocks. Information is carried from block to block via a weighted initial condition. This new block fast transversal filters (BFTF) algorithm is a numerically stable algorithm and can also be used to perform efficient least-squares system identification on any one data block, in which case it shows a moderate computational advantage over the previous most-efficient single-data-block algorithms of Morf et al. (1977), of Marple (1981), and of Kalouptsidis, Manolakis, and Carayannis (1984-1985). Mechanisms for tracking and varying block length from block to block are also presented and evaluated. Finally, we indicate how the new algorithm could be pipelined for maximum throughput with delay proportional to the number of parameters, after computation of the sample correlation lags.

A normalized frequency domain LMS adaptive algorithm

Abstract: A scheme is presented for obtaining an input power estimate for setting the algorithm gain parameter μ separately in each frequency bin in the frequency domain LMS adaptive algorithm. This is particularly important if the input has large spectral variations, and a single feedback parameter, set on the broad-band power, could result in instability in the adaptive filters in some frequency bins. The estimate is incorporated directly into the algorithm as a data dependent time-varying stochastic μ(n). Using a Gaussian data model and sample-to-sample data independence, first-order linear difference equations are derived and solved for the mean and misadjustment errors. The performance of the scheme is compared to the case for which the input power level is known a priori. For the same transient response, only about ten samples need be averaged to yield the same misadjustment error.

Adaptive identification of a time-varying ARMA speech model

Abstract: We propose an adaptive algorithm to estimate time-varying ARMA parameters for speech signals. It estimates both input excitations and underlying system parameters. The proposed algorithm is an extended form of the Kalman filter algorithm. We assume the input is either a white Gaussian process or a pseudoperiodical pulse-train as commonly adopted in LPC processing. The time variation of parameters is monitored by a likelihood function. In order to estimate optimal parameters in a small amount of data, AR and MA orders of an estimator are set to be higher than those of a true system. Parsimonious ARMA parameters are calculated from parameters obtained by the high-order ARMA model. Examples of synthetic and real speech sounds are given to demonstrate the tracking ability of this algorithm.

An integrated system optimization and parameter estimation technique for hierarchical control of steady-state systems

Abstract: This paper presents computer simulation results of an optimal adaptive algorithm (Brdyś and Roberts 1984) and develops a double iterative alternative. Both algorithms are optimal in the sense that Kuhn-Tucker necessary optimality conditions are satisfied. The aim of the latter is to reduce the number of times that information is required from the real system. Simulation results also show that it does not increase the total number of information exchanges during the iteration procedure and may even reduce it.

An Optimal Adaptive Scheme for Two Competing Queues with Constraints

Abstract: Two types of traffic, e. g., voice and data, share a single synchronous and noisy communication channel. This situation is modelled as a system of two discrete-time queues with geometric service requirements which compete for the attention of a single server. The problem is cast as one in Markov decision theory with long-run average cost and constraint. An optimal strategy is identified that possesses a simple structure, and its implementation is discussed in terms of an adaptive algorithm of the stochastic-approximations type. The proposed algorithm is extremely simple, recursive and easily implementable, with no a priori knowledge of the actual values of the statistical parameters. The derivation of the results combines martingale arguments, results on Markov chains, O.D.E. characterization of the limit of stochastic approximations and methods from weak convergence. The ideas developed here are of independent interest and should prove useful in studying broad classes of constrained Markov decision problems.

On almost sure convergence of adaptive algorithms

Abstract: We present an extension of the Furstenberg-Kesten theorem on the convergence of random matrices. This extension is applied to the study of almost sure convergence of certain adaptive algorithms. In particular, we establish that the NLMS algorithm is almost surely convergent under extremely weak necessary and sufficient conditions. We also discuss the relationship of sufficient conditions that have appeared in the literature with our results.

A complex adaptive algorithm for IIR filtering

Abstract: This correspondence generalizes the Gauss-Newton algorithm [1] for adaptive IIR filters to include complex coefficients. The resulting algorithm simultaneously updates the real and imaginary parts of the filter coefficients to minimize the average squared estimation error. It has application in frequency-domain adaptive IIR filtering [2] where the signals and filter coefficients are complex.

An SIMD Multiprocessor Ring Architecture for the LMS Adaptive Algorithm

Abstract: A new architecture for a single instruction stream, multiple data stream (SIMD) implementation of the LMS adaptive algorithm is investigated. This is denoted as a ring architecture, due to its physical configuration, and it effectively solves the latency problem often associated with prediction error feedback in adaptive filters. The multiprocessor ring efficiently updates the filter input vector by operating as a pipeline structure, while behaving as a parallel structure in computing the filter output and applying the weight adaptation algorithm. Last, individual processor timing and capacity considerations are examined.

A stability problem in sign-sign adaptive algorithms

Abstract: It has been shown by example that the often used sign-sign variant of the LMS can be unstable and produce unbounded parameter estimates. In this paper a modified sufficient excitation condition on the regressor vector for the sign-sign variant is introduced. Satisfaction of the excitation condition guarantees that there exists a sufficiently small step size to produce parameter estimates which converge exponentially to within a region of the correct parameters. The counter example to stability of sign-sign algorithms is reexamined in light of the new excitation condition and it is shown that the excitation condition correctly predicts when instability will occur in this example.

Recursive center-frequency adaptive filters for the enhancement of bandpass signals

Abstract: In some signal enhancement and tracking applications, where a priori information regarding the signal bandwidth and spectral shape is available, it is suggested to use a recursive center-frequency adaptive filter instead of a fully adaptive filter. A new adaptive algorithm, namely, the recursive maximum-mean-squares (RMXMS) algorithm, is developed based on the gradient ascent technique for the implementation of these filters. An adaptation mechanism based on the Gauss-Newton algorithm is also presented. This class of filters is found to have several advantages which include faster convergence and lesser computational complexity compared to the fully adaptive filters.

Adaptive filters realized with second order sections

Abstract: Adaptive digital filters are currently used in many communication systems for echo cancellation, channel equalization, and adaptive noise cancellation. Most practical applications presently use adaptive finite impulse response (FIR) digital filters because they are well behaved in terms of convergence and stability properties. This paper presents an adaptive algorithm that operates with a parallel form infinite impulse response (IIR) filter structure for applications in which an FIR filter requires too much computation. The new algorithm is derived mathematically and the results of computer experiments are presented to demonstrate its performance.

Linear Adaptive Control via Disturbance-Accommodation; Some Case Studies

Abstract: In [1], [2], [3] an essentially new approach to adaptive control was developed, using the principles and tools of disturbance-accommodating control (DAC) theory. This new approach to adaptive control design is unique in that the resulting adaptive controller is entirely linear and, for the case of "stationary" plants, has all constant parameters. In the present paper, the DAC adaptive control theory developed in [1]-[3] is applied to several specific examples (case-studies) and the resulting closed-loop adaptive systems are exercised on computer simulations to demonstrate the level of adaptive performance achieved. The latter results are somewhat striking and suggest that this new all-linear approach to adaptive controller design is a major advance in modern linear system theory.

Adaptive Control Robustness in Flexible Aircraft Application

Abstract: This paper presents the application of a model reference adaptive control (MRAC) algorithm to flexible aircraft flight control. The algorithm is an adaptive version of the Command Generator Tracking (CGT) control technique. This technique forces a dynamic system to follow a reduced-order model, allowing it to cope with the problem of unmodeled dynamics. The studies were made via simulation, using for the plant an aircraft dynamic model similar to the Bl bomber. This model is of a large aircraft with a reasonable amount of structural flexibility. In particular, flight configurations were analyzed where the influence of the flexible modes make it difficult to control the aircraft. The results indicate that the algorithm has good robustness properties vis-a-vis unmodeled dynamics and can force the flexible aircraft to follow rigid body responses.

Nonlinear quantization effects in the frequency domain complex scalar LMS adaptive algorithm

Abstract: Nonlinear quantization effects in the frequency domain complex scalar LMS adaptive algorithm are analyzed by using conditional expectations. The probability density function of the quantizer input, conditioned on the weight, is derived. The density is applied to finding the conditional characteristic function and the Mth conditional moment at the quantizer output. The first and second conditional moments of the quantizer output are used to derive difference equations that approximate the dynamical behavior of the first and second weight moments. These difference equations are solved numerically and compare favorably to simulation results. A model of the quantizer as an additive noise source is of no analytical value since the quantizatian noise has negligible effect on the mean square error when the model is valid. Finally, a design approach is proposed for selecting the number of bits in the weight accumulator. The moment equations are also used to determine the algorithm mean square error for different quantizer step sizes and the optimum algorithm step size μ when a fixed amount of input data is available for adaptation.

Detection of Frequency-Hop Signals

Abstract: This paper examines the performance and trade-offs associated with detecting frequency-hop signals by means of multiple observations in the presence of narrowband interfering signals. An adaptive algorithm is proposed for utilizing the outputs from a parallel filter bank observed over a number of time intervals to make decisions on the presence of one or more frequency-hop signals. Trade-offs among the number of filters, the number of time intervals, the time-bandwidth product of each energy detector, and the total observation time are explored by means of computer simulation. The probability of detection for a specified probability of false alarm is determined as a function of the frequency-hop signal power for various numbers of interfering signals. The degradation in performance that results from not observing the frequency-hop signal synchronously with the hops is evaluated, as is the effect of not knowing the hop rate.

Extensions of a Simplified Continuous-Time Multivariable Adaptive Control Algorithm

Abstract: A simplified adaptive control algorithm was recently shown to guarantee robustness with parasitic dynamics and disturbances. The algorithm uses parallel feedforward in order to satisfy necessary positive realness conditions. On the other hand, the order of the plant and the pole excess may be very large and unknown, while the model reference may be of very low order. This paper presents an attempt to reduce the prior knowledge needed for implementation of the adaptive algorithm. It is only assumed that a necessary feedforward of known order exists and the eigenvalues of this configuration are calculated adaptively. Although the stability analysis still arises some difficulties, the proposed algorithm seems to perform very well in difficult environments, including nonminimum-phase plants with rapidly changing parameters.

An adaptive algorithm for array processing

Abstract: A mathematical summary of the joint complex least squares lattice (JCLSL) adaptive algorithm is presented. The algorithm has as inputs two scalar discrete time series (primary. and reference channels). Output consists of the filtered reference channel subtracted from the primary channel. The convergence characteristics of the algorithm are illustrated experimentally for a problem where the reference channel time series consists of dual constant frequency sinusoids which undergo an instantaneous step in frequency. The primary channel time series consists of dual constant frequency sinusoids whose frequencies coincide with those of the reference channel after the step. Lastly, an application of the JCLSL algorithm to the rejection of ocean acoustic boundary reverberation is described.

Adaptive algorithms for eigenstructure based spectral estimation and filtering

Abstract: This paper considers the problem of adaptive estimation of the complete set of eigenvectors and eigenvalues of a data covariance matrix. After considering some applications of eigenstructure algorithms to spectral estimation and constrained filtering problems, the paper discusses a new approach to data adaptive eigenestimation. A new technique based on an adaptive implementation of the Q-R algorithm is presented. This algorithm offers a strategy for recursive estimation of the complete set of covariance matrix eigenvectors and eigenvalues, which is computationally efficient to implement.

CMA-based Techniques for Adaptive Interference Rejection

Abstract: This paper surveys several recent developments in the area of applying the Constant Modulus Algorithm (CMA) to the problem of rejecting interference from a signal deemed to be of interest This algorithm was originally developed for removing the dispersive effects of multipath propagation from constant envelope communications signals, but has proven useful in a variety of other applications, such as suppressing additive narrowband interference, combining diversity receiving channels to reject crosspolarized signal components, and steering nulls in a sensor array The paper first reviews the algorithm itself and its original application From this departure point, several applications, including those listed above, are examined and performance results cited where possible Some of these applications have encouraged the development of modified algorithms - several of these are described, including one employing real-valued data and another which allows "fast" convergence rather than the slower convergence characteristic of the gradient-search-based algorithms

On least square frequency-domain adaptive filters

Abstract: This paper presents a least square approach to the Dentino et al. [1] frequency-domain adaptive filter by minimizing a frequencydomain error criterion. The constant \mu that controls the LMS convergence behavior is replaced by an adaptive \mu that every new iteration achieves this least squared error. The proposed approach can be extended and then applied to modify other frequency-domain adaptive algorithms. For example, a modified version of the unconstrained frequency domain adaptive algorithm proposed by Mansour and Gray in [2] is presented. The advantage of our modified unconstrained frequency-domain adaptive algorithm is that it has only one convergence parameter as compared to two in the original algorithm.

An adaptation algorithm for parallel model reference adaptive bilinear systems

Abstract: An adaptation algorithm is presented for parallel model reference adaptive bilinear systems. The output error converges asymptotically to zero and the parameter estimates are bounded for stable reference models. The convergence criterion depends only upon the input sequence and a priori estimates of the maximum parameter values. A passivity condition, which is generally difficult to verify, is not required.

The Least Mean Squares (LMS) Algorithm

Abstract: The method of steepest descent described and developed in the previous chapter forms the mathematical basis for many current adaptive signal processing algorithms However, steepest descent was developed for iteratively solving the normal equations (235) for the optimal w N * For an actual signal processing application, this would be equivalent to requiring that the time series d(n) and x(n) be stationary and, additionally, that their second-order statistics be known Knowledge of the second-order statistics in (235) was conveyed by the autocorrelation matrix and cross-correlation vector However, in practical system implementations, these correlation values can only be estimated from available data, and this is often a source of computational delay, or error, or both This chapter develops an alternative to the method of steepest descent called the least mean squares (LMS) algorithm, which will then be applied to problems in which the second-order statistics of the signal are unknown Due to its simplicity, the LMS algorithm is perhaps the most widely used adaptive algorithm in currently implemented systems

Formulation and implementation of a practical algorithm for non-stationary adaptive state estimation

Abstract: Background information on the Kalman filter is given first. A discussion of the filter parameters and their a priori determination follows. The discussion points out the need for adaptive determination of the process noise statistics. The filter innovations are presented as a means for developing the adaptive criteria. The criteria center around the estimation of the true mean and covariance of the filter innovations. A method for the numerical approximation of the mean and covariance of a locally stationary random process is presented. The definition of a local stationarity is presented. Local stationarity allows for the separation of the process statistics into a stationary component and a time-varying component. The separation method is discussed. A method for estimating the stationary and time-varying components is presented. As an example of its application to real problems, the algorithm is applied to the problem to the problem of reentry trajectory estimation for the Space Shuttle. Both the adaptive algorithm and the steady-state Kalman filter are applied to the problem. The results of the reconstructions are presented. The adaptive algorithm exhibits superior performance.