Showing papers on "Kernel adaptive filter published in 1982"

Lattice filters for adaptive processing

Abstract: This paper presents a tutorial review of lattice structures and their use for adaptive prediction of time series Lattice filters associated with stationary covariance sequences and their properties are discussed The least squares prediction problem is defined for the given data case, and it is shown that many of the currently used lattice methods are actually approximations to the stationary least squares solution The recently developed class of adaptive least squares lattice algorithms are described in detail, both in their unnormalized and normalized forms The performance of the adaptive least squares lattice algorithm is compared to that of some gradient adaptive methods Lattice forms for ARMA processes, for joint process estimation, and for the sliding-window covariance case are presented The use of lattice structures for efficient factorization of covariance matrices and solution of Toeplitz sets of equations is briefly discussed

Signal cancellation phenomena in adaptive antennas: Causes and cures

Abstract: Conventional adaptive beamformers utilizing some form of automatic minimization of mean square error exhibit signal cancellation phenomena when adapting rapidly. These effects result from adaptive interaction between signal and interference, when signal and interference are received simultaneously. Similar phenomena have been observed and analyzed in relatively simple adaptive noise cancelling systems. A study of these phenomena in the simpler systems is used to provide insight into similar behavior in adaptive antennas. A method for alleviating signal cancellation has been devised by Duvall, whereby the signal components are removed from the adaptive process, then reinserted to form the final system output. Widrow has devised a different solution to the problem: to move the receiving array spatially (or electronically) to modulate emanations received off the look direction, without distorting useful signals incident from the look direction. This approach is called "spatial dither" and introduces the additional possibility of modulating "smart" jammer signals, thereby limiting their effectiveness.

Recursive adaptive filter design using an adaptive genetic algorithm

Abstract: An adaptive genetic algorithm for determining the optimum filter coefficients in a recursive adaptive filter is presented. The algorithm does not use gradient techniques and thus is appropriate for use in problems where the function to be optimized is non-unimodal or non-quadratic, such as the mean-squared error surface in a recursive adaptive filter. The mechanisms of the algorithm are inspired by adaptive processes observed in nature. After an initial set of possible filters is randomly selected, each filter is mapped to a binary string representation. Selected bit strings are then transformed using the operations of crossover and mutation to build new "generations" of filters. The probability of selecting a particular bit string to modify and/or replicate for the next "generation" is inversely proportional to its estimated mean-squared error value. Hence, the process not only examines new filter coefficient values, but also retains the advances made in previous "generations". Computer simulations of the algorithm's performance on unimodal and bimodal error surfaces are presented.

System identification techniques for adaptive signal processing

Abstract: Many problems in adaptive filtering can be approached from the point of view of system identification. The recursive maximum likelihood algorithm is proposed for estimating the parameters of the signal model. The parameter estimates are then used to form an adaptive infinite impulse response filter. Several examples are discussed including: adaptive line enhancement, adaptive deconvolution, adaptive noise cancelling, and adaptive time delay estimation.

ϵ‐separating nonlinear digital filter and its applications

Abstract: This paper proposes an ϵ-separating nonlinear digital filter (called an ϵ-filter). This filter is intended for effective filtering of low-amplitude noise superposed on the signal with sharp discontinuities and can be realized by combining a simple nonlinear element with a conventional linear filter. In this paper, the basic ϵ-filter and its modifications to a trend-adaptive filter and a two-dimensional filter are described. The effectiveness of the new filter is demonstrated by computer simulation. Some of its application to EEG analysis, image processing and coding are also presented.

On reduced-order adaptive output error identification and adaptive IIR filtering

Abstract: The reduced-order application of Landau's adaptive output error identifier results in a perturbed error system where the perturbation signal is a moving average of the unmodeled portion of the unknown plant output (or desired signal in adaptive filter parlance). It is proven in this paper that if this perturbation signal is sufficiently small and a reduced-order dimension model is sufficiently excited, then the output and parameter estimates of this adaptive identifier/filter remain bounded. The influence of various operating conditions on this quantitatively defined bound are noted. This robustness property is crucial in all real applications, which due to nonlinearities and distributed effects are subject to reduced-order modeling.

On the design of nonlinear discrete-time predictors (Corresp.)

Abstract: The problem of minimum mean-squared error prediction of a discrete-time random process using a nonlinear filter consisting of a zero-memory nonlinearity followed by a linear filter is studied. Classes of random processes for which the best predictor is realizable using a nonlinear filter of the above form are discussed. For those random processes for which the best predictor is not realizable using the above nonlinear filter, an iterative procedure is presented for finding a suboptimal nonlinear filter; special attention is directed to the case where the nonlinearity is a polynomial. Also, a noniterative approach based on nonlinear regression is presented.

Optimization of short digital linear filters for increased accuracy

Abstract: The accuracy of short length digital linear filter operators can be substantially increased if the sampling interval as well as the abscissa shift are properly adjusted. This may be done by a trial and error process of adjustment of these parameters until the error made by the filter operator, applied to a suitably chosen test function, is smallest. As an illustration of the application of this method, 7-, 11- and 19-point filters for the calculation of Schlumberger apparent resistivity from a known resistivity transform are designed. Errors with the new 7-point filter are seen to be less than those with a 19-point filter of conventional design. The errors with the new 19-point filter are two to three orders of magnitude smaller than those made by the conventional 19-point filter. The new method should provide digital linear operators that allow significant improvements in accuracy for comparable computation efforts, or substantial reduction in computation for comparable accuracy of results, or something of both.

The truncated second-order nonlinear filter revisited

Abstract: By rederiving the truncated second-order nonlinear filter, it is shown that the original derivations of this filter contain errors, or at least illogical approximations. The so-called modified truncated second-order nonlinear filter is, furthermore, shown to be the correct form of this filter provided a small correction is made in the discrete-time case.

Least squares algorithms for adaptive linear-phase filtering

Abstract: In many applications, it is desirable to use filters with linear-phase characteristics. This paper presents an approach for developing such filters for adaptive signal processing. Several least squares algorithms are derived for adjusting the coefficients of an adaptive linear phase filter. It is shown that smoothing filters, rather than the commonly used prediction filters, are a more natural choice if linear phase characteristics are required.

Two filter smoothing formulae by diagonalization of the Hamiltonian equations

Abstract: We present a new approach to two filter smoothing formulae via diagonalization of the general time variant hamiltonian equations of the linear estimation problem. This approach shows the special role of the famous Mayno-Fraser two filter formulae and also provides insight into certaini nvariance properties of backwards Kalman filter estimates.

System identification techniques for adaptive signal processing

Abstract: Many problems in adaptive filtering can be approached from the point of view of system identification. The close interconnection between these two disciplines is explored in some detail. This approach makes it possible to apply recursive parameter estimation algorithms to adaptive signal processing. Several examples are discussed including: adaptive line enhancement, generalized adaptive noise cancelling, adaptive deconvolution and adaptive TDOA estimation. It is shown how the recursive maximum likelihood algorithm can be used for both FIR and IIR filtering, and some preliminary results are presented. Several alternative algorithms are briefly discussed.

Adaptive filter including a far end energy discriminator

Abstract: ADAPTIVE FILTER INCLUDING AFAR END ENERGY DISCRIMINATOR Abstract of the Disclosure An energy discriminator is employed in conjunction with an adaptive filter to control updating of the filter transfer function characteristic. Specifically, the discriminator is employed to distinguish whether any significant received far end energy is only partial band or whole band. If the received energy is partial band the adaptive filter is inhibited from updating the transfer function characteristic during intervals that such energy is being received. On the other hand, if the received energy is determined not to be partial band and, hence, is whole band, the filter is enabled to update the transfer function characteristic during intervals that such energy is being received. In a specific example, the discriminator is employed in an adaptive echo canceler to inhibit updating an echo path estimate being generated by an adaptive transversal filter when partial band energy is being received and enabling updating of the echo path estimate when whole band energy is being received.

Combination speech synthesis and recognition apparatus

Abstract: A reconfigurable lattice filter is employed to permit the same circuitry to function as a speech synthesizer and as a speech analyzer or recognizer. The lattice filter can be configured both as an all-pole filter (for synthesis) and as an all-zero filter (for analysis), with the choice being determined by the state of an analysis/synthesis signal (i.e., mode control signal) provided thereto. The connections between various elements in the circuitry are controlled by the analysis/synthesis signal, also. In synthesis mode, partial correlation coefficients are supplied to the filter from a microprocessor. The filter is excited by a one of a number of stored patterns simulating a glottal pulse for voiced sounds and by a pseudo-random noise generator for unvoiced sounds. In analysis mode, appropriate feedback control paths are enabled so as to provide to the filter coefficients which change in response to changes in the input speech waveform. Coefficient values thus determined are averaged over fixed intervals and successions of such averaged coefficient sets produce representations of words or phrases which can then be used for speech recognition.

Adaptive filter update normalization

Abstract: Loop gain normalization is employed in adaptive filters to control weighting of the filter characteristic updates in order to converge properly to a desired filter characteristic. Filter stability and rapid high quality convergence is realized for a variety of received or inputted signals by employing both long term and fast attack estimates of a prescribed input signal characteristic to normalize the update gain. In one embodiment, both long term and fast attack input signal power estimates are generated and one of the two estimate values is selected to normalize the update gain. Specifically, the fast attack estimate is modified by a predetermined value and, then, the larger of the long term estimate and modified fast attack estimate is selected to normalize the update gain.

Adaptive echo canceller with AGC for transmission systems

Abstract: An adaptive echo canceller for a full duplex transmission system comprises a cascade arrangement of an adaptive digital filter and an automatic gain control device. The AGC device receives the output signal from the adaptive digital filter and delivers the estimate of the echo signal to the receive line for subtraction. It has a multiplier receiving the output signal and a signal representative of the multiplication factor from a gain adaptation circuit. A separate gain change circuit is connected to receive the output signal from the adaptive digital filter and simultaneously modifies the tap coefficients of said filter and the multiplication factor of the AGC device in opposite directions for maintaining the output of the adaptive digital filter in a predetermined range.

Adaptive techniques for automatic frequency determination and measurement.

Abstract: Various implementations of a technique are presented for capitalizing on signal correlation in a manner for providing usable frequency information. In a specific embodiment, a filter (51) is adapted to a signal component of an input signal using a variable generated by an adapter 58. The variable has a prescribed relationship to the frequency of the signal component. The variable is used to weight a combination of signal values derived from past signal history to form a prediction of a future signal. An adder 56 combines the new signal value with the prediction to form an error signal which is used by the filter (51) and the adapter (58). When the filter converges, a frequency indicator (59) using the variable provides an output signal indicative of the frequency of the signal component.

Fast recursive estimation using the lattice structure

Abstract: This paper presents the theory for a rapidly converging adaptive linear digital filter. The filter weights are updated for every new input sample. This way the filter is optimal (in the minimum mean square error sense) for all past data up to the present, at all instants of time. This adaptive filter has thus the fastest possible rate of convergence. Such an adaptive filter, which is highly desirable for use in dynamical systems, e.g., digital equalizers, used to require on the order of N2 multiplications for an N-tap filter at each instant of time. Recent “fast” algorithms have reduced this number to like 10 N. One of these algorithms has the lattice form, and is shown here to have some interesting properties: It decorrelates the input data to a new set of orthogonal components using an adaptive, Gram-Schmidt like, transformation. Unlike other fast algorithms of the Kalman form, the filter length can be changed at any time with no need to restart or modify previous results. It is conjectured that these properties will make it less sensitive to digital quantization errors in finite word-length implementation.

Applications of output error recursive estimation algorithms for adaptive signal processing

Abstract: Several problems in signal processing can be approached as recursive identification problems for AR, ARMA or ARMAX models. The output error with extended estimation model adaptive algorithm is proposed and evaluated for real-time estimation of the parameters of the signal model. The applications of these techniques for the adaptive signal processing are presented. The theoretical aspects related to the convergence properties of this algorithm are also discussed.

Nonlinear filtering using linear combinations of order statistics

Abstract: In this paper we consider a nonlinear filter whose output is given by a linear combination of the order statistics of the input sequence. Assuming a constant signal in white background noise, the coefficients in the linear combination are chosen to minimize the output MSE for several noise distributions. This new general filter is superior to the well-known median filter, since the median is just a special case.

Correlation function for the weight sequence of the frequency domain adaptive filter

Abstract: The statistical behavior of the single complex adaptive weight in the frequency domain adaptive filter is further investigated. In a previous note [8], an expression was evaluated for the expected value of the magnitude square of the weight sequence at any time. In this note, the covariance of the weight at different times is evaluated and, in steady state, shown to be geometric with the same time constant as the frequency domain adaptive filter algorithm itself. Using these results, the reduction in the fluctuations of the weight values are computed for an exponentially decaying post-algorithm filter.

Recursive lattice algorithms with finite-duration windows

Abstract: Most recursive adaptive lattice-filter algorithms use (IIR) exponential weighting of the signal elements necessary to calculate the filter parameters. In this paper, recursive algorithms for finite window (FIR) weighting are derived instead and applied to the parameter estimation process. Adaptation and steady state performance of adaptive lattice filters is calculated approximately for arbitrary weightings, allowing a comparison of the performance of different windows. As an example, a lattice filter with HAMMING windowing is compared to one with standard exponential weighting.

Kalman filter preprocessor

Abstract: An optical signal preprocessor for computing the input functions required to utilize an extended Kalman filter algorithm. An incoming stream of time-varying images is integrated to form a reference image, which is then subtracted from each subsequently sampled image. The result is digitized for use with the extended Kalman filter algorithm. The reference image is also fed through a spatial filter and then input to two light valve image subtraction systems to produce difference image approximations of two partial derivatives. These derivative functions are then digitized and utilized as inputs to the extended Kalman filter algorithm.

A model for signal detection based on an adaptive filter

Abstract: A model for the detection of brief stimuli based on a change detection algorithm and a random walk traversed by the residuals generated by an adaptive filter is proposed A linear relationship between mean RT and response proportion measures obtained in a simulation of the model was consistent with data obtained in psychophysical discrimination tasks using human observers In this way the role of the sensory system as a detector of change in ambient stimulation could be incorporated into a signal detection model

Estimation of magnitude-squared coherence function: An adaptive approach

Abstract: This paper concerns an adaptive approach for estimateing the magnitude-squared coherence (MSC) function via Widrow's least-mean-square (LMS) algorithm. Some theoretical aspects are addressed, and simulation results are presented to evaluate the performance of the adaptive approach.

Fast Cholesky algorithms and adaptive feedback filters

Abstract: In this paper, the Fast Cholesky algorithms, both by columns and by rows, are reviewed. It is shown that the algorithms lead naturally to a prediction error feedback filter. In addition, if this filter is used as the whitening filter for a moving average process, it is of fixed order but has time-varying coefficients. Simulation results for the case when the data came from the output of a moving average process driven by white Gaussian noise confirms theoretical results on convergence and stability of the triangular factors. In addition, the bandedness of the process being identified is revealed. Finally, from a VLSI implementation standpoint, it is shown that an array of CORDIC processors may be configured and controlled to factor a covariance matrix. In particular, there exists a method of factorization where the partial correlations associated with the given matrix are stored within the processors.

Survey of IIR adaptive filtering algorithms

Abstract: Several adaptive algorithms for IIR filters have been presented in recent years. These algorithms can be categorized as gradient search or non-gradient search. We present here an example in which a non-quadratic, multimodal error surface is possible. In particular, a case is presented which models a fourth-order FIR plant with a two-pole adaptive IIR filter. The resulting error surface has three distinct minima. Using this example, we compare the NRLMS (gradient search) algorithm with the Genetic (non-gradient search) Algorithm. A combination of the two algorithms is then presented which has improved performance over the individual algorithms.