Showing papers on "Kernel adaptive filter published in 1978"

Adaptive filtering in the frequency domain

Abstract: Adaptive filtering in the frequency domain can be accomplished by Fourier transformation of the input signal and independent weighting of the contents of each frequency bin. The frequency-domain filter performs similarly to a conventional adaptive transversal filter but promises a significant reduction in computation when the number of weights equals or exceeds 16.

An adaptive lattice structure for noise-cancelling applications

Abstract: This paper describes an adaptive filter structure which may be used in multi-channel noise-cancelling applications. The proposed structure differs from those presented previously in that it incorporates a lattice filter framework, rather than tapped-delay-lines. The successive orthogonalization provided by the lattice offers advantages in adaptive convergence rate which cannot be achieved with tapped-delay-lines. In the sections below, we present an explicit description of the general noise-cancelling lattice structure, together with the appropriate adaptive algorithms.

Adaptive line enhancer

Abstract: An input signal X(j) is fed directly to the positive port of a summing function and is simultaneously fed through a parallel channel in which it is delayed, and passed through an adaptive linear transversal filter, the output being then subtracted from the instantaneous input signal X(j). The difference, X(j)-Y(j), between these two signals is the error signal e(j). e(j) is multiplied by a gain μ and fed back to the adaptive filter to readjust the weights of the filter. The weights of the filter are readjusted until e(j) is minimized according to the recursive algorithm: ##EQU1## where the arrow above a term indicates that the term is a signal vector. Thus, when the means square error is minimized, W.sub.(j+1) =W.sub.(j), and the filter is stabilized.

Channel estimating reference signal processor for communication system adaptive antennas

Abstract: A spread spectrum communication adaptive array antenna processor is disclosed which can acquire and remain synchronized to a pseudo-noise (PN) signal transmitted in a multipath signal environment. The plurality of antennas which receive rf signals are individually associated with mixing circuitry which reduces the received signals to IF frequencies. The IF signals are fed into the adaptive filtering portion of the adaptive signal processor which contains circuits to generate an adaptive weight corresponding to each antenna element. An array signal is formed by summing the products of each IF signal with a filter weight corresponding to each antenna element generated within each respective adaptive loop. The adaptive signal processor utilizes the complex conjugate of the error feedback signal which is then multiplied by each respective IF signal. The complex conjugate of this integrated product forms each filter weight. A channel estimator generates an adaptive reference signal which inclues the essential multipath characteristics of the received signal. By using this reference signal in conjunction with the array signal generated by the adaptive filtering portion of the processor, the adaptive array can form an appropriate main beam without prior knowledge of the signal propagation direction.

Adaptive Tracking Filter for Maneuvering Targets

Abstract: A general method of continually restructuring an optimum Bayes-Kalman tracking filter is proposed by conceptualizing a growing tree of filters to maintain optimality on a target exhibiting maneuver variables. This tree concept is then constrained from growth by quantizing the continuously sensed maneuver variables and restricting these to a small value from which an average maneuver is calculated. Kalman filters are calculated and carried in parallel for each quantized variable. This constrained tree of several parallel Kalman filters demands only modest om; puter time, yet provides very good performance. This concept is implemented for a Doppler tracking system and the performance is compared to an extended Kalman filter. Simulation results are presented which show dramatic tracking improvement when using the adaptive tracking filter.

Adaptive lattice methods for linear prediction

Abstract: A general method for adaptive updating of lattice coefficients in the linear predictive analysis of nonstationary signals is presented. The method is given as one of two sequential estimation methods, the other being a block sequential estimation method. The fast convergence of adaptive lattice algorithms is seen to be due to the orthogonalization and decoupling properties of the lattice. These properties are useful in adaptive Wiener filtering. As an application, a new fast start-up equalizer structure is presented. In addition, a one-multiplier form of the lattice is presented, which results in a reduction of computations.

Convergence of an Adaptive Filter Algorithm

Abstract: A state-space representation of a dynamical, stochastic system is given. A corresponding model, parametrized in a particular way, is considered and an algorithm for the estimation of its parameters is analysed. The class of estimation algorithms thus considered contains general output error methods and model reference methods applied to stochastic systems. It also contains adaptive filtering schemes and, e.g. the extended least squares method. It is shown that if a certain transfer function associated with the true system is positive real, then the estimation algorithm converges with probability 1 to a value that gives a correct input-output model.

On an adaptive algorithm for IIR filters

Abstract: The purpose of this communication is to discuss an IIR adaptive filter algorithm developed by Stearns [1], in terms of an example that appeared in a recent article [2]. The example concerns the approximation of a fixed second-order filter by a first-order adaptive filter, when subjected to a white noise input.

An Improved Algorithm for Adaptive Processing

Abstract: The Widrow-Hoff least mean square (LMS) algorithm based on the method of steepest descent is conditionally stable. A modified algorithm is given which is unconditionally stable, capable of better performance when used in adaptive filter processing, and provides a more realistic means for simulating the Applebaum-Howells adaptive loop.

Frequency domain adaptive filter for detection of sonar signals

Abstract: An adaptive filter for sonar signals which operates on the complex spectral components of the received signal, which signal has been transformed into the frequency domain by means such as the Fast Fourier Transform The adaptive filter consists of a plurality of component filters, each of which operates on a single spectral component of the received signals The transfer coefficient of each component filter is described by a complex number and is adaptively adjusted by means of a computational feedback loop The feedback loop compares the product of the transfer coefficient and the complex spectral component of the received signal from a prior frequency transformation cycle, with the present spectral component to obtain an error signal The error signal, in turn, adaptively alters the magnitude and phase of the transfer coefficient A plurality of such component filters operate together to adaptively filter, in the frequency domain, the entire spectrum of the received signal

Adaptive filter network

Abstract: An adaptive filter network comprising a controllable filter having an adjustable cut-off frequency and adapted for varying the pass-band of the network. The adaptive filter network further includes a serial arrangement of an algebraic adder for generating control signals, connected to the controllable filter; a weighting filter for converting the control signal spectrum in response to the load sensitivity variation with frequency; a threshold limiter for setting the noise reduction threshold level of the adaptive filter network; a control signal frequency corrector; and an amplitude detector for shaping control signals applied to the control input of the controllable filter. The network analysis of the input audio signal spectrum and the width of its pass-band is varied depending on the present frequency limit of the input audio signal wanted components.

Bounding filter: A simple solution to lack of exact a priori statistics

Abstract: Weiner and Kalman—Bucy estimation problems assume that models describing the signal and noise stochastic processes are exactly known. When this modeling information, i.e., the signal and noise spectral densities for the Weiner filter and the signal and noise dynamic system and disturbing noise representations for Kalman—Bucy filtering, is inexactly known, then the filter's performance is suboptimal and may even exhibit apparent divergence. In this paper a system is designed whereby the actual estimation error covariance is bounded by the covariance calculated by the estimator. Therefore, the estimator obtains a bound on the actual error covariance which is not available, and also prevents, its apparent divergence. The bounding filter can be of lower order than the original stochastic models; hence, a technique is devised of reducing the order of the filtering system and concurrently obtaining a figure of merit for its performance. For many cases, the design conditions devised for the steady-state Weiner filter apply to transient Kalman—Bucy filter performance.

Convergence properties of an adaptive noise cancelling lattice structure

Abstract: This paper presents the results of a preliminary analysis designed to predict the properties of an adaptive noise-cancelling filter which is implemented using a lattice structure. Previous work in this area has been restricted to adaptive filters implemented using tapped-delay-lines. The comparison given shows that the lattice form has a time constant of convergence which is independent of the eigenvalue spread of the input data. Further, misadjustment values are shown to depend upon both filter length and the normalized adaptive step size.

Simple adaptive IIR filtering

Abstract: Several authors have suggested various methods of implementing an adaptive IIR filter. This paper suggests that hyperstability and associated positivity concepts can be used to determine the regions of assured convergence for adaptive IIR filter algorithms. This hyperstability interpretation is applied to the adaptive recursive LMS filter, for which it is demonstrated that convergence appears assured if the transfer function formed from the denominator (in z-1) of the transfer function effectively being modelled and a unity numerator is strictly positive real. Examples show that this plausibly sufficient condition, though not necessary, loosely approximates the region of applicability, which seriously restricts the utility of this attractively simple adaptive synthesis method. Slight modifications, suggested by the hyperstability approach, can favorably alter the positive-real "convergence" region with subsequent dramatic improvement in applicability and convergence speed.

Time Constants and Learning Curves of LMS Adaptive Filters.

Abstract: : This paper treats the convergence of adaptive LMS filters and, in particular, the adaptive line enhancer (ALE). The learning curves of such a filter are a sum of exponentially decaying modes with time constants given by the eigenvalues of the input correlation matrix and the relative initial magnitudes given by the projections of the filter on the eigenvectors. It is shown that, for large filter lengths, a simple correspondence may be set up between the discrete and continuous cases. Indexed by frequency, the eigenvalues of the correlation matrix correspond to the magnitude of the power spectrum, and the projections onto the eigenvectors to the filter transfer function. A detailed analysis is carried out for single pole spectra and evaluated through a computer simulation. In general, the techniques developed provide a physical context, i.e., the signal spectrum, in which to evaluate convergence. Thus, it is possible, with varying degrees of accuracy depending on knowledge of the input spectrum, to predict the convergence behavior of the system in general. (Author)

An iterative filter for solution of the inverse heat-conduction problem

Abstract: An iterative modification of the nonlinear Kalman filter is proposed for the determination of time-variable heat-transfer coefficients.

An Extended Kalman Filter for Use in a Shared Aperture Medium Range Tracker.

Abstract: : An extended Kalman filter algorithm, using outputs from a forward looking infrared (FLIR) sensor as measurements, is used to track a point source target in an open loop tracking problem The filter estimates the translational position changes of the target in the FLIR field of view due to two effects: actual target motion, and apparent motion caused by atmospheric turbulence Sixteen cases are examined to determine the performance of the filter as a function of signal-to-noise ratio, Gaussian beam, size, the ratio of RMS target motion to RMS atmospheric jetter, target correlation times, and mismatches between the true shape and the shape assumed by the filter The performance of the extended Kalman filter is compared to the performance of an existing correlation tracker under identical initial conditions A one sigma tracking error of 2 and 8 picture elements is obtained with signal-to-noise ratios of 20 and 1 respectively No degradation in performance is observed when the beam size is decreased or when the target correlation time is increased over a limited range, when filter parameters are adjusted to reflect this knowledge Sensitivity analysis shows that the filter is robust to minor changes in target intensity size (Author)

Implementation of a 64-point adaptive filter using an analogue c.c.d. programmable filter

Abstract: This letter describes the construction and operation of an adaptive filter based on the Widrow least-mean-square adaption algorithm using a 64-point analogue programmable c.c.d. transversal filter as the main processing element. Initial test results are presented to confirm the principle of the system and these results may be readily compared with previously published simulation results.

Nonlinear filter for inversion of channel distortion

Abstract: The ill-posed nature of direct deconvolution has prevented its use in applications such as channel equalization or inversion of transducer distortion. In this paper we discuss the use of a recursive nonlinear filter. The design of the proposed filter is accomplished in two stages. First, a constrained least-squares technique is employed to obtain, off-line, a filtered signal from a typical distorted signal. Then this pair of signals is used in a model identification scheme, to arrive at the nonlinear recursive filter. Since the final filter is recursive, and synthesized in one of the two alternative structures, both the memory and computation requirements are low enough to permit efficient on-line implementation.

On the Implementation of a Two-Dimensional FIR Filter Using a Single Multiplier

Abstract: A general scheme for implementing a two-dimensional FIR filter using only one multiplier is outlined. The realization is based on sequentially multiplexing the multiplier inputs and is illustrated with the aid of a block diagram and the sequence of operations for a 3 x 3 filter.

Selecting the length of an adaptive transversal filter

Abstract: Optimum in the mean-square error sense, the Wiener filter is the best linear filter which can be derived given known input statistics. Excellent results have been achieved for the filtering problem with the LMS adaptive filter when these same statistics are unknown. The gradient descent algorithm introduces an excess mean-square error which is proportional to the adaptive filter's length. In an adaptive array processor, the LMS filter can be configured as a noise canceller to partially remove a sidelobe interference source from a given receive beam. This paper derives the optimum length of the adaptive transversal filter such that the residual interference signal energy plus the excess mean-square error contributed by the LMS algorithm is minimized. Both narrowband and wideband interference signals are considered.

Detection performance of the adaptive line enhancer (ALE) with post-detection integration

Abstract: This paper discusses the detection performance of a data adaptive detector based on adaptive linear prediction filtering. The implementation considered utilizes the Widrow-Hoff LMS algorithm to provide continuous data adaptive estimates of the linear prediction filter coefficients. (This implementation is often denoted the Adaptive Line Enhancer (ALE).) Receiver-Operating Characteristic (ROC) curves are derived analytically for two distinct adaptive detector implementations for the case of a sinusoid of known frequency but unknown phase embedded in white Gaussian additive noise. The detection statistics and ROC curves of the ALE are obtained experimentally from extensive Monte Carlo simulations. The effect of post detection integration is evaluated analytically and experimentally. Comparative performance curves for adaptive and non-adaptive detector implementations are presented for this classical detection problem. The dependence on the frequency resolution and time constant of the adaptive filter is also discussed.

A well suited two-dimensional linear recursive filter for image processing

Abstract: In this paper, a fixed order two-dimensional linear recursive filter is obtained by matching the unit sample response of a fixed-order two-dimensional linear recursive operator with the unit sample response of an ideal circularly symmetric low pass filter. Such an operator thereby obtained possesses the desired circularly symmetric low pass filtering characteristic and is also stable. However, a direct application of this filter to the image processing is generally not well-suited. For this reason, a more appropriate filter called the flipped-filter, which utilizes the circularly symmetric filter, is designed. In order to demonstrate the effectiveness of the flipped-filter in image processing, a set of noise contaminated images are processed by this filter and the processed images are displayed.

Adaptive Filtering in the Frequency Domain Using the Complex LMS Algorithm.

Abstract: : Adaptive filtering in the frequency domain can be accomplished by Fourier transformation of the input signal and independent weighting of the contents of each frequency bin. The frequency-domain filter performs similarly to a conventional adaptive transversal filter but promises a significant reduction in computation when the number of weights equals or exceeds 16. (Author)

An adaptive matched filter

Abstract: A recursive estimator providing the best linear mean square estimate of an arbitrary signal is derived in a form which is readily implemented using a charge coupled device (CCD) realization of the sliding chirp-z-transform (CZT). This estimator forms the basis of the adaptive matched filter which is being developed for electro-optical sensor applications. A microprocessor is utilized to calculate the frequency domain filter characteristic based on updated noise spectrum estimates. In this manner, the filter characteristic is changed to maintain matched performance. The frequency domain characteristic is converted to a finite impulse response in the time domain via an inverse CZT. The impulse response and the signal to be filtered are used as inputs to a CCD analog-analog correlator to perform the matched filtering in the time domain.

Adaptive Kalman Type Estimation Applied to Image Processing.

Abstract: : Because of the stochastic and nonstationary nature of image processes, an adaptive estimation algorithm is proposed and evaluated for on-line filtering of an image scanned in a raster pattern. This algorithm combines a least squares parameter identification procedure with a two-dimensional reduced update Kalman filter. Results using an image with a 3 dB signal to noise ratio indicate that this adaptive algorithm is very effective for image restoration. (Author)