Showing papers on "Kernel adaptive filter published in 1990"

Federated square root filter for decentralized parallel processors

Abstract: An efficient, federated Kalman filter is developed for use in distributed multisensor systems. The design accommodates sensor-dedicated local filters, some of which use data from a common reference subsystem. The local filters run in parallel, and provide sensor data compression via prefiltering. The master filter runs at a selectable reduced rate, fusing local filter outputs via efficient square root algorithms. Common local process noise correlations are handled by use of a conservative matrix upper bound. The federated filter yields estimates that are globally optimal or conservatively suboptimal, depending upon the master filter processing rate. This design achieves a major improvement in throughput (speed), is well suited to real-time system implementation, and enhances fault detection, isolation, and recovery capability. >

Multidelay block frequency domain adaptive filter

Abstract: A flexible multidelay block frequency domain (MDF) adaptive filter is presented. The distinctive feature of the MDF adaptive filter is to allow one to choose the size of an FFT tailored to the efficient use of the hardware, rather than the requirements of a specific application. The MDF adaptive filter also requires less memory and thus reduces the hardware requirements and cost. In performance, the MDF adaptive filter introduces smaller block delay and is faster, making it ideal for a time-varying application such as modeling an acoustic path in a teleconference room. This is achieved by using a smaller block size, updating the weight vectors more often, and reducing the total execution time of the adaptive process. The MDF adaptive filter compares favorably to other frequency-domain adaptive filters when its adaptation speed and misadjustment are tested in computer simulations. >

Nonlinear techniques for interference suppression in spread-spectrum systems

Abstract: The binary nature of direct-sequence signals is exploited to obtain nonlinear filters that outperform the linear filters hitherto used for this purpose. The case of a Gaussian interferer with known autoregressive parameters is considered. Using simulations, it is shown that an approximate conditional mean (ACM) filter of the Masreliez type performs significantly better than the optimum linear (Kalman-Bucy) filter. For the case of interferers with unknown parameters, the nature of the nonlinearity in the ACM filter is used to obtain an adaptive filtering algorithm that is identical to the linear transversal filter except that the previous prediction errors are transformed nonlinearly before being incorporated into the linear prediction. Two versions of this filter are considered: one in which the filter coefficients are updated using the Widrow LMS algorithm, and another in which the coefficients are updated using an approximate gradient algorithm. Simulations indicate that the nonlinear filter with LMS updates performs substantially better than the linear filter for both narrowband Gaussian and single-tone interferers, whereas the gradient algorithm gives slightly better performance for Gaussian interferers but is rather ineffective in suppressing a sinusoidal interferer. >

Temporal backpropagation for FIR neural networks

Abstract: The traditional feedforward neural network is a static structure which simply maps input to output. To better reflect the dynamics in a biological system, a network structure which models each synapse by a finite-impulse response (FIR) linear filter is proposed. An efficient-gradient descent algorithm which is shown to be a temporal generalization of the familiar backpropagation algorithm is derived. By modeling each synapse as a linear filter, the neural network as a whole may be thought of as an adaptive system with its own internal dynamics. Equivalently, one may think of the network as a complex nonlinear filter. Applications should thus include areas of pattern recognition where there is an inherent temporal quality to the data, such as in speech recognition. The networks should also find a natural use in areas of nonlinear control, and other adaptive signal processing and filtering applications such as noise cancellation or equalization

Adaptive stack filtering under the mean absolute error criterion

Abstract: An adaptive filter algorithm is developed for the class of stack filters, which is a class of nonlinear filters obeying a weak superposition property. The adaptation algorithm can be interpreted as a learning algorithm for a group of decision-making units, the decisions of which are subject to a set of constraints called the stacking constraints. Under a rather weak statistical assumption on the training inputs, the decision strategy adopted by the group, which evolves according to the proposed learning algorithm, is shown to converge to an optimal strategy in the sense that it corresponds to an optimal stack filter under the mean absolute error-criterion, this adaptive algorithm requires only increment, decrement, and comparison operations and only local interconnections between the learning units. Implementation of the algorithm in hardware is therefore very feasible. An example is provided to show how the adaptive stack filtering algorithm can be used in an application in image processing. >

Performance analysis of LMS adaptive prediction filters

Abstract: The conditions required to implement real-time adaptive prediction filters that provide nearly optimal performance in realistic input conditions are delineated. The effects of signal bandwidth, input signal-to-noise ratio (SNR), noise correlation, and noise nonstationarity are explicitly considered. Analytical modeling, Monte Carlo simulations and experimental results obtained using a hardware implementation are utilized to provide performance bounds for specified input conditions. It is shown that there is a nonlinear degradation in the signal processing gain as a function of the input SNR that results from the statistical properties of the adaptive filter weights. The stochastic properties of the filter weights ensure that the performance of the adaptive filter is bounded by that of the optimal matched filter for known stationary input conditions. >

Tracking targets using adaptive Kalman filtering

Abstract: A simple algorithm for estimating the unknown process noise variance of an otherwise known linear plant, using a Kalman filter is suggested. The process noise variance estimator is essentially dead beat, using the difference between the expected prediction error variance, computed in the Kalman filter, and the measured prediction error variance. The estimate is used to adapt the Kalman filter. The use of the adaptive filter is demonstrated in a simulated example in which a wildly maneuvering target is tracked. >

Adaptive nonlinear digital filter with canonical piecewise-linear structure

Abstract: A novel adaptive nonlinear filter with the least-mean-square (LMS) error criterion is presented. It is based on the so-called canonical piecewise-linear structure. As an alternative to approaches based on the Wiener-Volterra series which have so far been widely employed for adaptive nonlinear filtering, the proposed approach can exhibit adaptive performance, especially in strongly nonlinear cases, while saving computation and implementation cost. The performance of this adaptive nonlinear filter is illustrated by computer simulation results. >

Generalization of the linear matched filter concept to nonlinear matched filters

Abstract: A nonlinear matched filter based image correlator is investigated. The linear matched filter is expressed as a bandpass function containing the amplitude and phase of the Fourier transform of the reference signal. The bandpass filter function is then applied to a kth law nonlinear device to produce the nonlinear matched filter function. Analytical expressions for the nonlinear matched filter are provided. The effects of the nonlinear transfer characteristics on the correlation signals at the output plane are investigated. The correlation signals are determined in terms of the nonlinear characteristics used to transform the filter. We show that the nonlinear filter results in a sum of infinite harmonic terms. Each harmonic term is envelope modulated due to the nonlinear characteristics of the device, and phase modulated by m times the phase modulation of the linear filter function. The correct phase information of the filter is recovered for the first-order harmonic of the series. The envelope of each harmonic term is proportional to the kth power of the Fourier transform magnitude of the reference signal. We show that various types of filter such as the continuous phase-only filters can be produced simply by varying the severity of the nonlinearity. Nonlinear filters provide higher correlation peak intensity and a better defined correlation spot.

Stochastic gradient adaptive filters with gradient adaptive step sizes

Abstract: Two adaptive step-size gradient adaptive filters are presented. The step sizes are changed using a gradient descent algorithm designed to minimize the squared estimation error. The first algorithm uses the same step-size sequence for all the filter coefficients, whereas the second algorithm uses different step-size sequences for different adaptive filter coefficients. An analytical performance analysis of the first algorithm is also presented. Analyses and experiments indicate that (1) the algorithms have fast convergence rates and small midadjustment errors and (2) in nonstationary environments, the algorithms tend to adjust the step sizes so as to give close to the best possible performance. Several simulation examples demonstrating the good properties of the adaptive filters are also presented. >

A parallel implementation of 3-D CT image reconstruction on hypercube multiprocessor

Abstract: A parallel is given of how image reconstruction in computerized tomography (CT) can be parallelized on a message-passing multiprocessor. In particular, the results obtained from parallel implementation of 3-D CT image reconstruction for parallel beam geometries on the Intel hypercube, iPSC/2, are presented. A two-stage pipelining approach is used for filtering (convolution) and backprojection. The conventional sequential convolution algorithm is modified such that the symmetry of the filter kernel is fully utilized for parallelization. In the backprojection stage, the 3-D incremental algorithm, a recently developed backprojection scheme which is shown to be faster than the conventional algorithm, is parallelized. The speed-up, defined as sequential processing time/parallel processing time, ranging from 5 to 27, and the efficiency, defined as speed-up/the number of processing elements, ranging from 60% to 92%, have been achieved, depending on the size of the image and the number of processing elements used. >

Adaptive recursive state-space filters using a gradient-based algorithm

Abstract: To aid in the search for better adaptive filter structures, a method is presented to obtain the gradients required to adapt general state-space filters. Unfortunately, the number of computations for this general case is quite high. To reduce the number of computations, two new state-space adaptive filters are introduced. One application where these new structures are shown to be useful is in oversampled filtering where an estimate of the final pole locations is known and the adaptive filter is required only to fine-tune the transfer function. It is shown that for this type of application, the new adaptive structures can have much improved adaptation rates and roundoff noise performance as compared to the corresponding direct-form realizations. >

Adaptive digital filter including low-pass filter

Abstract: ADAPTIVE DIGITAL FILTER INCLUDING LOW-PASS FILTER ABSTRACT OF THE DISCLOSURE An adaptive digital filter for estimating a response characteristic of a signal path by monitoring a sampled output signal of the signal path, estimating a predetermined number of filter coefficients which represent the response characteristic of the signal path, and generating an estimated output signal of the signal path using a plurality of successive sampled input signals of the signal path and the estimated filter coefficients, where the estimation is carried out so that a difference between the output signal and the estimated output signal is reduced. Each of the filter coefficients is extracted by a low-pass filter where the low-pass filter coefficient in the low-pass filter can be set to a constant. Normalization can be carried out in either the input side or the output side of the low-pass filter. Otherwise, the low-pass filter coefficient may be set to 1-K?Xj(m)2/r, where r is set equal to a norm of the sampled input signals in the beginning, and is then set to an integrated power of the sampled input signals.

A new approach to the analysis of nystagmus: an application for order-statistic filters.

Abstract: A computer program has been designed for the analysis of nystagmus This program employs a class of nonlinear digital filters called order-statistic (OS) filters Two OS filters and one linear filter are used First, the eye-movement signal is smoothed using a predictive finite-impulse response (FIR), median hybrid filter Then the smoothed signal is processed by a linear band-limited differentiating filter to calculate eye velocity And finally, the slow-phase velocity (SPV) envelope is extracted from the eye-velocity signal using an adaptive asymmetrically trimmed-mean filter This approach yields an evenly sampled SPV estimate without resorting to the various interpolation or extrapolation schemes generally used The adaptive filter estimates SPV based on the local statistical properties of the eye-velocity signal The adaptive strategy works under the assumption that, on the average, the eyes spend more time in slow-phase than in fast-phase No assumptions are made about the direction of the nystagmus or the nature of the stimulus used to elicit the nystagmus This method eliminates all the usual threshold tests and decision logic common to other nystagmus analysis programs The robust performance of OS filters and the use of adaptive filter structures totally eliminates the need to custom "tune" the program parameters for atypical data sets Language: en

An adaptive unit norm filter with applications to signal analysis and Karhunen-Loeve transformations

Abstract: An adaptive unit norm filter based on planar rotators, which offers a simpler implementation and better sensitivity properties than the transversal filter version, is proposed. By connecting the filter structure with the Schur eigenvalue deflation procedure, a triangular array is developed that adaptively estimates all the eigenvalues and eigenvectors of the input signal autocorrelation matrix; the converged triangular array thus realizes the Karhunen-Loeve transformation of the input signal. The signal operations are all orthogonal, resulting in robust numerical behavior. >

Nonrecursive and recursive stack filters and their filtering behavior

Abstract: It is shown that stack filters that are based on symmetric threshold functions and preserve median-filter roots make all inputs converge to roots or to cycles of period two. This is an important result, since these filters have useful roots (the median-filter roots), and they are time symmetric, i.e. time reversal of an input sequence of such a filter is equivalent to time reversal of the output sequence of the filter. In order to construct stack filters without cycles, the recursive stack filter, which is an extension of the recursive median filter, is introduced. It is shown that a recursive stack filter has the same roots as the corresponding nonrecursive stack filter; also, given a nonrecursive filter from the class mentioned above, the corresponding recursive filter will make every input signal of finite converge to a root in a finite number of passes. >

Modified matched filter for cloud clutter suppression

Abstract: The least-mean-square (LMS) filter has been developed as an alternative to the classical matched filter (MF) to address the clutter-spectrum issue. However, the output of the MF and the LMS processes is dependent on the scene energy and marginally dependent on the filter signal shape. An approach referred to as the modified matched filter (MMF) is presented. The MMF is a product of the LMS filter and a nonlinear operator known as the inverse Euclidean distance. The nonlinear operator modifies the LMS filter to improve its sensitivity to signal shape. A comparison indicates the relative merit of including shape detection in the LMS clutter-suppression process. Infrared cloud scenes from the background measurements and analysis program (BMAP) were used to demonstrate the relative clutter-suppression performance for both the LMS and the MMF processes. A performance metric is developed to measure cloud clutter suppression quantitatively. >

A new 2-D fast RLS algorithm

Abstract: A two-dimensional fast recursive least-squares algorithm is presented using a geometrical formulation based on the mathematical concepts of vector space, orthorgonal projection, and subspace decomposition. By appropriately ordering the 2-D data, the algorithm provides an exact least-squares solution to the deterministic normal equations. The method is further extended to the general FIR (finite impulse response) Wiener filter and the ARMA (autoregressive moving-average) modeling. The size and shape of the support region for both the MA and AR coefficients of the filter can be chosen arbitrarily. >

An improved median filter

Abstract: A modified median filtering technique offering improved smoothing performance while maintaining the edge-preserving ability of the conventional median filter is presented. It is shown how a mean filter outperforms a median filter in noise reduction except on or near the image boundaries. Along with the edge-preserving ability of the median filter, this observation forms the basis of the three-stage filtering algorithm which is described. >

Experimental verification of modified synthetic discriminant function filters for rotation invariance

Abstract: A modified binary synthetic discriminant function filter designed to recognize objects over a range of rotated views has been verified on a laboratory optical correlator. A binary synthetic discriminant function filter has been previously described that will produce a specified correlation response for a set of training images. [See D. A. Jared and D. J. Ennis, "Inclusion of Filter Modulation in Synthetic-Discriminant-Function Construction," Appl. Opt. 28, 232-239 (1989).] In the filter design, the modulation characteristics of the device onto which the filter is mapped are included in the synthesis equations. The system of nonlinear equations is then solved using an iteration procedure based on the Newton-Raphson algorithm. The development of the filter-SDF (fSDF) method was driven by the practical concern to make currently available spatial light modulators with limited modulation capabilities functional for distortion invariant pattern recognition. This technique is used to synthesize filters for a binary magnetooptic spatial light modulator (MOSLM), the Sight-MOD produced by Semetex. Two MOSLMs are used in the laboratory correlator, one in the filter plane and one in the input plane. We demonstrate that a single filter produces equal correlation peaks for a sample object (a Shuttle Orbiter in these tests) over in-plane and out-of-plane rotation ranges up to 75 degrees . The correlator is able to track dynamically the shuttle as it moves along a curved path across the input field. Views of the object in between those in the training set are also recognized when training images are sufficiently close in angle (~5 degrees apart).

The fast Householder filters-RLS adaptive filter

Abstract: A fast Householder filter (FHF) QR-RLS algorithm is presented that requires significantly less (by a factor of at least three) computation than previous fast QR-RLS adaptive algorithms. The essential feature of the new method is that it replaces the Givens rotations used in these fast QR algorithms by Householder transformations. A set of filters that characterize the QR factorization of a data matrix is derived, and time updates on this set are determined using a generic Householder updating identity. The FHF requires 7N computations per iteration for the standard prewindowed case, which is the same as the FTF (fast transversal filter) and FAEST fast (non-QR) RLS. >

An Adaptive Feedback Equalization Algorithm For The CID Digital Hearing Aid

Abstract: A method is described for adaptively equalizing the ubiquitous feedback path of a hearing aid in order to stabilize the system. The algorithm utilizes an LMS adaptive filter and is implemented in digital form. An additional 10 to 15 dB of stable gain margin has been demonstrated.

A robust approach to reliable real-time Kalman filtering

Abstract: A complete approach to reliable, robust, and adaptive Kalman filtering is presented. It has applications in all types of navigation systems. The starting point is a measurement editing and filter divergence protection scheme based on measurement residuals and their expected statistics. Rather than simply increasing the white measurement noise variance, certain error sources which are known to be present can be included in the filter model via a Schmidt-Kalman filter, which allows certain states to be considered without being estimated. This type of filter configuration has many advantages over the usual Kalman filter such as larger region of convergence, smoother transitions between over-determined solutions, and more conservative modeling when certain states are frozen, such as during clock or altitude hold. Details are given on how this type of filter can be used with a factorized covariance. The same statistics used for filter integrity are also used to assess how well the filter is tuned to a particular dynamic environment. A reasonable adaptive process noise matrix scheme based on these statistics is presented. Specific examples of the application of these techniques in Global Positioning System receiver are given. >

A function space model for digital image sampling and its application in image reconstruction

Abstract: A general mathematical model for digital signal processing, which is based onLp function spaces, is introduced. This model is used to derive a new class of reconstruction filters for the reconstruction ofN-dimensional images which are not necessarily band-limited. A basic proposition in this work is that the best reconstruction algorithm will depend on the pre-sample filter (or point spread) function. The reconstruction filters described here are optimal in the sense that they result in a reconstructed image which is as close as possible, with respect to a given measure of fidelity, to the unsampled image. The filter is similar in form to the optimal filter derived by Peterson and Middleton (Inform. and Control5, 1962 , 279–323) in their comprehensive paper on multidimensional sampling. However the reconstruction filter of Peterson and Middleton is optimal for random fields, whereas the filter described here is optimal for individual images. The optimal reconstruction filter has certain practical advantages over empirically derived reconstruction methods such as cubic interpolation. One of these advantages is that the method produces positive-valued images without loss of image resolution. The performance of the optimal reconstruction filter can be understood without reference to aliasing and truncation errors and is quantified in terms of a simple error metric.

A nonlinear digital filter using multi-layered neural networks

Abstract: A nonlinear digital filter utilizing multilayered neural networks is proposed. This filter significantly reduces random noises superimposed on signals which contain sharp edges, while preserving their sharpness. In addition, degradation of the capability for noise reduction due to the increase of the noise power is greatly suppressed compared to previously proposed nonlinear filters. The high performance of this neural filter is demonstrated in computer simulations and actual image processing. When the noise power is small, the performance of the neural filter is almost the same as that of the epsilon -filter, which corresponds to a simplified neural filter; however, when the noise power is large, the effectiveness of the neural filter is clearly demonstrated. >

Feedback cancellation in hearing aids

Abstract: Feedback cancellation in hearing aids is discussed. It involves estimating the feedback signal and subtracting it from the microphone input signal. The system described updates the estimated feedback path whenever changes are detected in the feedback behavior. The normal hearing-aid processing is then interrupted, a probe signal is injected into the system, and a set of filter coefficients is adjusted to give an estimate and the feedback path. Both LMS adaptive filter and Wiener filter approaches were simulated, with the Wiener filter giving better performance at poor signal-to-noise ratios. The simulation results indicate that feedback suppression in excess of 10 dB is possible. >

Gram-schmidt space-time adaptive filter using transverse orthonormal ladder filters

Abstract: A space-time adaptive filter system is provided for eliminating unwanted signals from a radar or communication system. The filter system receives a main channel and several auxiliary channels wherein the target signal is not correlated between the various signal channels. Correlated noise components are eliminated by decorrelating the signals. The adaptive filter includes a Gram-Schmidt processor for sequentially decorrelating the auxiliary signals from the main signal. Each decorrelation element of the Gram-Schmidt processor comprises a transverse orthonormal ladder filter.

An adaptive tuning circuit for integrated continuous-time filters

Abstract: A strategy for tuning continuous-time filters is presented. Instead of relying on matched integrated elements, this technique uses an adaptive algorithm to tune both the poles and zeros of the filter. Circuit details and experimental results are given. The tunable filter was fabricated with a 3- mu m CMOS process. The tuning circuit was implemented with an on-chip gradient filter and off-chip discrete components. Simulation and experimental results show the validity of the proposed tuning approach. >

A method for obtaining an approximate Wiener filter.

Abstract: The Wiener restoration filter yields the minimum mean‐square error between the restored image and the true object function. However, it has found limited use because, in its usual formulation, it requires information about the object power spectrum which is generally unknown. In this paper, it is shown that the Wiener filter can be derived from the noise‐free image power spectrum, and a method is presented for estimating this from the observed data. From this estimate an approximate Wiener filter was calculated. The method was tested on three sets of simulated data which included a constant background, rectangular defects, and Gaussian defects at varying contrast and noise levels. The performance of the approximate Wiener filter was compared both to the true Wiener filter and to the standard 1‐2‐1 three‐point smooth. The results confirmed that the approximate Wiener filter adapted to the information content of the observed data and closely matched the performance of the true Wiener filter. The approximate Wiener filter outperformed the three‐point smooth in all cases, especially at low contrast and high noise levels. The approximate Wiener filter can be calculated without operator intervention and requires little additional computation time over conventional Wiener filter techniques.