Showing papers on "Adaptive filter published in 1986"

Adaptive Filter Theory

Abstract: Background and Overview. 1. Stochastic Processes and Models. 2. Wiener Filters. 3. Linear Prediction. 4. Method of Steepest Descent. 5. Least-Mean-Square Adaptive Filters. 6. Normalized Least-Mean-Square Adaptive Filters. 7. Transform-Domain and Sub-Band Adaptive Filters. 8. Method of Least Squares. 9. Recursive Least-Square Adaptive Filters. 10. Kalman Filters as the Unifying Bases for RLS Filters. 11. Square-Root Adaptive Filters. 12. Order-Recursive Adaptive Filters. 13. Finite-Precision Effects. 14. Tracking of Time-Varying Systems. 15. Adaptive Filters Using Infinite-Duration Impulse Response Structures. 16. Blind Deconvolution. 17. Back-Propagation Learning. Epilogue. Appendix A. Complex Variables. Appendix B. Differentiation with Respect to a Vector. Appendix C. Method of Lagrange Multipliers. Appendix D. Estimation Theory. Appendix E. Eigenanalysis. Appendix F. Rotations and Reflections. Appendix G. Complex Wishart Distribution. Glossary. Abbreviations. Principal Symbols. Bibliography. Index.

Tracking properties and steady-state performance of RLS adaptive filter algorithms

Abstract: Adaptive signal processing algorithms derived from LS (least squares) cost functions are known to converge extremely fast and have excellent capabilities to "track" an unknown parameter vector. This paper treats analytically and experimentally the steady-state operation of RLS (recursive least squares) adaptive filters with exponential windows for stationary and nonstationary inputs. A new formula for the "estimation-noise" has been derived involving second- and fourth-order statistics of the filter input as well as the exponential windowing factor and filter length. Furthermore, it is shown that the adaptation process associated with "lag effects" depends solely on the exponential weighting parameter λ. In addition, the calculation of the excess mean square error due to the lag for an assumed Markov channel provides the necessary information about tradeoffs between speed of adaptation and steady-state error. It is also the basis for comparison to the simple LMS algorithm, in a simple case of channel identification, it is shown that the LMS and RLS adaptive filters have the same tracking behavior. Finally, in the last part, we present new RLS restart procedures applied to transversal structures for mitigating the disastrous results of the third source of noise, namely, finite precision arithmetic.

A variable step (VS) adaptive filter algorithm

Abstract: In recent work, a new version of an LMS algorithm has been developed which implements a variable feedback constant μ for each weight of an adaptive transversal filter. This technique has been called the VS (variable step) algorithm and is an extension of earlier ideas in stochastic approximation for varying the step size in the method of steepest descents. The method may be implemented in hardware with only modest increases in complexity ( \approx 15 percent) over the LMS Widrow-Hoff algorithm. It is shown that an upper bound for the convergence time is the classical mean-square-error time constant, and examples are given to demonstrate that for broad signal classes (both narrow-band and broad-band) the convergence time is reduced by a factor of up to 50 in noise canceller applications for the proper selection of variable step parameters. Finally, the VS algorithm is applied to an IIR filter and simulations are presented for applications of the VS FIR and IIR adaptive filters.

Robust model reference adaptive control

Abstract: We propose a new model reference adaptive control algorithm and show that it provides the robust stability of the resulting closed-loop adaptive control system with respect to unmodeled plant uncertainties. The robustness is achieved by using a relative error signal in combination with a dead zone and a projection in the adaptive law. The extra a priori information needed to design the adaptive law, are bounds on the plant parameters and an exponential bound on the impulse response of the inverse plant transfer function.

Continuous-time MOSFET-C filters in VLSI

Abstract: The desirable features of fully integrated, VLSI-compatible continuous-time filters are discussed. A recently proposed integrated continuous-time filter technique is reviewed, in which MOS transistors are used in place of resistors along with the nonlinearity cancellation and on-chip automatic tuning. The filters obtained using this technique are compared to switched-capacitor filters, digital filters, and continuous-time filters using different techniques. Representative experimental results are given, demonstrating the high performance that can be achieved.

Use of random noise for on‐line transducer modeling in an adaptive active attenuation system

Abstract: Active sound attenuation systems may be described using a system identification framework in which an adaptive filter is used to model the performance of an unknown acoustical plant. An error signal may be obtained from a location following an acoustical summing junction where the undesired noise is combined with the output of a secondary sound source. In order for the model output to properly converge to a value that will minimize the error signal, it is frequently necessary to determine the transfer function of the secondary sound source and the path to the error signal measurement. Since these transfer functions are continuously changing in a real system, it is desirable to perform continuous on‐line modeling of the output transducer and error path. In this paper, the use of an auxiliary random noise generator for this modeling is described. Based on a Galois sequence, this technique is easy to implement, provides continuous on‐line modeling, and has minimal effect on the final value of the error signal.

An adaptive generalized sidelobe canceller with derivative constraints

Abstract: An adaptive broad-band beamforming structure is presented which employs a gradient-based weight adjustment algorithm to minimize output variance subject to a set of J linear constraints on broadband directional derivatives in the desired look direction. A generalized sidelobe-cancelling structure is employed in which a nonadaptive (conventional) beamformer operates in parallel with an adaptive beamformer. The conventional portion has a broad-band beampattern which adheres to the specified constraints while the adaptive path is a cascade of a fixed signal blocking matrix and a set of tapped-delay line filters. Blocking is employed to ensure that all incident waveforms which meet the specified constraints do not reach the tapped-delay lines. As a result, an unconstrained least mean square (LMS) power minimization algorithm is employed to adapt the delay line weights. It is shown that with the addition of the directional derivative constraints, the beamformer quiescent bcampattern becomes a function of the location of the phase center used to specify the constraints. A design criterion for choosing this location is suggested and simulation experiments which illustrate the performance of this new adaptive beamformer are presented.

Adaptive comb filtering for harmonic signal enhancement

Abstract: A new algorithm is presented for adaptive comb filtering and parametric spectral estimation of harmonic signals with additive white noise. The algorithm is composed of two cascaded parts. The first estimates the fundamental frequency and enhances the harmonic component in the input, and the second estimates the harmonic amplitudes and phases. Performance analysis provides new results for the asymptotic Cramer-Rao bound (CRB) on the parameters of harmonic signals with additive white noise. Results of simulations indicate that the variances of the estimates are of the same order of magnitude as the CRB for sufficiently large data sets, and illustrate the performance in enhancing noisy artificial periodic signals.

Biomedical Signal Processing

Abstract: First published in 1986: The presentation of the material in the book follows the flow of events of the general signal processing system. After the signal has been acquired, some manipulations are applied in order to enhance the relevant information present in the signal. Simple, Optimal, and adaptive filtering are examples of such manipulations. The detection of wavelets is of importance in biomedical signals; they can be detected from the enhanced signal by several methods. The signal very often contains redundancies. When effective storing, transmission, or automatic classification are required, these redundancies have to be extracted.

Analysis of the normalized LMS algorithm with Gaussian inputs

Abstract: The LMS adaptive filter algorithm requires a priori knowledge of the input power level to select the algorithm gain parameter μ for stability and convergence. Since the input power level is usually one of the statistical unknowns, it is normally estimated from the data prior to beginning the adaptation process. It is then assumed that the estimate is perfect in any subsequent analysis of the LMS algorithm behavior. In this paper, the effects of the power level estimate are incorporated in a data dependent μ that appears explicitly within the algorithm. The transient mean and second-moment behavior of the modified LMS (NLMS) algorithm are evaluated, taking into account the explicit statistical dependence of μ upon the input data. The mean behavior of the algorithm is shown to converge to the Wiener weight. A constant coefficient matrix difference equation is derived for the weight fluctuations about the Wiener weight. The equation is solved for a white data covariance matrix and for the adaptive line enhancer with a single-frequency input in steady state for small μ. Expressions for the misadjustment error are also presented. It is shown for the white data covariance matrix case that the averaging of about ten data samples causes negligible degradation as compared to the LMS algorithm. In the ALE application, the steady-state weight fluctuations are shown to be mode dependent, being largest at the frequency of the input.

Performance of transform-domain LMS adaptive digital filters

Abstract: In this paper we analyze the performance, particularly the convergence behavior, of the transform-domain least mean-square (LMS) adaptive digital filter (ADF) using the discrete Fourier transform and discrete orthogonal transforms such as discrete cosine and sine transforms. We first obtain the optimum Wiener solution and the minimum mean-squared error (MSE) in the transform domain. It is shown that the two minimum MSE's in the time and transform domains are identical independently of the transforms used. We then study the convergence conditions and the steady-state excess MSE's of the transform-domain LMS (TRLMS) algorithms both for the cases of having a constant and a time-varying convergence factors. When a constant convergence factor is used, the convergence behaviors of the LMS and TRLMS ADF's appear to be almost identical, provided that each has an appropriate value of the convergence factor depending on the transform used. Also, based on the concept of a self-orthogonalizing algorithm in the transform domain, it is shown that the convergence speed of the TRLMS ADF can be improved significantly for the same excess MSE as that of the LMS ADF. In addition, we compare the computational complexities of the LMS and TRLMS ADF'S. Finally, we investigate by computer simulation the effects of system parameter values and different transforms on the convergence behavior of the TRLMS ADF.

Using spectral estimation techniques in adaptive processing antenna systems

Abstract: Improved spectral estimation techniques hold promise for becoming a valuable asset in adaptive processing array antenna systems. Their value lies in the considerable amount of additional useful information which they can provide about the interference environment, utilizing a relatively small number of degrees of freedom (DOF). The "superresolution" capabilities, estimation of coherence, and relative power level determination serve to complement and refine the data from faster conventional estimation techniques. Two conceptual application area examples for using such techniques are discussed; partially adaptive low-sidelobe arrays, and fully adaptive tracking arrays. For the partially adaptive area the information is utilized for efficient assignment of a limited number of DOF in a beamspace constrained adaptive system in order to obtain a stable main beam, retention of low sidelobes, considerably faster response, and reduction in overall cost. These benefits are demonstrated via simulation examples computed for a 16-element linear array. For the fully adaptive tracking array area the information is utilized in an all-digital processing system concept to permit stable hulling of coherent interference sources in the main beam region, efficient assignment/control of the available DOF, and greater flexibility in time-domain adaptive filtering strategy.

A recursive modified Gram-Schmidt algorithm for least- squares estimation

Abstract: This paper presents a recursive form of the modified Gram-Schmidt algorithm (RMGS). This new recursive least-squares (RLS) estimation algorithm has a computational complexity similar to the conventional RLS algorithm, but is more robust to roundoff errors and has a highly modular structure, suitable for VLSI implementation. Its properties and features are discussed and compared to other LS estimation algorithms.

A novel algorithm and architecture for adaptive digital beamforming

Abstract: A novel algorithm and architecture are described which have specific application to high performance, digital, adaptive beamforming. It is shown how a simple, linearly constrained adaptive combiner forms the basis for a wide range of adaptive antenna subsystems. The function of such an adaptive combiner is formulated as a recursive least squares minimization operation and the corresponding weight vector is obtained by means of the Q-R decomposition algorithm using Givens rotations. An efficient pipelined architecture to implement this algorithm is also described. It takes the form of a triangular systolic/wavefront array and has many desirable features for very large scale integration (VLSI) system design.

A new adaptive IIR filter

Abstract: A family of stochastic approximation variants of the Steiglitz-McBride identification scheme [1]-[3] is developed for adaptive IIR filtering. Parameter convergence is shown by computer simulation. An interesting phenomenon, global convergence regardless of local minima, is observed.

Adaptive filters with individual adaptation of parameters

Abstract: Conventional gradient-type adaptive filters use the fixed convergence factor \mu which is normally chosen to be the same for all the filter parameters. In this paper, we propose to use individual convergence factors which are optimally tailored to adapt individual filter parameters. Furthermore, we propose to adjust the individual convergence factors in real time so that their values are kept optimum for a new set of input variables. We call this approach "individual" adaptation as opposed to the conventional fixed "group" adaptation using the same fixed \mu for all the filter parameters. Computer simulation results show that the individual adaptation approach yields much better filters than the conventional fixed group adaptation approach. Optimization of individual time-varying convergence factors leads to a constraint which may be satisfied by several different algorithms. We propose and investigate here two algorithms satisfying the above constraint: individual adaptation (IA) and homogeneous adaptation (HA). The HA algorithm turns out to have the general form as some well known gradient algorithms that normalize the step size which were previously obtained either intuitively or using involved derivations. Both IA and HA are shown to provide much better performance than the conventional "group" adaptation. However, for several simulations, IA provides better performance than HA, at the expense of increased computation.

Adaptive filters suitable for real-time spectral analysis

Abstract: Some new cascade structures for adaptive filters are presented. They are especially suitable for real-time applications. Since the new structures are intended to be realized using single chip DSP IC's or single chip custom VLSI circuits the requirements for memory and divisions are minimized. The new structures are based on state-variable biquads that in addition to having good SNR's and low sensitivities (for fixed-point implementations) can also have their resonant frequencies and Q -factors independently tuned. The special cass of using the adaptive filters for tracking sinusoids corrupted by noise and for formant based speech compression are described in detail.

Synthesis and analysis of state-space active filters using intermediate transfer functions

Abstract: This paper is concerned with the realization of a given arbitrary filter transfer function as a network of resistively interconnected integrators. These state-space realizations are synthesized using a new technique called intermediate function (IF) synthesis. The technique is based on the selection of a set of functions to serve as either the transfer functions from the filter input to the integrator outputs or the transfer functions from the integrator inputs to the filter output. Relationships between the filter sensitivity and dynamic range and the intermediate functions are derived. A number of results are also given to aid in the selection of a set of IF's that yields structures with optimum performance.

Parameter drift in LMS adaptive filters

Abstract: We examine general conditions under which the LMS adaptive filter generates unbounded parameter estimates when driven by bounded sequences. This unexpected parameter divergence, or drift, is related to the inadequacy of excitation in the input sequence and is characterized by slow (i.e., nonexponential) escape of the parameter estimate vector to infinity in spite of all other signals (inputs, outputs, prediction errors) remaining bounded or even decaying to zero. The analysis proceeds by showing that, in a general adaptive filtering setting, the sequence of regressors (information vectors) provides a natural decomposition of the parameter estimate space into subspaces, each corresponding to a characteristic class of filter excitation. This subspace decomposition is applied to the LMS adaptive filter, yielding direct links between filter behavior and modes of excitation. In particular, stability and instability of the parameter estimates in the presence of bounded disturbances and prediction errors is obtained for various classes of excitation. This behavior is examined in detail for the first-and second-order cases, and is sufficient to characterize the behavior of higher order adaptive filters. The instability (drift) results are due to modes of "decaying" excitation, and bounds on the rates of drift are derived. This drift mechanism is inherent in the algorithm and is not due to numerical implementation problems or violation of small step-size conditions. Examples are presented where drift may occur in restricted complexity filtering and in the related stochastic gradient algorithm. An analysis of leakage in terms of input excitation reveals a tradeoff in performance between parameter and prediction errors. A modified form of leakage, using the subspace decomposition, is suggested to remove this difficulty.

An adaptive filter for estimating spatially-varying parameters: application to modeling police hours spent in response to calls for service

Abstract: The Spatial Adaptive Filter (SAF), introduced in this paper, uses generalized damped negative feedback to estimate spatially-varying parameters for multivariate models. Previous adaptive filters have been designed to estimate time-varying parameters and process data recursively in time sequence. SAF processes all data simultaneously in an iterative algorithm. Monte Carlo studies show that SAF is successful in automatically identifying and estimating step-jump and continuous spatial variation in the parameters of causal variables. A case study on census-tract data from Columbus, Ohio, relating police-vehicle hours spent in responding to calls to socio-economic indicators, has systematic spatial variation in estimated parameters. Independent variables that are significant in inner-city areas of Columbus become progressively less significant in moving to outlying areas.

Dual Sign Algorithm for Adaptive Filtering

Abstract: A new algorithm, which is a variant of the sign algorithm, is proposed for the adaptive adjustment of an FIR digital filter with an aim of improving the original convergence characteristics, yet retaining the advantage of hardware simplicity. Based on a recently proposed theory for the sign algorithm, a practical design method is derived for the new algorithm, and it is shown by computer simulation that the new algorithm in fact performs significantly better than the original algorithm.

Adaptive filter for dual energy radiographic imaging

Abstract: A radiographic scanner (A) generates a high energy image representation which is stored in a high energy image matrix (V) and a low energy image representation which is stored in a low energy image memory (U). A pair of filter functions selecting circuits (C) select a first or soft tissue specific filter function and second or bone specific filter function, respectively. The soft tissue filter function selecting circuit selects and adjusts the soft tissue filter function in accordance with the pixel value of the low energy image representation for each corresponding pair of pixel values. Convolvers (44, 46) convolve pixel values from the high and low energy image representations with the selected and adjusted filter functions. A soft tissue transform function (48) transforms the filtered high and low energy image representations into a soft tissue or other material specific image representation (42). The other filter selecting and adjusting circuit selects and adjusts the bone specific filter functions which are convolved with the high and low energy image representations by convolvers (54, 56). A bone specific transform function (58) transforms the filtered high and low energy image representations into a bone basis image.

Digital filter switch for data receiver

Abstract: A digital filter switch for use with a data receiver incorporates first and second squaring units connected to the outputs of first and second band-pass filters tuned to the separation and character frequencies in a signal transmission. The outputs of the squaring units are interconnected via an adder to the input of a low-pass filter, which produces the output data signal.

Efficient Approximation of Kalman Filter for Target Tracking

Abstract: A Kalman filter in the Cartesian coordinates is described for a maneuvering target when the radar sensor measures range, bearing, and elevation angles in the polar coordinates at high data rates. An approximate gain computation algorithm is developed to determine the filter gains for on-line microprocessor implementation. In this approach, gains are computed for three uncoupled filters and multiplied by a Jacobian transformation determined from the measured target position and orientation. The algorithm is compared with the extended Kalman filter for a typical target trajectory in a naval gun fire control system. The filter gains and the tracking errors for the proposed algorithm are nearly identical to the extended Kalman filter, while the computation requirements are reduced by a factor of four.

Pattern recognition system

Abstract: A self-categorizing pattern recognition system includes an adaptive filter for selecting a category in response to an input pattern A template is then generated in response to the selected category and a coincident pattern indicating the intersection between the expected pattern and the input pattern is generated The ratio between the number of elements and the coincident pattern to the number of elements in the input pattern determines whether the category is reset If the category is not reset, the adaptive filter and template may be modified in response to the coincident pattern Reset of the selected category is inhibited if no expected pattern is generated Weighting of the adaptive filter in response to a coincident pattern is inversely related to the number of elements in the input pattern The selected categories reset where a reset function is less than a vigilance parameter which may be varied in response to teaching events

Bandwidth compression for television signals

Abstract: A video signal received from a source (10) is bandwidth-compressed by filters (12, 14, 16), filter (14) being a temporal filter and filter (16) being a spatial filter. Selection of the filter to be used is dependent upon picture content. The transmitter reconstitutes in interpolators (44, 46) the signal which would be regenerated at the receiver, determines which filter gives the best results, and transmits an indication of which filter has been used in a digital signal associated with the analogue video signal. Preferably a determination of motion vectors associated with the signal is made and the digital signal indicates which of the determined motion vectors is applicable to different areas of te picture. By transmitting the control signal digitally with the analogue video signal the receiver circuitry is greatly simplified while its reliability is improved.

Noise updating repeated Wiener filter and other adaptive noise smoothing filters using local image statistics.

Abstract: We consider the restoration of images degraded by a class of signal-uncorrelated noise, which is possibly signal-dependent. Some adaptive noise smoothing filters, which assume a nonstationary mean, nonstationary variance image model implicitly or explicitly, are reviewed, and their performances are compared by the mean-squares errors (MSES) and by the human subjective judgment. We also present a new noise smoothing technique which is called the noise updating repeated Wiener (NURW) filter. Explicit noise variance updating formulas are derived for the NURW filter. The performance is improved both in the MSE sense and in the vicinity of edges by subjective observation.

Adaptive nonlinear digital filters using distributed arithmetic

Abstract: A nonlinear adaptive filter structure, based upon the theory of the truncated discrete Volterra series, is presented. A memory-oriented implementation exploiting distributed arithmetic is considered, and the conventional LMS adaptation algorithms are suitably modified. Memory-size reduction methods are developed to obtain simpler actual realizations. Computer simulation results are presented.