Showing papers on "Adaptive algorithm published in 1993"
TL;DR: The theoretical background for the design of deadlock-free adaptive routing algorithms for wormhole networks is developed and some basic definitions and two theorems are proposed, which create the conditions to verify that an adaptive algorithm is deadlocks-free, even when there are cycles in the channel dependency graph.
Abstract: The theoretical background for the design of deadlock-free adaptive routing algorithms for wormhole networks is developed. The author proposes some basic definitions and two theorems. These create the conditions to verify that an adaptive algorithm is deadlock-free, even when there are cycles in the channel dependency graph. Two design methodologies are also proposed. The first supplies algorithms with a high degree of freedom, without increasing the number of physical channels. The second methodology is intended for the design of fault-tolerant algorithms. Some examples are given to show the application of the methodologies. Simulations show the performance improvement that can be achieved by designing the routing algorithms with the new theory. >
831 citations
TL;DR: A self-tuning version of the robust control capable of achieving set point regulation is developed in which the control gains are tuned by an output-feedback adaptive algorithm.
Abstract: For pt.I, see ibid., p.17-32 (1993). The problem of designing global output-feedback robust stabilizing controls for a class of single-input single-output minimum-phase uncertain nonlinear systems with known and constant relative degree is addressed. They are assumed to be linear with respect to the input and nonlinear with respect to an unknown constant parameter vector. The nonlinearities depend on the output only. The nonlinearities may be uncertain and are only required to be bounded by known smooth functions. The order of the robust compensator is equal to the relative degree minus one and is static when the relative degree is one. A self-tuning version of the robust control capable of achieving set point regulation is developed in which the control gains are tuned by an output-feedback adaptive algorithm. When the parameter vector enters linearly, the self-tuning regulator does not require the knowledge of parameter bounds and guarantees set point regulation for the same class of systems considered in Part I. >
607 citations
TL;DR: It is shown that neural networks can be considered as general nonlinear filters that can be trained adaptively, that is, that can undergo continual training with a possibly infinite number of time-ordered examples.
Abstract: The paper proposes a general framework that encompasses the training of neural networks and the adaptation of filters. We show that neural networks can be considered as general nonlinear filters that can be trained adaptively, that is, that can undergo continual training with a possibly infinite number of time-ordered examples. We introduce the canonical form of a neural network. This canonical form permits a unified presentation of network architectures and of gradient-based training algorithms for both feedforward networks (transversal filters) and feedback networks (recursive filters). We show that several algorithms used classically in linear adaptive filtering, and some algorithms suggested by other authors for training neural networks, are special cases in a general classification of training algorithms for feedback networks.
196 citations
TL;DR: A comparative performance analysis of the two algorithms establishes some important theoretical properties of adaptive spectral detectors and leads to practical guidelines for applying the algorithms to multispectral sensor data.
Abstract: The fully adaptive hypothesis testing algorithm developed by I.S. Reed and X. Yu (1990) for detecting low-contrast objects of unknown spectral features in a nonstationary background is extended to the case in which the relative spectral signatures of objects can be specified in advance. The resulting background-adaptive algorithm is analyzed and shown to achieve robust spectral feature discrimination with a constant false-alarm rate (CFAR) performance. A comparative performance analysis of the two algorithms establishes some important theoretical properties of adaptive spectral detectors and leads to practical guidelines for applying the algorithms to multispectral sensor data. The adaptive detection of man-made artifacts in a natural background is demonstrated by processing multiband infrared imagery collected by the Thermal Infrared Multispectral Scanner (TIMS) instrument. >
169 citations
TL;DR: A normalized least-mean-squares (NLMS) adaptive algorithm with double the convergence speed, at the same computational load, of the conventional NLMS for an acoustic echo canceller is proposed and its fast convergence is demonstrated.
Abstract: A normalized least-mean-squares (NLMS) adaptive algorithm with double the convergence speed, at the same computational load, of the conventional NLMS for an acoustic echo canceller is proposed. This algorithm, called the ES (exponentially weighted stepsize) algorithm, uses a different stepsize (feedback constant) for each weight of an adaptive transversal filter. These stepsizes are time-invariant and weighted proportionally to the expected variation of a room impulse response. The algorithm adjusts coefficients with large errors in large steps, and coefficients with small errors in small steps. A transition formula is derived for the mean-squared coefficient error of the algorithm. The mean stepsize determines the convergence condition, the convergence speed, and the final excess mean-squared error. Modified for a practical multiple DSP structure, the algorithm requires only the same amount of computation as the conventional NLMS. The algorithm is implemented in a commercial acoustic echo canceller, and its fast convergence is demonstrated. >
148 citations
01 Apr 1993
TL;DR: A sliding-mode control algorithm combined with an adaptive scheme, which is used to estimate the unknown parameter bounds, is developed for the trajectory control of robot manipulators and shows that in the presence of the uncertainties, which are assumed to be unbounded and rapidly varying, the closed-loop system can still be stabilized.
Abstract: A sliding-mode control algorithm combined with an adaptive scheme, which is used to estimate the unknown parameter bounds, is developed for the trajectory control of robot manipulators. The major contribution of this methodology lies in the use of a special matrix, called the regressor, which makes it possible to isolate the unknown parameters from the robotic dynamics. Based on the upper bounds of those unknown parameters, which are estimated by a simple adaptive law, the proposed VSS (variable-structure-system) controller guarantees the stability of the closed-loop system. The robustness analysis shows that in the presence of the uncertainties, which are assumed to be unbounded and rapidly varying, the closed-loop system can still be stabilized. Chattering is reduced by using the boundary layer technique. Simulation results show the validity of the proposed algorithm. >
131 citations
TL;DR: Adaptive finite element methods for stationary convectiondiffusion problems are designed and analyzed based on a posteriori error estimates for the Shock-capturing Streamline Diffusion method to show that the algorithms are efficient in a certain sense.
Abstract: Adaptive finite element methods for stationary convectiondiffusion problems are designed and analyzed. The underlying discretization scheme is the Shock-capturing Streamline Diffusion method. The adaptive algorithms proposed are based on a posteriori error estimates for this method leading to reliable methods in the sense that the desired error control is guaranteed. A priori error estimates are used to show that the algorithms are efficient in a certain sense.
130 citations
TL;DR: Two CMOS implementations of the variable-step-size, power-of-two quantizer algorithm are presented to demonstrate that the performance gains are attainable with only a modest increase in circuit complexity.
Abstract: Stochastic gradient adaptive filtering algorithms using variable step sizes are investigated. The variable-step-size algorithm improves the convergence rate while sacrificing little in steady-state error. Expressions describing the convergence of the mean and mean-squared values of the coefficients are developed and used to calculate the mean-square-error evolution. The initial convergence rate and the steady-state error are also investigated. The performance of the algorithm is studied when a power-of-two quantizer algorithm is used, and finite-word-length effects are considered. The analytical results are verified with simulations encompassing variable applications. Two CMOS implementations of the variable-step-size, power-of-two quantizer algorithm are presented to demonstrate that the performance gains are attainable with only a modest increase in circuit complexity. >
122 citations
TL;DR: A frequency domain model of the filtered LMS algorithm is presented for analyzing the behavior of the weights during adaptation and expressions show that algorithm stability can be achieved over a frequency band of interest by inserting an appropriately chosen delay in the reference input to the L MS algorithm weight update equation.
Abstract: A frequency domain model of the filtered LMS algorithm is presented for analyzing the behavior of the weights during adaptation. In particular, expressions for stable operation of the algorithm are derived as a function of the algorithm step size, the input signal power, and the transfer functions of the linear filters. The expressions show that algorithm stability can be achieved over a frequency band of interest by inserting an appropriately chosen delay in the reference input to the LMS algorithm weight update equation. This result implies that it is not necessary to use a training mode to estimate the loop transfer functions before or during adaptation if the input is limited to a band of frequencies. It is only necessary to know the approximate delay introduced by the transfer functions in the band. The single delay parameter can be estimated much more easily than the entire transfer function. Simulations of the time domain algorithm are presented to support the theoretical predictions of the frequency domain model. >
109 citations
TL;DR: A special data structure based on octrees has been developed, which is flexible to handle all different types of cell division/deletion and can be applied to eliminate any possible hanging node configuration in a simple way.
Abstract: The paper describes the development and application of an adaptive algorithm for tetrahedral grids. An initial unstructured grid is adapted by employing local division, as well as deletion of the tetrahedral cells. The process is dynamic, and the adapted grid changes follow evolution of the solution. Adaptation of the cells consists of normal division of a tetrahedron into eight subcells, as well as directional division into two or four subcells. A major issue of such adaptive grid algorithms is elimination of hanging nodes that appear on the edges in the interface between the embedded and unembedded zones. A novel technique has been developed for treatment of such interface cells that can be applied to eliminate any possible hanging node configuration in a simple way. A special data structure based on octrees has been developed, which is flexible to handle all different types of cell division/deletion. Application cases include a moving source, as well as transonic flow around the ONERA M6 wing.
104 citations
TL;DR: A recursive equation that subsumes several common adaptive filtering algorithms is analyzed for general stochastic inputs and disturbances by relating the motion of the parameter estimate errors to the behavior of an unforced deterministic ordinary differential equation (ODE).
Abstract: A recursive equation that subsumes several common adaptive filtering algorithms is analyzed for general stochastic inputs and disturbances by relating the motion of the parameter estimate errors to the behavior of an unforced deterministic ordinary differential equation (ODE). The ODEs describing the motion of several common adaptive filters are examined in some simple settings, including the least mean square (LMS) algorithm and all three of its signed variants (the signed regressor, the signed error, and the sign-sign algorithms). Stability and instability results are presented in terms of the eigenvalues of a correlation-like matrix. This generalizes known results for LMS, signed regressor LMS, and signed error LMS, and gives new stability criteria for the sign-sign algorithm. The ability of the algorithms to track moving parameterizations can be analyzed in a similar manner, by relating the time varying system to a forced ODE. The asymptotic distribution about the forced ODE is an Ornstein-Uhlenbeck process, the properties of which can be described in a straightforward manner. >
07 Jun 1993
TL;DR: Self-adaptive algorithms for source separation based on a generalized criterion with the introduction of cross-cumulants and a new contrast function is defined whose maximum occurs when H is separating.
Abstract: Introduces self-adaptive algorithms for source separation based on a generalized criterion with the introduction of cross-cumulants. By adequate adaptive preprocessing it can be supposed that the observed source mixture x is 'white'. Then a separating matrix H (such that y=Hx has independent components) can be assumed unitary. A new contrast function is defined whose maximum occurs when H is separating. Its (simple) form admits an associated adaptive algorithm. Two different algorithms are proposed to estimate H, either directly or through its equivalent product of Givens rotations. Computer simulations illustrate the contribution of the cross-cumulants on the convergence of the algorithms. In the three-sources case, they show that the performances are improved substantially. >
TL;DR: In this paper, a second-order IIR adaptive notch filter (ANF) algorithm based on least-mean p-power (LMP) error criterion is investigated, which is used to cancel 60-Hz interference in the recording of electrocardiograms (ECG).
Abstract: A new second-order IIR adaptive notch filter (ANF) algorithm based on least-mean-p-power (LMP) error criterion is investigated. When the ANF is used to cancel 60-Hz interference in the recording of electrocardiograms (ECG), the performance of this adaptive algorithm with p=1 is better than that of the conventional least-mean-square (LMS, p=2) algorithm. Furthermore, when the ANF is applied to estimate the frequency of sinusoid embedded in white noise, this algorithm with p=3 has better statistical accuracy than the LMS algorithm. Simulation results are presented to demonstrate the effectiveness of the proposed ANF algorithm. >
TL;DR: An analysis and improvement of a data-adaptive signal estimation algorithm that leads to improvements of the methods and the predicted improvements are demonstrated by simulation and comparison with the Cramer-Rao bounds.
Abstract: An analysis and improvement of a data-adaptive signal estimation algorithm are presented. Perturbation analysis of a reduced-rank data matrix is used to reveal its statistical properties. The obtained information is used for calculating the performance of the Toeplitz-restoration algorithm of D. Tufts et al. (1982). This analysis leads to improvements of the methods, and the predicted improvements are demonstrated by simulation and comparison with the Cramer-Rao bounds. >
TL;DR: In this article, two adaptive feedforward control structures based on the filtered-x LMS algorithm have been developed for the active control of broadband vibration in structures, and the control signal is obtained in both configurations by filtering the reference signal through an adaptive finite impulse filter (FIR).
02 May 1993
TL;DR: The controller guarantees asymptotic motion and force tracking without any persistent excitation condition and has a proportional-integral force feedback control structure with a low P-gain, so that acausality is avoided.
Abstract: Adaptive motion, internal force, and external contact force control of multiple manipulators handling a constrained object is achieved. Parametric uncertainties may exist in the manipulator and in the object as well as in the friction coefficients of contact surfaces. A set of transformed dynamic equations are obtained in the joint space, in which internal force and external contact force have the same form and, thus, can be dealt with in the same way. Based on some particular properties of a reformulated motion and force equation, and adaptive algorithm is developed with unknown parameters updated by both motion and force tracking error. The controller guarantees asymptotic motion and force tracking without any persistent excitation condition and has a proportional-integral (PI) force feedback control structure with a low P-gain, so that acausality is avoided. Robustness to bounded velocity and force measurement noise as well as to disturbances of the controller is discussed. >
TL;DR: The pRAM is realizable in hardware, and the third-generation VLSI pRAM chip is described, which is adaptive since learning algorithms have been incorporated on-chip, using reinforcement training.
Abstract: The pRAM (probabilistic RAM) is a nonlinear stochastic device with neuron like behavior. The pRAM is realizable in hardware, and the third-generation VLSI pRAM chip is described. This chip is adaptive since learning algorithms have been incorporated on-chip, using reinforcement training. The pRAM chip is also adaptive with respect to the interconnections between neurons. Results achieved from a small net of pRAM's performing a pattern-recognition task using reinforcement training are presented. >
TL;DR: In this paper, an adaptive structure based on a generalized structural subband decomposition of FIR (finite-impulse-response) filters is presented, which implements an adaptive FIR filter of length N as a parallel connection of L branches, with each branch composed of a cascade of a fixed interpolator and a sparse adaptive subfilter containing at least L nonzero coefficients.
Abstract: An adaptive structure based on a generalized structural subband decomposition of FIR (finite-impulse-response) filters is presented. The proposed structure implements an adaptive FIR filter of length N as a parallel connection of L branches, with each branch composed of a cascade of a fixed interpolator and a sparse adaptive subfilter containing at least L nonzero coefficients. There is no sampling rate alteration in this structure, and therefore no problems with aliasing occur. The interpolators are implemented by a computationally efficient transform (e.g., DCT, DFT). The proposed structure presents superior convergence performance for colored input signals when compared to the conventional direct-form LMS (least-mean-square) structure, with a very small increase in the number of operations. The advantages of using the subband structure in the adaptive line enhancer, acoustic echo canceller, and channel equalizer applications are shown through computer simulations. >
01 Jun 1993
TL;DR: A concurrent adaptive conjugate gradient learning algorithm has been developed for training of multilayer feed-forward neural networks and implemented in C on a MIMD shared-memory machine (CRAY Y-MP/8- 864 supercomputer).
Abstract: A concurrent adaptive conjugate gradient learning al gorithm has been developed for training of multilayer feed-forward neural networks and implemented in C on a MIMD shared-memory machine CRAY Y-MP/8- 864 supercomputer. The learning algorithm has been applied to the domain of image recognition. The per formance of the algorithm has been evaluated by ap plying it to two large-scale training examples with 2,304 training instances. The concurrent adaptive neural networks algorithm has superior convergence property compared with the concurrent momentum back-propagation algorithm. A maximum speedup of about 7.9 is achieved using eight processors for a large network with 4,160 links as a result of microtask ing only. When vectorization is combined with micro tasking, a maximum speedup of about 44 is realized using eight processors.
TL;DR: An adaptive genetic algorithm, which has its rates of genetic operators changed automatically during the iterative optimization process, is described, which uses a Wilcoxon signed rank test to show its performance improvement over the fixed-rate genetic algorithm.
TL;DR: A fast-adaptive coding algorithm is given which tracks the local data statistics more quickly, thus yielding better compression efficiency and performing badly when segmenting data into relatively small segments.
Abstract: The Huffman code in practice suffers from two problems: the prior knowledge of the probability distribution of the data source to be encoded is necessary, and the encoded data propagate errors. The first problem can be solved by adaptive coding, while the second problem can be partly solved by segmenting data into segments. However, the adaptive Huffman code performs badly when segmenting data into relatively small segments because of its relatively slow adaptability. A fast-adaptive coding algorithm which tracks the local data statistics more quickly, thus yielding better compression efficiency, is given. >
14 Jun 1993
TL;DR: This paper presents a deadlock-free adaptive routing algorithm obtained from the application of the theory proposed in [4] to the 3D-torus, and shows that this algorithm is very fast, also increasing the network throughput considerably.
Abstract: In this paper, a deadlock-free adaptive routing algorithm, obtained from the application of the theory proposed in [4] to the 3D-torus, is evaluated under different load conditions and compared with other algorithms. The results show that this algorithm is very fast, also increasing the network throughput considerably. Nevertheless, this adaptive algorithm has cycles in its channel dependency graph. As a consequence, when the network is heavily loaded messages may temporarily block cyclically, drastically reducing the performance of the algorithm. Two mechanisms are proposed to avoid this problem.
TL;DR: An adaptive link assignment algorithm for the distributed optimization of dynamically changing network topologies is presented and is designed to recover from predictable link outages as well as massive unpredictable failures.
Abstract: An adaptive link assignment algorithm for the distributed optimization of dynamically changing network topologies is presented The algorithm is responsible for determining the network connectivity by controlling the selection of links to be established and disconnected This algorithm is designed to recover from predictable link outages as well as massive unpredictable failures To minimize computational time complexity as well as to improve transient response Some known graph-theoretic algorithms are utilized >
Journal Article•
TL;DR: A new approach to feedback equalization for hearing aids is described that involves the use of an adaptive algorithm that estimates and tracks the characteristic of the hearing aid feedback path.
Abstract: This paper describes a new approach to feedback equalization for hearing aids. The method involves the use of an adaptive algorithm that estimates and tracks the characteristic of the hearing aid feedback path. The algorithm is described and the results of simulation studies and bench testing are presented.
TL;DR: An adaptive algorithm for adjusting the gains of a vehicle speed control system is presented, which helps the design of a single speed control module that does not need additional calibration or sacrifices in performance for certain car lines.
Abstract: An adaptive algorithm for adjusting the gains of a vehicle speed control system is presented. By continuously adjusting the proportional-integral control gains, speed control performance can be optimized for each vehicle and operating condition. This helps the design of a single speed control module that does not need additional calibration or sacrifices in performance for certain car lines. It also allows improved performance for changing road conditions not possible with a fixed-gain control or other types of adaptive control. The results of initial vehicle testing confirm the performance improvements and robustness of the adaptive controller. >
TL;DR: In this paper, a parallel theory of algorithms for dynamically adapting windows on networks having multiple paths with different propagation delays and multiple virtual circuits (VCs) on each path is developed.
Abstract: Recently the optimal design of windows for virtual circuits has been studied for high speed, wide area data networks in an asymptotic framework in which the delay bandwidth product is the large parameter. Based on the results of this analysis we have previously proposed and evaluated a new class of algorithms for dynamically adapting windows in single path, multi-hop networks. Here we complement our previous work by first developing a parallel theory of algorithms for dynamically adapting windows on networks having multiple paths with different propagation delays and multiple virtual circuits (VCs) on each path. A common feature of these algorithms is that the source of each VC measures the round trip response time of its packets and uses these measurements to adjust its window with the goal of satisfying certain asymptotic identities that have been proven to hold in stationary asymptotically optimal designs. These identities, which hold for all values of cross traffic intensities, serve as “design equations” for the algorithms. A major part of the work reported here is the evaluation of the performance of the new adaptive algorithms in realistic, nonstationary conditions by simulations of networks with data rates of 45 Mbps and propagation delays of up to 47 ms. One of two networks studied has 3 nodes, 2 paths and up to 16 VCs on each path; the level of cross traffic determines whether a path has 1 or 2 bottlenecks. The simulation results generally confirm that the realizations of the adaptive algorithms give stable, efficient performance and are close to theoretical expectations.
TL;DR: The new results agree with the existing ones when reduced to the finite impulse response (FIR) case, and the explosive behavior of pertinent error variances of Newton-type IIR algorithms when the forgetting factor /spl lambda/=1 is concluded.
Abstract: For pt.I see ibid., vol.41, no.4, p.1493-1517, 1993. Finite precision (FP) implementation is the ultimately inevitable reality of all adaptive filters, including adaptive infinite impulse response (IIR) filters. This paper continues to examine the asymptotic convergence speed of adaptive IIR filters of various structures and algorithms, including the simple constant gain type and the Newton type, but under FP implementation. A stochastic differential equation (SDE) approach is used in the analysis. Such an approach not only greatly simplifies the FP analysis, which is traditionally very involved algebraically, but it also provides valuable information about the first-order as well as the second-order moments that (the latter) are not available using the ordinary differential equation (ODE) approach. The asymptotic convergence speed, as well as the convergent values, of the pertinent moments of FP errors are examined in terms of unknown system pole-zero locations. The adverse effects of lightly damped low-frequency (LDLF) poles resulting from fast sampling on the local transient and convergent behavior of various structures and algorithms are analyzed and compared. The new results agree with the existing ones when reduced to the finite impulse response (FIR) case. In particular, the explosive behavior of pertinent error variances of Newton-type IIR algorithms when the forgetting factor /spl lambda/=1 is also concluded. Computer simulation verifies the predicted theoretical results.
Book•
01 Sep 1993
TL;DR: Signal processing for linear instrumental systems with noise - a general theory with illustrations from optical imaging and light scattering problems, M.M. Bertero and E.R.R Pike boundary implication results in parameter space, N.K. Bose sampling of bandlimited signals - fundamental results and some extensions.
Abstract: Signal processing for linear instrumental systems with noise - a general theory with illustrations from optical imaging and light scattering problems, M. Bertero and E.R. Pike boundary implication results in parameter space, N.K. Bose sampling of bandlimited signals - fundamental results and some extensions, J.L. Brown Jr localization of sources in a sector - algorithms and statistical analysis, K. Buckley and X-L Xu the signal subspace direction-of-arrival algorithm, J.A. Cadzow digital differentiators, S.C. Dutta Roy and B. Kumar VLSI in signal processing, A. Ghouse constrained beam forming and adaptive algorithm, L.C. Godara bispectral speckle interferometry to reconstruct extended objects from turbulence-degraded telescope images, D.M. Goodman et al multi-dimensional signal processing, K. Hirano on the assessment of visual communication, F.O. Huck et al VLSI implementations of number theoretic concepts with applications in signal processing, G.A. Jullien et al decision-level neural net sensor fusion, R.Y. Levine and T.S. Khuon statistical algorithms for non-causal Gauss Markov fields, J.M.F. Moura and N. Balram subspace methods for directions-of-arrival estimation, A. Paulraj et al closed form solution to the estimates of directions of arrival using data from an array of sensors, C.R. Rao and B. Zhou high-resolution direction-finding, S.V. Schell and W.A. Gardner multiscale signal processing techniques - a review, A.H. Tewfik et al sampling theorens and wavelets, G.G. Walter image and video coding research, J.W. Woods fast algorithms for structured matrices in signal processing, A.E. Yagle.
TL;DR: A QR-recursive-least squares (RLS) adaptive algorithm for non-linear filtering is presented that retains the fast convergence behavior of the RLS Volterra filters and is numerically stable.
Abstract: A QR-recursive-least squares (RLS) adaptive algorithm for non-linear filtering is presented. The algorithm is based solely on Givens rotation. Hence the algorithm is numerically stable and highly amenable to parallel implementations. The computational complexity of the algorithm is comparable to that of the fast transversal Volterra filters. The algorithm is based on a truncated second-order Volterra series model; however, it can be easily extended to other types of polynomial nonlinearities. The algorithm is derived by transforming the nonlinear filtering problem into an equivalent multichannel linear filtering problem with a different number of coefficients in each channel. The derivation of the algorithm is based on a channel-decomposition strategy which involves processing the channels in a sequential fashion during each iteration. This avoids matrix processing and leads to a scalar implementation. Results of extensive experimental studies demonstrating the properties of the algorithm in finite and 'infinite' precision environments are also presented. The results indicate that the algorithm retains the fast convergence behavior of the RLS Volterra filters and is numerically stable. >
Patent•
24 Aug 1993
TL;DR: In this article, the Least Mean Square (LMS) adaptive algorithm is used to provide effective normalization when the background noise is locally non-stationary and when the target may be subject to time spread of unknown extent.
Abstract: A normalizer based on a Least Mean Square (LMS) adaptive algorithm configured to provide effective normalization when the background noise is locally non-stationary and when the target may be subject to time spread of unknown extent. The LMS algorithm used in the normalizer includes an adaptive filter in both the primary and reference inputs as a means of adapting to variations in both the signal and noise statistics. The LMS algorithm is implemented on the logarithm of the data, so that the difference minimized in the LMS structure drives the ratio of the signal power to noise power to a constant value. The algorithm can be used as a range normalizer by running it over range in each doppler bin, or as a frequency normalizer by operating across doppler in each range bin. By continually adapting to the statistics present in the data, the normalizer more effectively deals with the variations in the noise and signal statistics.