Showing papers on "Adaptive filter published in 1973"

Theory of Adaptive Radar

Abstract: This paper reviews the principles of adaptive radar in which both the spatial (antenna pattern) and temporal (Doppler filter) responses of the system are controlled adaptively. An adaptive system senses the angular-Doppler distribution of the external noise field and adjusts a set of radar parameters for maximum signal-to-interference ratio and optimum detection performance. A gradient technique for control of the radar array/filter weights is described and shown to generate weights which asymptotically approach optimum values. Simulation results illustrate the convergence rate of adaptive systems and the performance improvement which can be achieved.

Digital lattice and ladder filter synthesis

Abstract: There is evidence that in addition to standard digital filter forms such as the direct, parallel, and cascade forms, digital lattice and ladder filters may play an important role in finite word length implementation problems. In this paper, techniques are developed in detail for efficiently synthesizing digital lattice and ladder filters from any stable direct form. In one form, a lattice filter canonic in terms of multiplies and delays is obtained. An internal scaling procedure is also introduced that will be of importance for optimizing one of the lattice forms for finite word length implementation.

Optimum Mismatched Filters for Sidelobe Suppression

Abstract: This paper discusses the application of least-mean-squares approximate inverse filtering techniques to radar range sidelobe reduction. The method is illustrated by application to the 13-element Barker code. The performance of the least-mean-square inverse filter is compared with the matched filter and with the simplified sidelobereducing filters of Rihaczek and Golden. A filter which completely suppresses the range sidelobes of a 13-element Barker sequence is only 0.2 dB worse than a matched filter in noise.

Practical design rules for optimum finite impulse response low-pass digital filters

Abstract: Although a great deal is known about design techniques for optimum (in a minimax error sense) finite impulse response (FIR) low-pass digital filters, there have not been established any practical design rules for such filters. Thus, a user is unable to easily decide on the (approximate or exact) filter order required to meet his design specifications and must resort to tables or trial and error procedures. In this paper, such a set of design rules is given. In the case of very narrow bandwidth or very wide bandwidth filters, analytic relations between the filter parameters can be readily obtained. In all other cases, exceedingly good linear and nonlinear fits to the data can be obtained over somewhat restricted ranges of the parameters. These fitting procedures lead to a practical set of simple design rules for estimating filter order from the desired specifications.

On the design of gradient algorithms for digitally implemented adaptive filters

Abstract: The effect of digital implementation on the gradient (steepest descent) algorithm commonly used in the mean-square adaptive equalization of pulse-amplitude modulated data signals is considered. It is shown that digitally implemented adaptive gradient algorithms can exhibit effects which are significantly different from those encountered in analog (infinite precision) algorithms. This is illustrated by considering the often quoted result of stochastic approximation that to achieve the optimum rate of convergence in an adaptive algorithm the step size should be proportional to 1/n , where n is the number of iterations. On closer examination one finds that this result applies only when n is large and is relevant only for analog algorithms. It is shown that as the number of iterations becomes large one should not continually decrease the step size in a digital gradient algorithm. This result is a manifestation of the quantization inherent in any digitally implemented system. A surprising result is that these effects produce a digital residual mean-square error that is minimized by making the step size as large as possible. Since the analog residual error is minimized by taking small step sizes, the optimum step-size sequence reflects a compromise between these competing goals. The performance of a time-varying gain sequence suggested by stochastic approximation is contrasted with the performance of a constant step-size sequence. It is shown that in a digital environment the latter sequence is capable of attaining a smaller residual error.

Analysis of quantization errors in the direct form for finite impulse response digital filters

Abstract: An analysis of the three possible types of quantization effects in the direct form realization of finite impulse response (FIR) digital filters is presented. These quantization effects include roundoff noise, A-D noise, and filter frequency response errors due to coefficient quantization. Since the analysis of roundoff noise and A-D noise for the direct form is straightforward, this paper concentrates on an analysis of the effects of quantized coefficients on the resulting filter frequency response. Based on this analysis, statistical bounds on the error incurred in the frequency response of a filter due to coefficient quantization are developed and verified by extensive experimental data. Using these bounds, a procedure for applying known techniques for FIR filter design to the design of filters with finite word length coefficients is presented. On the whole, the direct form is shown to be a very attractive structure for realizing FIR filters.

Stability criterion for N -dimensional digital filters

Abstract: The stability requirement for one-dimensional recursive filters is well known. A stability theorem for n -dimensional recursive filters is proved wherein the denominator of the filter is an n -dimensional power series. A Tauberian theorem due to Wiener yields the desired result in the general case.

On the stability of two-dimensional digital filters

Abstract: This correspondence proposes a method to check the stability of two-dimensional recursive filters. In this method the Jury table is modified and used to check the first condition of Huang's theorem. Some examples are solved to illustrate the method.

New Hardware Realizations of Nonrecursive Digital Filters

Abstract: Analysis of the bit-level operations involved in the convolution realizing a nonrecursive digital filter leads to hardware designs of digital filters based on the operation of counting.

Coordinated adaptive washout for motion simulators

Abstract: This paper introduces a new method of providing motion cues to a moving base six-degree-of-freedom flight simulator utilizing nonlinear filters. Coordinated adaptive filters, used to coordinate translational and rotational motion, are derived based on the method of continuous steepest descent, and the basic concept of the digital controllers used for the uncoordinated heave and yaw cues is also presented. The coordinated adaptive washout method is illustrated by an application in a six-degree-of-freedom fixed-base environment.

Adaptive digital filters

Abstract: Both analog and equivalent digital filters having adaptive capability are discussed. The analysis is restricted to second order sections but is extendable. Simple to implement gradient procedures using energy or phase information are used. Neither require supervised adaption. Applications include tracking nonstationary signals such as in seismic and acoustical sensing. Aside from the results shown, the tutorial nature of the paper establishes the need for further study to determine the optimum transformation that will minimize the interaction of the analog parameters (center frequency and bandwidth) in the transformed digital domain. It is suggested that this be realized by adaptive decorrelation, modification of the topological structures, and design of sm appropriate equivalent transformation.

Second-order digital filter with only one magnitude-truncation quantiser and having practically no limit cycles

Abstract: A 2nd-order digital filter with only one magnitude-truncation quantiser is discussed, and results are given that indicate that limit cycles are almost absent in this filter.

Least pth optimization of recursive digital filters

Abstract: The application of the Bandler-Charalambous method using extremely large values of p, typically 10,000 to the problem of choosing the coefficients of a recursive digital filter to meet arbitrary specifications on the magnitude characteristics, is described. The Fletcher (1970) method is used in conjunction with least pth optimization and is compared with the well-known Fletcher-Powell method. Some relevant design ideas, such as local optimality checking by perturbation, increasing the order complexity of the filter through growing filter sections, and meeting the stability requirements by using a pole inversion technique, have been implemented. A general description of a computer program package that uses these ideas, along with some illustrative examples are given.

Unsupervised Tracking of Maneuvering Vehicles

Abstract: The design of adaptive filters for the tracking of high-performance maneuvering targets is a fundamental problem in real-time surveillance systems. As is well known, a filter which provides heavy smoothing can not accurately track an evasive maneuver, and conversely. Consequently, one is led to the consideration of adaptive methods of filter design. This paper presents an improved self-adaptive filter algorithm for on-line solution of the above problem. Basically, this algorithm utilizes the orthogonality property of the residual time series to force the filter to automatically track the optimal gain levels in a changing environment.

Recursive digital filter design by linear programming

Abstract: A technique is presented for the design of recursive digital filters by means of linear programming. Examples of low-pass and bandpass filters designed with this technique are included.

An Examination of the Use of Adaptive Filtering in Forecasting

Abstract: Adaptive filtering is a technique for preparing short- to medium-term forecasts based on the weighting of historical observations, in a similar way to moving average and exponential smoothing. However, adaptive filtering, as it has been developed in electrical engineering, attempts to distinguish a signal pattern from random noise, rather than simply smoothing the noise of past data. This paper reviews the technique of adaptive filtering and investigates its applications and limitations for the forecasting practitioner. This is done by looking at the performance of adaptive filtering in forecasting a number of time series and by comparing it with other forecasting techniques.

A note on the linear filter method of computing electromagnetic sounding curves

Abstract: The values of the filter coefficients used for the computation of electromagnetic sounding curves are studied in conjunction with the values of the input function to the filter, or the range of values which the input function may assume, and the filters are broken off at such a place that the error in the sum of the products of filter coefficient and input function does not exceed a prescribed value. This analysis is carried out for the horizontal coils system, the perpendicular coils system, and the vertical coplanar coils system. The lengths of the filters so derived depend on the layer parameters, the frequency and the coil spacing. Even in the most unfavourable cases the filters are shorter than the filters published by Koefoed, Ghosh, and Polman (1972).

The Design and Application of Digital Filters

Abstract: The advantages of digital circuits and the frequency-response design procedures that are available for specifying the coefficients of the digital-filter transfer function are discussed. The hardware design of a digital filter is discussed, and an example is given of the application of the filter in a servo loop. Further application of the filter to generate a notch network characteristic is illustrated.

On nonlinear filters involving transformation of the time variable

Abstract: A new type of nonlinear filter, called the E -filter, is introduced that involves a transformation of the independent variable of the input function. It is shown how an E -filter can be designed to filter out superimposed "noise" on a signal, leaving the large peaks of the signal unattenuated. Unlike a Iow-pass linear filter, the low-pass E -filter is almost frequency independent and so does not affect the amplitudes of large sharp peaks of the signal. It is shown that the E -filter can be realized in real time and that a wide class of E -filters have a filtering action which is independent of the dc level of the input signal.

An Experimental Study of Roundoff Effects in a Tenth-Order Recursive Digital Filter

Abstract: This paper reports experimental measurements of limitcycle amplitude and period in digital recursive filters. The results that were obtained on two cascaded forms of a tenth-order filter show good agreement with existing theoretical bounds. (The bounds only apply to single second-order sections because analysis of cascaded sections is difficult.) Roundoff noise of the filter was measured and it agreed both in spectral shape and total power with that predicted by computer simulation. Some preliminary observations on relative magnitude of limit cycle and roundoff noise were made. In addition, the gradual buildup of a signal through a limit cycle was observed and 1 bit of noise in the least significant bit (LSB) in the filter was seen to break up limit cycles.

A Mobile Radio Single-Frequency "Two-Way" Diversity System Using Adaptive Retransmission from the Base

Abstract: This paper describes an adaptive retransmission system capable of providing a UHF (1 GHz) mobile radio channel with "twoway diversity." The system is unique in that all signal processing associated with the diversity combining is done at the base station. A two-branch prototype of the system, without modulation, was field tested to determine its adaptive retransmission performance. These tests indicate that the statistics of the fading envelope at both the base and mobile stations closely agree with those predicted by theory for an equal gain combiner with correlation between the branches.

A direct approximation technique for digital filters and equalizers

Abstract: A direct approximation method is given for periodic frequency-domain characteristics, such as magnitude and delay, leading to digital-filter functions. Dependence on lumped-element designs or on optimization methods is therefore not necessary. The approximation method is simple, with predictable error. For recursive filter functions it can be shown that stability is achieved.

The utilization of data measurement residuals for adaptive kalman filtering

Abstract: In recent years the Kalman filter has been utilized extensively for passive target motion analysis (TMA). Unfortunately, in these applications divergence is a common problem. Available methods for eliminating divergence ultimately involve increasing filter sensitivity by discounting the influence of past data. However, this procedure makes the filter more susceptible to random errors; therefore to avoid unnecessarily sacrificing noise performance, adaptive control is required. In this paper the Kalman filter equations are derived and the associated data measurement residuals are examined to determine their suitability for providing adaptive control. An important relationship between the system performance index and the data residuals is established. By exploiting this relationship, pertinent statistical properties of the performance index are deduced and are subsequently utilized as a basis for formulating practical adaptive control criteria. A simulated example is presented to demonstrate divergence (e. g., tracking of a maneuvering target) and significant improvement in performance is noted when adaptive control is appended.

Magnitude equalization using digital filters

Abstract: A method of designing digital fiters to directly equalize log gain functions of frequency is presented. Two methods of estimating the error are also given.

Nonlinear and Adaptive Estimation in Re-Entry

Abstract: The problem of real-time estimation of a lifting reentry vehicle trajectory of the shuttle orbiter type is considered. Simulations feature large position and velocity uncertainties at radar acquisition and realistic model errors in lift, drag and other model parameters. Radar tracking and accelerometer data are simulated. Significant nonlinearities are found to exist on spacecraft acquisition. An iterated nonlinear filter is shown to perform optimally during the radar acquisition phase. An adaptive filter is shown to track time-varying model errors, such as errors in the lift and drag coefficients, down to the noise level. Such real-time model tracking (identification) is frequently required for guidance and control implementation.

Cascade transversal-filter phase-compensation network

Abstract: A phase-compensation network, capable of modifying the phase response of a filter or network while leaving unchanged the amplitude response, comprising a cascaded combination of simple transversal filters, each of which comprises a delay line; at least one tapped weighted element whose input is connected to the delay line; and a signal summer whose input is connected to the outputs of the weighted elements. The elements of each simple transversal filter correspond to the values of the Bessel function of fixed argument and for successive integral indices of the order, including the zeroth order, only significant values of positive and negative indices of the order being used, the element corresponding to the zeroth order being in the center of its specific transversal filter. The output of one transversal filter constitutes the input to the next succeeding filter in the cascade, each transversal filter corresponding to one of a set of fixed arguments of a Bessel function of the first kind, the set of fixed arguments being obtained from the coefficients of a phase function when expressed in Fourier series form.

Optimum Signal and Filter Design in Underwater Acoustic Echo Ranging Systems

Abstract: Optimization of the filter, the signal, and the signal and filter jointly are studied in the sonar environment under noise and reverberation limited conditions. The maximization of the receiver output signal-to-interference ratio is used as a performance criterion with unit energy constraint on both signal and filter. In the filter design problem, the optimum filter function is the solution of a linear integral equation. The kernel of the integral equation is a function of the target and medium scattering functions and the reverberation distribution. In the signal design problem, a similar type of integral equation is obtained as in the filter optimization problem. In the joint signal and filter design problem, it is shown that the optimum signal and filter functions are the solutions to a pair of linear integral equations with the largest (SIR)O. Several examples are investigated for different mediums and reverberation distributions with the finite matrix approximation method. An interative technique is used to compute the joint optimization of signal and filter.