Showing papers on "Kernel adaptive filter published in 1970"

Optimal adaptive estimation: Structure and parameter adaptation

Abstract: Optimal structure and parameter adaptive estimators have been obtained for continuous as well as discrete data gaussian process models with linear dynamics. Specifically, the essentially nonlinear adaptive estimators are shown to be decomposable (partition theorem) into two parts, a linear non-adaptive part consisting of a bank of Kalman-Bucy filters, and a nonlinear part that incorporates the learning or adaptive nature of the estimator. The conditional-error-covariance matrix of the estimator is also obtained in a form suitable for on-line performance evaluation. The adaptive estimators are applied to the problem of state-estimation with nongaussian initial state and also to estimation under measurement uncertainty (joint detection-estimation). Examples are given of the application of the proposed adaptive estimators to structure and parameter adaptation indicating their applicability to practical engineering problems.

Digital filter using weighting

Abstract: Digital filter apparatus in which a set of weighting signal samples to be multiplied in the filter has values which are exactly powers of two such that the filter multiplier network may be comprised of simple signal routing circuits

Prediction of economic time-series by means of the Kalman filter†

Abstract: The principal objective of this paper is to indicate the use of the well-known Kalman filter as a technique for prediction of time-series and its similarities to optimal adaptive forecasting. It is shown that for a single time-series consisting of trend and trend-change and stochastic disturbances, the filter gives predictions identical to those of Thoil-Nerlove-Wage who in 1964 developed optimal adaptive forecasting for such a series. A numerical example illustrates the use of the filter and verifies the analytical results.

Frequency domain adaptive equalizer

Abstract: A frequency domain adaptive equalizer employs a first filter, having a plurality of periodically spaced zeros in its transfer characteristics, coupled to a second filter that includes a plurality of tuned circuits, each circuit having two poles in its transfer characteristics. The two filters are designed such that each of the zeros of the first filter are coincident with the poles of a separate tuned circuit of the second filter. Associated with each tuned circuit is a compensation circuit coupled to a summation circuit which combines the output signals of all of the compensation circuits to form a composite signal. A comparator circuit compares the composite signal thus generated with a stored reference signal to generate an error signal which is directed back to the compensation circuits to automatically adjust its parameters such that the error signal is minimized.

Adaptive digital filters for equalization of telephone channels

Abstract: An application of digital filtering to communication over a channel having amplitude and phase distortion in the frequency band occupied by the transmitted signal is presented. Described are a nonrecursive and a recursive digital filter which can serve as adaptive equalizers in compensating for the amplitude and phase distortion caused by the channel. The filter coefficients are adjusted automatically by the use of a test signal which is transmitted over the channel. The adjustment of the coefficients is carried out in the presence of noise with the aid of a steepest descent algorithm. The recursive filter, consisting of a comb filter in cascade with a bank of parallel two-pole filters, is shown to be especially suited for performing equalization. By choosing as a test signal sinusoids whose frequencies coincide with the poles of the two-pole filters, the coefficients of the recursive filter are easily adjusted.

Frequency-Domain Maximum-Likelihood Adaptive Filtering

Abstract: : Recent intensive study of adaptive (gradient-search) filtering in the time domain has not solved the problems with rate-of-convergence problem, which is a major difficulty with this technique. A recent study based on a set of time-stationary synthetic data shows that the time-domain maximum-likelihood adaptive filter converges very slowly to the optimum filter. After 3300 iterations of adaption with an adaptive rate of 10 percent of maximum value, the adaptive filter is still about 4 db away from the optimum filter in the sense of mean-square outputs. Time-domain adaptive filtering necessitates using only one convergence parameter for all filter coefficients, which may cause slow convergence for some data. Frequency-domain adaptive filtering may solve this problem, since different convergence parameters can be used for different frequency components. This report describes a frequency-domain maximum- likelihood adaptive-filtering algorithm analogous to the time-domain adaptive algorithm. This algorithm was used with a set of synthetic stationary data previously used for a time-domain adaptive-filtering study. Different filter lengths and convergence parameters were used. Results are compared with beamsteer and time-domain adaptive filter.

Adaptive signal processing through stochastic approximation

Abstract: One of the problems in signal processing is estimating the impulse response function of an unknown system. The well-known Wiener filter theory has been a powerful method in attacking this problem. In comparison, the use of stochastic approximation method as an adaptive signal processor is relatively new. This adaptive scheme can often be described by a recursive equation in which the estimated impulse response parameters are adjusted according to the gradient of a pre-determined error function. This paper illustrates by means of simple examples the application of stochastic approximation method as a single-channel adaptive processor. Under some conditions the expected value of its weight sequence converges to the corresponding Wiener optimum filter when the least-mean-square (LMS) error criterion is used.