Showing papers on "Kernel adaptive filter published in 1968"

Suboptimal state estimation for continuous-time nonlinear systems from discrete noisy measurements

Abstract: This paper presents the derivation of the dynamical equations of a second-order filter which estimates the states of a non-linear plant on the basis of discrete noisy measurements. The filter equations contain terms involving the second-order partial derivatives of the plant and output equations. Simulation results are presented which yield a comparison of the performance of the first-versus the second-order filter when applied to a nonlinear third-order system. The results indicate that the inclusion of second-order terms can markedly improve the filter performance.

Coefficient Accuracy and Digital Filter Response

Abstract: The frequency response of a digital filter realized by a finite word-length machine deviates from that which would have been obtained with an infinite word-length machine. An "ideal" or "errorless" filter is defined as a realization of the required pulse transfer function by an infinite word-length machine. This paper shows that quantization of a digital filter's coefficients in an actual realization can be represented by a "stray" transfer function in parallel with the corresponding ideal filter. Also, by making certain statistical assumptions, the statistically expected mean-square difference between the real frequency responses of the actual and ideal filters can be readily evaluated by one short computer program for all widths of quantization. Furthermore, the same computations may be used to evaluate the rms value of output noise due to data quantization and multiplicative rounding errors. Experimental measurements verify the analysis in a practical case. The application of the results to the design of the digital filters is also considered.

Optimum radar signal processing in clutter

Abstract: This paper considers the joint optimization of a class of radar signals and filters in a number of clutter-pins-noise environments. The radar signal processor in this case will be optimum in the sense that its output at the time of target detection yields the maximum ratio of peak signal power to total interference power. If the interference at the input to this signal processor is a Gaussian random process, this processor also yields the maximum probability of detection for a given value of false-alarm probability. The signals used are pulse trains and the filters are tapped delay lines. The purpose of signal design is to determine the optimum complex weighting for each pulse of the pulse train. Filter design yields the optimum complex weighting for the output taps of the delay line. Filter design for a specified signal is considered first. This is followed by combined signal and filter design and matched filter design. Constrained signal and filter design is investigated last. It should be emphasized that the optimizations require a knowledge of the clutter time-frequency distribution. For practical situations, when the clutter distribution is unknown, an adaptive filter is proposed that automatically provides the optimum filter weights for a given transmitted signal. When the clutter has a range-time extent less than the equivalent range-time extent of the signal, filter design alone yields nearly optimum performance. As the clutter becomes extended in range-time, it is necessary to consider jointly the design of signal and filter to obtain an optimum radar signal processor. In this report it is suggested that the signal be designed under the assumption of the clutter being extended over a broad range of Dopplers and that the signal processor consist of a bank of adaptive filters. Then each filter output yields the maximum ratio of peak signal to total interference power for this signal design.

A summary, by illustrations, of least-squares filters with constraints

Abstract: Several methods of combining a number of time series into a single series are discussed. They are all individual filtering followed by summation and are somewhat like Wiener filtering in that a least-squares criterion is used to design the filter coefficients. They differ from Wiener filtering in that signal information is given in the form of various constraints on the filter coefficients rather than being given as a signal correlation function. The equations are worked out explicitly for the case of two time series and three filter points and presented in such a way as to make generalization clear.

Design and Application of an Adaptive Tracking Filter Control System

Abstract: The design of an adaptive tracking filter control system and its application to large flexible booster vehicles is described. The problem of elastic vehicle stability is considered along with its solution by conventional and adaptive techniques. The improvement in vehicle stability, which may be achieved with the adaptive tracking filter technique as compared to conventional techniques, is shown. The control system evolved uses two adaptive tracking filters to phase stabilize the first and second bending modes, in addition to conventional compensation techniques. The application of this adaptive technique to a vehicle in which the modal frequencies are in close proximity (<2.5 percent separation) is discussed. The mechanization of the adaptive control system involves the selection of design techniques and components that are electrically and physically compatible with the intended airborne application. The development of a suitable frequency tracking technique and tracking filter is described, in addition to the electronic and mechanical design of the adaptive control system prototype.

Online digital filtering

Abstract: The advantages of the recursive digital filter as a real-time signal processor are stated, and, as an example, a fourth-order Cheby?shev lowpass filter has been synthetised and programmed into an online computer. Typical responses are shown for pulse, step and low-frequency mixed sinusoidal signals.