Showing papers on "Kernel adaptive filter published in 1967"

A direct derivation of the optimal linear filter using the maximum principle

Abstract: The purpose of this paper is to present an alternate derivation of optimal linear filters. The basic technique is the use of a matrix version of the maximum principle of Pontryagin coupled with the use of gradient matrices to derive the optimal values of the filter coefficients for minimum variance estimation under the requirement that the estimates be unbiased. The optimal filter which is derived turns out to be identical to the well-known Kalman-Bucy filter.

Discrete Programming by the Filter Method

Abstract: In this paper (section 1) a two-phase procedure, the filter method or accelerated additive algorithm, is proposed for solving linear programs with zero-one variables. In Phase I an auxiliary problem is constructed that, in Phase II, is used to “filter” the solutions to which the tests of the additive algorithm are to be applied. The filter method is then extended (section 2) by J. F. Benders’ partitioning procedure to the mixed-integer zero-one case, as well as to general integer and mixed-integer programs. Finally, a specialized version of this method is used (section 3) to tackle a general machine-sequencing model, formulated as the problem of finding a minimaximal path in a disjunctive graph.

Application of the extended kalman filter to ballistic trajectory estimation.

Abstract: : In this report an extended Kalman filter for ballistic trajectory estimation is presented The filter equations are basically the same as those in the previous Final Report on this contract The several modifications are explained in detail, and values for all filter parameters are given The filter was tested against simulated radar data for a number of different cases; performance was excellent in all cases For comparison purposes a second-order exponentially weighted polynomial filter was used on the same data; the performance was significantly worse than for the extended Kalman filter The extended Kalman filter was also run at slower data rates and with multiple interruptions of data with only a slight degradation in performance A precomputed approximation to the weighting matrix was calculated on the basis of several runs; this approximation performed nearly as well as the fully implemented filter Use of this approximation reduced computational requirements by an order of magnitude (Author)

The optimal discrete filter corresponding to a given analog filter

Abstract: In this paper, the discrete filter to be used in place of a given analog filter so as to result in minimum mean-square error at the sampling instants is derived. The spectra of the signals to be filtered are assumed to be either 1) band limited, or 2) of known rational form. The condition which the optimal discrete filter must satisfy is obtained by minimizing the expected value of the square of the error, formed by the difference between a digital and sampled analog channel. For rational spectra, the optimum discrete filter is a function of both the frequency characteristics of the analog filter and the spectrum of the process. The optimal discrete filter for this case can be placed in rational form. For band-limited spectra, it is demonstrated that the corresponding optimal discrete filter is dependent only upon the frequency characteristics of the analog filter. The optimal discrete filter for this case, however, cannot, in general, be placed in rational form. Two methods are described for placing this optimal discrete filter in rational form. One of these methods, which involves obtaining the best first-order rational approximation to the optimum transformation, reduces to the well-known Tustin transformation.

An Adaptive Tracking Filter for Bending-Mode Stabilization

Abstract: Simulation results of adaptive tracking filter application to stabilization of structural bending modes of SI-B launch vehicle

Complex spatial filter synthesis

Abstract: An optical filter in the form of a synthetic hologram of an aggregation of point sources recorded on a photographic plate using a standard two-beam holographic system. The required filter function of the optical filter is established and generalized into a periodic function which is then synthesized by a finite number of harmonics in a spatial frequency domain. Where the filter function has a degree of symmetry, the synthesis process is comparatively simple with only the first several harmonics needed to construct the optical filter. Both the amplitude and phase of the desired function are recorded on the synthetically generated hologram.

Adaptive filtering Interim report

Abstract: Adaptive filter with inaccuracies approximated by Gaussian white noise input and determination of covariance for most probable residual sequence

System Design for Improved Extra-Terrestrial Communications

Abstract: This paper describes a proposed system for improved exo-ionospheric communications. The dynamic magneto-ionic character of the channel is considered, in particular, the multipath situation arising therefrom. An ideal matched filter is found, matched to the multipath structure and the dynamics of the exo-ionospheric channel. The improvement in the signal-to-noise ratio through the matched filter is calculated. It is seen to depend on the quotient of the input signal to the bandwidths of the ``measuring'' filter and the ``integrating'' filter. Further advantages are shown to accrue from signal processing at the transmitter involving both increases in range, and, in particular, secure coding possibilities.

The human controller as an adaptive, low pass filter.

Abstract: Data is presented on the ability of a human controller to track a signal contaminated with noise. Signal frequencies and signal-to-noise ratio are the independent variables. An optimal, adaptive filter is presented for comparison. A descriptive model is derived based on known human characteristics in manual control. Future research needs are discussed.