Showing papers on "Kernel adaptive filter published in 1969"
TL;DR: The single stage iteration filter has superior mean squared error performance under all conditions, followed by the second-order filter, which appears to be more of an unbiased estimator than the other filters.
146 citations
TL;DR: The purpose of this paper is to determine the linear optimal filtering algorithm for a message generated by noisy observations of a linear dynamic system with state-dependent, stochastic disturbances and shows that one approximation reduces to thelinear optimal filter.
Abstract: The purpose of this paper is to determine the linear optimal filtering algorithm for a message generated by noisy observations of a linear dynamic system with state-dependent, stochastic disturbances. These disturbances can be considered as stochastic parameter variations. As a consequence of the state-dependent noiso the message process is non-Gaussian. Hence the filter obtained by solving the Wiener-Hopf equation is only the optimal linear operation on the data. The optimal filter is non-linear. Unfortunately the dynamical equations for optimal nonlinear filtering can only be solved approximately. We show that one approximation reduces to the linear optimal filter. As an application we determine the linear optimal filter for a second-order system. This example provides us with a comparison of the performance of the linear optimal filter with a filter designed neglecting the presence of the state-dependent disturbances.
47 citations
TL;DR: In this article, a simple algorithm for nonlinear filtering of a time series composed of a gaussian component, pulses and steps is presented, where the main advantage is a scheme for adaptation of the filter parameters.
Abstract: A simple algorithm is presented for nonlinear filtering of a time series composed of a gaussian component, pulses and steps. The method used is a combination of simple statistical techniques. The main advantage is claimed to be a scheme for adaptation of the filter parameters.
6 citations
3 citations
TL;DR: This paper proposes a method for synthesizing digital filters in the time domain based on the assumption that the pulsed transfer function of the digital filter is a ratio of two rational polynomials.
Abstract: In designing digital systems, one often faces the task of replacing a given analog filter by an equivalent digital filter. This paper proposes a method for synthesizing such digital filters in the time domain. It is assumed that the pulsed transfer function of the digital filter is a ratio of two rational polynomials. The coefficients are then determined by least-square fitting the digital filter to the analog filter's sampled input and output data. The resulting equations for computing the coefficients are linear. It is shown that the digital filter is essentially related to the analog filter, the sampling time, and the power spectrum of the signal being processed. If the signal is band-limited and the sampling frequency is sufficiently high, the digital filter can then be simply approximated by the Z transform of the analog filter multiplied by the sampling period.
1 citations
TL;DR: In this paper, an integral formula is given which enables the unique determination of the pulse-transfer function (p.t.f.) of a linear-time-invariant (l.i.) digital filter from its real or imaginary part defined on the unit circle in the z−1 plane.
Abstract: An integral formula is given which enables the unique determination of the pulse-transfer function (p.t.f.) of a linear-time-invariant (l.t.i.) digital filter from its real or imaginary part defined on the unit circle in the z−1 plane.