Showing papers on "Maximum a posteriori estimation published in 1968"

An upper bound on average estimation error in nonlinear systems

Abstract: An upper bound is obtained on the probability density of the estimate of the parameter m when a nonlinear function s(t, m) is transmitted over a channel that adds Gaussian noise, and maximum likelihood or maximum a posteriori estimation is used. If this bound is integrated with a loss function, an upper bound on the average error is obtained. Nonlinear (below threshold) effects are included. The problem is viewed in a Euclidean space. Evaluation of the probability density can be reduced to integrating the probability density of the observation over part of a hyperplane. By bounding the integrand, and using a larger part of the hyperplane, an upper bound is obtained. The resulting bound on mean-square error is quite close for the cases calculated.

Estimation of linear weighting functions in Gaussian noise

Abstract: The measurement of linear time-varying systems and the mapping of densely distributed radar targets provide the motivation for the problem of estimation of linear multidimensional weighting functions in Gaussian noise. The assumption that the weighting function to be estimated is a sample of a Gaussian process of known autocorrelation function, and the adoption of either a maximum a posteriori probability or a minimum mean-square error criterion for the excellence of the estimate reduces the estimation problem to that of the solution of a Fredholm equation, the kernel of which is a generalization of Woodward's ambiguity function. A unique solution is assured if the statistics involved have sufficiently short correlation intervals. Closed-form solutions to the Fredholm equation, in particular two-dimensional cases of time- and frequency-shifted signals, are obtained over infinite domains of the weighting function by using Fourier and Wiener-Hopf techniques, and over finite domains by solving the eigenvalue problem of the ambiguity function. Generally speaking, the estimation error decreases with the decrease in the domain area; within a domain of unit area, perfect reproduction can be approached by increasing the SNR, in agreement with previous resuits on strictly noiseless measurement of linear systems. The appropriate "optimum" signal processor performs on the received signal a linear operation that is, essentially, an "inversion" of the eigenvalue spectrum of the ambiguity function; the extent of inversion is,limited:by its accentuation of the additive noise of the interference from neighboring areas of the domain. Only under extreme circumstances of constant eigenvalue spectra or of vanishing signal-to-noise ratios is the optimum processor equivalent to a "matched filter." The performances of the optimum processor and of the matched filter are compared in several examples.

Optimum Realizable Continuous Range Estimation

Abstract: The ability to detect the presence or absence of a target is no longer the fundamental design criterion when the vehicle to be tracked is cooperative. In spacecraft tracking or navigation systems, for example, emphasis is placed on post-acquisition performance. Therefore, classical radar theory and design techniques are not specifically applicable. On the other hand, there are optimization techniques for extracting the tracking data from noise that are more to the point. In particular, optimum demodulation theory is directed specifically to the problem of continuously extracting data from a nonlinear modulation process. In this paper, the tracking properties of a multitone PM ranging signal are reviewed and are shown to be nearly optimum for cooperative vehicles. An optimum, but nonrealizable, maximum a posteriori (MAP) continuous estimator of range is derived for this signal. The linearized model of this receiver is the optimum nonrealizable Wiener filter for the data. Interpretation of this optimum nonrealizable estimator leads to a receiver design that is both practical and intuitively satisfying. With the aid of post-detection processing in the Wiener-Hopf sense, almost optimum performance is obtained from the resulting receiver, above threshold.

On the maximum likelihood estimation of rational pulse transfer-function parameters

Abstract: Thus The prediction error at anfinstant k is E(R) = 3t(k + 1)-~ (k 4-1) or E(2) = B(z)X(z)-Z X (Z) =-e-X(2) =-sY(2)