Neural networks can be viewed as nonlinear models, where the weights are parameters to be estimated. In general two parameter estimation methods are used: nonlinear regression, corresponding to the standard backpropagation algorithm, and Bayesian estimation, in which the model parameters are considered as being random variables drawn from a prior distribution, which is updated based on the obse...

By combining strong tracking filter theory with state fusion estimation algorithm, we put forward a new algorithm of state fusion estimation for a class of nonlinear dynamic systems with all sensors having different sampling rates on the basis of distributed information. The algorithm is also extended to the joint state and parameter estimation of a class of nonlinear systems having time-varyin...

Recursive estimation of constrained nonlinear dynamical systems has attracted the attention of many researchers in recent years. For nonlinear/non-Gaussian state estimation problems, particle filters have been widely used. As pointed out by Daum (2005), particle filters require a proposal distribution and the choice of proposal distribution is the key design issue. In this paper, a novel approa...

An innovation model is derived for a nonlinear stochastic system described by a state variable representation. The problem of state and system parameter estimation is solved through identification of the innovation model. A recursive prediction error (RPE) algorithm is derived for the joint system parameter and state estimation through minimization of the innovation variance (MIV). The algorith...

Reverse correlation techniques have been extensively used in physiology (Marmarelis & Marmarelis 1978; Sakai, Naka, & Korenberg, 1988), allowing characterization of both linear and nonlinear aspects of neuronal processing (e.g., Emerson, Bergen, & Adelson, 1992; Emerson & Citron 1992). Over the past decades, Ahumada (1996) developed a psychophysical reverse correlation technique, termed noise i...

This paper is concerned with the parameter estimation of a relatively general class of nonlinear dynamic systems. A Maximum Likelihood (ML) framework is employed in the interests of statistical efficiency, and it is illustrated how an Expectation Maximisation (EM) algorithm may be used to compute these ML estimates. An essential ingredient is the employment of so-called “particle smoothing” met...

We propose a new estimation procedure for covariate adjusted nonlinear regression models for situations where both the predictors and response in a nonlinear regression model are not directly observed, however distorted versions of the predictors and response are observed. The distorted versions are assumed to be contaminated with a multiplicative factor that is determined by the value of an un...

Methods are developed and analyzed for estimating the distance to a local minimizer of a nonlinear programming problem. One estimate, based on the solution of a constrained convex quadratic program, can be used when strict complementary slackness and the second-order sufficient optimality conditions hold. A second estimate, based on the solution of an unconstrained nonconvex, nonsmooth optimiza...

Based on the techniques of high gain observer and adaptive estimation, an algorithm is proposed in this paper for sensor fault estimation in nonlinear systems. It is essentially assumed that a high gain observer exists for the fault-free system. A high gain adaptive observer is then designed for sensor fault estimation. The convergence of the algorithm is established under a persistent excitati...

Estimation on a noisy signal observed by a nonlinear sensor taking the form of a threshold quantizer is considered. The optimal Bayesian estimator with minimal error is derived in this nonlinear setting. The existence of conditions where the performance of this estimator can be improved by raising the level of noise is established, both theoretically and numerically. These results constitute a ...