Nonlinear Filtering Method Research Articles

A Nonlinear Filter for Estimation of States of a Continuous-Time System with Discrete Measurements

A method is presented for estimating the states of a nonlinear system for which the state process is described by a stochastic differential equation and the measurements by a stochastic difference equation. The estimates are obtained from the condition of minimization of the mean-square error criterion. The estimator equations are differential and difference equations which are specified by so-called preassignable structural functions [1]. The method provides theoretical solution to the nonlinear filtering problem for continuous system with discrete measurements (CSDM). The computations of optimal gains can be carried out before the availability of observations. The subsequent processing of observations for estimation of states is considerably simpler by the present method than other nonlinear filtering methods. As a special case continuous discrete Kalman Filter for a linear system is derived.

An extension of the Beneš filter and some identification problems solved by nonlinear filtering methods

An extension of Benneš' filtering theorem to time dependent, parameter dependent and unknown initial conditions filtering problems is proved. A new approach for the identification of linear diffusions with unknown drift coefficients follows. New finite dimensional filters, which may also be regarded as identification filters, are derived and related to W.S. Wong's earlier work which used algebraic methods.

Conditionally optimal estimation in stochastic differential systems

The theory of conditionally optimal estimation of the state and parameters and of conditionally optimal extrapolation of the state of a stochastic system described by differential equations is given. Previous results obtained by the author follow from this theory as special cases. Classes of admissible estimates in this new theory are constructed in such a way that any specific estimate defined as a result of some linear transform of the solution of a stochastic differential equation can be enclosed in the respective class of admissible estimates and compared with the conditionally optimal estimate in this class. This enables one to study the accuracy of any such estimate, in particular the accuracy of any known approximate method of nonlinear filtering, and to improve the accuracy without any complications by optimizing the coefficients in the respective differential equation. As a special case the filtering and prediction theory is developed for linear systems with white noises in the coefficients.

A sequential method for nonlinear filtering: Numerical implementation and comparisons

Exact equations are presented for sequentially updating the optimal solution for a discrete-time analog of the basic Sridhar nonlinear filtering problem as the process length increases and new observations are obtained. A tabular method is described for implementing numerically the sequential filtering equations. The accuracy and efficiency of the tabular method are illustrated by means of several numerical examples.

Digital image processing applied to scintillation images from biomedical systems.

Several nonlinear filtering methods have been developed for two-dimensional image signals obtained from an Anger Scintillation camera. The first method termed "pruning" is implemented in the frequency domain and filters out certain components of the two-dimensional amplitude spectrum. The other methods called "E-filtering" and "P-filtering" utilize a nonlinear transformation of the spatial coordinates which is proportional to the two-dimensional signal amplitude and energy spectrum, respectively. These nonlinear filtering techniques have been applied to phantom scintigrams as well as brain and heart scans of normal and abnormal patients. In addition, the detection of boundaries using the hexagonal Golay transform on filtered and unfiltered images is included. Finally, these filtering and edge detection techniques were for the first time applied to a new technique for the detection of acute myocardial infarcts.

System Identification of Frames under Seismic Loads

In this paper system identification algorithms are employed to construct appropriate nonlinear models of real structures, undergoing seismic disturbances. A three-story half-scale steel frame of the moment resisting type is modeled as a “shear” frame. The data for this frame were obtained from the Earthquake Engineering Research Center of the University of California. The restoring forces in this model are assumed to be of the viscous differential type, containing four unknown parameters. The solution of the problem, that is, the identification of state parameters, is sought by nonlinear filtering methods. The invariant imbedding filter is presented as a special case of a novel dynamic programming filter. In a purely experimental fashion, it is shown that the adopted model is identifiable and stable by utlizing simulated and real data. Abundant numerical experiments are performed; some of the results are presented. By adding corrective nonlinear terms to the basic linear model, the predictive ability of the model is demonstrated.