Takashi Soeda

Optimal sensor location problem for a linear distributed parameter system

This paper studies an optimal sensor location problem for a linear distributed parameter system. It is assumed that a criterion for the optimal sensor location is to minimize the trace of the optimal filtering error covariance function. The existence and uniqueness theorem concerning a solution of the optimal filtering error covariance function for the pointwise observation case is considered. Then by using the existence and uniqueness theorem, the comparison theorem for the partial differential equations of Riccati type is proved. By using the theorems obtained here, the existence theorem concerning a solution of the optimal sensor location problem is proved and the necessary and sufficient conditions for optimality are derived. Finally, some numerical examples for the optimal sensor location problem are illustrated.

A sequential failure detection approach and the identification of failure parameters

This paper is concerned with the problem of a failure diagnosis for a discrete-time system with parametric failure, in which the occurrence time and mode of parametric failure cannot be estimated in advance. The failure diagnosis system which is proposed consists of three parts : (i) a normal mode filter, (ii) a detector for anomaly states, and (iii) an adaptive extended Kalman filter. The normal mode filter is called the optimal Kalman filter and transports the information of its innovation sequence to the detector. The detector which is based on the SPRT approach detects anomaly states affected by the parametric failure. The adaptive extended Kalman filter estimates simultaneously system parameters and the states under the failure mode. The adaptive procedure is directed by increasing the calculated covariance on the basis of hypothesis tests for the estimation errors of unknown parameters. Numerical results for a simple plant model illustrate the effectiveness of the proposed failure diagnosis system.

An application of the information theory to estimation problems

The purpose of this paper is to study estimation problems from the viewpoint of the information theory. It is proved that the necessary and sufficient condition for maximizing the mutual information between a state and the estimate is to minimize the entropy of the estimation error. Based on this relation between the mutual information and the error entropy, the Kalman filter for a discrete-time linear system is derived by an application of the information theory. Furthermore, the optimal filter for a continuous-time linear system is also constructed by an analogous approach.

Estimation of nitrogen dioxide concentrations in the vicinity of a roadway by optimal filtering theory

Abstract Distributed filtering theory and maximum likelihood estimation are applied to the joint estimation of atmospheric diffusion parameters and of nitrogen dioxide (NO 2 ) concentration levels in the vicinity of a heavily travelled roadway in Tokushima, Japan. An optimal estimator for the air pollution problem is derived in the case of time-averaged and pointwise observations. Based on the NO 2 measurement data in the study area, traffic volumes and weather conditions, an algorithm is developed that can be used in conjunction with urban air pollution models to estimate the spatial and temporal distribution of airborne NO 2 levels.

An application of the information theory to filtering problems

Abstract The purpose of this paper is to study the filtering problems from the viewpoint of the information theory. For a linear system it is proved that the necessary and sufficient condition for maximizing the mutual information between a state and the estimate is to minimize the entropy of the estimation error. Then we derive the Kalman-Bucy filter for both the discrete-time and the continuous-time systems by an application of the information theory. Furthermore, the approach is extended to the nonlinear dynamical systems with noisy observations and then the information structures of the optimal filter for a continuous-time nonlinear system are made clear, which has been presented as the interesting open problems by Bucy.

Technical communique: A modified extended Kalman filter for linear discrete-time systems with unknown parameters

This technical communique presents a modified extended Kalman filter for estimating the states and unknown parameters in discrete-time, multi-input multi-output linear systems. The hyperstability of the filter is guaranteed by introducing a compensator into the estimation mechanism. It is proved that the estimates for the states and unknown parameters converge to the exact values if some conditions are assumed to the estimation mechanism. A numerical example shows that the proposed filter is much more effective than the extended Kalman filter in the estimation of unknown parameters.

Optimal filtering for discrete-time nonlinear systems

This correspondence is concerned with estimating a state variable for a discrete-time nonlinear system in the presence of random disturbance and measurement noise. A Bayesian approach is adopted in which the state conditioned upon the available measurement data is computed recursively. The new feature of the present method is that the stochastic differential rules can be applied for deriving the optimal nonlinear filter for a discrete-time system described by difference equations. Based on this estimator, the Kalman-Bucy filter and the Kushner filter are derived by the appropriate procedures.

Optimal non-linear estimation for distributed-parameter systems via the partition theorem

Abstract This paper considers the estimation problem for non-linear distributed-parameter systems via the ‘Partition Theorem’. First, the a posterioriprobability for the state is derived for the estimation of non-linear distributed-parameter systems. Secondly, linear systems excited by a white gaussian noise and with non-gaussian initial state are considered as a special class of the problem. The a posterioriprobability for the state, the optimal estimates and corresponding error covariance matrices are obtained by using the properties of the fundamental solution for the differential operator. Finally, it is shown that on approximate expression for the solution of the problem is also derived by applying a gaussian sum approximation technique.

A method of predicting failure or life for stochastic systems by using autoregressive models

This paper discusses on-line detection and prediction problems of the failure or life of stochastic systems by using autoregression (AR) models. We regard the change of the equipment from an ordinary state to failure as a variation of the characteristics of a time aeries signal. An AR model is fitted to the time aeries signal and the change is detected by variations of the model. Using four types of performance index of the variations, we detect the failure of a cutting tool of a lathe and predict the width of flank wear.

Fixed-point smoothing in Hilbert spaces

The fixed-point smoothing estimator and smoothing error covariance operator equations are derived for infinite-dimensional linear systems using both the Wiener-Hoph theory in Hilbert spaces developed by Falb and the abstract evolution theory. Since it is clear that the prediction problems can be solved by the same approach, the present results in conjunction with the work of Falb on filtering give a complete treatment of the infinite-dimensional linear estimation problem from the viewpoint of Wiener-Hoph theory. Finally, based on the optimal smoothing estimator in Hilbert space, the fixed-point smoothing estimator is derived for a linear distributed parameter system of parabolic type.