Distortion correction of NOAA image by statistical method

Remote sensing technique by satellite has been well-developed in recent years. In this paper two kinds of statistical correction methods are proposed to clarify observation data by NOAA with atmospheric scattering. The first method is the deletion of the path radiance effect by the least squares method. The second uses a smoothing filter. These methods are applied to the original remote sensing data collected on 26 July 1987.     

Distributed parameter identification by regularization and its application to prediction of air pollution

An identification algorithm is considered for unknown spatially varying diffusivities in the diffusion equation by using the regularization method. The diffusion equation is expressed by a parabolic partial differential equation and the identification for the system possesses ill-posedness. To solve this problem we use the regularization method which was proposed by Kravaris (1984) and Kravaris and Seinfeld (1985). The diffusivities for air pollution problems are identified under the assumption that the diffusivities are affected by the wind velocity, Using this algorithm, the NO, concentrations caused by motor vehicles near a roadway in Tokushima, Japan are estimated.     

The optimal smoothing estimators based on the Wiener-Hopf theory

It is well known that the Wiener-Hopf theory plays a fundamental role in estimation problems. In this paper, we derive the basic equations for the optimal smoothing estimators by using the Wiener-Hopf theory. The interrelation between the Wiener-Hopf theory and the innovation theory is also considered. Finally based on the basic equations three kinds of the smoothing estimators, that is, the fixed-point, fixed-interval, and fixed-lag smoothing estimators are derived.     

Temperature control of a water bath by self-tuning PI controller

Although there have been several reports of various self-tuning proportional-plus-integral (STPI) schemes and proportional-plus-integral-plus-derivative (STPID) schemes for controllers in recent years, their theory and practice are still immature. The capabilities of this type of controller to control real physical processes need to be proven in more detail. In this light, the paper presents an application of an STPI controller proposed by Cameron and Seborg (1983) to a microcomputer-controlled water bath system. The water bath is an example of an important component in many industrial chemical processes. Experiments are conducted to test the STPI controller and to compare its performance with two other controllers, namely a self-tuning controller (STC) due to Clarke and Gawthrop (1975, 1979) and a conventional PI controller. The reliability of the STPI controller is tested by artificially adding load disturbances, simulating a change in the process dynamics, and artificially adding a variable delay element in the control loop of the process. The results prove that the performance of the STPI controller is as good as a self-tuning controller with the added advantage of having a PI-like structure. Moreover, the STPI controller performs better than the conventional PI controller, especially when there are changes in the process dynamics.     

Fixed-interval smoothing for a linear distributed parameter system

The fixed-interval smoothing estimator for a linear distributed parameter system with a noisy observation at discrete points on the spatial domain or its boundary is derived from the Wiener-Hopf theoretical viewpoint. The present derivation of the smoothing estimator is based on the Wiener-Hopf theory. Thus, using the Wiener-Hopf equations both for the optimal smoothing problem and for the optimal filtering problem, the optimal fixed-interval smoothing estimator which corresponds to the results obtained by using Kalman's limiting procedure is derived. Finally, for the convenience of the numerical computation, we rewrite the results for the optimal fixed-interval smoothing estimator and the error covariance function by using the Fourier expansion method.     

The optimal filtering problem for a discrete-time distributed parameter system

In this paper, the optimal filtering problem for a discrete-time linear distributed parameter system is considered. Using the least squares estimation error criterion, the Wiener-Hopf equation for the discrete-time distributed parameter system is derived. Based on the Wiener-Hopf equation, the equations satisfied by the optimal filtering estimate and the minimum error covariance matrix function are derived by using the matrix inversion lemma for a distributed parameter system. Finally, we show that the approximation of the results obtained for a distributed parameter system by using the Fourier expansion method produces those of the Kalman filtering problem for the lumped parameter system.     

Comparison of the approximate solutions of a noisy non-linear system based on Monte Carlo simulation

This paper is concerned with the comparison of the approximate methods in order to evaluate the values of state variables of a noisy nonlinear system by Monte Carlo simulation. The approximate methods considered here are (1) the stochastic linearisation, (2) the first-order approximation and (3) the second-order approximation. It is shown that the order of the accuracies of the covariance based on the approximate equation of Riccati type does not always coincide with the order of the practical error covariance of the original system which is obtained by using Monte Carlo simulation. Therefore the comparison of the accuracies should not be carried out by the solution obtained from the covariance equation but by the practical error covariance of the original system directly. This result is demonstrated with numerical examples. The characteristics of the random numbers which are used for Monte Carlo simulation are examined by various kinds of tests.     

Optimal estimators for time-averaged measurement systems

The optimal linear prediction estimator and filter are derived for dynamic systems with time-averaged measurements using the Wiener-Hopf theory. The estimates are compared with other optimal estimators for various measurement systems.     

A design method for a self-tuning regulator for a distributed-parameter system

A design method for a self-tuning regulator for a distributed-parameter system is presented. This system is assumed to have some actuators fixed in the spatial domain. The power of each actuator is estimated by a least-squares algorithm. Some numerical examples are given.