Suboptimal Smoothers Research Articles

Application of Unscented Transformation for Nonlinear State Smoothing

AbstractMotivated by the well-known fact that the state estimate of a smoother is more accurate than that of the corresponding filter, this paper is concerned with the state smoothing problem for a class of nonlinear stochastic discrete systems. Firstly, a novel type of optimal smoother, which provides a unified theoretical framework for the solution of state smoothing problem no matter that system is linear or nonlinear, is derived on the basis of minimum mean squared error (MMSE) estimation theory. Further, in the case that the dynamic model and measurement functions are all nonlinear, a new suboptimal smoother is developed by applying the unscented transformation for approximately computing the smoothing gain in the optimal smoothing framework. Finally, the superior performance of the proposed smoother to the existing extended Kalman smoother (EKS) is demonstrated through a simulation example.

Locally monotonic regression

The concept of local monotonicity appears in the study of the set of root signals of the median filter and provides a measure of the smoothness of the signal. The median filter is a suboptimal smoother under this measure of smoothness, since a filter pass does necessarily yield a locally monotonic output; even if a locally monotonic output does result, there is no guarantee that it will possess other desirable properties such as optimal similarity to the original signal. Locally monotonic regression is a technique for the optimal smoothing of finite-length discrete real signals under such a criterion. A theoretical framework in which the existence of locally monotonic regression is proved and algorithms for their computation are given. Regression is considered as an approximation problem in R/sub n/, the criterion of approximation is derived from a semimetric, and the approximating set is the collection of signals sharing the property of being locally monotonic.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Applying a smoothing criterion to the Kalman filter

A performance measure is suggested for evaluating the performance of a given optimal estimator at other lags than the design lag. Applying this idea, suboptimal smoothers are found for both continuous-and discrete-time systems, combining low complexity and good performance. Several examples are considered. Suboptimal-smoothing improvement is related to optimal improvement and interpreted in terms of input-output transfer-function properties. A special class of discrete-time systems is also discussed where the optimal smoother is of the same complexity as the zero-lag filter.

Smoothing properties of discrete-time zero-lag Kalman filter

In this paper it is shown than an estimate generated in a discrete time Kalman filter can, under certain circumstances, give better performance if some delay is allowed in the system. This fact is utilized to construct three simple suboptimal smoothers, all based on the structure of a Kalman filter. These smoothers are of low complexity as compared with the optimal ones. The conditions are given under which the performance of these suboptimal smoothers is better than that of a zero-lag Kalman filter. The methods of suboptimal smoothing considered give, in many cases, a possibility of obtaining results close to the optimal smoother. Several examples are presented.

A Model of the Human as a Suboptimal Smoother

Estimation theory is used to develop a model of a human decision maker in a self-paced, visual data smoothing task. The model is basically a noisy fixed-point smoother combined with a weighting function that discounts data in relation to its distance (in time) from the point being smoothed. Experimental data is used to estimate the parameters of the model. Applications of the model to the design of information displays and man-computer interactive decision making systems are considered.

Stable fixed-lag smoothing of continuous time processes

Attempts to realize optimal fixed-lag smoothers for continuous-time processes have encountered two major difficulties: the presence of delay lines in the smoother, and the instability of most smoothers. This paper considers suboptimal smoothers which still outperform filters and have performance very close to the optimum. Design procedures are exhibited for smoothers that are both finite-dimensional and asymptotically stable, with the procedures depending on the delay line being approximated by a finite-dimensional dynamical system.

Outline designs for stable continuous-time fixed-lag smoothers

Three basic methods for constructing suboptimal continuous-time linear fixed-lag smoothers are described. In contrast to the optimal smoother, all the suboptimal smoothers are stable. The degree of complexity allowed in the suboptimal smoothers determines how closely they perform to the limit obtainable from the theoretical optimal linear fixed-lag smoother.