Estimation and control with censored data
Date
2015
Authors
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Journal ISSN
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Publisher
University of Delaware
Abstract
Censored measurements are a particular form of output nonlinearity in which the measured output is a continuous function of the state within a certain dynamic range, and is constant outside this range. Such measurements can take the form of output saturation, dead zone, occlusion, and limit of detection. Common systems that may produce censored measurements include low cost inertial sensors with limited dynamic range, imagers with fixed field of view, chemical and biological measurements with limit-of-detection constraints, analog to digital converters, and received signal strength from transmission sources. Estimating the true state of the underlying dynamic system via these censored outputs is a challenging problem that is often overlooked or avoided. Traditional optimal state estimators such as the Kalman filter become biased when presented with the output nonlinearity induced by censored measurements. As a consequence, when output feedback is implemented using these estimators the resulting closed-loop system may become unstable if the system output approaches or enters the censored region. The Tobit Kalman filter is a novel adaptation of the classical standard Kalman filter for optimal state estimation in the presence of output censoring. With known cen- soring limits, using a Tobit Kalman filter will result in stable, unbiased state estimation despite censoring. This allows for the application of new and traditional control techniques for system regulation. In this defense new developments of the Tobit Kalman filter and its applications towards control will be reviewed. It will be shown that the Tobit Kalman estimator is a stable unbiased estimator under certain constraints. It will be demonstrated that a Tobit Kalman observer can be used in conjunction with linear output feedback techniques to perform set-point control to values that may not be directly measurable. Applications of such capability towards novel vision based target tracking and mobile receiver localization and control will be explored. Novel estimation techniques in the presence of output censoring will be introduced, including the use of multiple fields of view and variable censoring limits. It will be shown that the Tobit Kalman filter can be used to effectively alter censoring limits in order to meet desired state estimation specifications. Advantages of time varying control of censoring limits include minimization of state estimation uncertainty vs. actuation cost, autonomous tracking of multiple targets, and optimal power consumption for measurement systems. Continuation of this work will be to optimally distribute multiple censoring limits, with seamless integration of differing censoring models, in order minimize state uncertainty over a given region. Optimal control laws will be formulated to alter the trajectory of censoring limits in order to minimize total state uncertainty while tracking multiple states over a given time. Extension to non-linear estimation and control will be performed.