A Combined Stochastic and Greedy Hybrid Estimation Capability for Concurrent Hybrid Models with Autonomous Mode Transitions

Robotic and embedded systems have become increasingly pervasive in applicationsranging from space probes and life support systems to robot assistants. In order to act robustly in the physical world, robotic systems must be able to detect changes in operational mode, such as faults, whose symptoms manifest themselves only in the continuous state. In such systems, the state is observed indirectly, and must therefore be estimated in a robust, memory-efficient manner from noisy observations.Probabilistic hybrid discrete/continuous models, such as Concurrent Probabilistic Hybrid Automata (CPHA) are convenient modeling tools for such systems. In CPHA, the hidden state is represented with discrete and continuous state variables that evolve probabilistically. In this paper, we present a novel method for estimating the hybrid state of CPHA that achieves robustness by balancing greedy and stochastic search. The key insight is that stochastic and greedy search methods, taken together, are often particularly effective in practice.To accomplish this, we first develop an efficient stochastic sampling approach for CPHA based on Rao-Blackwellised Particle Filtering. We then propose a strategy for mixing stochastic and greedy search. The resulting method is able to handle three particularly challenging aspects of real-world systems, namely that they 1) exhibit autonomous mode transitions, 2) consist of a large collection of concurrently operating components, and 3) are non-linear. Autonomous mode transitions, that is, discrete transitions that depend on thecontinuous state, are particularly challenging to address, since they couple the discrete and continuous state evolution tightly. In this paper we extend the class of autonomous mode transitions that can be handled to arbitrary piecewise polynomial transition distributions.We perform an empirical comparison of the greedy and stochastic approaches to hybrid estimation, and then demonstrate the robustness of the mixed method incorporated with our HME (Hybrid Mode Estimation) capability. We show that this robustness comes at only a small performance penalty

State estimation of probabilistic hybrid systems with particle filters

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.Includes bibliographical references (p. 117-123).Robotic and embedded systems have become increasingly pervasive in every-day applications, ranging from space probes and life support systems to autonomous rovers. In order to act robustly in the physical world, robotic systems must handle the uncertainty and partial observability inherent in most real-world situations. A convenient modeling tool for many applications, including fault diagnosis and visual tracking, are probabilistic hybrid models. In probabilistic hybrid models, the hidden state is represented with discrete and continuous state variables that evolve probabilistically. The hidden state is observed indirectly, through noisy observations. A challenge is that real-world systems are non-linear, consist of a large collection of concurrently operating components, and exhibit autonomous mode transitions, that is, discrete state transitions that depend on the continuous dynamics. In this thesis, we introduce an efficient algorithm for hybrid state estimation that combines Rao-Blackwellised particle filtering with a Gaussian representation. Conceptually, our algorithm samples trajectories traced by the discrete variables over time and, for each trajectory, estimates the continuous state with a Kalman Filter. A key insight to handling the autonomous transitions is to reuse the continuous estimates in the importance sampling step. We extended the class of autonomous transitions that can be efficiently handled by Gaussian techniques and provide a detailed empirical evaluation of the algorithm on a dynamical system with four continuous state variables. Our results indicate that our algorithm is substantially more efficient than non-RaoBlackwellised approaches. Though not as good as a k-best filter in nominal scenarios, our algorithm outperforms(cont.) a k-best filter when the correct diagnosis has too low a probability to be included in the leading set of trajectories. Through these accomplishments, the thesis lays ground work for a unifying stochastic search algorithm that shares the benefits of both methods.by Stanislav Funiak.M.Eng

An Extension to the Kalman Filter for an Improved Detection of Unknown Behavior

The use of Kalman filter (KF) interferes with fault detection algorithms based on the residual between estimated and measured variables, since the measured values are used to update the estimates. This feedback results in the estimates being pulled closer to the measured values, influencing the residuals in the process. Here we present a fault detection scheme for systems that are being tracked by a KF. Our approach combines an open-loop prediction over an adaptive window and an information-based measure of the deviation of the Kalman estimate from the prediction to improve fault detection

A Rao-Blackwellized Particle Filter for EigenTracking

©2004 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.Presented at the 2004 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 27 June-2 July 2004, Washington, D.C.DOI: 10.1109/CVPR.2004.1315271Subspace representations have been a popular way to model appearance in computer vision. In Jepson and Black’s influential paper on EigenTracking, they were successfully applied in tracking. For noisy targets, optimization-based algorithms (including EigenTracking) often fail catastrophically after losing track. Particle filters have recently emerged as a robust method for tracking in the presence of multi-modal distributions. To use subspace representations in a particle filter, the number of samples increases exponentially as the state vector includes the subspace coefficients. We introduce an efficient method for using subspace representations in a particle filter by applying Rao-Blackwellization to integrate out the subspace coefficients in the state vector. Fewer samples are needed since part of the posterior over the state vector is analytically calculated. We use probabilistic principal component analysis to obtain analytically tractable integrals. We show experimental results in a scenario in which we track a target in clutter

Group-SMA Algorithm Based Joint Estimation of Train Parameter and State

The braking rate and train arresting operation is important in the train braking performance. It is difficult to obtain the states of the train on time because of the measurement noise and a long calculation time. A type of Group Stochastic M-algorithm (GSMA) based on Rao-Blackwellization Particle Filter (RBPF) algorithm and Stochastic M-algorithm (SMA) is proposed in this paper. Compared with RBPF, GSMA based estimation precisions for the train braking rate and the control accelerations were improved by 78% and 62%, respectively. The calculation time of the GSMA was decreased by 70% compared with SMA

Survey of Bayesian Models for Modelling of Stochastic Temporal Processes

This survey gives an overview of popular generative models used in the modeling of stochastic temporal systems. In particular, this survey is organized into two parts. The first part discusses the discrete-time representations of dynamic Bayesian networks and dynamic relational probabilistic models, while the second part discusses the continuous-time representation of continuous-time Bayesian networks

Developing Prognostic Models Using Duality Principles for DC-to-DC Converters

Within the field of Integrated System Health Management, there is still a lack of technological approaches suitable for the creation of adequate prognostic model for large applications whereby a number of similar or even identical subsystems and components are used. Existing similarity among a number of different systems, which are comprised of similar components but with different topologies, can be employed to assign the prognostics of one system to other systems using an inference engine. In the process of developing prognostics, this approach will thereby save resources and time. This paper presents a radically novel approach for building prognostic models based on system similarity in cases where duality principle in electrical systems is utilized. In this regard, unified damage model is created based on standard Tee/Pi models, prognostics model based on transfer functions, and remaining useful life (RUL) estimator based on how energy relaxation time of system is changed due to degradation. An advantage is that the prognostic model can be generalized such that a new system could be developed on the basis and principles of the prognostic model of other systems. Simple electronic circuits, dc-to-dc converters, are to be used as an experiment to exemplify the potential success of the proposed technique validated with prognostics models from particle filter

Bayesian Condition Monitoring in Neonatal Intensive Care

Institute for Adaptive and Neural ComputationThe observed physiological dynamics of an infant receiving intensive care contain a great deal of information about factors which cannot be examined directly, including the state of health of the infant and the operation of the monitoring equipment. This type of data tends to contain both common, recognisable patterns (e.g. as caused by certain clinical operations or artifacts) and some which are rare and harder to interpret. The problem of identifying the presence of these patterns using prior knowledge is clinically significant, and one which is naturally described in terms of statistical machine learning. In this thesis I develop probabilistic dynamical models which are capable of making useful inferences from neonatal intensive care unit monitoring data. The Factorial Switching Kalman Filter (FSKF) in particular is adopted as a suitable framework for monitoring the condition of an infant. The main contributions are as follows: (1) the application of the FSKF for inferring common factors in physiological monitoring data, which includes finding parameterisations of linear dynamical models to represent common physiological and artifactual conditions, and adapting parameter estimation and inference techniques for the purpose; (2) the formulation of a model for novel physiological dynamics, used to infer the times in which something is happening which is not described by any of the known patterns. EM updates are derived for the latter model in order to estimate parameters. Experimental results are given which show the developed methods to be effective on genuine monitoring data