Recursive Bayesian estimation

Abstract: Recursive model selection can be addressed within the Bayesian framework, the multiple model algorithm being one such approach for linear Gaussian systems. The recent advances in nonlinear non-Gaussian estimation with the sequential Monte Carlo algorithms, such as the particle filter, allow the application of Bayesian inference to the development of recursive model selection algorithms for general nonlinear non-Gaussian systems. Such an algorithm is developed in this paper and applied to a linear autoregressive and nonlinear autoregressive systems.

Abstract: Nuclear facilities require wide-area surveys and remote response to the detection of abnormal radiation levels. These typically require a large number of measurement locations using fixed search patterns. Such approaches are time-consuming, require extended radiation exposure, and are difficult to routinely replicate by technicians. This paper presents an automated method of detecting and locating single or multiple small gamma-ray sources in an unstructured environment, requiring significantly fewer measurements than traditional methods and without a need for post-processing. A mobile robot can collect higher-precision data than practically possible by a human and removes the technician from the radiation area. This is enabled by addressing complexities that previously made automation difficult including supervisory control, obstacle avoidance, sensor positioning over a large height range, recognizing environmental complexities (shielding, etc and modifying survey parameters based on aberrant readings. The developed solution uses a mobile platform with a height-adjustable (up to 2.44 meters) radiation detector. Recursive Bayesian Estimation (RBE) is used to update a probability distribution of the location and intensity of source(s) after each measurement. The likelihood function is determined using radiation transport and detector models. Isotopic identification via a gamma library search aids data analysis by distinguishing counts from different sources. Computation considerations are discussed including predicting and localizing multiple sources.

Abstract: This paper presents theoretical and experimental results for the estimation of large position and orientation inaccuracies during force-controlled compliant motion. This is a significant improvement over previous results. The estimation is based on position, velocity and force measurements. For large position and orientation inaccuracies, the non-linear estimation problem is not satisfactorily solved by existing Kalman filters. Therefore, a new Bayesian estimator is derived. The filter is derived independently of our application and is valid for static systems (parameter estimation) with any kind of non-linear measurement equation subject to Gaussian measurement uncertainty and for a limited class of dynamic systems. Experimental results for the estimation of the inaccurately known positions and orientations of contacting objects during autonomous compliant motion are presented.

Abstract: Hidden Markov models (HMM) are a powerful tool in signal modelling. In an HMM, the probability that signal leaves a state is constant, and hence the duration that signal stays in each state has an exponential distribution. However, this exponential density is not appropriate for a large class of physical signals. Hence, a more sophisticated model, called hidden semiMarkov models (HSMM), are used where the state durations are modelled in some form. This paper presents new signal model for hidden semiMarkov models. This model is based on state duration dependant transition probabilities, where the state duration densities are modelled with parametric distribution functions. An adaptive algorithm for online identification of HSMMs based on our signal model is presented. This algorithm is based on the 'recursive prediction error' technique, where the parameter estimates are updated adaptively in a direction that maximizes the likelihood of parameter estimates. From the numerical results it is shown that the proposed algorithms can successfully estimate the true value of parameters. These results also show that our algorithm can adaptively track the parameter's changes in time.