Bayesian State Estimation in Sensorimotor Systems With Particle Filtering

A robust Cubature Kalman filter for nonlinear systems subject to randomly occurring measurement anomalies without a priori statistic

In this work, we investigate the problem of state estimation for a class of nonlinear systems subjected to randomly occurring measurement anomalies (ROMAs) without a priori statistic. To address the problem, first, a novel measurement model is constructed, in which the anomalous measurements and anomaly probability are modeled as Gaussian mixture distribution (GMD) and Beta distribution, respectively. Different from the existing researches assuming that the statistical information of anomalous measurements is known in advance, the model does not require a priori statistical knowledge of anomalous measurements. Moreover, by adaptive learning of the anomaly probability, the measurement model is identical with the classical cubature Kalman filter (CKF) in the absence of measurement anomalies. Then, the variational Bayesian inference (VBI) is employed to approximately calculate the joint posterior distribution of the system state and unknown parameters, and a robust filter is derived. Finally, the effectiveness of our filter is demonstrated by the numerical simulation.

Towards a cross-level understanding of Bayesian inference in the brain

Perception emerges from unconscious probabilistic inference, which guides behaviour in our ubiquitously uncertain environment. Bayesian decision theory is a prominent computational model that describes how people make rational decisions using noisy and ambiguous sensory observations. However, critical questions have been raised about the validity of the Bayesian framework in explaining the mental process of inference. Firstly, some natural behaviours deviate from Bayesian optimum. Secondly, the neural mechanisms that support Bayesian computations in the brain are yet to be understood. Taking Marr's cross level approach, we review the recent progress made in addressing these challenges. We first review studies that combined behavioural paradigms and modelling approaches to explain both optimal and suboptimal behaviours. Next, we evaluate the theoretical advances and the current evidence for ecologically feasible algorithms and neural implementations in the brain, which may enable probabilistic inference. We argue that this cross-level approach is necessary for the worthwhile pursuit to uncover mechanistic accounts of human behaviour.