An auxiliary particle filtering algorithm with inequality constraints

For nonlinear non-Gaussian stochastic dynamic systems with inequality state constraints, this paper presents an efficient particle filtering algorithm, constrained auxiliary particle filtering algorithm. To deal with the state constraints, the proposed algorithm probabilistically selects particles such that those particles far away from the feasible area are less likely to propagate into the next time step. To improve on the sampling efficiency in the presence of inequality constraints, it uses a highly effective method to perform a series of constrained optimization so that the importance distributions are constructed efficiently based on the state constraints. The caused approximation errors are corrected using the importance sampling method. This ensures that the obtained particles constitute a representative sample of the true posterior distribution. A simulation study on vehicle tracking is used to illustrate the proposed approach

New multiple target tracking strategy using domain knowledge and optimisation

This paper proposes an environment-dependent vehicle dynamic modeling approach considering interactions between the noisy control input of a dynamic model and the environment in order to make best use of domain knowledge. Based on this modeling, a new domain knowledge-aided moving horizon estimation (DMHE) method is proposed for ground moving target tracking. The proposed method incorporates different types of domain knowledge in the estimation process considering both environmental physical constraints and interaction behaviors between targets and the environment. Furthermore, in order to deal with a data association ambiguity problem of multiple-target tracking in a cluttered environment, the DMHE is combined with a multiple-hypothesis tracking structure. Numerical simulation results show that the proposed DMHE-based method and its extension could achieve better performance than traditional tracking methods which utilize no domain knowledge or simple physical constraint information only

Particle filtering with soft state constraints for target tracking

In practice, additional knowledge about the target to be tracked, other than its fundamental dynamics, can often be modelled as a set of soft constraints and utilised in a filtering process to improve the tracking performance. This paper develops a general approach to the modelling of soft inequality constraints, and investigates particle filtering with soft state constraints for target tracking. We develop two particle filtering algorithms with soft inequality constraints, i.e. a sequential-importanceresampling particle filter and an auxiliary sampling mechanism. The latter probabilistically selects the candidate particles from the soft inequality constraints of the state variables so that they are more likely to comply with the soft constraints. The performances of the proposed algorithms are evaluated using Monte Carlo simulations in a target tracking scenario

Particle filtering for EEG source localization and constrained state spaces

Particle Filters (PFs) have a unique ability to perform asymptotically optimal estimation for non-linear and non-Gaussian state-space models. However, the numerical nature of PFs cause them to have major weakness in two important areas: (1) handling constraints on the state, and (2) dealing with high-dimensional states. In the first area, handling constraints within the PF framework is crucial in dynamical systems, which are often required to satisfy constraints that arise from basic physical laws or other considerations. The current trend in constrained particle filtering is to enforce the constraints on all particles of the PF. We show that this approach leads to more stringent conditions on the posterior density that can cause incorrect state estimates. We subsequently describe a novel algorithm that restricts the mean estimate without restricting the posterior pdf, thus providing a more accurate state estimate. In the second area, we tackle the curse of dimensionality, which causes the PF to require an exponential increase in computational complexity as the dimension of the state increases. The application of interest is localization of the brain neural generators that create the Electroencephalogram (EEG) signal. Specifically, we describe a state-space model that tracks the position and moments of multiple dynamic dipoles and apply the marginalized PF, which alleviates the curse of dimensionality for tracking multiple dynamic dipoles. This modified framework allows us to consider dynamic dipoles, which were historically considered time-invariant

Clustering for filtering: multi-object detection and estimation using multiple/massive sensors

Advanced multi-sensor systems are expected to combat the challenges that arise in object recognition and state estimation in harsh environments with poor or even no prior information, while bringing new challenges mainly related to data fusion and computational burden. Unlike the prevailing Markov-Bayes framework that is the basis of a large variety of stochastic filters and the approximate, we propose a clustering-based methodology for multi-sensor multi-object detection and estimation (MODE), named clustering for filtering (C4F), which abandons unrealistic assumptions with respect to the objects, background and sensors. Rather, based on cluster analysis of the input multi-sensor data, the C4F approach needs no prior knowledge about the latent objects (whether quantity or dynamics), can handle time-varying uncertainties regarding the background and sensors such as noises, clutter and misdetection, and does so computationally fast. This offers an inherently robust and computationally efficient alternative to conventional Markov–Bayes filters for dealing with the scenario with little prior knowledge but rich observation data. Simulations based on representative scenarios of both complete and little prior information have demonstrated the superiority of our C4F approach

Belief Space Scheduling

This thesis develops the belief space scheduling framework for scheduling under uncertainty in Stochastic Collection and Replenishment (SCAR) scenarios. SCAR scenarios involve the transportation of a resource such as fuel to agents operating in the field. Key characteristics of this scenario are persistent operation of the agents, and consideration of uncertainty. Belief space scheduling performs optimisation on probability distributions describing the state of the system. It consists of three major components---estimation of the current system state given uncertain sensor readings, prediction of the future state given a schedule of tasks, and optimisation of the schedule of the replenishing agents. The state estimation problem is complicated by a number of constraints that act on the state. A novel extension of the truncated Kalman Filter is developed for soft constraints that have uncertainty described by a Gaussian distribution. This is shown to outperform existing estimation methods, striking a balance between the high uncertainty of methods that ignore the constraints and the overconfidence of methods that ignore the uncertainty of the constraints. To predict the future state of the system, a novel analytical, continuous-time framework is proposed. This framework uses multiple Gaussian approximations to propagate the probability distributions describing the system state into the future. It is compared with a Monte Carlo framework and is shown to provide similar discrimination performance while computing, in most cases, orders of magnitude faster. Finally, several branch and bound tree search methods are developed for the optimisation problem. These methods focus optimisation efforts on earlier tasks within a model predictive control-like framework. Combined with the estimation and prediction methods, these are shown to outperform existing approaches