Analysis of error propagation in particle filters with approximation

This paper examines the impact of approximation steps that become necessary when particle filters are implemented on resource-constrained platforms. We consider particle filters that perform intermittent approximation, either by subsampling the particles or by generating a parametric approximation. For such algorithms, we derive time-uniform bounds on the weak-sense $L_p$ error and present associated exponential inequalities. We motivate the theoretical analysis by considering the leader node particle filter and present numerical experiments exploring its performance and the relationship to the error bounds.Comment: Published in at http://dx.doi.org/10.1214/11-AAP760 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

On particle filters in radar target tracking

The dissertation focused on the research, implementation, and evaluation of particle filters for radar target track filtering of a maneuvering target, through quantitative simulations and analysis thereof. Target track filtering, also called target track smoothing, aims to minimize the error between a radar target's predicted and actual position. From the literature it had been suggested that particle filters were more suitable for filtering in non-linear/non-Gaussian systems. Furthermore, it had been determined that particle filters were a relatively newer field of research relating to radar target track filtering for non-linear, non-Gaussian maneuvering target tracking problems, compared to the more traditional and widely known and implemented approaches and techniques. The objectives of the research project had been achieved through the development of a software radar target tracking filter simulator, which implemented a sequential importance re-sampling particle filter algorithm and suitable target and noise models. This particular particle filter had been identified from a review of the theory of particle filters. The theory of the more conventional tracking filters used in radar applications had also been reviewed and discussed. The performance of the sequential importance re-sampling particle filter for radar target track filtering had been evaluated through quantitative simulations and analysis thereof, using predefined metrics identified from the literature. These metrics had been the root mean squared error metric for accuracy, and the normalized processing time metric for computational complexity. It had been shown that the sequential importance re-sampling particle filter achieved improved accuracy performance in the track filtering of a maneuvering radar target in a non-Gaussian (Laplacian) noise environment, compared to a Gaussian noise environment. It had also been shown that the accuracy performance of the sequential importance re-sampling particle filter is a function of the number of particles used in the sequential importance re-sampling particle filter algorithm. The sequential importance re-sampling particle filter had also been compared to two conventional tracking filters, namely the alpha-beta filter and the Singer-Kalman filter, and had better accuracy performance in both cases. The normalized processing time of the sequential importance re-sampling particle filter had been shown to be a function of the number of particles used in the sequential importance re-sampling particle filter algorithm. The normalized processing time of the sequential importance re-sampling particle filter had been shown to be higher than that of both the alpha-beta filter and the Singer-Kalman filter. Analysis of the posterior Cramér-Rao lower bound of the sequential importance re-sampling particle filter had also been conducted and presented in the dissertation

Non Parametric Distributed Inference in Sensor Networks Using Box Particles Messages

This paper deals with the problem of inference in distributed systems where the probability model is stored in a distributed fashion. Graphical models provide powerful tools for modeling this kind of problems. Inspired by the box particle filter which combines interval analysis with particle filtering to solve temporal inference problems, this paper introduces a belief propagation-like message-passing algorithm that uses bounded error methods to solve the inference problem defined on an arbitrary graphical model. We show the theoretic derivation of the novel algorithm and we test its performance on the problem of calibration in wireless sensor networks. That is the positioning of a number of randomly deployed sensors, according to some reference defined by a set of anchor nodes for which the positions are known a priori. The new algorithm, while achieving a better or similar performance, offers impressive reduction of the information circulating in the network and the needed computation times

A novel high-fidelity unscented particle filtering method for the accurate state of charge estimation of lithium-ion batteries.

Power Li-ion batteries are one of the core "three powers" systems of new energy vehicles, and its accurate batteries modeling and state prediction have become the core technology of the scientific and technological progress in the industry. This paper takes the ternary Li-ion batteries as the research subject. Aiming at the mathematical expressions of different structural features, innovatively construct a second-order Thevenin equivalent circuit model with autoregressive effect. This model can characterize the internal reaction mechanism of Li-ion batteries and fit the complex electrochemical reactions inside the battery. An improved particle filter model, namely a new high-fidelity unscented particle filter method, is designed and established. By introducing a suitable suggested density function, the model can accurately calculate the mean and variance, solve the particle degradation problem, and find out the Li-ion batteries state of charge, which is suitable for complex charging and discharging conditions. By further improving the theoretical analysis and combining with experiments under different working conditions, this method studies the Li-ion batteries state of charge. The test results show that the average absolute error of the improved equivalent circuit model is reduced by 0.00457 V, and the error rate is stably kept within 1%, which has the ability to describe Li-ion batteries well. When using the high-fidelity unscented particle filter algorithm to estimate the state of charge of the lithium battery, the robustness of the system is improved, the following effect is better, and the estimation error is controlled within 1.5%, which brings good practical value to the power Li-ion batteries

Multilevel Estimation of Normalization Constants Using the Ensemble Kalman-Bucy Filter

In this article we consider the application of multilevel Monte Carlo, for the estimation of normalizing constants. In particular we will make use of the filtering algorithm, the ensemble Kalman-Bucy filter (EnKBF), which is an N-particle representation of the Kalma-Bucy filter (KBF). The EnKBF is of interest as it coincides with the optimal filter in the continuous-linear setting, i.e. the KBF. This motivates our particular setup in the linear setting. The resulting methodology we will use is the multilevel ensemble Kalman-Bucy filter (MLEnKBF). We provide an analysis based on deriving Lq-bounds for the normalizing constants using both the single-level, and the multilevel algorithms. Our results will be highlighted through numerical results, where we firstly demonstrate the error-to-cost rates of the MLEnKBF comparing it to the EnKBF on a linear Gaussian model. Our analysis will be specific to one variant of the MLEnKBF, whereas the numerics will be tested on different variants. We also exploit this methodology for parameter estimation, where we test this on the models arising in atmospheric sciences, such as the stochastic Lorenz 63 and 96 model.Comment: 33 pages, 21 figure