A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking

Damage detection of civil infrastructure has gained significant momentum in the last decade due to aging and being more prone to failure of infrastructure. New advances in sensing technology have made it possible to detect damage in giant infrastructure more effectively. As the size of structure increases, the number of installed sensors on the structure increases significantly. This increase in the number of sensors makes it more challenging to collect and interpret the data. Therefore, utilizing the minimum number of sensors at any time of detection while maintaining an effective monitoring system is of great interest. In this paper, we will develop an innovative on/off sensors methodology using the sequential importance sampling technique to choose the sensors to be turned on at any given time while tracking the potential damage. This method will be used on a cable stayed bridge over Mississippi River called Luling Bridge. The finite element (FE) model of the bridge is developed to introduce the damage at different girder locations in the bridge. This model will be used to show the effectiveness of the proposed sequential importance sampling method in providing effective monitoring with minimal number of turned activated sensors at any given time.

Publication in the conference proceedings of EUSIPCO, Toulouse, France, 2002

This paper presents a Hybrid Particle Filter based RNN method for state estimation of non-linear dynamical system with knowledge of its input and output measurements. Particle filters are sequential Monte Carlo methods based on point mass (or particle) representations of probability densities, which is used to train Recurrent Neural Networks for estimation problems. The performance this method is compared with EKF based estimation and RNN based estimation. An Induction motor is considered as typical non-linear system and is implemented in MATLAB environment.

Assimilating real-time sensor data into large-scale spatial-temporal simulations, such as simulations of wildfires, is a promising technique for improving simulation results. This asks for advanced data assimilation methods that can work with the complex structures and nonlinear behaviors associated with the simulation models. This article presents a data assimilation framework using Sequential Monte Carlo (SMC) methods for wildfire spread simulations. The models and algorithms of the framework are described, and experimental results are provided. This work demonstrates the feasibility of applying SMC methods to data assimilation of wildfire spread simulations. The developed framework can potentially be generalized to other application areas where sophisticated simulation models are used.

Residual and stratified branching particle filters

A note on auxiliary particle filters

Sequential importance sampling for structural reliability analysis

Random graphs with given degrees are a natural next step in complexity beyond the Erdős–Renyi model, yet the degree constraint greatly complicates simulation and estimation. We use an extension of a combinatorial characterization due to Erdős and Gallai to develop a sequential algorithm for generating a random labeled graph with a given degree sequence. The algorithm is easy to implement and allows for surprisingly efficient sequential importance sampling. The resulting probabilities are easily computed on the fly, allowing the user to reweight estimators appropriately, in contrast to some ad hoc approaches that generate graphs with the desired degrees but with completely unknown probabilities. Applications are given, including simulating an ecological network and estimating the number of graphs with a given degree sequence.

This paper considers the object tracking problem in three dimensional (3-D) space when the azimuth and elevation of the object are available from the passive acoustic sensor. The particle filtering technique can be directly applied to estimate the 3-D object location, but we propose to decompose the 3-D particle filter into the three planes particle filters, which are individually designed for the 2-D bearings-only tracking problems. 2-D bearing information is derived from the azimuth and elevation of the object to be used for the 2-D particle filter. Two estimates of three planes particle filters are selected based on the characterization of the acoustic sensor operation in a noisy environment. The Cramer-Rao Lower Bound of the proposed 2-D particle filter-based algorithm is derived and compared against the algorithm that is based on the direct 3-D particle filter.

Based on the concept of sequential importance sampling (SIS) and the use of Bayesian theory, particle filter is particularly useful in dealing with nonlinear and non-Gaussian problems. In this paper, a new particle filter is proposed that uses a divided difference filter to generate the importance proposal distribution is proposed. The proposal distribution integrates the latest measurements into system state transition density so it can match the posterior density well. The simulation results show that the new particle filter performs superior to the generic particle filter and other particle filters such as the extended Kalman particle filter and the unscented particle filter.

This article addresses the target tracking problem based on the received signal strength (RSS) and angle of arrival (AOA) in wireless sensor networks (WSNs). The tracking problem is formulated in the framework of the maximum a posteriori (MAP), in which the prior knowledge of moving target nodes (TNs) is exploited. Due to the fact that the cost function of the tracking problem is highly nonlinear and nonconvex, most of the existing algorithms tend to approximate and relax the cost function. As a result, the tracking accuracy is usually compromised. In this article, we propose a tracking algorithm based on evolutionary techniques that do not require an approximation of the cost function, resulting in a considerable improvement in tracking accuracy. The proposed tracking algorithm is compared with state-of-the-art algorithms such as the MAP, particle filter (PF), and Kalman filter (KF). Simulation and real experiment results demonstrate that the proposed tracking algorithm provides an improvement roughly by 16%, 11%, and 18% over the MAP, PF, and KF, respectively, in the tracking accuracy.

A novel approach to Bayesian structure from motion (SfM) using inertial information and sequential importance sampling (SIS) is presented. The inertial information is obtained from camera-mounted inertial sensors and is used in the Bayesian SfM approach as prior knowledge of the camera motion in the sampling algorithm. Experimental results using both synthetic and real images show that, when inertial information is used, more accurate results can be obtained or the same estimation accuracy can be obtained at a lower cost.

The reliability polynomial of a graph gives the probability that a graph is connected as a function of the probability that each edge is connected. The coefficients of the reliability polynomial count the number of connected subgraphs of various sizes. Algorithms based on sequential importance sampling (SIS) have been proposed to estimate a graph's reliability polynomial. We develop a new bottom-up SIS algorithm for estimating the reliability polynomial by choosing a spanning tree and adding edges. This algorithm improves on existing bottom-up algorithms in that it has lower complexity ≈ O(E2) as opposed to O(EV3), and it uses importance sampling to reduce variance.

A novel particle filter, enhancing particle swarm optimization based particle filter (EPSOPF), is proposed for visual tracking. Particle filter (PF) is sequential Monte Carlo simulation based on particle set representations of probability densities, which can be applied to visual tracking. However, PF has the impoverishment phenomenon which limits its application. To improve the performance of PF, particle swarm optimization with mutation operator is introduced to form new filtering, in which mutation operator maintain multiple modes of particle set and optimization-seeking procedure drives particles to their neighboring maximum of the posterior. When applied to visual tracking, the proposed approach can realize more efficient function than PF.

Critical events that occur rarely in biological processes are of great importance, but are challenging to study using Monte Carlo simulation. By introducing biases to reaction selection and reaction rates, weighted stochastic simulation algorithms based on importance sampling allow rare events to be sampled more effectively. However, existing methods do not address the important issue of barrier crossing, which often arises from multistable networks and systems with complex probability landscape. In addition, the proliferation of parameters and the associated computing cost pose significant problems. Here we introduce a general theoretical framework for obtaining optimized biases in sampling individual reactions for estimating probabilities of rare events. We further describe a practical algorithm called adaptively biased sequential importance sampling (ABSIS) method for efficient probability estimation. By adopting a look-ahead strategy and by enumerating short paths from the current state, we estimate the reaction-specific and state-specific forward and backward moving probabilities of the system, which are then used to bias reaction selections. The ABSIS algorithm can automatically detect barrier-crossing regions, and can adjust bias adaptively at different steps of the sampling process, with bias determined by the outcome of exhaustively generated short paths. In addition, there are only two bias parameters to be determined, regardless of the number of the reactions and the complexity of the network. We have applied the ABSIS method to four biochemical networks: the birth-death process, the reversible isomerization, the bistable Schlögl model, and the enzymatic futile cycle model. For comparison, we have also applied the finite buffer discrete chemical master equation (dCME) method recently developed to obtain exact numerical solutions of the underlying discrete chemical master equations of these problems. This allows us to assess sampling results objectively by comparing simulation results with true answers. Overall, ABSIS can accurately and efficiently estimate rare event probabilities for all examples, often with smaller variance than other importance sampling algorithms. The ABSIS method is general and can be applied to study rare events of other stochastic networks with complex probability landscape.