Aspects of particle filtering in high-dimensional spaces

Nonlinear data assimilation is high on the agenda in all fields of the geosciences as with ever increasing model resolution and inclusion of more physical (biological etc.) processes, and more complex observation operators the data-assimilation problem becomes more and more nonlinear. The suitability of particle filters to solve the nonlinear data assimilation problem in high-dimensional geophysical problems will be discussed. Several existing and new schemes will be presented and it is shown that at least one of them, the Equivalent-Weights Particle Filter, does indeed beat the curse of dimensionality and provides a way forward to solve the problem of nonlinear data assimilation in high-dimensional systems.

Mice and larvae tracking using a particle filter with an auto-adjustable observation model

This paper proposes a novel way to combine different observation models in a particle filter framework. This, so called, auto-adjustable observation model, enhance the particle filter accuracy when the tracked objects overlap without infringing a great runtime penalty to the whole tracking system. The approach has been tested under two important real world situations related to animal behavior: mice and larvae tracking. The proposal was compared to some state-of-art approaches and the results show, under the datasets tested, that a good trade-off between accuracy and runtime can be achieved using an auto-adjustable observation model. (C) 2009 Elsevier B.V. All rights reserved.

Range-based Weighted-likelihood Particle Filter for RSS-based Indoor Tracking

Attractive business cases in various application fields contribute to the sustained long-term interest in indoor localization and tracking by the research community. Location tracking is generally treated as a dynamic state estimation problem, consisting of two steps: (i) location estimation through measurement, and (ii) location prediction. For the estimation step, one of the most efficient and low-cost solutions is Received Signal Strength (RSS)-based ranging. However, various challenges - unrealistic propagation model, non-line of sight (NLOS), and multipath propagation - are yet to be addressed. Particle filters are a popular choice for dealing with the inherent non-linearities in both location measurements and motion dynamics. While such filters have been successfully applied to accurate, time-based ranging measurements, dealing with the more error-prone RSS based ranging is still challenging. In this work, we address the above issues with a novel, weighted likelihood, bootstrap particle filter for tracking via RSS-based ranging. Our filter weights the individual likelihoods from different anchor nodes exponentially, according to the ranging estimation. We also employ an improved propagation model for more accurate RSS-based ranging, which we suggested in recent work. We implemented and tested our algorithm in a passive localization system with IEEE 802.15.4 signals, showing that our proposed solution largely outperforms a traditional bootstrap particle filter.

Improved detection and tracking of objects in surveillance video

Surveillance networks are typically monitored by a few people, viewing several monitors displaying the camera feeds. It is then very difficult for a human operator to effectively detect events as they happen. Recently, computer vision research has begun to address ways to automatically process some of this data, to assist human operators. Object tracking, event recognition, crowd analysis and human identification at a distance are being pursued as a means to aid human operators and improve the security of areas such as transport hubs. The task of object tracking is key to the effective use of more advanced technologies. To recognize an event people and objects must be tracked. Tracking also enhances the performance of tasks such as crowd analysis or human identification. Before an object can be tracked, it must be detected. Motion segmentation techniques, widely employed in tracking systems, produce a binary image in which objects can be located. However, these techniques are prone to errors caused by shadows and lighting changes. Detection routines often fail, either due to erroneous motion caused by noise and lighting effects, or due to the detection routines being unable to split occluded regions into their component objects. Particle filters can be used as a self contained tracking system, and make it unnecessary for the task of detection to be carried out separately except for an initial (often manual) detection to initialise the filter. Particle filters use one or more extracted features to evaluate the likelihood of an object existing at a given point each frame. Such systems however do not easily allow for multiple objects to be tracked robustly, and do not explicitly maintain the identity of tracked objects. This dissertation investigates improvements to the performance of object tracking algorithms through improved motion segmentation and the use of a particle filter. A novel hybrid motion segmentation / optical flow algorithm, capable of simultaneously extracting multiple layers of foreground and optical flow in surveillance video frames is proposed. The algorithm is shown to perform well in the presence of adverse lighting conditions, and the optical flow is capable of extracting a moving object. The proposed algorithm is integrated within a tracking system and evaluated using the ETISEO (Evaluation du Traitement et de lInterpretation de Sequences vidEO - Evaluation for video understanding) database, and significant improvement in detection and tracking performance is demonstrated when compared to a baseline system. A Scalable Condensation Filter (SCF), a particle filter designed to work within an existing tracking system, is also developed. The creation and deletion of modes and maintenance of identity is handled by the underlying tracking system; and the tracking system is able to benefit from the improved performance in uncertain conditions arising from occlusion and noise provided by a particle filter. The system is evaluated using the ETISEO database. The dissertation then investigates fusion schemes for multi-spectral tracking systems. Four fusion schemes for combining a thermal and visual colour modality are evaluated using the OTCBVS (Object Tracking and Classification in and Beyond the Visible Spectrum) database. It is shown that a middle fusion scheme yields the best results and demonstrates a significant improvement in performance when compared to a system using either mode individually. Findings from the thesis contribute to improve the performance of semi-automated video processing and therefore improve security in areas under surveillance.

Multi-sensor tracking using a scalable condensation filter

Surveillance and tracking systems typically use a single colour modality for their input. These systems work well in controlled conditions but often fail with low lighting, shadowing, smoke, dust, unstable backgrounds or when the foreground object is of similar colouring to the background. With advances in technology and manufacturing techniques, sensors that allow us to see into the thermal infrared spectrum are becoming more affordable. By using modalities from both the visible and thermal infrared spectra, we are able to obtain more information from a scene and overcome the problems associated with using visible light only for surveillance and tracking. Thermal images are not affected by lighting or shadowing and are not overtly affected by smoke, dust or unstable backgrounds. We propose and evaluate three approaches for fusing visual and thermal images for person tracking. We also propose a modified condensation filter to track and aid in the fusion of the modalities. We compare the proposed fusion schemes with using the visual and thermal domains on their own, and demonstrate that significant improvements can be achieved by using multiple modalities.

Multi-spectral fusion for surveillance systems

Surveillance systems such as object tracking and abandoned object detection systems typically rely on a single modality of colour video for their input. These systems work well in controlled conditions but often fail when low lighting, shadowing, smoke, dust or unstable backgrounds are present, or when the objects of interest are a similar colour to the background. Thermal images are not affected by lighting changes or shadowing, and are not overtly affected by smoke, dust or unstable backgrounds. However, thermal images lack colour information which makes distinguishing between different people or objects of interest within the same scene difficult. ----- By using modalities from both the visible and thermal infrared spectra, we are able to obtain more information from a scene and overcome the problems associated with using either modality individually. We evaluate four approaches for fusing visual and thermal images for use in a person tracking system (two early fusion methods, one mid fusion and one late fusion method), in order to determine the most appropriate method for fusing multiple modalities. We also evaluate two of these approaches for use in abandoned object detection, and propose an abandoned object detection routine that utilises multiple modalities. To aid in the tracking and fusion of the modalities we propose a modified condensation filter that can dynamically change the particle count and features used according to the needs of the system. ----- We compare tracking and abandoned object detection performance for the proposed fusion schemes and the visual and thermal domains on their own. Testing is conducted using the OTCBVS database to evaluate object tracking, and data captured in-house to evaluate the abandoned object detection. Our results show that significant improvement can be achieved, and that a middle fusion scheme is most effective.

Capping computation time and storage requirements for appearance-based localization with CAT-SLAM

Appearance-based localization is increasingly used for loop closure detection in metric SLAM systems. Since it relies only upon the appearance-based similarity between images from two locations, it can perform loop closure regardless of accumulated metric error. However, the computation time and memory requirements of current appearance-based methods scale linearly not only with the size of the environment but also with the operation time of the platform. These properties impose severe restrictions on longterm autonomy for mobile robots, as loop closure performance will inevitably degrade with increased operation time. We present a set of improvements to the appearance-based SLAM algorithm CAT-SLAM to constrain computation scaling and memory usage with minimal degradation in performance over time. The appearance-based comparison stage is accelerated by exploiting properties of the particle observation update, and nodes in the continuous trajectory map are removed according to minimal information loss criteria. We demonstrate constant time and space loop closure detection in a large urban environment with recall performance exceeding FAB-MAP by a factor of 3 at 100% precision, and investigate the minimum computational and memory requirements for maintaining mapping performance.

Assessing the Impact of Sensor Accuracy and Sensor Choice on Air Traffic Conflict Risk Estimation using Risk-Ratio Concepts

One of the primary desired capabilities of any future air traffic separation management system is the ability to provide early conflict detection and resolution effectively and efficiently. In this paper, we consider the risk of conflict as a primary measurement to be used for early conflict detection. This paper focuses on developing a novel approach to assess the impact of different measurement uncertainty models on the estimated risk of conflict. The measurement uncertainty model can be used to represent different sensor accuracy and sensor choices. Our study demonstrates the value of modelling measurement uncertainty in the conflict risk estimation problem and presents techniques providing a means of assessing sensor requirements to achieve desired conflict detection performance.

Alive SMC^2: Bayesian model selection for low-count time series models with intractable likelihoods

In this paper we present a new method for performing Bayesian parameter inference and model choice for low count time series models with intractable likelihoods. The method involves incorporating an alive particle filter within a sequential Monte Carlo (SMC) algorithm to create a novel pseudo-marginal algorithm, which we refer to as alive SMC^2. The advantages of this approach over competing approaches is that it is naturally adaptive, it does not involve between-model proposals required in reversible jump Markov chain Monte Carlo and does not rely on potentially rough approximations. The algorithm is demonstrated on Markov process and integer autoregressive moving average models applied to real biological datasets of hospital-acquired pathogen incidence, animal health time series and the cumulative number of poison disease cases in mule deer.

Time variant reliability model updating in instrumented dynamical systems based on Girsanov's transformation

The problem of updating the reliability of instrumented structures based on measured response under random dynamic loading is considered. A solution strategy within the framework of Monte Carlo simulation based dynamic state estimation method and Girsanov's transformation for variance reduction is developed. For linear Gaussian state space models, the solution is developed based on continuous version of the Kalman filter, while, for non-linear and (or) non-Gaussian state space models, bootstrap particle filters are adopted. The controls to implement the Girsanov transformation are developed by solving a constrained non-linear optimization problem. Numerical illustrations include studies on a multi degree of freedom linear system and non-linear systems with geometric and (or) hereditary non-linearities and non-stationary random excitations.

A novel filtering framework through Girsanov correction for the identification of nonlinear dynamical systems

Using a Girsanov change of measures, we propose novel variations within a particle-filtering algorithm, as applied to the inverse problem of state and parameter estimations of nonlinear dynamical systems of engineering interest, toward weakly correcting for the linearization or integration errors that almost invariably occur whilst numerically propagating the process dynamics, typically governed by nonlinear stochastic differential equations (SDEs). Specifically, the correction for linearization, provided by the likelihood or the Radon-Nikodym derivative, is incorporated within the evolving flow in two steps. Once the likelihood, an exponential martingale, is split into a product of two factors, correction owing to the first factor is implemented via rejection sampling in the first step. The second factor, which is directly computable, is accounted for via two different schemes, one employing resampling and the other using a gain-weighted innovation term added to the drift field of the process dynamics thereby overcoming the problem of sample dispersion posed by resampling. The proposed strategies, employed as add-ons to existing particle filters, the bootstrap and auxiliary SIR filters in this work, are found to non-trivially improve the convergence and accuracy of the estimates and also yield reduced mean square errors of such estimates vis-a-vis those obtained through the parent-filtering schemes.

Time variant reliability model updating in instrumented dynamical systems based on Girsanov’s transformation

The problem of updating the reliability of instrumented structures based on measured response under random dynamic loading is considered. A solution strategy within the framework of Monte Carlo simulation based dynamic state estimation method and Girsanov’s transformation for variance reduction is developed. For linear Gaussian state space models, the solution is developed based on continuous version of the Kalman filter, while, for non-linear and (or) non-Gaussian state space models, bootstrap particle filters are adopted. The controls to implement the Girsanov transformation are developed by solving a constrained non-linear optimization problem. Numerical illustrations include studies on a multi degree of freedom linear system and non-linear systems with geometric and (or) hereditary non-linearities and non-stationary random excitations.

A scaled unscented transformation based directed Gaussian sum filter for nonlinear dynamic system identification

Impoverishment of particles, i.e. the discretely simulated sample paths of the process dynamics, poses a major obstacle in employing the particle filters for large dimensional nonlinear system identification. A known route of alleviating this impoverishment, i.e. of using an exponentially increasing ensemble size vis-a-vis the system dimension, remains computationally infeasible in most cases of practical importance. In this work, we explore the possibility of unscented transformation on Gaussian random variables, as incorporated within a scaled Gaussian sum stochastic filter, as a means of applying the nonlinear stochastic filtering theory to higher dimensional structural system identification problems. As an additional strategy to reconcile the evolving process dynamics with the observation history, the proposed filtering scheme also modifies the process model via the incorporation of gain-weighted innovation terms. The reported numerical work on the identification of structural dynamic models of dimension up to 100 is indicative of the potential of the proposed filter in realizing the stated aim of successfully treating relatively larger dimensional filtering problems. (C) 2013 Elsevier Ltd. All rights reserved.

A Kushner-Stratonovich Monte Carlo filter applied to nonlinear dynamical system identification

A Monte Carlo filter, based on the idea of averaging over characteristics and fashioned after a particle-based time-discretized approximation to the Kushner-Stratonovich (KS) nonlinear filtering equation, is proposed. A key aspect of the new filter is the gain-like additive update, designed to approximate the innovation integral in the KS equation and implemented through an annealing-type iterative procedure, which is aimed at rendering the innovation (observation prediction mismatch) for a given time-step to a zero-mean Brownian increment corresponding to the measurement noise. This may be contrasted with the weight-based multiplicative updates in most particle filters that are known to precipitate the numerical problem of weight collapse within a finite-ensemble setting. A study to estimate the a-priori error bounds in the proposed scheme is undertaken. The numerical evidence, presently gathered from the assessed performance of the proposed and a few other competing filters on a class of nonlinear dynamic system identification and target tracking problems, is suggestive of the remarkably improved convergence and accuracy of the new filter. (C) 2013 Elsevier B.V. All rights reserved.

An Ensemble Kushner-Stratonovich-Poisson Filter for Recursive Estimation in Nonlinear Dynamical Systems

We propose a Monte Carlo filter for recursive estimation of diffusive processes that modulate the instantaneous rates of Poisson measurements. A key aspect is the additive update, through a gain-like correction term, empirically approximated from the innovation integral in the time-discretized Kushner-Stratonovich equation. The additive filter-update scheme eliminates the problem of particle collapse encountered in many conventional particle filters. Through a few numerical demonstrations, the versatility of the proposed filter is brought forth.