Ba-Tuong Vo

A Consistent Metric for Performance Evaluation of Multi-Object Filters

The concept of a miss-distance, or error, between a reference quantity and its estimated/controlled value, plays a fundamental role in any filtering/control problem. Yet there is no satisfactory notion of a miss-distance in the well-established field of multi-object filtering. In this paper, we outline the inconsistencies of existing metrics in the context of multi-object miss-distances for performance evaluation. We then propose a new mathematically and intuitively consistent metric that addresses the drawbacks of current multi-object performance evaluation metrics.

Analytic Implementations of the Cardinalized Probability Hypothesis Density Filter

The probability hypothesis density (PHD) recursion propagates the posterior intensity of the random finite set (RFS) of targets in time. The cardinalized PHD (CPHD) recursion is a generalization of the PHD recursion, which jointly propagates the posterior intensity and the posterior cardinality distribution. In general, the CPHD recursion is computationally intractable. This paper proposes a closed-form solution to the CPHD recursion under linear Gaussian assumptions on the target dynamics and birth process. Based on this solution, an effective multitarget tracking algorithm is developed. Extensions of the proposed closed-form recursion to accommodate nonlinear models are also given using linearization and unscented transform techniques. The proposed CPHD implementations not only sidestep the need to perform data association found in traditional methods, but also dramatically improve the accuracy of individual state estimates as well as the variance of the estimated number of targets when compared to the standard PHD filter. Our implementations only have a cubic complexity, but simulations suggest favorable performance compared to the standard Joint Probabilistic Data Association (JPDA) filter which has a nonpolynomial complexity.

Joint Detection and Estimation of Multiple Objects From Image Observations

The problem of jointly detecting multiple objects and estimating their states from image observations is formulated in a Bayesian framework by modeling the collection of states as a random finite set. Analytic characterizations of the posterior distribution of this random finite set are derived for various prior distributions under the assumption that the regions of the observation influenced by individual objects do not overlap. These results provide tractable means to jointly estimate the number of states and their values from image observations. As an application, we develop a multi-object filter suitable for image observations with low signal-to-noise ratio (SNR). A particle implementation of the multi-object filter is proposed and demonstrated via simulations.

The Labeled Multi-Bernoulli Filter

This paper proposes a generalization of the multi- Bernoulli filter called the labeled multi-Bernoulli filter that outputs target tracks. Moreover, the labeled multi-Bernoulli filter does not exhibit a cardinality bias due to a more accurate update approximation compared to the multi-Bernoulli filter by exploiting the conjugate prior form for labeled Random Finite Sets. The proposed filter can be interpreted as an efficient approximation of the δ-Generalized Labeled Multi-Bernoulli filter. It inherits the advantages of the multi-Bernoulli filter in regards to particle implementation and state estimation. It also inherits advantages of the δ-Generalized Labeled Multi-Bernoulli filter in that it outputs (labeled) target tracks and achieves better performance.

Labeled Random Finite Sets and the Bayes Multi-Target Tracking Filter

An analytic solution to the multi-target Bayes recursion known as the δ-Generalized Labeled Multi-Bernoulli ( δ-GLMB) filter has been recently proposed by Vo and Vo in [“Labeled Random Finite Sets and Multi-Object Conjugate Priors,” IEEE Trans. Signal Process., vol. 61, no. 13, pp. 3460-3475, 2014]. As a sequel to that paper, the present paper details efficient implementations of the δ-GLMB multi-target tracking filter. Each iteration of this filter involves an update operation and a prediction operation, both of which result in weighted sums of multi-target exponentials with intractably large number of terms. To truncate these sums, the ranked assignment and K-th shortest path algorithms are used in the update and prediction, respectively, to determine the most significant terms without exhaustively computing all of the terms. In addition, using tools derived from the same framework, such as probability hypothesis density filtering, we present inexpensive (relative to the δ-GLMB filter) look-ahead strategies to reduce the number of computations. Characterization of the L1-error in the multi-target density arising from the truncation is presented.

A Metric for Performance Evaluation of Multi-Target Tracking Algorithms

Performance evaluation of multi-target tracking algorithms is of great practical importance in the design, parameter optimization and comparison of tracking systems. The goal of performance evaluation is to measure the distance between two sets of tracks: the ground truth tracks and the set of estimated tracks. This paper proposes a mathematically rigorous metric for this purpose. The basis of the proposed distance measure is the recently formulated consistent metric for performance evaluation of multi-target filters, referred to as the OSPA metric. Multi-target filters sequentially estimate the number of targets and their position in the state space. The OSPA metric is therefore defined on the space of finite sets of vectors. The distinction between filtering and tracking is that tracking algorithms output tracks and a track represents a labeled temporal sequence of state estimates, associated with the same target. The metric proposed in this paper is therefore defined on the space of finite sets of tracks and incorporates the labeling error. Numerical examples demonstrate that the proposed metric behaves in a manner consistent with our expectations.

A Random-Finite-Set Approach to Bayesian SLAM

This paper proposes an integrated Bayesian frame work for feature-based simultaneous localization and map building (SLAM) in the general case of uncertain feature number and data association. By modeling the measurements and feature map as random finite sets (RFSs), a formulation of the feature-based SLAM problem is presented that jointly estimates the number and location of the features, as well as the vehicle trajectory. More concisely, the joint posterior distribution of the set-valued map and vehicle trajectory is propagated forward in time as measurements arrive, thereby incorporating both data association and feature management into a single recursion. Furthermore, the Bayes optimality of the proposed approach is established. A first-order solution, which is coined as the probability hypothesis density (PHD) SLAM filter, is derived, which jointly propagates the posterior PHD of the map and the posterior distribution of the vehicle trajectory. A Rao-Blackwellized (RB) implementation of the PHD-SLAM filter is proposed based on the Gaussian-mixture PHD filter (for the map) and a particle filter (for the vehicle trajectory). Simulated and experimental results demonstrate the merits of the proposed approach, particularly in situations of high clutter and data association ambiguity.

Adaptive Target Birth Intensity for PHD and CPHD Filters

The standard formulation of the probability hypothesis density (PHD) and cardinalised PHD (CPHD) filters assumes that the target birth intensity is known a priori. In situations where the targets can appear anywhere in the surveillance volume this is clearly inefficient, since the target birth intensity needs to cover the entire state space. This paper presents a new extension of the PHD and CPHD filters, which distinguishes between the persistent and the newborn targets. This extension enables us to adaptively design the target birth intensity at each scan using the received measurements. Sequential Monte-Carlo (SMC) implementations of the resulting PHD and CPHD filters are presented and their performance studied numerically. The proposed measurement-driven birth intensity improves the estimation accuracy of both the number of targets and their spatial distribution.

A Tutorial on Bernoulli Filters: Theory, Implementation and Applications

Bernoulli filters are a class of exact Bayesian filters for non-linear/non-Gaussian recursive estimation of dynamic systems, recently emerged from the random set theoretical framework. The common feature of Bernoulli filters is that they are designed for stochastic dynamic systems which randomly switch on and off. The applications are primarily in target tracking, where the switching process models target appearance or disappearance from the surveillance volume. The concept, however, is applicable to a range of dynamic phenomena, such as epidemics, pollution, social trends, etc. Bernoulli filters in general have no analytic solution and are implemented as particle filters or Gaussian sum filters. This tutorial paper reviews the theory of Bernoulli filters as well as their implementation for different measurement models. The theory is backed up by applications in sensor networks, bearings-only tracking, passive radar/sonar surveillance, visual tracking, monitoring/prediction of an epidemic and tracking using natural language statements. More advanced topics of smoothing, multi-target detection/tracking, parameter estimation and sensor control are briefly reviewed with pointers for further reading.

Visual tracking of numerous targets via multi-Bernoulli filtering of image data

This paper presents a novel Bayesian method to track multiple targets in an image sequence without explicit detection. Our method is formulated based on finite set representation of the multi-target state and the recently developed multi-Bernoulli filter. Experimental results on sport player and cell tracking studies show that our method can automatically track numerous targets, and it outperforms the state-of-the-art in terms of false positive (false alarm) and false negative (missing) rates as detection error measures, and in terms of label switching rate and lost tracks ratio as tracking error measures.