Karl Granström

A Gaussian mixture PHD filter for extended target tracking

In extended target tracking, targets potentially produce more than one measurement per time step. Multiple extended targets are therefore usually hard to track, due to the resulting complex data association. The main contribution of this paper is the implementation of a Probability Hypothesis Density (PHD) filter for tracking of multiple extended targets. A general modification of the PHD filter to handle extended targets has been presented recently by Mahler, and the novelty in this work lies in the realisation of a Gaussian mixture PHD filter for extended targets. Furthermore, we propose a method to easily partition the measurements into a number of subsets, each of which is supposed to contain measurements that all stem from the same source. The method is illustrated in simulation examples, and the advantage of the implemented extended target PHD filter is shown in a comparison with a standard PHD filter.

An Extended Target CPHD Filter and a Gamma Gaussian Inverse Wishart Implementation

This paper presents a cardinalized probability hypothesis density (CPHD) filter for extended targets that can result in multiple measurements at each scan. The probability hypothesis density (PHD) filter for such targets has been derived by Mahler, and different implementations have been proposed recently. To achieve better estimation performance this work relaxes the Poisson assumptions of the extended target PHD filter in target and measurement numbers. A gamma Gaussian inverse Wishart mixture implementation, which is capable of estimating the target extents and measurement rates as well as the kinematic state of the target, is proposed, and it is compared to its PHD counterpart in a simulation study. The results clearly show that the CPHD filter has a more robust cardinality estimate leading to smaller OSPA errors, which confirms that the extended target CPHD filter inherits the properties of its point target counterpart.

Learning to close loops from range data

In this paper we address the loop closure detection problem in simultaneous localization and mapping ( slam ), and present a method for solving the problem using pairwise comparison of point clouds in both two and three dimensions. The point clouds are mathematically described using features that capture important geometric and statistical properties. The features are used as input to the machine learning algorithm AdaBoost, which is used to build a non-linear classifier capable of detecting loop closure from pairs of point clouds. Vantage point dependency in the detection process is eliminated by only using rotation invariant features, thus loop closure can be detected from an arbitrary direction. The classifier is evaluated using publicly available data, and is shown to generalize well between environments. Detection rates of 66%, 63% and 53% for 0% false alarm rate are achieved for 2D outdoor data, 3D outdoor data and 3D indoor data, respectively. In both two and three dimensions, experiments are performed using publicly available data, showing that the proposed algorithm compares favourably with related work.

Learning to detect loop closure from range data

Despite significant developments in the Simultaneous Localisation and Mapping (SLAM) problem, loop closure detection is still challenging in large scale unstructured environments. Current solutions rely on heuristics that lack generalisation properties, in particular when range sensors are the only source of information about the robots surrounding environment. This paper presents a machine learning approach for the loop closure detection problem using range sensors. A binary classifier based on boosting is used to detect loop closures. The algorithm performs robustly, even under potential occlusions and significant changes in rotation and translation. We developed a number of features, extracted from range data, that are invariant to rotation. Additionally, we present a general framework for scan-matching SLAM in outdoor environments. Experimental results in large scale urban environments show the robustness of the approach, with a detection rate of 85% and a false alarm rate of only 1%. The proposed algorithm can be computed in real-time and achieves competitive performance with no manual specification of thresholds given the features.

Multiple Extended Target Tracking With Labeled Random Finite Sets

Targets that generate multiple measurements at a given instant in time are commonly known as extended targets. These present a challenge for many tracking algorithms, as they violate one of the key assumptions of the standard measurement model. In this paper, a new algorithm is proposed for tracking multiple extended targets in clutter, which is capable of estimating the number of targets, as well the trajectories of their states, comprising the kinematics, measurement rates, and extents. The proposed technique is based on modeling the multi-target state as a generalized labeled multi-Bernoulli (GLMB) random finite set (RFS), within which the extended targets are modeled using gamma Gaussian inverse Wishart (GGIW) distributions. A cheaper variant of the algorithm is also proposed, based on the labelled multi-Bernoulli (LMB) filter. The proposed GLMB/LMB-based algorithms are compared with an extended target version of the cardinalized probability hypothesis density (CPHD) filter, and simulation results show that the (G)LMB has improved estimation and tracking performance.

New prediction for extended targets with random matrices

This paper presents a new prediction update for extended targets whose extensions are modeled as random matrices. The prediction is based on several minimizations of the Kullback-Leibler divergence (KL-div) and allows for a kinematic state dependent transformation of the target extension. The results show that the extension prediction is a significant improvement over the previous work carried out on the topic.

On Spawning and Combination of Extended/Group Targets Modeled With Random Matrices

In extended/group target tracking, where the extensions of the targets are estimated, target spawning and combination events might have significant implications on the extensions. This paper investigates target spawning and combination events for the case that the target extensions are modeled in a random matrix framework. The paper proposes functions that should be provided by the tracking filter in such a scenario. The results, which are obtained by a gamma Gaussian inverse Wishart implementation of an extended target probability hypothesis density filter, confirms that the proposed functions improve the performance of the tracking filter for spawning and combination events.

Gamma Gaussian Inverse Wishart Probability Hypothesis Density for Extended Target Tracking Using X-Band Marine Radar Data

X-band marine radar systems represent a flexible and low-cost tool for the tracking of multiple targets in a given region of interest. Although suffering several sources of interference, e.g., the sea clutter, these systems can provide high-resolution measurements, both in space and time. Such features offer the opportunity to get accurate information not only about the target position/motion but also about the targets size. Accordingly, in this paper, we exploit emergent extended target tracking (ETT) methodologies in which the target state, typically position/velocity/acceleration, is augmented with the target length and width. In this paper, we propose an ETT procedure based on the popular probability hypothesis density filter, and in particular, we describe the extended target state through the gamma Gaussian inverse Wishart model. The comparative simplicity of the used models allows us to meet the real-time processing constraint required for the practical surveillance purposes. Real-world data from an experimental and operational campaign, collected during the recovery operations of the Costa Concordia wreckage in October 2013, are used to assess the performance of the proposed target tracking methodology. The full signal processing chain is implemented, and considerations of the experimental results are provided. Important nonideal effects, common to every marine radar, are observed and discussed in relation to the assumptions made for the tracking procedure.

Random Set Methods: Estimation of Multiple Extended Objects

Random set-based methods have provided a rigorous Bayesian framework and have been used extensively in the last decade for point object estimation. In this article, we emphasize that the same methodology offers an equally powerful approach to estimation of so-called extended objects, i.e., objects that result in multiple detections on the sensor side. Building upon the analogy between Bayesian state estimation of a single object and random finite set (RFS) estimation for multiple objects, we give a tutorial on random set methods with an emphasis on multiple-extended-object estimation. The capabilities are illustrated on a simple yet insightful real-life example with laser range data containing several occlusions.

Greedy Reduction Algorithms for Mixtures of Exponential Family

In this letter, we propose a general framework for greedy reduction of mixture densities of exponential family. The performances of the generalized algorithms are illustrated both on an artificial example where randomly generated mixture densities are reduced and on a target tracking scenario where the reduction is carried out in the recursion of a Gaussian inverse Wishart probability hypothesis density (PHD) filter.