Poisson multi-Bernoulli conjugate prior for multiple extended object filtering

This paper presents a Poisson multi-Bernoulli mixture (PMBM) conjugate prior for multiple extended object filtering. A Poisson point process is used to describe the existence of yet undetected targets, while a multi-Bernoulli mixture describes the distribution of the targets that have been detected. The prediction and update equations are presented for the standard transition density and measurement likelihood. Both the prediction and the update preserve the PMBM form of the density, and in this sense the PMBM density is a conjugate prior. However, the unknown data associations lead to an intractably large number of terms in the PMBM density, and approximations are necessary for tractability. A gamma Gaussian inverse Wishart implementation is presented, along with methods to handle the data association problem. A simulation study shows that the extended target PMBM filter performs well in comparison to the extended target d-GLMB and LMB filters. An experiment with Lidar data illustrates the benefit of tracking both detected and undetected targets

Extended Object Tracking: Introduction, Overview and Applications

This article provides an elaborate overview of current research in extended object tracking. We provide a clear definition of the extended object tracking problem and discuss its delimitation to other types of object tracking. Next, different aspects of extended object modelling are extensively discussed. Subsequently, we give a tutorial introduction to two basic and well used extended object tracking approaches - the random matrix approach and the Kalman filter-based approach for star-convex shapes. The next part treats the tracking of multiple extended objects and elaborates how the large number of feasible association hypotheses can be tackled using both Random Finite Set (RFS) and Non-RFS multi-object trackers. The article concludes with a summary of current applications, where four example applications involving camera, X-band radar, light detection and ranging (lidar), red-green-blue-depth (RGB-D) sensors are highlighted.Comment: 30 pages, 19 figure

Mono-Camera 3D Multi-Object Tracking Using Deep Learning Detections and PMBM Filtering

Monocular cameras are one of the most commonly used sensors in the automotive industry for autonomous vehicles. One major drawback using a monocular camera is that it only makes observations in the two dimensional image plane and can not directly measure the distance to objects. In this paper, we aim at filling this gap by developing a multi-object tracking algorithm that takes an image as input and produces trajectories of detected objects in a world coordinate system. We solve this by using a deep neural network trained to detect and estimate the distance to objects from a single input image. The detections from a sequence of images are fed in to a state-of-the art Poisson multi-Bernoulli mixture tracking filter. The combination of the learned detector and the PMBM filter results in an algorithm that achieves 3D tracking using only mono-camera images as input. The performance of the algorithm is evaluated both in 3D world coordinates, and 2D image coordinates, using the publicly available KITTI object tracking dataset. The algorithm shows the ability to accurately track objects, correctly handle data associations, even when there is a big overlap of the objects in the image, and is one of the top performing algorithms on the KITTI object tracking benchmark. Furthermore, the algorithm is efficient, running on average close to 20 frames per second.Comment: 8 pages, 2 figures, for associated videos, see https://goo.gl/Aoydg

Multi-Scan Implementation of the Trajectory Poisson Multi-Bernoulli Mixture Filter

The Poisson multi-Bernoulli mixture (PMBM) and the multi-Bernoulli mixture (MBM) are two multitarget distributions for which closed-form filtering recursions exist. The PMBM has a Poisson birth process, whereas the MBM has a multi-Bernoulli birth process. This paper considers a recently developed formulation of the multitarget tracking problem using a random finite set of trajectories, through which the track continuity is explicitly established. A multiscan trajectory PMBM filter and a multiscan trajectory MBM filter, with the ability to correct past data association decisions to improve current decisions, are presented. In addition, a multiscan trajectory MBM01 filter, in which the existence probabilities of all Bernoulli components are either 0 or 1, is presented. This paper proposes an efficient implementation that performs track-oriented N-scan pruning to limit computational complexity, and uses dual decomposition to solve the involved multiframe assignment problem. The performance of the presented multitarget trackers, applied with an efficient fixed-lag smoothing method, is evaluated in a simulation study

Trajectory Poisson multi-Bernoulli filters

This paper presents two trajectory Poisson multi-Bernoulli (TPMB) filters for multi-target tracking: one to estimate the set of alive trajectories at each time step and another to estimate the set of all trajectories, which includes alive and dead trajectories, at each time step. The filters are based on propagating a Poisson multi-Bernoulli (PMB) density on the corresponding set of trajectories through the filtering recursion. After the update step, the posterior is a PMB mixture (PMBM) so, in order to obtain a PMB density, a Kullback-Leibler divergence minimisation on an augmented space is performed. The developed filters are computationally lighter alternatives to the trajectory PMBM filters, which provide the closed-form recursion for sets of trajectories with Poisson birth model, and are shown to outperform previous multi-target tracking algorithms

Multiple Object Trajectory Estimation Using Backward Simulation

This paper presents a general solution for computing the multi-object posterior for sets of trajectories from a sequence of multi-object (unlabelled) filtering densities and a multi-object dynamic model. Importantly, the proposed solution opens an avenue of trajectory estimation possibilities for multi-object filters that do not explicitly estimate trajectories. In this paper, we first derive a general multi-trajectory backward smoothing equation based on random finite sets of trajectories. Then we show how to sample sets of trajectories using backward simulation for Poisson multi-Bernoulli filtering densities, and develop a tractable implementation based on ranked assignment. The performance of the resulting multi-trajectory particle smoothers is evaluated in a simulation study, and the results demonstrate that they have superior performance in comparison to several state-of-the-art multi-object filters and smoothers.Comment: Accepted for publication in IEEE Transactions on Signal Processin