To enable safe and efficient autonomous driving in an urban environment, accurate knowl- edge of the vehicle’s position, as well as of other road users is needed. On one hand, this is enabled by having highly accurate on-board sensors and on the other hand, through fusion of information collected by other vehicles.
In Paper C, we proposed a Bayesian filtering formulation to jointly track the positions of multiple cooperative vehicles and of observed moving targets (called features in this work). In doing so, measurements from two kinds of sensors were utilized: a Global
6.2 Multitarget Tracking with Uncertain Sensor State (Papers C, D and E)
Positioning System (GPS)-like sensor to obtain the vehicles absolute position, and a radar-like sensor to obtain the relative positions of targets. The radar-sensors’ peculiarity of an unknown target-to-measurement association, was incorporated in the factor graph (FG) formulation and the minimum mean square error (MMSE) estimate was found by running nonparametric belief propagation (BP).
When multiple vehicle with different location uncertainties observe the same set of targets, the positioning quality of vehicles with uncertain location can be improved by target tracking. Furthermore, we saw that the accuracy of the target measurements determines how much global information can be transferred from a well localized vehicle to vehicles with lower accuracy by means of target tracking. Thereby, the number of observed targets has an impact on the amount of information which can be transferred between the vehicles within one time step. It is interesting to point out that well-localized vehicles do not benefit by target tracking. The reason for this is simply that no new information in terms of a measurement of an absolute coordinate/position is introduced. In Paper D and E, we followed a different path to tackle this tracking problem, where we proposed a multisensor Poisson multi-Bernoulli filter for joint target and vehicle state tracking. To enable the usage of standard MTT frameworks, and to achieve a tractable implementation, we performed an approximation of the joint posterior density by mini- mizing the Kullback-Leibler divergence (KLD). This allowed to maintain an independent structure of the vehicle and of the target state densities. The result of this approach is that a standard Poisson multi-Bernoulli mixture (PMBM) MTT filter can be applied for target tracking, with the modification that the single target likelihood considers the present vehicle (sensor) uncertainty. Furthermore, due to the symmetry in the approxi- mations, an update of the sensor state is possible by means of target tracking.
In a single vehicle scenario, the vehicle’s location uncertainty is incorporated in the MTT filter, which allows to produce stable target estimates compared to the case when this uncertainty is ignored (c.f. Paper E). We observed that in terms of target tracking performance, the vehicle state should not be updated by the target measurements. The reason for this is that after the measurement update step, target and vehicle states become correlated, which is not modeled by the proposed filter.
In a multiple vehicle scenario, target measurements from vehicles with different location uncertainties are incorporated sequentially utilizing an iterator-corrector approach. This allows not only accurate target tracking, but also to convey information from targets to vehicles, with the result of an improved position quality compared to the case of vehicle state tracking alone. We demonstrated this not only in simulations but also in an experiment involving real vehicles. Furthermore, we observed that vehicles with high location uncertainty can improve their positioning quality by target tracking only when the observed target set intersected with the target set of observed by vehicles with low location uncertainty is non-empty.
Chapter 6 Scientific Achievements, Conclusions and Outlook
Possible Extensions
The proposed approach of Paper C neither considers target appearance and disappear- ance nor non-overlapping field-of-views (FoVs) of the radar-like sensors. A natural ex- tension would be to consider them. Note that target appearance and disappearance was addressed in [48], [53]. Furthermore, prior knowledge of the measurement-to-target correspondence, if available, could be incorporated in the FG for the radar-like sensor.
The implementation of the proposed MTT filter of Paper D and E utilizes linear dynamical and measurement models. An extension of this work could consider non- linear models, e.g., through a sequential Monte-Carlo implementation, thus allowing to model the vehicles orientation. Furthermore, no target labels are maintained by the proposed filter implementation and therefore there are no trajectories for individual targets available. Labels can be added as discussed in [58] or alternative descriptions of the multi-Bernoulli mixture (MBM) filter should be considered when the target tracks are of interest (c.f. Sec. 5.4). The problem of MTT from a vehicle with uncertain location can also be cast as a simultaneous localization and mapping (SLAM) problem, where the whole vehicle trajectory and not only the current vehicle state is of interest. Accordingly, the multi-vehicle scenario would then result in a cooperative SLAM problem. Furthermore, the proposed filter is a centralized approach, which is not desirable for autonomous driving scenarios. The filter could also be extended to that effect allowing to address issues like time synchronization among different vehicles and dealing with the error prone wireless communication channel.
6.3 Decentralized Extended Target Tracking (Paper F)
In Paper F, we adapted a state-of-the art ETT filter to track targets with star-convex shape. Thereby, a GP was used to model the target shape. The ETT filter, together with the GP target shape model, enables to accurately estimate and track the shape and kinematic state of multiple ETs from target contour measurements, where the filter’s posterior is modeled by a Poisson multi-Bernoulli (PMB).
We proposed a method to fuse posterior information from multiple independent ETT filters in a way such that the fused density does not underestimate the true uncertainty of the targets (robust fusion). In doing so, fusing the multitarget posteriors was performed separately by fusion of the Poisson random finite sets (RFSs) describing the hypothesized, but not yet detected targets, and by fusing the multi-Bernoulli (MB) RFSs modeling the detected targets. Through utilization of a map for individual Bernoulli components between the MB RFSs, which is described in the minimum KLD sense and found by solving a linear assignment problem, complexity in the fusion step is reduced. After the fusion step, the obtained multitarget posterior can be utilized as a prior density for the independent filters in the next time step.