The Mahalanobis distance is commonly used in multi-object trackers for measurement-to-track association. Starting with the original definition of the Mahalanobis distance we review its use in association. Given that there is no principle in multi-object tracking that sets the Mahalanobis distance apart as a distinguished statistical distance we revisit the global association hypotheses of multiple hypothesis tracking as the most general association setting. Those association hypotheses induce a distance-like quantity for assignment which we refer to as association log-likelihood distance. We compare the ability of the Mahalanobis distance to the association log-likelihood distance to yield correct association relations in Monte-Carlo simulations. Here, we use a novel method to generate multi-track scenarios that make the association evaluation independent of a specific track management scheme. We also explore the influence of the term proportional to the measurement dimension in the association log-likelihood distance on the assignment performance. It turns out that on average the distance based on association log-likelihood performs better than the Mahalanobis distance, confirming that the maximization of global association hypotheses is a more fundamental approach to association than the minimization of a certain statistical distance measure.

Many driver assistance systems such as Adaptive Cruise Control require the identification of the closest vehicle that is in the host vehicle's path. This entails an assignment of detected vehicles to the host vehicle path or neighboring paths. After reviewing approaches to the estimation of the host vehicle path and lane assignment techniques we introduce two methods that are motivated by the rationale to filter measured data as late in the processing stages as possible in order to avoid delays and other artifacts of intermediate filters. These filters generate discrete posterior probability distributions from which a path or “lane” index is extracted by a median estimator. The relative performance of those methods is illustrated by a ROC using experimental data and labeled ground truth data.

In safety-critical driver assistance systems such as automatic emergency braking that require the estimation of the vehicle's environment usually a measure of confidence or probability of existence for tracked objects is required. We review and assess existing approaches of obtaining such measures. We propose a new method of computing a probability of existence by relaxing the underlying assumption of a Bayes estimator. The benefits of this approach compared to a standard Bayes estimator are demonstrated and illustrated by experimental results.

In this paper, we report on a new stability analysis for hybrid legged locomotion systems based on factorization of return maps. We apply this analysis to a family of models of the spring loaded inverted pendulum (SLIP) with different leg recirculation strategies. We obtain a necessary condition for the asymptotic stability of those models, which is formulated as an exact algebraic expression despite the non-integrability of the SLIP dynamics. We outline the application of this analysis of other models of legged locomotion and it importance for the stability of legged robots and animals.