# Data association algorithms and metric design for trajectory estimation

[Doktorsavhandling]

This thesis is concerned with trajectory estimation, which finds applications in various fields such as automotive safety and air traffic surveillance. More specifically, the thesis focuses on the data association part of the problem, for single and multiple targets, and on performance metrics.

Data association for single-trajectory estimation is typically performed using Gaussian mixture smoothing. To limit complexity, pruning or merging approximations are used. In this thesis, we propose systematic ways to perform a combination of merging and pruning for two smoothing strategies: forward-backward smoothing (FBS) and two-filter smoothing (TFS). We present novel solutions to the backward smoothing step of FBS and a likelihood approximation, called smoothed posterior pruning, for the backward filtering in TFS.

For data association in multi-trajectory estimation, we propose two iterative solutions based on expectation maximization (EM). The application of EM enables us to independently address the data association problems at different time instants, in each iteration. In the first solution, the best data association is estimated at each time instant using 2-D assignment, and given the best association, the states of the individual trajectories are immediately computed using Gaussian smoothing. In the second solution, we average the states of the individual trajectories over the data association distribution, which in turn is approximated using loopy belief propagation. Using simulations, we show that both solutions provide good trade-offs between accuracy and computation time compared to multiple hypothesis tracking.

For evaluating the performance of trajectory estimation, we propose two metrics that behave in an intuitive manner, capturing the relevant features in target tracking. First, the generalized optimal sub-pattern assignment metric computes the distance between finite sets of states, and addresses properties such as localization errors and missed and false targets, which are all relevant to target estimation. The second metric computes the distance between sets of trajectories and considers the temporal dimension of trajectories. We refine the concepts of track switches, which allow a trajectory from one set to be paired with multiple trajectories in the other set across time, while penalizing it for these multiple assignments in an intuitive manner. We also present a lower bound for the metric that is remarkably accurate while being computable in polynomial time.

**Nyckelord: ** smoothing, metrics, data association, Gaussian mixtures, expectation maximization, Trajectory estimation

Denna post skapades 2016-09-28. Senast ändrad 2016-09-28.

CPL Pubid: 242484