A New Data Association Method Using Kalman Filter Innovation Vector Projections

This paper describes the derivation, analysis and implementation of a new data association method that provides a tight bound on the risk of incorrect association for LiDAR feature-based localization. Data association (DA) is the process of assigning currently-sensed features with ones that were previously observed. Most DA methods use a nearest-neighbor criterion based on the normalized innovation squared (NIS). They require complex algorithms to evaluate the risk of incorrect association because sensor state prediction, prior observations, and current measurements are uncertain. In contrast, in this work, we derive a new DA criterion using projections of the extended Kalman filter's innovation vector. The paper shows that innovation projections (IP) are signed quantities that not only capture the impact of an incorrect association in terms of its magnitude, but also of its direction. The IP-based DA criterion also leverages the fact that incorrect associations are known and well-defined fault modes. Thus, as compared to NIS, IPs provide a much tighter bound on the predicted risk of incorrect association. We analyze and evaluate the new IP method using simulated and experimental data for autonomous inertial-aided LiDAR localization in a structured lab environment.