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Navigation, mapping, and tracking are state estimation problems relevant to a wide range of applications. These problems have traditionally been formulated using random vectors in stochastic filtering, smoothing, or optimization-based approaches. Alternatively, the problems can be formulated using random finite sets, which offer a more robust solution in poor detection conditions (i.e., low probabilities of detection, and high clutter intensity). This paper mathematically shows that the two estimation frameworks are related, and equivalences can be determined under a set of ideal detection conditions. The findings provide important insights into some of the limitations of each approach. These are validated using simulations with varying detection statistics, along with a real experimental dataset.

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In robotic mapping and simultaneous localization and mapping, the ability to assess the quality of estimated maps is crucial. While concepts exist for quantifying the error in the estimated trajectory of a robot, or a subset of the estimated feature locations, the difference between all current estimated and ground-truth features is rarely considered jointly. In contrast to many current methods, this paper analyzes metrics, which automatically evaluate maps based on their joint detection and description uncertainty. In the tracking literature, the optimal subpattern assignment (OSPA) metric provided a solution to the problem of assessing target tracking algorithms and has recently been applied to the assessment of robotic maps. Despite its advantages over other metrics, the OSPA metric can saturate to a limiting value irrespective of the cardinality errors and it penalizes missed detections and false alarms in an unequal manner. This paper therefore introduces the cardinalized optimal linear assignment (COLA) metric, as a complement to the OSPA metric, for feature map evaluation. Their combination is shown to provide a robust solution for the evaluation of map estimation errors in an intuitive manner. Index Terms-Map metric, simultaneous localization and mapping, mobile robots. I. INTRODUCTION F UNDAMENTAL to any state estimation problem is the concept of estimation error. Solutions to robotic mapping and simultaneous localization and mapping (SLAM), in which usually the location of an unknown number of features should be estimated, are numerous offering various degrees of performance. Examples include classical methods such as recursive EKF SLAM [1], [2], multihypothesis (MH) FastSLAM [3],