Pose estimation is central to several robotics applications such as registration, hand-eye calibration, and simultaneous localization and mapping (SLAM). Online pose estimation methods typically use Gaussian distributions to describe the uncertainty in the pose parameters. Such a description can be inadequate when using parameters such as unit quaternions that are not unimodally distributed. A Bingham distribution can effectively model the uncertainty in unit quaternions, as it has antipodal symmetry, and is defined on a unit hypersphere. A combination of Gaussian and Bingham distributions is used to develop a truly linear filter that accurately estimates the distribution of the pose parameters. The linear filter, however, comes at the cost of state-dependent measurement uncertainty. Using results from stochastic theory, we show that the state-dependent measurement uncertainty can be evaluated exactly. To show the broad applicability of this approach, we derive linear measurement models for applications that use position, surface-normal, and pose measurements. Experiments assert that this approach is robust to initial estimation errors as well as sensor noise. Compared with state-of-the-art methods, our approach takes fewer iterations to converge onto the correct pose estimate. The efficacy of the formulation is illustrated with a number of examples on standard datasets as well as real-world experiments.

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Real-time traffic status information provides good references for urban traffic control and management. Travel time is easy to understand and widely employed in representing traffic status. With significantly improved positioning accuracy and coverage, trajectory data collected from GPS-equipped probe vehicles have great potential for traffic state recognition. This paper presents a machine learning enabled travel time estimation method based on the GPS-equipped probe vehicles data. This research considers the spatial-temporal relevancy while solving the travel time allocation problem: the travel time of target segment might be associated with its previous travel times and/or the traffic states of nearby relevant segments. After data normalization and network clustering, an artificial neural network (ANN) algorithm considering such spatial-temporal relevancy was conducted to infer the travel time distribution among the traveled segments within one path. Furthermore, a weighted summation of the travel time estimation result from various trajectories was calculated to better represent the segment travel time in one time step. The proposed method was evaluated by evaluating the estimation results with automatic vehicle identification obtained ground truth. The experimental results illustrated that by utilizing the ANN to consider the spatialtemporal relevancy, the proposed method is effective and efficient in estimating the travel time. INDEX TERMS Artificial neural network (ANN), data clustering, global positioning system (GPS) equipped probe vehicle, travel time estimation, travel time allocation.

Global positioning system (GPS) trajectory map matching projects GPS coordinates to the road network. Most existing algorithms focus on the geometric and topological relationships of the road network, while did not make full use of the historical road network information and floating car data. In this study, the authors proposed a deep learning enabled vehicle trajectory map-matching method with advanced spatial-temporal analysis (DST-MM). The algorithm mainly focused on the following three aspects: (i) analyse the spatial relevancy from the prospective of geometric analysis, topology analysis and intersection analysis; (ii) to make full use of the historical and real-time data, a deep learning model was conducted to extract the road network and vehicle trajectory features and (iii) establish a speed prediction model and nest it in the temporal analysis structure. It narrows down the path search range through establishing the dynamic candidate graph. Experimental results show that the proposed DST-MM algorithm outperforms the existing algorithms in terms of matching accuracy for low-sampling frequencies GPS data, especially in the central urban area.

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