This paper presents a joint trajectory smoothing and tracking framework for a specific class of targets with smooth motion. We model the target trajectory by a continuous function of time (FoT), which leads to a curve fitting approach that finds a trajectory FoT fitting the sensor data in a sliding time-window. A simulation study is conducted to demonstrate the effectiveness of our approach in tracking a maneuvering target, in comparison with the conventional filters and smoothers. Note to Practitioners —Estimation, such as automatically tracking and predicting the movement of an aircraft, a train, or a bus, plays a key role in our daily life. In this paper, we provide a new approach for the online estimation of the target trajectory function by means of fitting the time-series observation, which accommodates the lack of quantifiable knowledge about the target motion and of the statistical property of the sensor observation noise. The resulting trajectory function can be used to infer either the past or the present state of the target. Engineering-friendly strategies are provided for computationally efficient implementation. The proposed approach is particularly appealing to a broad range of real-world targets that move in smooth courses, such as passenger aircraft and ships.
Target trajectory estimation and analysis do not only allow recording the history of past locations and predicting the future but also provide a means to specify behavioral patterns or relationships between locations observed in time series and to guide target detection in future frames @cite_17 , to name a few. Most existing works however are based on either deterministic or stochastic HMM assumption of the target motion and need statistical property of the observation, which forms the key difference to our approach. In addition, no explicit attempts explicitly unify the tasks of smoothing, filtering, tracking and forecasting, fully based on data fitting learning.
@cite_17
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We present a novel approach for multi-object tracking which considers object detection and spacetime trajectory estimation as a coupled optimization problem. Our approach is formulated in a minimum description length hypothesis selection framework, which allows our system to recover from mismatches and temporarily lost tracks. Building upon a state-of-the-art object detector, it performs multiview multicategory object recognition to detect cars and pedestrians in the input images. The 2D object detections are checked for their consistency with (automatically estimated) scene geometry and are converted to 3D observations which are accumulated in a world coordinate frame. A subsequent trajectory estimation module analyzes the resulting 3D observations to find physically plausible spacetime trajectories. Tracking is achieved by performing model selection after every frame. At each time instant, our approach searches for the globally optimal set of spacetime trajectories which provides the best explanation for the current image and for all evidence collected so far while satisfying the constraints that no two objects may occupy the same physical space nor explain the same image pixels at any point in time. Successful trajectory hypotheses are then fed back to guide object detection in future frames. The optimization procedure is kept efficient through incremental computation and conservative hypothesis pruning. We evaluate our approach on several challenging video sequences and demonstrate its performance on both a surveillance-type scenario and a scenario where the input videos are taken from inside a moving vehicle passing through crowded city areas. We present a novel approach for multi-object tracking which considers object detection and spacetime trajectory estimation as a coupled optimization problem. It is formulated in a hypothesis selection framework and builds upon a state-of-the-art pedestrian detector. At each time instant, it searches for the globally optimal set of spacetime trajectories which provides the best explanation for the current image and for all evidence collected so far, while satisfying the constraints that no two objects may occupy the same physical space, nor explain the same image pixels at any point in time. Successful trajectory hypotheses are fed back to guide object detection in future frames. The optimization procedure is kept efficient through incremental computation and conservative hypothesis pruning. The resulting approach can initialize automatically and track a large and varying number of persons over long periods and through complex scenes with clutter, occlusions, and large-scale background changes. Also, the global optimization framework allows our system to recover from mismatches and temporarily lost tracks. We demonstrate the feasibility of the proposed approach on several challenging video sequences. In order to track moving objects in long range against occlusion, interruption, and background clutter, this paper proposes a unified approach for global trajectory analysis. Instead of the traditional frame-by-frame tracking, our method recovers target trajectories based on a short sequence of video frames, e.g., 15 frames. We initially calculate a foreground map at each frame obtained from a state-of-the-art background model. An attribute graph is then extracted from the foreground map, where the graph vertices are image primitives represented by the composite features. With this graph representation, we pose trajectory analysis as a joint task of spatial graph partitioning and temporal graph matching. The task can be formulated by maximizing a posteriori under the Bayesian framework, in which we integrate the spatio-temporal contexts and the appearance models. The probabilistic inference is achieved by a data-driven Markov chain Monte Carlo algorithm. Given a period of observed frames, the algorithm simulates an ergodic and aperiodic Markov chain, and it visits a sequence of solution states in the joint space of spatial graph partitioning and temporal graph matching. In the experiments, our method is tested on several challenging videos from the public datasets of visual surveillance, and it outperforms the state-of-the-art methods. Location is a key context ingredient and many existing pervasive applications rely on the current locations of their users. However, with the ability to predict the future location and movement behavior of a user, the usability of these applications can be greatly improved. In this paper, we propose an approach to predict both the intended destination and the future route of a person. Rather than predicting the destination and future route separately, we have focused on making prediction in an integrated way by exploiting personal movement data (i.e. trajectories) collected by GPS. Since trajectories contain daily whereabouts information of a person, the proposed approach first detects the significant places where the person may depart from or go to using a clustering-based algorithm called FBM (Forward-Backward Matching), then abstracts the trajectories based on a space partitioning method, and finally extracts movement patterns from the abstracted trajectories using an extended CRPM (Continuous Route Pattern Mining) algorithm. Extracted movement patterns are organized in terms of origin-destination couples. The prediction is made based on a pattern tree built from these movement patterns. With the real personal movement data of 14 participants, we conducted a number of experiments to evaluate the performance of our system. The results show that our approach can achieve approximately 80 and 60 accuracy in destination prediction and 1-step prediction, respectively, and result in an average deviation of approximately 60 m in continuous future route prediction. Finally, based on the proposed approach, we implemented a prototype running on mobile phones, which can extract patterns from a user's historical movement data and predict the destination and future route.