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...t states Ψ (s) t on the associated trajectories. This results in many hypotheses which often lie closely together. To condense this set into a small number of hypotheses, we apply a mean shift method =-=[16]-=-, [17]. The key idea is to estimate the local densities of the predicted states φ (s) T by constructing a kernel over each state and then to shift the states iteratively towards higher densities with ...

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... signatures [8]. Matching methods based on string matching techniques for raw trajectories (i.e. without change in representation) have been proven to be successful. Examples are Dynamic Time Warping =-=[9]-=-, the Longest Common Subsequence [10], and the Levenshtein Distance on Trajectories [5]. We will further explore this idea in the following sections. A concept strongly related to the topic of traject...

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...based on trajectories is more widely used. Echo State Networks are applied in [3] to obtain a motion prediction of a robotic system in local surroundings with main focus on real-time applications. In =-=[4]-=-, a body-tracking system is presented where the motion is predicted with a particle filter approach based on a motion database. Similarly, a set of motion hypotheses is used in [5] to track a hand-for...

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...|Ψt−1)p(Ψt−1|M1:t−1) dΨt−1 (16) with η as a normalisation constant. This distribution is represented by a set of samples or particles {Ψ (s) t }S, which are propagated in time using a particle filter =-=[15]-=-. Therefore, each particle Ψ (s) t represents a sub-trajectory for the current state. The distribution p(M1:t|Ψt) represents the likelihood that the measurement trajectory M1:t can be observed when th...

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... each trajectory as a feature vector of length n. These vectors are used as input to a standard classifier architecture. For this purpose, we applied the well-known second-order polynomial classifier =-=[14]-=- with ideal output vectors τ = [1, 0] for trajectories of class “turn left” and τ = [0, 1] for trajectories of class “straight on”. This straightforward feature extraction and classification approach,...

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...is an efficient matching technique to compare the vehicle history with the dataset. A lot of research has been done in this field, starting from different representations, e.g. polynomial descriptors =-=[6]-=-, turning angle representation [7], and curve signatures [8]. Matching methods based on string matching techniques for raw trajectories (i.e. without change in representation) have been proven to be s...

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...lated to the topic of trajectory matching are classifiers applied to trajectories. Often a trajectory is converted into a feature representation, such that it can be processed by standard classifiers =-=[11]-=-. III. TRAJECTORIES Motion patterns are the core issue of this study. We present them as trajectories X which consist of ordered tuples X = ((x1, t1), . . . , (xN, tN)) combining states xi with a time...

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... to compare the vehicle history with the dataset. A lot of research has been done in this field, starting from different representations, e.g. polynomial descriptors [6], turning angle representation =-=[7]-=-, and curve signatures [8]. Matching methods based on string matching techniques for raw trajectories (i.e. without change in representation) have been proven to be successful. Examples are Dynamic Ti...

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... to be an adequate metric and can handle these stated requirements, except the last two issues. We thus adopted the LCS metric and applied the property of rotational invariance by using the method in =-=[12]-=- which finds the optimal orthogonal transformation to superimpose two point sets based on quaternions. B. Longest Common Subsequence (LCS) The LCS metric originates in the field of string matching alg...

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...ased on a set of labelled trajectories. II. RELATED WORK To our knowledge, the problem of predicting a vehicle state several seconds into the future has not yet been addressed by many researchers. In =-=[1]-=- an explicit motion model is used to gain a stochastic threat assessment of road objects populating the environment. Similarly, in [2] a motion model is learned from given trajectories using a cluster...

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...es Ψ (s) t on the associated trajectories. This results in many hypotheses which often lie closely together. To condense this set into a small number of hypotheses, we apply a mean shift method [16], =-=[17]-=-. The key idea is to estimate the local densities of the predicted states φ (s) T by constructing a kernel over each state and then to shift the states iteratively towards higher densities with the me...

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...sed on string matching techniques for raw trajectories (i.e. without change in representation) have been proven to be successful. Examples are Dynamic Time Warping [9], the Longest Common Subsequence =-=[10]-=-, and the Levenshtein Distance on Trajectories [5]. We will further explore this idea in the following sections. A concept strongly related to the topic of trajectory matching are classifiers applied ...

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...nto the future has not yet been addressed by many researchers. In [1] an explicit motion model is used to gain a stochastic threat assessment of road objects populating the environment. Similarly, in =-=[2]-=- a motion model is learned from given trajectories using a clustering technique to predict the object’s behaviour. In the field of body-tracking, motion prediction based on trajectories is more widely...

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...story with the dataset. A lot of research has been done in this field, starting from different representations, e.g. polynomial descriptors [6], turning angle representation [7], and curve signatures =-=[8]-=-. Matching methods based on string matching techniques for raw trajectories (i.e. without change in representation) have been proven to be successful. Examples are Dynamic Time Warping [9], the Longes...

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...me applications. In [4], a body-tracking system is presented where the motion is predicted with a particle filter approach based on a motion database. Similarly, a set of motion hypotheses is used in =-=[5]-=- to track a hand-forearm model of a worker in an industrial scenario. A key to predict motion based on trajectories is an efficient matching technique to compare the vehicle history with the dataset. ...

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...ectories using a clustering technique to predict the object’s behaviour. In the field of body-tracking, motion prediction based on trajectories is more widely used. Echo State Networks are applied in =-=[3]-=- to obtain a motion prediction of a robotic system in local surroundings with main focus on real-time applications. In [4], a body-tracking system is presented where the motion is predicted with a par...