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...needs to calculate the probability density of each snapshot: An appropriate application-specific distribution (e.g., skewed-normal random distribution) can be used to estimate the probability density =-=[1,2,9]-=-. [13] provides some non-linear methods that can significantly reduce the errors associated with the peak point of the probability density. If the snapshots can be further minimized, the spatiotempora...

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... of the actual derivatives. Processing a query with uncertainty means that each result data item is associated with the probability (or likelihood) that the item really satisfies the query predicates =-=[3]-=-. To support probabilistic query processing, one needs to calculate the probability density of each snapshot: An appropriate application-specific distribution (e.g., skewed-normal random distribution)...

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... object is within a certain distance d, of its last reported location. If the object moves further than d, it reports its new location and possibly changes the distance threshold d for future updates =-=[12]-=-. Given a point in time, the uncertainty is a circle with a radius d, bounding all possible locations of the object. Another model assumes that an object always moves along straight lines (linear rout...

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... along a straight line, but can deviate from this path by a certain distance [10, 11]. An important study on the issues of uncertainty in the recorded past trajectories (history) of CCDOs is found in =-=[6]-=-. Assuming that the maximum velocity of an object is known, they prove that all possible locations of the object during the time interval between two consecutive observations (reported states) lie on ...

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...needs to calculate the probability density of each snapshot: An appropriate application-specific distribution (e.g., skewed-normal random distribution) can be used to estimate the probability density =-=[1,2,9]-=-. [13] provides some non-linear methods that can significantly reduce the errors associated with the peak point of the probability density. If the snapshots can be further minimized, the spatiotempora...

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...needs to calculate the probability density of each snapshot: An appropriate application-specific distribution (e.g., skewed-normal random distribution) can be used to estimate the probability density =-=[1,2,9]-=-. [13] provides some non-linear methods that can significantly reduce the errors associated with the peak point of the probability density. If the snapshots can be further minimized, the spatiotempora...

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... reports whenever the object’s speed or direction changes. Other models assume that an object travels with a known velocity along a straight line, but can deviate from this path by a certain distance =-=[10, 11]-=-. An important study on the issues of uncertainty in the recorded past trajectories (history) of CCDOs is found in [6]. Assuming that the maximum velocity of an object is known, they prove that all po...

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... range queries for trajectories. The error ellipse defined and proved in [6] is the projection of a three-dimensional spatiotemporal uncertainty region onto the two-dimensional data space. Similarly, =-=[4]-=- represents the set of all possible locations based on the intersection of two half cones that constraint the maximum deviation from two known locations. It also introduces multiple granularities to p...

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... reports whenever thesobject’s speed or direction changes. Other models assume that an object travels with asknown velocity along a straight line, but can deviate from this path by a certain distances=-=[10, 11]-=-.sAn important study on the issues of uncertainty in the recorded past trajectoriess(history) of CCDOs is found in [6]. Assuming that the maximum velocity of an object issknown, they prove that all po...

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...within a certain interval, centered at its last reported location, along the line of movement [12]. Different CCDO trajectory models that have no uncertainty consideration are found in the literature =-=[7]-=-. These models make sure that the exact velocity is always known by requiring reports whenever the object’s speed or direction changes. Other models assume that an object travels with a known velocity...

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... reports whenever the object’s speed or direction changes. Other models assume that an object travels with a known velocity along a straight line, but can deviate from this path by a certain distance =-=[10, 11]-=-. An important study on the issues of uncertainty in the recorded past trajectories (history) of CCDOs is found in [6]. Assuming that the maximum velocity of an object is known, they prove that all po...

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...calculate the probability density of each snapshot: An appropriate application-specific distribution (e.g., skewed-normal random distribution) can be used to estimate the probability density [1,2,9]. =-=[13]-=- provides some non-linear methods that can significantly reduce the errors associated with the peak point of the probability density. If the snapshots can be further minimized, the spatiotemporal regi...

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...d thus variably affecting the set of possible states of the CCDO, one can further reduce the snapshots through a separate processing steps of contextualizing (modifying) the probability distributions =-=[8]-=-. In the two-phase (filtering-refinement) query processing, the smaller the uncertainty regions are, the lower the rate of false-drops (i.e., the objects that are selected in thesfiltering-phase but d...