We study algorithms for matching user tracks, consisting of time-ordered location points, to paths in the road network. Previous work has focused on the scenario where the location data is linearly ordered and consists of fairly dense and regular samples. In this work, we consider the , where the location data comes from different trips on the same route, each with very sparse samples. This captures the realistic scenario where users repeatedly travel on regular routes and samples are sparsely collected, either due to energy consumption constraints or because samples are only collected when the user actively uses a service. In the multi-track problem, the total set of combined locations is only partially ordered, rather than globally ordered as required by previous map-matching algorithms. We propose two methods, the iterative projection scheme and the graph Laplacian scheme, to solve the multi-track problem by using a single-track map-matching subroutine. We also propose a boosting technique which may be applied to either approach to improve the accuracy of the estimated paths. In addition, in order to deal with variable sampling rates in single-track map matching, we propose a method based on a particular regularized cost function that can be adapted for different sampling rates and measurement errors. We evaluate the effectiveness of our techniques for reconstructing tracks under several different configurations of sampling error and sampling rate.
Another line of research does not use any statistical methods to address the problem. Authors in @cite_4 use curve simplification for approximating the Fr 'echet distance of curves. Given a polygonal curve @math and an embedded graph @math with edges embedded as straight line segments, they attack the problem of finding the closest path in @math to the curve @math with respect to the Fr 'echet distance. @cite_9 , the average Fr 'echet distance is used to reduce the effect of outliers.
@cite_9 @cite_4
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We extend recent results using curve simplification for approximating the Frechet distance of realistic curves in near linear time to map matching: the problem of matching a curve in an embedded graph. We show that the theoretical bounds on the running time of the previous result still hold if only one of the curves is simplified during the course of the approximation algorithm. This enables our extension to the case of map matching under the assumption that the graph is p-low density for a constant p. We present experimental evidence for this assumption and implement the extended approximate matching algorithm. We show that it performs well on real world data, such as GPS traces and road networks of urban areas. In particular, it is able to perform matching tasks that took several hours with the exact matching algorithm in under a second. We consider the problem of approximating a polygonal curve P under a given error criterion by another polygonal curve P? whose vertices are a subset of the vertices of P. The goal is to minimize the number of vertices of P? while ensuring that the error between P? and P is below a certain threshold. We consider two fundamentally different error measures -- Hausdorff and Frechet error measures. For both error criteria, we present near-linear time approximation algorithms that, given a parameter ? > 0, compute a simplified polygonal curve P? whose error is less than ? and size at most the size of an optimal simplified polygonal curve with error ? 2. We consider monotone curves in the case of Hausdorff error measure and arbitrary curves for the Frechet error measure. We present experimental results demonstrating that our algorithms are simple and fast, and produce close to optimal simplifications in practice.