An adaptive Markov chain algorithm applied over map-matching of vehicle trip GPS data

Abstract

Markov chains have frequently been applied to match the probable routes with a set of GPS trip data that a pilot vehicle is emitting over a specific graph road network. This class of mapmatching (MM) algorithms presently demonstrates and involve statistical and ad-hoc measures to drive the Markov chain transitional probabilities in picking the best route combinations constrained over the graph road network. In this study, we have devised an adaptive scheme to modify the Markov Chain (MC) kernel window as we move along the GPS samples to reduce the mistakes that can happen by the use of narrower MC widths. The measure for temporarily increasing the MC window width is chosen to be the ratio between the geodesic distance of current route to the actual geodesic distance between each pair of GPS samples. This adaptive use of MC has shown to have hardened the results significantly with tolerable computational cost increase. The details of the overall algorithm are depicted by the example routes extracted from various vehicle trips and the results are shown to validate the usefulness of the algorithm in practice.

A fixed storage distributed graph database hybrid with at-scale OLAP expression and I/O support of a relational DB: Kinetica-Graph

“…Map matching solver using hidden Markov chains deserves a special mention among many noteworthy Kinetica-Graph solvers since its success stems mainly from graph database's efficient doubly link topology structure explained in Section 2. This patented in-house capability determines the route of thousands of GPS emitting vehicles using a novel adaptive width Hidden Markov Chain algorithm [19] shown in Figure 26. On one test batch consisted of more than 300K sample points belonging to 370 individual trips of varying degrees of sampling frequencies between 0.5 seconds and 5 seconds, we were able to obtain results in less than 24 seconds using 8 cores where 95 percent of the trips had match scores well below 1 meter over a graph of approximately 7 million edges.…”

“…For a billion node graph where each node goes to every other, the conventional graph data structures require hundred million GBytes (formidable) storage whereas Kinetica Graph requires only ten GBytes. Key differ-entiator of Kinetica Graph DB is its efficient data representation supporting a very large number of edges/nodes that has no memory degradation under dynamic updates [18,19]. Our optimized parallel graph solvers are built on top of this representation.…”

“…We have opted a priority queue implementation for our version of the Dijkstra solver which seems to supersede parallel queue implementations [19,25]. In general, the Dijkstra Condition (DC) on each node v i can be specified by Equation ( 1) which states that the cost d i can not be greater than the minimum of the cost of any incoming nodes connected to v i via the edge's weight w ij .…”

“…Figure 26: Noise in the GPS samples is quite visible by the void red circles zoomed in on a portion of the Microsoft's Seattle data set. The Map matching algorithm finds the best route by screening possible path sequences under the constraints of the graph road network topology [19]. …”

Optimal routing algorithm for trips involving thousands of ev-charging stations using Kinetica-Graph

“…When this one-tomany (lower order) and one-to-one (higher order) adjacency constraints are respected, only one vector of the size three times the data items is enough to spatially index the entire data as a doubly link list (dls); previous and next items, so that the removal and the addition of an item to the bin structure has constant time complexity. This lightweight structure is first devised by the author for numerical preprocessors, simulations and solvers [11,12], and later successfully adapted for the construction of a fixed size graph topology for the Kinetica-Graph itself [8,13].…”