Calculation of the parameters of Hidden Markov models used in the navigation systems of surface transportation for map matching: A review

This article provides an overview of the mathematical methods for calculating the parameters of Hidden Markov Models (HMM) used in conjunction with the map coordinates measured by the global positioning systems (GPSs) of mobile navigation systems. These methods are analyzed and compared. There is considered an example of calculating of emission probability of observations emissions and transition probabilities for the Hidden Markov Model of a road network. The example is accompanied by the construction of a states diagram of the HMM and a trellis diagram of the Viterbi algorithm. Using the example, there is estimated the influence of the choice of the value of the standard deviation for the probability density distribution of the minimum distances and the angles difference between the direction of the road element and the direction of the velocity of the vehicle on the probability of the path on the Viterbi trellis. It is proposed to use the functional dependence of the optimal path on the standard deviations and the orthogonal distances for the correction in the process of testing and the practical application of the algorithm of map matching based on the HMM.