An Integrated Likelihood Formulation for Characterizing the Proximity of Position Measurements to Road Segments

The analysis of spatial proximity between objects can yield useful insights for a variety of problems. A common application is found in map matching problems, where noisy position measurements collected from a receiver on a network-bound mobile object is analyzed for estimating the original road segments traversed by the object. Motivated by this problem, we take a detailed look at proximity measures that quantify the spatial closeness between points and curves in non-deterministic problems, where the given points are noisy observations of a stochastic process defined on a given set of curves. Starting with a critical review of traditional pointwise approaches, we introduce the integral proximity measure for quantifying proximity, so as to better represent the statistical likelihoods of a process' states. Assuming a generic stochastic model with additive noise, we discuss the correct proximity function for the proximity measures, and the relationship between a posteriori probabilities of the process and the proximity measures for a comparison of both measures. Later, we prove that the proposed measure can provide better inferences about the process' states, when the process is under the influence of uncorrelated bivariate Gaussian noise. Finally, we conduct an extensive Monte Carlo analysis, which shows significant inference improvements over traditional proximity measures, particularly under high noise levels and dense road settings.