Aspects of Theoretical and Experimental Map-Matching

This paper is a tutorial development of both new and old results of theoretical and experimental techniques which are applicable to map-matching, the recognition of previously observed results in experimental data. This development of a theory for treating 2-valued maps deals with the manipulation of maps with Boolean functions and the corresponding manipulation with optical equipment. The use of a modulo-2 operation defines the identity condition. Binary weighting functions produce conditional identity conditions and a relation between symmetrical and asymmetrical correlation of maps. Sampled maps introduce the concept of essentially identical maps so as to make possible the calculation of error probabilities from a sample population of essentially similar maps. The use of loss functions in accepting or rejecting the identity of two maps produces a decision-theoretic criteria for threshold detection. The threshold is a nontrivial threshold in the cases where system noise is present. The construction of composite maps is treated from the standpoint of minimum average discrepancy error. Numerical examples based on exponential bounds indicate the effectiveness of these techniques.