Localization-based sensor validation using the Kullback-Leibler divergence

A sensor validation criteria based on the sensor's object localization accuracy is proposed. Assuming that the true probability distribution of an object or event in space f(x) is known and a spatial likelihood function (SLF) psi(x) for the same object or event in space is obtained from a sensor, then the expected value of the SLF E[psi(x)] is proposed as a suitable validity metric for the sensor, where the expectation is performed over the distribution f(x). It is shown that for the class of increasing linear log likelihood SLFs, the proposed validity metric is equivalent to the Kullback-Leibler distance between f(x) and the unknown sensor-based distribution g(x) where the SLF psi(x) is an observable increasing function of the unobservable g(x). The proposed technique is illustrated through several simulated and experimental examples.