Learning the Parameters of Spatially-Referring Natural Language Likelihoods in Binary Models

Despite imprecision and possible ambiguity expressed by spatially referring natural language statements, they are potentially useful “measurements” (also known as soft data) for target localisation and tracking. The likelihood functions of such measurements typically include the parameters that model the inherent uncertainty in soft data. Adopting a binary model for spatially referring statements involving the word “near”, the paper derives the theoretical posterior Cramér-Rao bound for the estimation (learning) of the parameter which features in the likelihood function. A numerical analysis of the bound is presented with an example demonstrating estimation/learning in practice.