Bayesian filtering with wavefunctions

This paper describes a general framework for performing Bayesian filtering on probability density functions represented by the modulus squared of a wavefunction in an orthogonal function basis. The objective of this work is to find a sparse representation for high-dimensional non-Gaussian density functions enabling tractable implementations of the general Bayesian filtering problem. The general form of the Bayesian filtering algorithms employing the modulus squared of a wavefunction is presented without specification of a particular basis. A simple 0-th order implementation of this formulation for a bearing only sensor is also demonstrated.