A method allows for determining the quality of a vessel's moment estimate and track information derived from a suite of sensors measuring the local magnitude of the magnetic field. A Bayesian treatment, employing a Markov Chain Monte Carlo approach with Gibbs sampling is applied with reduced magnetic noise spatio-temporal correlation models and implied whitening procedures. Vessel moment parameters are handled with a Gaussian prior leading to conditional densities that are Gaussian and posterior marginal densities that are mixture-Gaussian. Other conditional quantile functions for track parameters are computed with a grid procedure. From these, the Markov chain is determined and the resulting joint density of all variates is constructed. The method allows for determining posterior marginal densities and dependencies associated with magnetic moment and track parameters. The method may be stored in a storage device in a sensor and may be executed by a processor within the sensor.