A Horizontal Accuracy Metric for Magnetic Navigation

This paper develops a navigation accuracy metric for magnetic navigation when adapted to civil aviation. Metrics that are currently used may not directly apply to magnetic navigation because the assumptions behind these metrics are based on the statistics of more conventional navigation modalities where the uncertainty distribution in the horizontal plane is typically radially symmetric. Magnetic navigation challenges these assumptions. New standard deviation limits based on the probability of exceedance of radial error are derived. Use is made of quadratic forms over random variables, specifically the Hoyt distribution and its associated probability density function and cumulative density function. Although the density functions lack closed-form solutions, new approximations for this distribution are utilized in order to make rapid computation possible, enabling their use for navigation purposes. When used in conjunction with robust numerical methods, the new approach accurately calculates the bounds on error distributions that would meet the requirements associated with Performance Based Navigation.