Analytical Reformulation of Angles-Only Measurements with Application to Cislunar Object Tracking

This paper proposes a robust alternative approach to fusing information from angles-only measurements into sequential filters. It has become common practice to work directly with the azimuth and elevation of an object in the local visual field to construct measurement residuals for use within batch or sequential filters. While easy to obtain, these values can prove troublesome, particularly in scenarios where measurements are scarce and intermittently available. This is due primarily to the linear approximation of the measurement function breaking down when the residual is too large. This study introduces a filter working measurement and associated error covariance, constructed from the measured azimuth and elevation, that eliminates the nonlinearity in the measurement function while preserving the angular uncertainty. Additionally, it will be shown that this approach can be generalized to work with received range-only measurements and a fusion of independent range and angular measurements. A final comparison between the traditional nonlinear measurement equations and the proposed variable-range pointing vector is performed for cislunar uncooperative object-tracking scenarios with intermittent measurements due to various observation exclusion zones.