Adaptive Filtering for Multisatellite Relative Navigation with Quantized Measurements

In non-cooperative close-proximity operations, onboard optical measurements of a nearby space object can be used to determine its relative state. If the target geometry is known a priori, range information can be inferred from the apparent target extent in the image plane using a process known as stadiametric range finding. However, quantization errors of the target extent can dominate the indirect range measurement, thus violating standard modeling assumptions. This paper develops a new probabilistic measurement model to account for quantized and imprecise measurements. A Bayesian adaptive Gaussian mixture filter is derived for single- and multisatellite relative navigation that splits mixands about the quantization set boundaries. The navigation filter is shown to produce accurate and consistent relative state estimates in single- and multi-inspector scenarios involving a geostationary-orbiting target.