Astrometric and Photometric Data Fusion for Mass and Surface Material Estimation using Refined Bidirectional Reflectance Distribution Functions-Solar Radiation Pressure Model

摘要

CONFERENCE PAPER This paper studies the inference of space object mass, which is made possible due to the coupled influence of solar radiation pressure (SRP) acceleration on the orbit of satellites and their observed brightness. This effect takes time to be observed in optical angle measurements given the combination of a priori kinematic state uncertainties and the magnitude of this effect relative to them and the sensor data noise. Therefore, multiple nights of observations are typically required to extract this "weak" signal from collected measurements. From angles data alone, only effective albedo-area-to-mass can be estimated since this term appears in the SRP acceleration equation, but when photometric data is fused with the astrometric angle measurements, it provides observability of, and thus constrains, the albedo-area estimates. This inferred constraint makes mass the most open degree of freedom and thus the fused data eventually informs the filter of the mass. The observability of albedo-area products is provided by the photometric brightness measurements, since the brightness of the space object is a strong function of the albedo-areas. However, the relationship between the albedo-areas and both the photometric return and SRP involves knowledge of the Bidirectional Reflectance Distribution Function (BRDF) for the surface of the space object. If the BRDF in the photometric measurement model and the BRDF in the SRP model are not consistent with each other, then the resulting estimated albedo-areas and mass are inaccurate and biased. This work studies the use of physically consistent BRDF-SRP models for mass estimation. Simulation studies are used to provide an indication of the benefits of using these new models. An unscented Kalman filter approach that includes BRDF and mass parameters in the state vector is used. The full set of estimated parameters includes position, velocity, attitude, angular rates, mass, exponential factor (parameter in Ashikhmin-Shirley BRDF related to sharpness of specular reflection), specular coefficient and diffuse coefficient. The challenge of adding these additional parameters is the fact that they are constrained, where all must be positive and the specular and diffuse coefficients must be less than unity. Two approaches are adopted to account for the constraints; the first approach projects the sigma points onto the constraint boundary if any violate the constraints on the parameters, and the second approach defines proxy parameters that are unconstrained version of the original parameters. The results for estimating mass are promising and show that the addition of consistent BRDF-SRP models benefits the estimation process.