Comparing Antenna Conical Scan Algorithms for Spacecraft Position Estimation

I NTHISNote,wewill examine nonlinear estimation techniques to solve nonlinear problems that have been traditionally solved by linear methods. In the area of nonlinear estimation, a class of sampling algorithms known asMarkov chainMonte Carlo (MCMC) was extensively used to obtain a solution that is often a general, nonGaussian, nonunimodal probability distribution. Therefore, there is a natural question to ask regarding problems that have been solved in practice by linear/Gaussian approximations: Canwe do better with nonlinear methods such asMCMC? If so, how much better? This Note examines the problem of estimating spacecraft position using scanning techniques for NASA’s Deep Space Network antennas and compares different algorithms through numerical studies. As described in [1–3], the NASA Deep Space Network antennas have spacecraft trajectory programmed into them to form the antenna command. To compensate for disturbances and determine the true position of the spacecraft, circular movements are added to the antenna command trajectory in a technique known as conical scanning (ConScan). From the sinusoidal variations in the power of the signal received from the spacecraft by the antenna, the true spacecraft position can then be estimated. A least-squares method was reported in literature and used in practice for the batch processing mode. We compare this method with two other possible methods: the general linear method, which uses prior distribution of spacecraft position, and the MCMCmethod, which tries to solve the nonlinear problem directly by representing the desired distribution of spacecraft position with samples. Simulations show that for the amount of data collected for ConScan batch processing in practice, all three algorithms perform essentially the same. When we artificially reduce the amount of available data, performance improvement manifests itself but the amount is dependent upon the noise level. For a low level of noise, general linear is significantly better than least squares, whereas MCMC is marginally better than general linear. For a high level of noise, general linear is marginally better than least squares, whereas MCMC is significantly better than general linear.