Advanced Filtering Techniques Applied to Spaceflight

IST-Rolla developed two nonlinear filters for spacecraft orbit determination during the Phase I contract. The theta-D filter and the cost based filter, CBF, were developed and used in various orbit determination scenarios. The scenarios were application to low Earth orbit, range only, and range and range rate estimation. The modified state observer was also developed to estimate uncertainty in the dynamic model besides estimation of orbital states. Phase I research showed that there is a problem with the linear-like form that is used by many nonlinear filters such as the State Dependant Riccati Equation filter (SDRE filter), and the theta-D and CBF. A study of the observability led to important discoveries about the lack of observabilty in some formulations. Detailed study of the working of the proposed nonlinear filters in terms of observability and their application to more precise orbit determination and model uncertainty estimation will be undertaken in Phase II. Also learned from Phase I, IST-Rolla will focus more on how and where these nonlinear filters can help NASA. There will be three main applications studied during Phase II: interplanetary orbit determination, space debris tracking, and interplanetary landing spacecraft tracking. These applications were chosen because of their relevance to current NASA missions and the nonlinearity of the measurements involved should show the need for the nonlinear filters. Furthermore, working algorithms and software will be given to NASA to test on ongoing applications.

Most of the applications for NASA apply here as well. Once packaged, these algorithms will provide a powerful tool to spacecraft designers and will be easy to implement and test. IST-Rolla strives to make all commercial products as user friendly, and applicable in as many cases as possible. Furthermore, these set of algorithms along with the EKF, the unscented Kalman filter will be made into a tool box that can be sold to educational organizations for teaching courses on estimation and orbit determination as well as companies like aerospace, automotive industry for use in design.

The algorithms provided by IST-Rolla, the theta-D, CBF and neural network estimator, will be set up so that the end user can provide the current estimate and the measurements, then the filter will adjust to those measurements and provide an estimate. This will be packaged into a C code, and an attempt will be made to create a filtering toolbox for MATLAB as well. These steps will allow the end user to apply and adapt these filters and with the analysis provided by IST-Rolla in Phase I and Phase II, the user will know exactly what to expect from the algorithms. The accuracy and efficiency will be a valuable asset to NASA's repertoire of orbit determination technologies.

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