Adaptive and Dynamically Constrained Process Noise Estimation for Orbit Determination

Abstract: This paper introduces two new algorithms to accurately estimate the process noise covariance of a discrete-time Kalman filter online for robust orbit determination in the presence of dynamics model uncertainties. Common orbit determination process noise techniques, such as state noise compensation and dynamic model compensation, require offline tuning and a priori knowledge of the dynamical environment. Alternatively, the process noise covariance can be estimated through adaptive filtering. However, many adaptive filtering techniques are not applicable to onboard orbit determination due to computational cost or the assumption of a linear time-invariant system. Furthermore, existing adaptive filtering techniques do not constrain the process noise covariance according to the underlying continuous-time dynamical model, and there has been limited work on adaptive filtering with colored process noise. To overcome these limitations, a novel approach is developed which optimally fuses state noise compensation and dynamic model compensation with covariance matching adaptive filtering. This yields two adaptive and dynamically constrained process noise covariance estimation techniques. Unlike many adaptive filtering approaches, the new techniques accurately extrapolate over measurement outages and do not rely on ad hoc methods to ensure the process noise covariance is positive semi-definite. The benefits of the proposed algorithms are demonstrated through two case studies: an illustrative linear system and the autonomous navigation of two spacecraft orbiting an asteroid.