Adaptive square-root cubature-quadrature Kalman particle filter via KLD-sampling for orbit determination

Orbit determination (OD) problem utilizing onboard sensors is a key requirement for many current and future space missions. Though there exists ample research and work on this subject, a novel algorithm is presented in this paper for the nonlinear problem of OD. In this regard, initially a new cubature-quadrature particle filter (CQPF) that uses the square-root cubature-quadrature Kalman filter (SR-CQKF) to generate the importance proposal distribution is developed. The developed CQPF scheme avoids the limitation of the standard particle filter (PF) concerning new measurements. Subsequently, CQPF is enhanced to take advantage of the relative entropy (Kullback-Leibler Distance) criterion to adaptively select the number of particles thus enhancing the efficiency and accuracy of the newly proposed adaptive CQPF (ACQPF). The current study also applies ACQPF for the OD of a low Earth orbit (LEO) satellite equipped with a three-axis magnetometer (TAM) sensor pack that provides noisy geomagnetic field measurements. The results and performance of the proposed filter are compared with a variety of Gaussian approximation filters as well as different versions of PF via a Monte Carlo simulation. It is demonstrated that the proposed ACQPF outperforms the comparative estimators in terms of the root mean square of the estimation error. Moreover, a sensitivity analysis on the orbital elements, plants' and the estimators' parameters is conducted to verify the feasibility and robustness of the ACQPF over a wider acceptable range of operating system and environment.