Dual-Quaternion-Based Multiplicative Unscented Kalman Filtering (DQ-MUKF) for Relative Navigation in Small Groups of Interacting Objects
Year: 2026
Type: conference-paper
Abstract: Our project develops a computationally efficient and numerically stable Multiplicative Unscented Kalman Filter (MUKF) specifically designed for the relative navigation of three interacting PocketQube spacecraft. By leveraging dual quaternion, the algorithm unifies translational and rotational dynamics into a single algebraic framework, effectively managing the high degree of nonlinearity inherent in coupled orbital and attitude motion. Our research first establishes a dual-quaternion kinematic state propagation model and a error formulation that preserves the unit constraints of the manifold. Subsequently, a stochastic sigma point mapping technique is implemented via the Unscented Transform (UT) to propagate uncertainties without the linearization errors typical of Extended Kalman Filters. Finally, numerical simulations demonstrate that the MUKF achieves superior convergence and robustness compared to traditional methods. Results indicate that the estimation errors remain consistently within the covariance bounds, with minimal relative distance errors and zero-mean innovation sequence, confirming the filter's unbiased performance and closed-loop stability for small-scale satellite swarms.
Institution: Saint Petersburg State Electrotechnical University
Language: English
Subfield: Aerospace Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7203662328