Central Difference Variational Filtering Based on Conjugate Gradient Method for Distributed Imaging Application

The airborne distributed position and orientation system (ADPOS), which integrates multi-inertia measurement units (IMUs), a data-processing computer, and a Global Navigation Satellite System (GNSS), serves as a key sensor in new higher-resolution airborne remote sensing applications, such as array SAR and multi-node imaging loads. ADPOS can provide reliable, high-precision and high-frequency spatio-temporal reference information to realize multinode motion compensation with the various nonlinear filter estimation methods such as Central Difference Kalman Filtering (CDKF), and modified CDKF. Although these known nonlinear models demonstrate good performance, their noise estimation performance with its linear minimum variance estimation criterion is limited for ADPOS. For this reason, in this paper, Central Difference Variational Filtering (CDVF) based on the variational optimization process is presented. This method adopts the conjugate gradient algorithm to enhance the estimation performance for mean correction in the filtering update stage. On one hand, the proposed method achieves adaptability by estimating noise covariance through the variational optimization method. On the other hand, robustness is implemented under the minimum variance estimation criterion based on the conjugate gradient algorithm to suppress measurement noise. We conducted a real ADPOS flight test, and the experimental results show that the accuracy of the slave motion parameters has significantly improved compared to the current CDKF. Moreover, the compensation performance shows a clear enhancement.