A state-constrained and noise-separated pseudo-linear Kalman filtering algorithm for 3D-AOA model

Abstract

In the context of three-dimensional angle-of-arrival (3D-AOA) target tracking, this study proposes a state-constrained and noise-separated pseudo-linear Kalman filtering (SC-NS-PLKF) algorithm to address nonlinear filtering challenges. Whereas existing bias-compensated (BC), instrumental-variable (IV) and unbiased (UB) PLKF methods only correct the pseudo-linear bias, SC-NS-PLKF achieves high-precision unbiased estimation with enhanced algorithmic stability. Specifically, this method (i) derives a new pseudo-linear measurement model through nonlinear equivalent transformation and noise separation; (ii) employs auxiliary filtering to supply the target position required by NS-PLKF and constructs an ellipsoidal constraint domain that guarantees divergence prevention; (iii) provides a rigorous proof of bounded estimation error and includes a complexity analysis to validate computational efficiency. Extensive Monte-Carlo simulations demonstrate significant gains in accuracy and stability compared to state-of-the-art methods.