Composite adaptive cubature kalman filter with hierarchical bayesian noise estimation and NIS-gated Q-adaptation

Le résumé fourni par la source

Abstract Navigation and tracking systems for aerospace and low-altitude platforms suffer from significant noise uncertainties: platform maneuvering leads to time-varying process noise covariance Q, while sensor aging and atmospheric propagation interference cause drift in measurement noise covariance R. Nevertheless, the standard Cubature Kalman Filter (CKF) assumes constant and known noise covariances, which limits its performance in complex aerospace detection environments. Most existing adaptive filtering methods only optimize a single noise source, and seldom consider extra estimation errors introduced by the adaptive adjustment mechanism itself. To meet the demands of intelligent autonomous flight vehicle navigation and integrated aerospace environmental perception, this paper proposes a Composite Adaptive Cubature Kalman Filter (CACKF). A multi-layer square-root filtering framework is adopted to simultaneously handle uncertainties in both Q and R. The algorithm consists of two core covariance regularization modules with rigorous theoretical foundations: (1) Hierarchical Bayesian Noise Estimation (HBN). Hierarchical conjugate posteriors of global inverse-Wishart and dimension-wise inverse-Gamma distributions are constructed. By explicitly eliminating prediction uncertainty terms to separate contributions of process noise and measurement noise, the mixed noise bias inherent in the classic Sage-Husa method is eliminated. (2) Normalized Innovation Squared-gated (NIS-gated) Variational Bayesian Q-adaptation (VB-Q). The exponential moving average of NIS is used to dynamically adjust the learning rate. An m-related dead zone [ χ m 2 ( 0.10 ) / m , χ m 2 ( 0.90 ) / m ] is set to avoid invalid updates of Q when noise states remain stable. Meanwhile, an autocorrelation-based freeze detection mechanism is introduced to mitigate filter convergence stagnation. Auxiliary mechanisms, including multiple fading factors, iterative CKF (ICKF), Student’s t-distribution modelling, and Joseph update, form a complete numerical stability guarantee system. Ablation simulation results demonstrate that HBN is the most critical component of the overall framework; removing HBN degrades the aggregate tracking Root Mean Square Error(RMSE) by 24.7%. The VB-Q module works conditionally: when the prior process noise is accurate, VB-Q without NIS gate control instead deteriorates RMSE by 21.6%. Benchmark simulations covering four motion scenarios and seven comparative filters with 30 Monte Carlo runs are carried out. In the constant-velocity linear scenario, position RMSEs of all algorithms fall within the narrow range of 2.76–3.13 m. However, the UKF suffers severe covariance collapse with a Normalized Estimation Error Squared (NEES) up to 1504.7, where the covariance shrinks to only 1/250 of the true error. The proposed CACKF achieves a steady NEES of 5.00, making it the only filter among all candidates that maintains statistical consistency under 𝜒 2 (6) distribution, with a confidence interval coverage rate of 92.8%. With a four-stage speed scheduling strategy, the single-frame computation time reduces from 7.45 ms to 0.55 ms, yielding a 13.5-fold acceleration. A high-speed aerospace platform trajectory is established based on the publicly available US 1976 standard atmospheric model and general polar curve aerodynamic model for further verification under nonlinear radar detection simulation conditions. The tracking RMSE of CACKF reaches 646 m, whereas that of the standard square-root CKF (SCKF) is as high as 8667 m. This paper also analyzes how the solution order of triangular decomposition in square-root filtering affects numerical accuracy. Multiple open-source implementations mishandle this step, resulting in a systematic NIS bias of 15%–25%. The research can provide references for the engineering implementation of filtering modules in autonomous navigation and integrated avionics systems for aerospace vehicles.

Ce résumé expose les affirmations des auteurs. BNTIC ne l’interprète pas comme une validation indépendante des résultats.