Heave measurement for SINS using attitude complementary filtering and all-pass compensated multi-stage low-pass filters

Accurate and low-latency measurement of ship heave displacement under dynamic ocean excitations remains a challenging problem in measurement science. In complex sea states, ship heave exhibits broadband spectral content and multi-period superposition, which can induce phase distortion and dynamic measurement errors when conventional single-frequency filtering methods are employed. In this work, we propose a heave measurement algorithm for strapdown inertial navigation system based on attitude complementary filtering and all-pass compensated multi-stage low-pass filters (ACF-APC-MLP). First, AFC is employed to fuse gyroscope and accelerometer data, suppress low-frequency attitude drift, and eliminate systematic bias in heave estimation. Subsequently, a main extraction channel for the heave signal is constructed using a cascade of MLP. Through progressive segmented filtering and complementary reconstruction, frequency components within the 5–20 s heave period are efficiently extracted. Finally, an analytically designed all-pass filter is introduced to globally compensate for frequency dependent phase lag caused by the low-pass filter chain to improve dynamic measurement fidelity. Simulation and experimental results demonstrate that the proposed algorithm maintains heave measurement errors within 4 cm under complex sea conditions, achieving at least 20% improvement in accuracy compared to conventional methods. The algorithm is suitable for ship motion monitoring, offshore platform operation, and other civilian marine measurement applications in complex marine environments.