A Dynamic-Gain Gradient-Descent-Based Complementary Filter for Attitude Estimation

This paper presents a gradient-descent-based complementary filter with dynamically adjustable gain for attitude estimation using gyroscope, accelerometer, and magnetometer measurements. The proposed method adaptively adjusts the complementary-filter gain through a bilinear transformation of the cost function already available within the gradient-descent optimization procedure, thereby increasing the correction aggressiveness during large orientation mismatches while preserving gyroscope-dominated propagation near steady-state operation. By leveraging the already computed cost function, the proposed method avoids the need for an additional error metric or computationally demanding optimization procedure. In contrast to conventional complementary filters with fixed gain, the proposed formulation accelerates convergence from incorrect initial conditions without a substantial increase in the average arithmetic workload. Simulation, Monte Carlo, and experimental results demonstrate substantially faster convergence relative to constant-gain complementary filtering, the Madgwick algorithm, and the Mahony filter, while maintaining comparable steady-state performance. The operation-count analysis, together with average numbers of gradient-descent iterations below one in most tested configurations, demonstrates that the improved transient convergence is achieved with low average arithmetic workload, while retaining characteristics favorable for computationally constrained embedded and real-time attitude estimation systems.