Trust–Region Nonlinear Optimization Algorithm for Orientation Estimator and Visual Measurement of Inertial–Magnetic Sensor

Abstract

This paper proposes a novel robust orientation estimator to enhance the accuracy and robustness of orientation estimation for inertial–magnetic sensors of the small consumer–grade drones. The proposed estimator utilizes a trust–region strategy within a nonlinear optimization framework, transforming the orientation fusion problem into a nonlinear optimization problem based on the maximum likelihood principle. The proposed estimator employs a trust–region Dogleg gradient descent strategy to optimize orientation precision and incorporates a Huber robust kernel to minimize interference caused by acceleration during the maneuvering process of the drone. In addition, a novel method for evaluating the performance of orientation estimators is also presented based on visuals. The proposed method consists of two parts: offline calibration of the basic cube using Augmented Reality University of Cordoba (ArUco) markers and online orientation measurement of the sensor carrier using a nonlinear optimization solver. The proposed measurement method’s accuracy and the proposed estimator’s performance are evaluated under low–dynamic (rotation) and high–dynamic (shake) conditions in the experiment. The experimental findings indicate that the proposed measurement method obtains an average re–projection error of less than 0.1 pixels. The proposed estimator has the lowest average orientation error compared to conventional orientation estimation algorithms. Despite the time–consuming nature of the proposed estimator, it exhibits greater robustness and precision, particularly in highly dynamic environments.