Complementary Filtering on SO(3) for Attitude Estimation with Scalar Measurements
I3S, CNRS, Université Côte d’Azur（法国国家科学研究中心蔚蓝海岸大学I3S实验室）；Institut Universitaire de France（法国大学研究院）；Department of Computer Science and Engineering, Université du Québec en Outaouais (UQO)（魁北克大学乌塔韦校区计算机科学与工程系）
Alessandro Melis, Soulaimane Berkane, Robert Mahony, Tarek Hamel
备注：
Accepted to the 65th IEEE Conference on Decision and Control (CDC 2026)
This paper proposes a complementary filter on SO(3) for attitude estimation from scalar measurements corresponding to projections of known inertial vectors onto body-frame sensing directions. The observer evolves directly on SO(3) and employs a constant-gain innovation tailored to the scalar-output structure. Under suitable persistence-of-excitation conditions, almost-global asymptotic stability is established when at least three inertial vectors are measured along a common body-frame direction. For configurations involving only two scalar measurements, sufficient conditions for asymptotic convergence are derived together with an explicit characterization of the region of attraction. Numerical simulations illustrate the proposed results.
On Fast Attitude Filtering Using Matrix Fisher Distributions with Stability Guarantee
School of Astronautics, Shenyuan Honors College, Beihang University（北京航空航天大学宇航学院、深空探测学院）；School of Astronautics and the MOE Key Laboratory of Spacecraft Design, Optimization and Dynamic Simulation, Beihang University（北京航空航天大学宇航学院、航天器设计与优化动态仿真教育部重点实验室）；School of Astronautics, Beihang University（北京航空航天大学宇航学院）
Attitude estimation is the process of computing the orientation angles of an object with respect to a fixed frame of reference. Gyroscope, accelerometer, and magnetometer are some of the fundamental sensors used in attitude estimation. The orientation angles computed from these sensors are combined using the sensor fusion methodologies to obtain accurate estimates. The complementary filter is one of the widely adopted techniques whose performance is highly dependent on the appropriate selection of its gain parameters. This paper presents a novel cascaded architecture of the complementary filte…
To obtain a high-accuracy position with SINS(Strapdown Inertial Navigation System), initial alignment needs to determine initial attitude rapidly and accurately. High-accuracy grade IMU(Inertial Measurement Uint) can obtain the initial attitude indenpendently, however, the low-accuracy grade gyroscope doesn't adapt to determine the heading angle, hence the initial attitude matrix will not be obtained. If using large misalignment angle model to estiamting heading angle, the convergence time will become much longer. For solving these two problems, a novel alignment algorithm combined backtrackin…
Accurate state estimation using low-cost MEMS (Micro Electro- Mechanical Systems) sensors present on Commercial-off-the-shelf (COTS) drones is a challenging problem. Most UAV systems use a combination of a gyroscope, an accelerometer, and a magnetometer to obtain measurements and estimate attitude. Under this paradigm of sensor fusion, the Extended Kalman Filter (EKF) is the most popular algorithm for attitude estimation in UAVs. In this work, we propose a novel estimation technique called extended H2 filter that can overcome the limitations of the EKF, specifically with respect to computation…
A geometric estimator is proposed for the rigid body attitude under multi-rate measurements using discrete-time Lyapunov stability analysis in this work. The angular velocity measurements are assumed to be sampled at a higher rate compared to the attitude. The attitude determination problem from two or more vector measurements in the body-fixed frame is formulated as Wahba's problem. In the case when measurements are absent, a discrete-time model for attitude kinematics is assumed in order to propagate the measurements. A discrete-time Lyapunov function is constructed as the sum of a kinetic e…
Department of Computer Science and Engineering, University of Quebec in Outaouais（计算机科学与工程系，魁北克大学 Outaouais分校）；Department of Electrical Engineering, Lakehead University（电气工程系，拉克希德大学）；I3S-UniCA-CNRS, University Cote d’Azur and the Insitut Universitaire de France（I3S-UniCA-CNRS，大学海岸阿兹尔分校和法国国家科学院）
The rigid body attitude estimation problem is treated using the discrete-time Lagrange-d'Alembert principle. Three different possibilities are considered for the multi-rate relation between angular velocity measurements and direction vector measurements for attitude: 1) integer relation between sampling rates, 2) time-varying sampling rates, 3) non-integer relation between sampling rates. In all cases, it is assumed that angular velocity measurements are sampled at a higher rate compared to the inertial vectors. The attitude determination problem from two or more vector measurements in the bod…
The problem of $H_{\infty}$ filtering for attitude estimation using rotation matrices and vector measurements is studied. Starting from a storage function on the Special Orthogonal Group $SO(3)$, a dissipation inequality is considered, and a deterministic nonlinear $H_{\infty}$ filter is derived which respects a given upper bound $γ$ on the energy gain from exogenous disturbances and initial estimation errors to a generalized estimation error. The results are valid for all estimation errors which correspond to an angular error of less than $π/2$ radians in terms of the axis-angle representatio…
Symbiosis International (Deemed University)（共生国际大学）；Central Scientific Instruments Organisation（中央科学仪器组织）；Council of Scientific and Industrial Research（科学与工业研究理事会）
This paper presents a novel method for attitude estimation of an object in 3D space by incremental learning of the Long-Short Term Memory (LSTM) network. Gyroscope, accelerometer, and magnetometer are few widely used sensors in attitude estimation applications. Traditionally, multi-sensor fusion methods such as the Extended Kalman Filter and Complementary Filter are employed to fuse the measurements from these sensors. However, these methods exhibit limitations in accounting for the uncertainty, unpredictability, and dynamic nature of the motion in real-world situations. In this paper, the ine…
On the Optimized Use of Non-Orthonormality Constraints for the Quasi-Static INS Alignment of Autonomous Underwater and Surface Vehicles
Federal University of Lavras（拉夫拉斯联邦大学）；University of Haifa（海法大学）；Fluminense Federal Institute of Education, Science and Technology（弗卢米嫩塞联邦教育科学技术学院）；Federal Institute of Education, Science and Technology of Amazonas（亚马逊联邦教育科学技术学院）；University of São Paulo（圣保罗大学）；Zoox, Inc.（Zoox公司）
Thompson Rivers University（汤普森河大学）；The Hong Kong Polytechnic University（香港理工大学）
Simultaneous Localization and Mapping (SLAM) is a process of concurrent estimation of the vehicle's pose and feature locations with respect to a frame of reference. This paper proposes a computationally cheap geometric nonlinear SLAM filter algorithm structured to mimic the nonlinear motion dynamics of the true SLAM problem posed on the matrix Lie group of $\mathbb{SLAM}_{n}\left(3\right)$. The nonlinear filter on manifold is proposed in continuous form and it utilizes available measurements obtained from group velocity vectors, feature measurements and an inertial measurement unit (IMU). The …
