Nonlinear Complementary Filters on the Special Orthogonal Group

Abstract

16International audienceThis paper considers the problem of obtaining good attitude estimates from measurements obtained from typical low cost inertial measurement units. The outputs of such systems are characterized by high noise levels and time varying additive biases. We formulate the filtering problem as deterministic observer kinematics posed directly on the special orthogonal group SO(3) driven by reconstructed attitude and angular velocity measurements. Lyapunov analysis results for the proposed observers are derived that ensure almost global stability of the observer error. The approach taken leads to an observer that we term the direct complementary filter. By exploiting the geometry of the special orthogonal group a related observer, termed the passive complementary filter, is derived that decouples the gyro measurements from the reconstructed attitude in the observer inputs. Both the direct and passive filters can be extended to estimate gyro bias online. The passive filter is further developed to provide a formulation in terms of the measurement error that avoids any algebraic reconstruction of the attitude. This leads to an observer on S(3), termed the explicit complementary filter, that requires only accelerometer and gyro outputs; is suitable for implementation on embedded hardware; and provides good attitude estimates as well as estimating the gyro biases online. The performance of the observers are demonstrated with a set of experiments performed on a robotic test-bed and a radio controlled unmanned aerial vehicle

Design of inertial navigation systems for marine craft with adaptive wave filtering aided by triple‐redundant sensor packages

“…This is important since f n = −g n due to wave excitation of the vessel. The attitude observer, Σ 1 , by Grip et al [22], developed from [23], is given as…”

Nonlinear observer for GNSS-aided inertial navigation with quaternion-based attitude estimation

“…Hua [16] used the vector-based attitude observer of Hamel and Mahony [17] and Mahony, Hamel, and Pflimlin [8] as the basis for an attitude and velocity observer that depends only on inertial measurements, GNSS velocity measurements, and magnetometer measurements. Hua's observer exploits the fact that the vehicle's acceleration vector in the navigation frame is implicitly available in the derivative of the GNSS velocity.…”

State Estimation for Shore Monitoring Using an Autonomous Surface Vessel

“…For this purpose we use the Complementary filter (CF) [13], which integrates the gyroscopic measurements ω and corrects them with measurements of known directions v i . The state of the filter consists of the attitude represented by a unit quaternionq and a vector of additive gyroscope biasesb g .…”

“…To overcome this problem, EKFs using the Inertia Measurement Unit (IMU) directly in the prediction step were proposed [12]. Focussing only on the attitude estimation based on an IMU, Mahony et al [13] introduced the concept of the Complementary filter (CF) and demonstrated its performance on a micro aerial vehicle. This variety of solutions require a deeper investigation on how the IMU should be used in an EKF.…”