Evaluation of Murrell's EKF-Based Attitude Estimation Algorithm for Exploiting Multiple Attitude Sensor Configurations.

Requirements of highly precise pointing performance have been imposed on recently developed spacecrafts for a variety of missions. The stringent requirements have called on on-orbit estimation of spacecraft dynamics parameters and calibration of on-board sensors as indispensible practices. Consequently, on-orbit estimation of the mass moment of inertia of spacecraft has been a major issue mostly due to the changes by solar panel deployment and a large portion of fuel consumption (Creamer et al., 1996; Ahmed et al., 1998; Bordany et al., 2000; VanDyke et al., 2004; Myung et al., 2007; Myung & Bang, 2008; Sekhavat et al., 2009). As for measurement sensors, on-board calibration of alignment and bias errors of attitude and rate sensors is one of the main concerns of attitude sensor calibration researches (Pittelkau, 2001 & 2002, Lai et al., 2003). Pittelkau (2002) proposed an attitude estimator based on the Kalman filter (Kalman, 1960), in which spacecraft attitude quaternion, rate sensor misalignment and bias, and star tracker misalignments are taken into consideration as states, whereas the body rate is dealt as a synthesized signal by the estimates. Lai at al. (2003) derived a method for alignment estimation of attitude and rate sensors based on the unscented Kalman filter (UKF) (Julier and Uhlmann, 1997). Ma and Jiang (2005) presented spacecraft attitude estimation and calibration based only magnetometer measurements using an UKF. An interesting point is that we need predesigned 3-axis excitation manoeuvres of spacecraft for both dynamics parameter estimation and sensor calibration. Therefore, this study is motivated to merge above estimation and calibration processes into a single filtering problem. It is noteworthy that poor information of moments of inertia is to be treated as a system uncertainty while the rate sensor model errors are to be incorporated into the measurement process. As a filtering algorithm, this study employs a UKF. Extended Kalman filters (EKFs) have been successfully applied to the nonlinear attitude estimation problem (Crassidis et al., 2007). Hybrid estimation using the EKF has been reported by Myung at al. (2007). However, the EKF estimates using the first order linearization, which may lead to instability of the filter (ValDyke et al., 2004). The UKF approximates the nonlinear model to the second order by spreading points 1 sigma apart from the a priori mean. Performing nonlinear

Robust adaptive smooth variable structure Kalman filter for spacecraft attitude estimation

In navigation and motion control of an autonomous vehicle, estimation of attitude and heading is an important issue, especially when the localization sensors such as global positioning system (GPS) are not available and the vehicle is navigated by the dead reckoning (DR) strategies. In this paper, based on a new modeling framework, an extended Kalman filter (EKF) is utilized for estimation of attitude, heading, and gyroscope sensor bias using a low-cost microelectromechanical system (MEMS) inertial sensor. The algorithm is developed for accurate estimation of attitude and heading in the presence of external disturbances including external body accelerations and magnetic disturbances. In this study, using the proposed attitude and heading reference system (AHRS) and an identified surge dynamic model of an autonomous underwater vehicle, a low-cost model-aided DR navigation system has been designed for an AUV. The proposed algorithm application is evaluated by experimental tests in different acceleration bound and existence of external magnetic disturbances for an AUV. The results indicate that the roll, pitch, and heading are estimated by mean value errors about 0.35°, 0.29°, and 1.27°, respectively. Moreover, they indicate that a relative navigation error about 8% of the traveling distance can be achieved using the developed approach in during GPS outages.

This paper describes a quaternion implementation of an Unscented Kalman Filter for attitude estimation on CubeSats using measurements of a sun vector, a magnetic field vector and angular velocity. Using unit quaternions provides a singularity free attitude parameterization. However, the unity constraint requires a redesign of the Unscented Kalman Filter. Therefore, a quaternion error state is introduced. Emphasis has been put in making the implementation accessible to other CubeSat by using realistic models of COTS components used for attitude sensing and simulations have shown that the extra computational cost of estimating bias in measurements is worthwhile. The simulations where performed in a simulation environment for the CubeSat AAUSAT3, where robustness has been an important factor during tuning of the attitude estimators. The results indicate that it is possible to achieve acceptable CubeSat attitude estimation, even during eclipse, on a limited budget and using COTS components, without the need of expensive high precision sensor setups.

Legged robots operating in irregular environments are often subjected to compound disturbances such as tilts and vibrations, which can degrade attitude stability and motion reliability. This paper presents a real-time disturbance-adaptive control framework for a hexapod robot. The proposed system integrates quaternion-based attitude estimation using an extended Kalman filter (EKF), a double-threshold pose classifier, and a modular gait library and is implemented on an embedded controller with a 2 ms control-loop latency. Analytical verification and laboratory experiments demonstrate that the proposed control loop achieves uniform ultimate boundedness (UUB) under deterministic hybrid disturbances composed of controlled tilt and vibration, with a mean recovery time of 5.7 s. These results demonstrate that a lightweight rule-based controller can ensure reliable posture recovery within the experimentally validated laboratory scenarios, providing a foundation for future extensions to more complex environments. The main contributions of this work are (1) a disturbance-adaptive gait selection architecture for quasi-static stabilization, (2) a noise-robust EKF-based attitude estimation and double-threshold pose determination scheme, and (3) a concise Lyapunov-based stability analysis demonstrating UUB of the closed-loop system.

This paper presents a novel adaptive iterated extended Kalman filter (AIEKF) for relative position and attitude estimation, taking into account the influence of model uncertainty. Considering a nonlinear stochastic discrete‐time system with unknown disturbance, the AIEKF algorithm adopts the Gauss‐Newton iterative optimization steps to implement a maximum a posteriori (MAP) estimation, and the switch‐mode combination technique is used to achieve the adaptive capability. The mean‐square estimation error (MSE) of the state estimate is derived. It is proved that the AIEKF can yield a smaller MSE than that of the traditional extended Kalman filter (EKF) or iterated extended Kalman filter (IEKF). The performance advantage of the AIEKF is illustrated via Monte Carlo simulations on a typical relative position and attitude estimation application. Through comparisons in different scenarios, the presented algorithm is shown to improve adaptability and ensure estimation accuracy.

Relative position and attitude estimation for satellite formation with coupled translational and rotational dynamics

This paper describes an integral scheme of the design and simulation of the Attitude Determination and Control Subsystem (ADCS) of CubeSat. CubeSat is an educational low-cost, cube-shaped Pico spacecraft. Attitude Determination (AD) is the problem of expressing the orientation of a spacecraft with respect to a given coordinate system. Three axis magneto-resistive digital magnetometer is selected as an attitude sensor. The International Geomagnetic Reference Field (IGRF) is used as reference for magnetometer to obtain attitude information. An enhanced orbit estimate/propagator is implemented to provide position information to IGRF model. Satellite environmental torque is modeled along with satellite kinematics and dynamics. Attitude estimation is done using Extended Kalman Filter (EKF) while the magnetic coils are used as actuators. Attitude Control is applied using Linear Quadratic Regulation (LQR) Controller. The designed ADCS is implemented in Matlab/Simulink.

A deterministic attitude estimation problem for a rigid body in an attitude dependent potential field with bounded measurement errors is studied. An attitude estimation scheme that does not use generalized coordinate representations of the attitude is presented here. Assuming that the initial attitude, angular velocity and measurement noise lie within given ellipsoidal bounds, an uncertainty ellipsoid that bounds the attitude and the angular velocity of the rigid body is obtained. The center of the uncertainty ellipsoid provides point estimates, and its size gives the accuracy of the estimates. The point estimates and the uncertainty ellipsoids are propagated using a Lie group variational integrator and its linearization, respectively. The estimation scheme is optimal in the sense that the attitude estimation error and the size of the uncertainty ellipsoid is minimized at each measurement instant, and it is global since the attitude is represented by a rotation matrix.

We consider the attitude and gyro-bias estimation as well as the attitude stabilization problem of a rigid body in space using low-cost sensors. We assume that a biased measurement of the angular velocity of the rigid body is provided by a low-cost gyroscope, and the attitude measurements are obtained using low-cost (low-pass) sensors such as accelerometers and magnetometers. We provide an attitude and gyro-bias estimation algorithm using the biased gyro measurement and the attitude measurements - which represent the true attitude only at low frequencies - provided by the low-cost attitude sensors. Finally, the proposed estimation algorithm is coupled with a quaternion-based attitude stabilization scheme, and simulation results are provided to show the effectiveness of the proposed algorithm.

Current emphasis on low-budget missions involving small spacecraft leads to a need for an efficient and effective algorithm for attitude and rate estimation. This paper investigates the performance of a Pseudo-Linear Kalman Filter (plkf) with continuous-time dynamics for attitude and rate estimation. The plkf differs from the traditional Extended Kalman Filter (ekf) with its continuous-time dynamics performing estimation using a pseudo-linear state-dependent dynamic model. Both quaternion-based and vector-based measurements have been considered and the dynamic model of the spacecraft accounts for external environmental disturbances. Using computer simulations, the designed filter is shown to overcome large initial errors and yields accurate estimates. The performance indices used for evaluation are based on robustness against plant, measurement and initial estimate errors. While the ekf remains more robust for some cases of angular velocity estimation, the plkf, in general, outperforms the ekf in attitude estimation.

A three-axis attitude estimation scheme is presented using a set of albedo interfered coarse sun sensors (CSSs) of Earth, which are inexpensive, small in size, and light in power consumption. For modeling the interference, a two-stage albedo estimation algorithm based on autoregressive model is proposed. The algorithm does not require any data, such as albedo coefficients, spacecraft position, sky condition, or ground coverage, other than albedo measurements. The results are compared with five albedo models on the basis of two reference conditions. The estimated albedo is fed to the CSS measurements for correction. The corrected CSS measurements are processed under three estimation techniques with two different sensor configurations. The relative performance of the attitude estimation schemes when using different albedo models is examined.

<div class="section abstract"><div class="htmlview paragraph">The attitude of autonomous marine, land, air or space vehicles can be determined from the state estimation by means of mathematical tools such as Extended Kalman filter. In the process of calculation of this value, three-axis inertial and non-inertial sensors are used. From the knowledge of the orientation of the main axis, it is implemented the automatic control of the vehicle.</div><div class="htmlview paragraph">The solid-state magnetometer is a non-inertial sensor with three axes that provides both the direction and the magnitude of the magnetic field vector which it is being submitted. However, measurements of the Earth's magnetic field vector, obtained using the three-axis magnetometer, are not accurate. In the vehicle itself, the presence of ferrous materials creates disturbances in the Earth's magnetic field, distorting the measured field. The accuracy of the magnetometer can be improved by means of various calibration methods, which, in summary, calculate the vector components of the bias, the systematic error, which can be modeled as a magnetic field that overlaps and distorts the actual terrestrial magnetic field. More than 90% of the measured geomagnetic field is generated in the earth's outer core and can be described by mathematical models that serve as reference to some of the magnetometer calibration algorithms.</div></div>

Stability of catheter-tissue contact in the robotic magnetic navigation (RMN) system is one of the key features that distinguishes this system from manually guided catheters. Numerous studies have shown that contact force (CF) in manually controlled catheters is as crucial for forming an optimal lesion as the duration of application or power. Catheters used in the RMN system lack a quantitative method for intraoperative monitoring of this parameter. Our study aims to partially address this gap in scientific knowledge. We conducted a total of 1200 CF measurements using the RMN system (Stereotaxis, St. Louis, MO, USA), a magnetic-guided 8 Fr RF ablation catheter (THERMOCOOL RMT Catheter, Biosense Webster, Irvine, CA, USA) inserted through a long sheath (SR0, Abbott Cardiovascular, Nathan Lane North, Plymouth, MN, USA), and a precision jewelry scale (IKEME, Guangdong, CN). We analyzed the impact on the obtained CF values of four different magnetic field vectors (transverse, sagittal, caudal, and cranial), two field strengths (0.1T and 0.08T), and three catheter extension configurations from the long sheath (with Position 1 being the least extended and Position 3 the most extended). The contact force values varied significantly across the different magnetic field vectors, field strengths, and catheter extensions from the vascular sheath. The greatest differences in achieved values were observed across the different magnetic field vectors in the Position 1, ranging from 3.52 ± 0.1 g (caudal plane) to 15.15 ± 0.05 g (cranial plane) at 0.08 Tesla (T) field strength (p < 0.001), and from 4.10 ± 0.06 g (caudal) to 15.01 ± 0.07 g (cranial) at 0.1 T, p < 0.001. Differences in other vectors reached approximately 20%. The highest CF values were obtained in Position 1, intermediate values in Position 2, and the lowest in Position 3. An exception was the transverse vector, where, particularly with a magnetic field of 0.1 T, more similar values were observed across Positions 1-3, with respective values of 8.61 ± 0.14 g, 9.36 ± 0.06 g, and 8.31 ± 0.05 g. A stronger magnetic field (0.1 T compared to 0.08 T) resulted in higher CF values, especially during measurements in the transverse vector. This effect was most pronounced in the most extended catheter from the sheath - Position 3 (with respective values of 4.54 ± 0.09 g vs. 8.31 ± 0.05 g, p < 0.001). In the sagittal, cranial, and caudal vectors, the differences were less noticeable. Different magnetic field vectors, catheter extensions from the sheath, and magnetic field strengths result in varying contact force values. For effective radiofrequency ablation lesions, these factors should be considered alongside power, duration, and other established parameters.

Study of Relative Position and Attitude Estimation and Control Scheme for the Final Phase of an Autonomous Docking Mission