Attitude Estimation Problem Research Articles

Light curve attitude estimation using particle swarm optimizers

Knowledge of the attitude of a space object is useful in space situational awareness for independently evaluating a satellite’s health and characterizing unknown objects. In cases where only non-resolved optical observations are available, the object’s attitude may be estimated using a time sequence of brightness observations, also known as the light curve. This attitude estimation problem is plagued with multiple difficulties: even in the absence of noise and when all other relevant factors are perfectly known, the non-uniqueness of the problem means that multiple attitude time histories may fit the light curve equally well. In addition, there is often insufficient information about the object to generate an initial state guess for an estimator. This paper presents a method that estimates an observed object’s attitude and angular velocity while accounting for ambiguities and without needing any initial state guess. The only inputs are the light curve, the object’s albedo shape, and the object’s position relative to the Sun and the observer. The ability of the estimator to resolve attitude time histories is demonstrated using simulated light curves by comparing state estimates against known true states.

Unscented Schmidt-Kalman filter on Lie groups with application to spacecraft attitude estimation

This paper addresses the estimation problem of nonlinear systems evolving on Lie groups with unknown parameters. More precisely, some parameters in the equations of motion or sensor measurements are unknown, such as gravitational anomalies and measurement biases, and are infeasible to estimate with available observations. The unscented Schmidt-Kalman filter (USKF) approach in Euclidean space is incorporated with exponential maps from Lie algebra to Lie groups, to develop USKF algorithms on Lie groups. Two types of USKFs are derived, respectively, from left-invariant and right-invariant state estimation errors. The two USKFs, not only account for the effect of unknown parameters but also provide estimates preserving the geometry of state manifold. They are advantageous over the extended Schmidt-Kalman filter for nonlinear systems in the sense of avoiding the computation of Jacobian and achieving higher or comparable estimation accuracy depending on the magnitude of parameters uncertainties. The proposed method is then applied to a spacecraft attitude estimation problem based on quaternion representation, where the magnitude of the gyroscope bias noise is unknown. Simulations are conducted to illustrate the effectiveness of the proposed algorithms in comparison with other methods.

A precise localization algorithm for unmanned aerial vehicles integrating visual-internal odometry and cartographer

Accurate positioning in space is an important foundation for ensuring the stability of autonomous flight and successful mapping and navigation of unmanned aerial vehicles (UAVs). At present, the SLAM algorithm based on the Cartographer algorithm for real-time positioning and mapping is widely used in fields such as robot navigation and autonomous driving. However, in the context of UAV applications, this algorithm has a high dependence on the amount of point cloud information in the surrounding environment, and cannot achieve precise positioning in open spaces with insufficient lighting and fewer feature points, resulting in significant mapping errors. In order to solve the problem of low positioning estimation accuracy in the Cartographer algorithm in above environment, this paper proposes a precise positioning algorithm for UAVs that integrates VIO and Cartographer. This algorithm can continuously output more accurate position estimation information during UAV flight, compensating for the problem of inaccurate position estimation caused by partial feature loss or coordinate system drift in point clouds. In addition, this algorithm ensures navigation obstacle avoidance in narrow spaces by improving positioning accuracy and mapping accuracy, making it more applicable in the field of UAVs. Finally, the effectiveness of the proposed positioning algorithm was verified through experimental analysis of the Cartographer dataset and practical testing of UAVs in real scenarios.

Attitude Estimation From Vector Measurements: Necessary and Sufficient Conditions and Convergent Observer Design

The paper addresses the problem of attitude estimation for rigid bodies using (possibly time-varying) vector measurements, for which we provide a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">necessary and sufficient</i> condition of distinguishability. Such a condition is shown to be strictly weaker than those previously used for attitude observer design. Thereafter, we show that even for the single vector case the resulting condition is sufficient to design almost globally convergent attitude observers, and two explicit designs are obtained. To overcome the weak excitation issue, the first design employs to make full use of historical information, whereas the second scheme dynamically generates a virtual reference vector, which remains non-collinear to the given vector measurement. Simulation results illustrate the accurate estimation despite noisy measurements.

Geometric Data Fusion for Collaborative Attitude Estimation

In this paper, we consider the collaborative attitude estimation problem for a multi-agent system. The agents are equipped with sensors that provide directional measurements and relative attitude measurements. We present a bottom-up approach where each agent runs an extended Kalman filter (EKF) locally using directional measurements and augments this with relative attitude measurements provided by neighbouring agents. The covariance estimates of the relative attitude measurements are geometrically corrected to compensate for relative attitude between the agent that makes the measurement and the agent that uses the measurement before being fused with the local estimate using the convex combination ellipsoid (CCE) method to avoid data incest. Simulations are undertaken to numerically evaluate the performance of the proposed algorithm.

Noncontacting Position and Orientation Estimation of a Centimeter-Scale Robot Using an Active Electromagnet

This article focuses on estimating the position and orientation of a three degree-of-freedom (DoF) robot using a novel electromagnet-based active control system. The electromagnet is mounted on a servo motor and its orientation is controlled in real time so that it always points at the robot. A two-axis magnetic sensor on the robot helps determine both its radial distance from the electromagnet and its orientation. The active pointing control of the electromagnet highly simplifies the position estimation problem. Instead of requiring a magnetic field model that is a function of all three DoF, the radial distance and robot orientation estimation tasks become decoupled and independent problems. The radial distance is estimated using an asymptotically stable nonlinear observer designed using a linear matrix inequality. The analytical principles of the estimation system are first presented using key technical lemmas and proofs. Extensive experimental results are then presented on the performance of the estimation system, including real-time estimation of the moving robot's position and orientation.

Sensorless control of a PMSM based on an RBF neural network-optimized ADRC and SGHCKF-STF algorithm

For the problem of the rotor position estimation and control accuracy of permanent magnet synchronous motor (PMSM), this paper proposes a PMSM sensorless based on radial basis function (RBF) neural network optimized Automatic disturbance rejection control (RBF-ADRC) and strong tracking filter (STF) improved square root generalized fifth-order cubature Kalman filter (SGHCKF-STF). The Automatic disturbance rejection control (ADRC) has strong robustness, but there are many parameters and difficult to adjust. Now we use RBF neural network to adjust the parameters in ADRC online so as to improve the robustness and anti-disturbance ability. In order to improve the estimation accuracy of rotor position and speed, the orthogonal triangle (QR) decomposition and STF are introduced on the basis of the generalized fifth-order cubature Kalman filter (GHCKF) to design the SGHCKF-STF algorithm that not only ensure the non-positive nature of the covariance matrix but also improve the ability to cope with sudden changes in state during the filtering process. Experimental results show that the combination of RBF-ADRC and SGHCKF-STF improve the sensorless control effect of the PMSM to some extent.

Robust filtering for spacecraft attitude estimation systems with multiplicative noises, unknown measurement disturbances and correlated noises

Unknown measurement disturbances and correlated noise caused by jitter or vibration phenomena during spacecraft operation and the complex external environment are important topics for spacecraft attitude estimation. This paper studies the problem of spacecraft attitude estimation for nonlinear systems with multiplicative noises, unknown measurement disturbances and correlated noises. In addition, a two-step prediction framework is used to complete the noise decoupling. This paper aims to design a robust filter that minimizes the upper bound of the prediction error covariance and estimation error covariance in the presence of multiplicative noises, correlated noises and unknown measurement disturbances. The prediction gain and filtering gain of the robust filter are designed to minimize the upper bound. Finally, the simulation results verify the effectiveness of the proposed filter.

Vision-based particle filtering for quad-copter attitude estimation using multirate delayed measurements.

In this paper, the problem of attitude estimation of a quad-copter system equipped with a multi-rate camera and gyroscope sensors is addressed through extension of a sampling importance re-sampling (SIR) particle filter (PF). Attitude measurement sensors, such as cameras, usually suffer from a slow sampling rate and processing time delay compared to inertial sensors, such as gyroscopes. A discretized attitude kinematics in Euler angles is employed where the gyroscope noisy measurements are considered the model input, leading to a stochastic uncertain system model. Then, a multi-rate delayed PF is proposed so that when no camera measurement is available, the sampling part is performed only. In this case, the delayed camera measurements are used for weight computation and re-sampling. Finally, the efficiency of the proposed method is demonstrated through both numerical simulation and experimental work on the DJI Tello quad-copter system. The images captured by the camera are processed using the ORB feature extraction method and the homography method in Python-OpenCV, which is used to calculate the rotation matrix from the Tello's image frames.

Three-axis high-accuracy spacecraft attitude estimation via sequential extended Kalman filtering of single-axis magnetometer measurements

Magnetometer is a highly advantageous sensor for determining a spacecraft’s attitude. This article provides a solution to the problem of spacecraft attitude estimation using magnetometer measurements only. To ensure full observability of spacecraft attitude states, it is necessary to use at least two types of sensors. Consequently, utilizing a single sensor, such as the magnetometer, poses a significant challenge for any attitude estimation algorithm, including the extended Kalman filter (EKF). Moreover, implementing the EKF algorithm, or any other attitude estimation algorithm, is computationally intensive. To address these issues, an algorithm has been developed that estimates spacecraft attitude angles and attitude rates using a sequential extended Kalman filter (SEKF). This algorithm offers numerous benefits over those found in the literature such as high accuracy, low computational resource requirements, the ability to converge even with large initial attitude and angular velocity estimation errors, and the ability to function even if two of the three measurement channels of the magnetometer are not functioning. With these benefits, the developed SEKF algorithm is capable of operating in all spacecraft operational modes, delivering accurate performance and computation time. In spite of measurements with large noise values, the high accuracy achieved by the SEKF algorithm enables the magnetometer to serve as the sole source of attitude information, even if one or two magnetometer measurement channels are not functioning.

Distributed decentralized EKF for very large-scale networks with application to satellite mega-constellations navigation

The design of a decentralized and distributed filtering solution for large-scale networks of interconnected systems is addressed considering (i) generic nonlinear dynamics and (ii) generic coupled nonlinear outputs in a generic, possibly time-varying, topology. The local filters, which follow the structure of the extended Kalman filter, are implemented in each system, which estimates its own state exclusively. To be suitable for the heavily restricted implementation to very large-scale systems, a novel algorithm is proposed, which: (i) does not rely on instantaneous data transmission; (ii) allows local communication exclusively; and (iii) requires computational, memory, and data transmission resources for each system that do not scale with the dimension of the network. The scalability of the proposed algorithm allows for its application to the cooperative localization problem of very large-scale systems. In particular, it is applied herein to the on-board position estimation problem of LEO mega-constellations using GNSS featuring numerical simulations for the Starlink constellation.

Single 24-GHz FMCW Radar-Based Indoor Device-Free Human Localization and Posture Sensing With CNN

The position information and posture information of a device-free human in a confined indoor environment have multiple uses in health monitoring and other areas. In this study, we aim to use a single-input-single-output (SISO) frequency-modulated continuous-wave (FMCW) radar at 24-GHz band for simultaneous localization and posture estimation of one device-free human target. This device is easy to deploy in new setups. We use image formation to convert temporal measurements of the radar signal into image-like data and convert the problem of simultaneous position estimation and posture perception into an image classification problem. Leveraging the use of convolutional neural networks (CNNs) for image classification, we design a variety of tests to explore the most favorable parameters of the CNN model and then use the best practice model to accomplish the classification task involving a fusion of localization and pose recognition. To explain the primary causes of inaccuracies, we examine not only cases based on a fused position and posture dataset but also cases based on position-only and posture-only datasets. On both real-life datasets, our proposed scheme can achieve 98% classification accuracy and less than 1-m localization accuracy within 0.95 cumulative error probability within the area of interest, outperforming traditional classification methods.

Uniting Attitude Estimation With Global Asymptotic Stability

This paper approaches the problem of attitude estimation using biased gyro and body-referenced measurements of inertial vectors. First, a new observer for attitude estimation is proposed through introducing a family of synergistic potential functions with explicit expression of synergistic gap. Furthermore, it is convenient to adjust the design by adding additional state-dependent gains without adapting the switching rules. The proposed observer exhibits faster convergence for large attitude estimation errors than similar work in literature. Second, to achieve better steady-state performance, we unite this global observer with a traditional local observer, i.e., multiplicative extended Kalman filter. The new uniting observer inherits the desired transient and steady-state performance from the two sub-observers respectively. The performance of proposed methods has been evaluated via simulation and experiments.

Attitude Estimation from Vector Measurements: Necessary and Sufficient Conditions and Convergent Observer Design

The paper addresses the problem of attitude estimation for rigid bodies using (possibly time-varying) vector measurements, for which we provide a necessary and sufficient condition of distinguishability. Such a condition is shown to be strictly weaker than those previously used for attitude observer design. Thereafter, we show that even for the single vector case the resulting condition is sufficient to design almost globally convergent attitude observers, and an explicit design is obtained. To overcome the weak excitation issue, the design makes full use of historical information. Simulation results illustrate the accurate estimation despite with noisy measurements.

Asymptotically stable optimal multi-rate rigid body attitude estimation based on lagrange-d'alembert principle

&lt;abstract&gt;&lt;p&gt;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 body-fixed frame is formulated as Wahba's problem. At instants when direction vector measurements are absent, a discrete-time model for attitude kinematics is used to propagate past measurements. A discrete-time Lagrangian is constructed as the difference between a kinetic energy-like term that is quadratic in the angular velocity estimation error and an artificial potential energy-like term obtained from Wahba's cost function. An additional dissipation term is introduced and the discrete-time Lagrange-d'Alembert principle is applied to the Lagrangian with this dissipation to obtain an optimal filtering scheme. A discrete-time Lyapunov analysis is carried out to show that the optimal filtering scheme is asymptotically stable in the absence of measurement noise and the domain of convergence is almost global. For a realistic evaluation of the scheme, numerical experiments are conducted with inputs corrupted by bounded measurement noise. These numerical simulations exhibit convergence of the estimated states to a bounded neighborhood of the actual states.&lt;/p&gt;&lt;/abstract&gt;

On the attitude estimation of nonholonomic wheeled mobile robots

This paper addresses the attitude estimation problem of wheeled mobile robots (WMRs) with nonholonomic constraints moving in a plane. We consider the case that only the robot’s Cartesian position and linear velocity are available from sensor measurements. Based on the kinematic model, three attitude observers are proposed. The first observer is designed directly on the Special Orthogonal group SO(2) and guarantees that for almost all initial conditions, the estimated attitude converges to the actual one with an exponential convergence rate. The second observer estimates the heading direction of the mobile robot, i.e., its dynamics evolves on the unit circle S1. The first and second observers rely on linear velocity measurements. On the other hand, the third observer presents a globally exponentially stable error dynamics and requires only Cartesian position measurements but does not evolve on S1. Additionally, a control-observer algorithm is proposed to solve the trajectory-tracking problem of WMRs. Finally, the performances of the proposed attitude observers and control law were evaluated by a set of experiments on a commercial WMR.

A Novel Visual-Based Terrain Relative Navigation System for Planetary Applications Based on Mask R-CNN and Projective Invariants

In the framework of autonomous spacecraft navigation, this manuscript proposes a novel vision-based terrain relative navigation (TRN) system called FederNet. The developed system exploits a pattern of observed craters to perform an absolute position measurement. The obtained measurements are thus integrated into a navigation filter to estimate the spacecraft state in terms of position and velocity. Recovering crater locations from elevation imagery is not an easy task since sensors can generate images with vastly different appearances and qualities. Hence, several problems have been faced. First, the crater detection problem from elevation images, second, the crater matching problem with known craters, the spacecraft position estimation problem from retrieved matches, and its integration with a navigation filter. The first problem was countered with the robust approach of deep learning. Then, a crater matching algorithm based on geometric descriptors was developed to solve the pattern recognition problem. Finally, a position estimation algorithm was integrated with an Extended Kalman Filter, built with a Keplerian propagator. This key choice highlights the performance achieved by the developed system that could benefit from more accurate propagators. FederNet system has been validated with an experimental analysis on real elevation images. Results showed that FederNet is capable to cruise with a navigation accuracy below 400 meters when a sufficient number of well-distributed craters is available for matching. FederNet capabilities can be further improved with higher resolution data and a data fusion integration with other sensor measurements, such as the lunar GPS, nowadays under investigation by many researchers.

Distributed fusion fault-tolerant attitude estimation scheme for nanosatellite using commercial off-the-shelf sensors

The highly reliable nanosatellite platforms have broad application prospects in the construction of satellite Internet. Obtaining accurate attitude information is crucial to enhance the reliability of nanosatellite platforms. However, the traditional attitude sensors are not suitable for nanosatellite and attitude sensor faults are the main ones in space field. Therefore, sensor fault detection and fault-tolerant processing are essential to improve the reliability of platforms. In this paper, the distributed fusion fault-tolerant attitude estimation (FTAE) problems for nanosatellite with commercial off-the-shelf (COTS) sensors are investigated. Considering the low development cost of nanosatellite platforms, a FTAE scheme using COTS sensors is developed, which can acquire high-precision attitude information and improve the fault tolerance of nanosatellite platforms. Moreover, a novel fault detection method is designed and strict mathematical analysis is applied to fault threshold in FTAE scheme, which can significantly reduce complicated debugging work in engineering application and improve the design efficiency of FTAE scheme. Some case studies are given to illustrate the efficacy of the designed distributed fusion FTAE scheme.

Adaptive invariant Kalman filtering for lie groups attitude estimation with biased and heavy-tailed process noise

Attitude determination is fundamental for spacecraft missions in aerospace engineering. Kalman filter (KF) is the optimal estimator in least square sense and, using the symmetry properties of matrix Lie groups system, the invariant Kalman filter (IKF) has been developed to boost the filtering performance for attitude estimation. However, due to presence of frequent and severer maneuvers, the Lie groups attitude dynamics is usually corrupted by significant biases and heavy-tailed outliers, which usually leads to decreased precision of IKF. For attitude estimation problem troubled by biased and heavy-tailed process noise, this work proposes a new invariant Kalman filter (VBAIKF) by constructing the hierarchical Gaussian system model: the probability density function of prior estimate state is first described using the student’s t distribution, while the unknown scale covariance matrix and degrees of freedom (dof) of the employed student’s t distribution are defined as the inverse Wishart distribution (IWD) and Gamma distribution. In VBAIKF, the Lie groups rotation matrix of spacecraft, the biased mean, the parameters of dof and scale covariance matrix are online estimated together by variational Bayesian fixed-point iterations. The simulation results with Lie groups attitude estimation system further verify the superior filtering adaptability and precision of proposed approach VBAIKF than other methods for attitude determination with biased mean and heavy-tailed process noise.

Direct Position Determination for Noncooperative Source with Fast Moving Receivers

The problem of position estimation for a noncooperative source has always been widely discussed in the field of wireless communication. Direct position determination (DPD) for a noncooperative source with fast moving receivers is discussed in this paper. The sinc function is used to reconstruct the signals, which is an important step in DPD for wideband signals. A DPD method based on the baseband signal is proposed which is more practical in communication signal with high carrier frequency. And based on the proposed DPD method, a DPD method for multiple noncooperative stationary sources by single-channel receivers is presented. In order to evaluate the performance of the proposed DPD method, the Cramér-Rao lower bound (CRLB) for DPD based on baseband signal is derived. Several numerical investigations are carried out to evaluate the performance of the proposed method.