Attitude Estimation Problem Research Articles

State Estimation for a Class of Linear Systems with Quadratic Output

This paper deals with the problem of state estimation for a class of linear time-invariant systems with quadratic output measurements. An immersion-type approach is presented that transforms the system into a state-affine system by adding a finite number of states to the original system. Under suitable persistence of excitation conditions on the input and its higher derivatives, global state estimation is exhibited by means of a Kalman-type observer. A numerical example is provided to illustrate the applicability of the proposed observer design for the problem of position and velocity estimation for a vehicle navigating in the n— dimensional Euclidean space using a single position range measurement.

Attitude Estimation Method of High-Spinning Body Through Onboard Sensor Fusion Under Uniaxial Gyroscope Saturation Environment

This article deals with a 3-D attitude estimation problem of a dynamic object that involves a uniaxial, high-speed rotational motion. As a high spinning dynamics typically causes an angular rate saturation in most gyros, it is also challenging to determine the object's attitude of the principal rotation axis and correspondingly the attitude of other orthogonal axes. To solve this problem, this article proposes two techniques to accomplish the attitude estimation under uniaxial gyro saturation condition. First, this article develops a new integrated filter scheme based on a reduced state model and attitude kinematics. The proposed estimation algorithm takes advantage of the magnetic measurement and gyro's partial rates to obtain a posteriori attitude estimate in the orthogonal axes and further develops to derive the principal axis attitude deterministically. Despite decent estimation performance, a measurement degeneracy may be caused in the reduced state model theoretically. To suppress the degeneracy effect, this study also exploits an augmented attitude estimation method, which adopts a post-processing computational rate in the principal axis through a time-frequency analysis on magnetic measurements. Finally, the proposed technique's performance was demonstrated through both simulation and experiment with the high spinning rate of 10846 and 2880°/s, respectively, where the error level was measured at the sub-degree in the orthogonal axes and slightly higher in the principal axis.

Robust Attitude Estimation Using IMU-Only Measurements

This article proposes two novel covariance-tuning methods to form a robust Kalman filter (RKF) algorithm for attitude (i.e., roll and pitch) estimation using the measurements of only an inertial measurement unit (IMU). KF-based and complementary filtering (CF)-based approaches are the two common methods for solving the attitude estimation problem. Efficiency and optimality of the KF-based attitude filters are correlated with appropriate tuning of the covariance matrices. Manual tuning process is a difficult and time-consuming task. Specifically, the IMU-only attitude estimation filters are prone to the external accelerations unless their covariances are adapted to gain robustness. The proposed algorithms provide an adaptive method for tuning the measurement noise covariance such that they can accurately estimate the attitude in the two axes. The first method relies on a single tuning factor, whereas the second one tunes the covariance with different (multiple) factors for each measurement axis. The proposed methodologies are tested and compared with other existing filtering algorithms in the literature under different dynamical conditions and using real-world experimental datasets in order to validate their effectiveness. Results show that highly dynamic scenarios, especially the multiple tuning factor strategy, can increase the attitude estimation accuracy more than two-times compared to the competitive algorithms.

Cramér–Rao Bounds for Beam Tracking With Photon Counting Detector Arrays in Free-Space Optical Communications

Optical beam center position on an array of detectors is an important parameter that is essential for estimating the angle-of-arrival of the incoming signal beam. In this paper, we have examined the beam position estimation problem for photon-counting detector arrays, and to this end, we have derived and analyzed the Cramer-Rao lower bounds on the mean-square error of unbiased estimators of beam position. Furthermore, we have also derived the Cramer-Rao lower bounds of other system parameters such as signal peak intensity, and dark current noise power, on the array. In this sense, we have considered robust estimation of beam position in which none of the parameters are assumed to be known beforehand. Additionally, we have derived the Cramer-Rao lower bounds of beam and noise parameters for observations based on both pilot and data symbols of a pulse position modulation (PPM) scheme. Finally, we have considered a two-step estimation problem in which the signal peak and dark current noise intensities are estimated using a method of moments estimator, and the beam center position is estimated with the help of a maximum likelihood estimator.

Hybrid Nonlinear Observers for Inertial Navigation Using Landmark Measurements

This paper considers the problem of attitude, position and linear velocity estimation for rigid body systems relying on landmark measurements. We propose two hybrid nonlinear observers on the matrix Lie group $SE_2(3)$, leading to global exponential stability. The first observer relies on fixed gains, while the second one uses variable gains depending on the solution of a continuous Riccati equation (CRE). These observers are then extended to handle biased angular velocity measurements. Both simulation and experimental results are presented to illustrate the performance of the proposed observers.

Neural Network-Based Pose Estimation for Noncooperative Spacecraft Rendezvous

This article presents the Spacecraft Pose Network (SPN), the first neural network-based method for on-board estimation of the pose, i.e., the relative position and attitude, of a known noncooperative spacecraft using monocular vision. In contrast to other state-of-the-art pose estimation approaches for spaceborne applications, the SPN method does not require the formulation of hand-engineered features and only requires a single grayscale image to determine the pose of the spacecraft relative to the camera. The SPN method uses a convolutional neural network (CNN) with three branches to solve the problem of relative attitude estimation. The first branch of the CNN bootstraps a state-of-the-art object detection algorithm to detect a 2-D bounding box around the target spacecraft in the input image. The region inside the 2-D bounding box is then used by the other two branches of the CNN to determine the relative attitude by initially classifying the input region into discrete coarse attitude labels before regressing to a finer estimate. The SPN method then estimates the relative position by using the constraints imposed by the detected 2-D bounding box and the estimated relative attitude. Further, with the detection of 2-D bounding boxes of subcomponents of the target spacecraft, the SPN method is easily generalizable to estimate the pose of multiple target geometries. Finally, to facilitate integration with navigation filters and perform continuous pose tracking, the SPN method estimates the uncertainty associated with the estimated pose. The secondary contribution of this article is the generation of the Spacecraft PosE Estimation Dataset (SPEED), which is used to train and evaluate the performance of the SPN method. SPEED consists of synthetic as well as actual camera images of a mock-up of the Tango spacecraft from the PRISMA mission. The synthetic images are created by fusing OpenGL-based renderings of the spacecraft's 3-D model with actual images of the Earth captured by the Himawari-8 meteorological satellite. The actual camera images are created using a seven degrees-of-freedom robotic arm, which positions and orients a vision-based sensor with respect to a full-scale mock-up of the Tango spacecraft with submillimeter and submillidegree accuracy. The SPN method, trained only on synthetic images, produces degree-level relative attitude error and cm-level relative position errors when evaluated on the actual camera images with a different distribution not used during training.

Attitude trajectory tracking of quadrotor UAV using super-twisting observer-based adaptive controller

The successful implementation of high-level decision algorithm on quadrotor depends on the accurate trajectory tracking performance. In this paper attitude estimation and trajectory tracking control problem of quadrotor unmanned aerial vehicle (UAV) with endogenous and exogenous disturbance are considered, where the lumped disturbance characteristic does not have a probabilistic illustration but instead the dynamics are known to have a bound. The problem is handled by developing disturbance estimator and control strategy. In order to estimate lumped disturbance precisely, a globally finite time stable extended state observer is proposed based on super-twisting algorithm. Stability analysis and observer’s parameters selection rule are discussed by using Lyapunov’s stability theory. The proposed observer strategy achieves accurate observing performance of disturbance without increasing observer’s order, and chattering effect is also reduced by applying super-twisting algorithm. Furthermore, a super-twisting sliding mode control law is proposed to guarantee the asymptotic convergence of the drone’s orientation with respect to the reference. Finally, a numerical study based on simulations is presented to analyze the performance of proposed approach.

Wireless Localization Based on Deep Learning: State of Art and Challenges

The problem of position estimation has always been widely discussed in the field of wireless communication. In recent years, deep learning technology is rapidly developing and attracting numerous applications. The high-dimension modeling capability of deep learning makes it possible to solve the localization problems under many nonideal scenarios which are hard to handle by classical models. Consequently, wireless localization based on deep learning has attracted extensive research during the last decade. The research and applications on wireless localization technology based on deep learning are reviewed in this paper. Typical deep learning models are summarized with emphasis on their inputs, outputs, and localization methods. Technical details helpful for enhancing localization ability are also mentioned. Finally, some problems worth further research are discussed.

A quantified approach of predicting suitability of using the Unscented Kalman Filter in a non-linear application

A mathematical framework to predict the Unscented Kalman Filter (UKF) performance improvement relative to the Extended Kalman Filter (EKF) using a quantitative measure of non-linearity is presented. It is also shown that the range of performance improvement the UKF can attain, for a given minimum probability depends on the Non-linearity Indices of the corresponding system and measurement models. Three distinct non-linear estimation problems are examined to verify these relations. A launch vehicle trajectory estimation problem, a satellite orbit estimation problem and a re-entry vehicle position estimation problem are examined to verify these relations. Using these relations, a procedure is suggested to predict the estimation performance improvement offered by the UKF relative to the EKF for a given non-linear system and measurement without designing, implementing and tuning the two Kalman Filters.

Relative Position Estimation for Formation Control with the Fusion of Predicted Future Information and Measurement Data

This paper addresses a relative position estimation problem for formation control of multiple robots. In the authors' previous paper, a relative position estimation method has been proposed, w...

Simultaneous Position and Orientation Estimation for Visible Light Systems With Multiple LEDs and Multiple PDs

Visible light communication (VLC) is seen as a supplement for fifth-generation (5G) wireless communication in short-range high data rate communication applications [1]. A reliable VLC system relies on an accurate estimate of the position and orientation of the receiver, which corresponds to the six-dimensional positioning problem mentioned in [2]. In this paper, we investigate the simultaneous position and orientation estimation (SPO) problem using received signal strength (RSS), for a visible light system containing multiple LEDs and multiple photodiodes (PDs) (MLMP). Although in general, the position and orientation of the receiver can be represented by a vector and a rotation matrix, respectively, the constraints imposed by the rotation matrix make the numerical optimization in the estimation process cumbersome, e.g, the commonly used constrained optimization method is often very complex and non-robust. Therefore, in this paper, we design two SPO algorithms using the principle of optimization on manifolds, which alleviates the constraints from the rotation matrix. In addition, we propose an initialization algorithm, based on the direct linear transformation (DLT) principle, to obtain an initial estimate in closed-form for the iterative algorithms. To evaluate the performance of the proposed RSS-based SPO algorithms, we derive the Cramer-Rao bound (CRB). In particular, the orientation error component of the CRB corresponds to the intrinsic CRB or the CRB on manifolds, which measures the error in the estimated rotation matrix in a physically meaningful way. Finally, computer simulations show an asymptotic tightness between the performance of the proposed algorithms and the theoretical lower bound, demonstrating the effectiveness of the proposed solutions.

Design and Demonstration of Robust Visible Light Positioning Based on Received Signal Strength

In this article, we consider indoor visible light positioning (VLP) based on received signal strength (RSS). Under the assumption of unknown receiver coefficient, we propose a robust VLP scheme which jointly estimates the receiver position and receiver coefficient. Through mathematical derivations, the original estimation problem is equivalently transformed into the position estimation problem of maximizing the angle between the received signal vector and RSS feature vector, where the direction of RSS feature vector is shown to be a one-to-one feature characterizing the receiver position. Compared with existing schemes, the proposed VLP scheme is more robust to the variations of transmission environments, as it only requires the ratios of transmitter coefficients rather than specific values of transceiver coefficients. Besides, for implementation of the proposed scheme, we also present a method for estimating the required parameters. Experimental and simulation results demonstrate the robustness of the proposed VLP scheme. Specifically, experimental results show that the proposed VLP scheme retains a stable positioning accuracy about 4 cm in a 150 × 60 × 60 cm $^3$ space and about 8 cm in a 200 × 60 × 60 cm $^3$ space.

Inertial Navigation and Position Uncertainty During a Blind Safe Stop of an Autonomous Vehicle

This work considers the problem of position and position-uncertainty estimation for atonomous vehicles during power black-out, where it cannot be assumed that any position data is accessible. To tackle this problem, the position estimation will instead be performed using power separated and independent measurement devices, including one inertial 6 Degrees of Freedom (DOF) measurement unit, four angular wheel speed sensors and one pinion angle sensor. The measurement unit's sensors are initially characterized in order to understand conceptual limitations of the inertial navigation and also to be used in a filtering process. Measurement models are then fused together with vehicle dynamics process models using the architecture of an Extended Kalman Filter (EKF). Two different EKF filter concepts are developed to estimate the vehicle position during a safe stop; one simpler filter for smooth manoeuvres and a complex filter for aggressive manoeuvres. Both filter designs are tested and evaluated with data gathered from an experimental vehicle for selected manoeuvres of developed safe-stop scenarios. The experimental results from a set of use-case manoeuvres show a trend where the size of the position estimation errors significantly grows above an initial vehicle speed of 70 km/h. This paper contributes to develop vehicle dynamics models for the purpose of a blind safe stop.

On the need for switched-gain observers for non-monotonic nonlinear systems

This paper focuses on the challenges in observer design for nonlinear systems which are non-monotonic. A class of nonlinear systems is considered in which the process dynamics and output equations are both composed of nonlinear vector functions of scalar combinations of the states. The nonlinear functions are assumed to be differentiable with bounded derivatives. An observer design algorithm that requires solving just a single linear matrix inequality for exponentially convergent state estimation is developed. The developed algorithm works effectively when the involved nonlinear functions are monotonic. However, it fails when all or even some of the system functions are non-monotonic. Both numerical computation and analytical results show that the observer design LMI has no feasible solutions when either all output functions or all process dynamics functions are non-monotonic. Further, other constant gain LMI-based observer design methods from literature also fail when the involved nonlinear functions are all non-monotonic, no matter how small the Lipschitz constant or the Jacobian bounds of the nonlinearities. This limitation has not previously been recognized in observer design literature. To overcome this limitation, a hybrid observer that switches between multiple constant observer gains is developed that can provide global asymptotic stability for systems with non-monotonic nonlinear functions. Hybrid observers with switched gains enable existing observer design methods to be utilized for non-monotonic nonlinear functions with finite local extrema. The application of the developed hybrid observer to two motion estimation applications, one a vehicle position tracking problem on roads and another a piston position estimation problem for an industrial actuator, are demonstrated.

Deception Attack Detection and Estimation for a Local Vehicle in Vehicle Platooning Based on a Modified UFIR Estimator

In this article, the position sensor deception attack detection and estimation problem is investigated for a local vehicle in a vehicle platoon. In a platoon system, the position measurement is critical as the distances between neighboring vehicles are relatively small. However, the position measurement of vehicles is usually vulnerable to deception attacks as it relies on external information, such as GPS and environment information from cameras. Therefore, position sensor deception attack detection and estimation should be addressed for local vehicles in a platoon. To deal with this problem, a linearized model is presented to describe the longitudinal dynamics of a local vehicle. Moreover, modeling uncertainties, measurement noises, and piecewise constant deception attacks injected in position measurement are specified along with this model. Based on this model, a scheme based on a modified unbiased finite impulse response (UFIR) estimator is proposed to generate an intermediate estimated value related only to the attack. Then, the deception attack is recovered based on this value through a function fitting strategy. Based on analysis results, simulations are conducted to verify the effectiveness of the proposed attack detection and estimation scheme.

OriNet: Robust 3-D Orientation Estimation With a Single Particular IMU

Estimating the robot's heading is a crucial requirement in odometry systems which are attempting to estimate the movement trajectory of a robot. Small errors in the orientation estimation result in a significant difference between the estimated and real trajectory, and failure of the odometry system. The odometry problem becomes much more complicated for micro flying robots since they cannot carry massive sensors. In this manner, they should benefit from the small size and low-cost sensors, such as IMU, to solve the odometry problem, and industries always look for such solutions. However, IMU suffers from bias and measurement noise, which makes the problem of position and orientation estimation challenging to be solved by a single IMU. While there are numerous studies on the fusion of IMU with other sensors, this study illustrates the power of the first deep learning framework for estimating the full 3D orientation of the flying robots (as yaw, pitch, and roll in quaternion coordinates) accurately with the presence of a single IMU. A particular IMU should be utilized during the training and testing of the proposed system. Besides, a method based on the Genetic Algorithm is introduced to measure the IMU bias in each execution. The results show that the proposed method improved the flying robots’ ability to estimate their orientation displacement by approximately 80% with the presence of a single particular IMU. The proposed approach also outperforms existing solutions that utilize a monocular camera and IMU simultaneously by approximately 30%.

A Novel Roll and Pitch Estimation Approach for a Ground Vehicle Stability Improvement Using a Low Cost IMU.

Onboard attitude estimation for a ground vehicle is persuaded by its application in active anti-roll bar design. Conventionally, the attitude estimation problem for a ground vehicle is a complex one, and computationally, its solution is very intensive. Lateral load transfer is an important parameter which should be taken in account for all roll stability control systems. This parameter is directly related to vehicle roll angle, which can be measured using devices such as dual antenna global positioning system (GPS) which is a costly technique, and this led to the current work in which we developed a simple and robust attitude estimation technique that is tested on a ground vehicle for roll mitigation. In the first phase Luenberger and Sliding mode observer is implemented using simplest roll dynamics model to measure the roll angle of a vehicle and the validation of results is carried using commercial software, CarSim® (CarSim, Ann Arbor, MI, USA). In the second phase of research, complementary and Kalman filters have been designed for attitude estimation. In the third phase, a low-cost inertial measurement unit (IMU) is mounted on a vehicle, and both the complementary filter (CF) and Kalman filter (KF) are applied independently to measure the data for both smooth and uneven terrains at four different frequencies. We compared the simulated and real-time results of roll and pitch angles obtained using the complementary and Kalman filters. Using the proposed method, the achieved root mean square error (RMSE) is less than 0.73 degree for pitch and 0.68 degree for roll, with a sample time of 2 ms. Thus, a warning signal can be generated to mitigate roll over. Hence, we claim that our proposed method can provide a low-cost solution to the roll-over problem for a road vehicle.

Cascaded Kalman Filtering-Based Attitude and Gyro Bias Estimation With Efficient Compensation of External Accelerations

We consider the problem of attitude estimation of rigid bodies in motion using low cost inertial measurement unit (IMU). An efficient scheme is proposed using two different Kalman filters by deriving their measurement models for precise attitude (pitch and roll) estimation in the presence of high and prolonged dynamic conditions and gyro bias. Both filters work in a coupled fashion where one of the filters provides accurate estimates of rigid body attitude and external acceleration using the accelerometer in conjunction with the gyroscope while the second filter is responsible to estimate the gyro bias, allowing the proposed scheme to be used in any application with minimal calibration. A new threshold based external acceleration detection module is also introduced to change the confidence level on external acceleration prediction to assist the estimation process. The proposed scheme is tested and compared with other existing estimators in the literature under different dynamical conditions and real-world experimental data sets in order to validate its effectiveness.

Accurate Position Estimation of Mobile Robot Based on Cyber-Physical-Social Systems (CPSS)

When planning the trajectory of a mobile robot, it is usually necessary to use sensors to collect a large amount of position information. Because traditional computing methods cannot effectively use huge data sources, an edge computing that implements edge intelligent services on the side of network edge near the data source is proposed, which speeds up the process of data processing. However, the data collected through sensors may contain gross errors. In general, the influence of gross errors on state estimation are rarely considered when using particle filter algorithms for state estimation. In fact, the measurements of dynamic systems are often affected by different types of gross errors in the actual application process. Therefore, it is a problem worth studying that how to detect and compensate for different types of gross errors. In this paper, an improved particle filter algorithm is proposed for the position estimation of mobile robot dynamic system. Firstly, the gross error identification method is used to identify the types of gross errors, and then the various gross errors are compensated. Finally, the particle filter algorithm based on the measurements compensation is obtained. Simulation experiments on the position estimation of mobile robots are carried out to verify the effectiveness of the proposed method in solving the measurements with gross errors. The precise position estimation of the mobile robot is achieved. Through the simulation experiments on the position estimation problem of mobile robots, it is verified that the proposed method is effective in solving the measurements with gross errors. And the accurate position estimation of the mobile robot is realized.

A higher-order robust correlation Kalman filter for satellite attitude estimation

A higher-order robust correlation Kalman filtering approach is presented to achieve attitude estimation for satellites with unknown modeling errors. A robust correlation Kalman filter (RCKF) is preliminarily derived by using the sequence orthogonal principle. To improve its performance further, a higher-order sigma version of the RCKF is designed by incorporating a novel sigma point generation algorithm. This modified filter can capture the third and the fourth central moment’s information of the system posteriori probability density function. It is proved that the proposed filter achieves better estimation accuracy and robustness. The effectiveness of the developed filter is demonstrated by simulation results with it applied to the satellite attitude estimation problem.