Optimal Position Estimation Research Articles

A simulated fusion localization algorithm with adaptive error covariance matrix for closed corridor seamless positioning

Due to the blocking and reflection of buildings, the received Beidou satellite navigation signal (BDS) in the closed corridor will be getting weaker, which results in poor positioning accuracy or positioning failure. Introducing Ultra-Wide Band (UWB) positioning technology and establishing BDS/UWB integrated positioning system is an effective method to achieve seamless positioning. The positioning accuracy obtained by the Least Square-Kalman Filter (LS-KF) algorithm is below m level. However, the prior error covariance matrix of the KF correction process is easily contaminated, which affects the proportion of system observations and state prediction values to the optimal position estimation. A LS-KF fusion positioning algorithm based on adaptive error covariance matrix is proposed, the algorithm adjusts the state prior error covariance matrix by constructing an adaptive factor, improves the Kalman gain and the optimal estimation of the position, balances the trust of the filter estimation value to the observation value and the state prediction value of the integrated positioning system. Theoretical analysis and experimental results show that compared with LS-KF, EKF, UKF and improved LS-KF algorithm, the proposed LS-AKF algorithm not only has higher positioning accuracy, stronger anti-interference ability, but also has faster convergence speed.

Optimal vehicle position estimation using adaptive unscented Kalman filter based on sensor fusion

Precise position recognition systems are actively used in various automotive technology fields such as autonomous vehicles, intelligent transportation systems, and vehicle driving safety systems. In line with this demand, this paper proposes a new vehicle position estimation algorithm based on sensor fusion between low-cost standalone global positioning system (GPS) and inertial measurement unit (IMU) sensors. In order to estimate accurate vehicle position information using two complementary sensor types, adaptive unscented Kalman filter (AUKF), an optimal state estimation algorithm, is applied to the vehicle kinematic model. Since this AUKF includes an adaptive covariance matrix whose value changes under GPS outage conditions, it has high estimation robustness even if the accuracy of the GPS measurement signal is low. Through comparison of estimation errors with both extended Kalman filter (EKF) and UKF, which are widely used state estimation algorithms, it can be confirmed how improved the estimation performance of the proposed AUKF algorithm in real-vehicle experiments is. The given test course includes roads of various shapes as well as GPS outage sections, so it is suitable for evaluating vehicle position estimation performance.

Optimization of Gradient Descent Parameters in Attitude Estimation Algorithms.

Attitude estimation methods provide modern consumer, industrial, and space systems with an estimate of a body orientation based on noisy sensor measurements. The gradient descent algorithm is one of the most recent methods for optimal attitude estimation, whose iterative nature demands adequate adjustment of the algorithm parameters, which is often overlooked in the literature. Here, we present the effects of the step size, the maximum number of iterations, and the initial quaternion, as well as different propagation methods on the quality of the estimation in noiseless and noisy conditions. A novel figure of merit and termination criterion that defines the algorithm's accuracy is proposed. Furthermore, the guidelines for selecting the optimal set of parameters in order to achieve the highest accuracy of the estimate using the fewest iterations are proposed and verified in simulations and experimentally based on the measurements acquired from an in-house developed model of a satellite attitude determination and control system. The proposed attitude estimation method based on the gradient descent algorithm and complementary filter automatically adjusts the number of iterations with the average below 0.5, reducing the demand on the processing power and energy consumption and causing it to be suitable for low-power applications.

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

<abstract><p>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.</p></abstract>

Sensor fault-tolerant attitude determination system based on the nonlinear interacting-multiple-model approach

This paper presents a methodology for satellite sensors' fault detection and diagnosis (FDD) in a fault-tolerant attitude determination system using a nonlinear interacting-multiple-model approach (IMM). Moreover, the fault-tolerant attitude determination system utilizes the IMM approach in the presence of sensors' total fault to estimate faulty sensors and attitude states. This methodology relies on the most conventional satellite attitude sensors including magnetometer, sun sensor, and gyroscope measurements. The presented scheme leads to a significant computational time-saving method due to considering a pre-filter Kalman for fault detection, hence, the proposed FDD approach consists of two stages. In the first stage, the pre-filter Kalman detects any sensor fault and attitude states. In contrast, in the next stage, fault diagnosis and optimal attitude estimation are obtained through the IMM approach. Therefore, the IMM algorithm will be activated to extract the optimal estimation and identify faulty sensor(s). A Monte Carlo type approach is used to verify this technique for various initial conditions. Through numerical and Monte Carlo simulations, it is shown that the proposed scheme is robust against sensors' total fault, and the system is capable of detecting and isolating accurately the faulty sensor. Hardware in the loop tests using satellite dynamics simulator are also used to validate the presented system performance.

Active suspension control strategy of heavy rescue vehicle based on multi-sensor information fusion

This study proposes the active suspension control strategy of heavy rescue vehicles based on multi-sensor information fusion to address the problem of poor ride comfort and stability of heavy rescue vehicles on unstructured pavement. Firstly, an attitude fusion algorithm with acceleration compensation is designed. According to the driving speed, the appropriate cut-off frequency of acceleration filter is selected, and the extended Kalman filter is designed to complete the optimal estimation of position and attitude information. Secondly, the vehicle nine degree of freedom model is established, and the inverse matrix of attitude control is solved to obtain the suspension actuator output. Lastly, an active suspension control strategy based on multi-sensor information fusion is designed. The body attitude information after the information fusion is used for the control of active suspension system to realize the real-time adjustment of body attitude. Test results show that the root mean square values of vertical displacement, pitch angle, and roll angle under active suspension are reduced by 37.01%, 26.96%, and 38.90%, respectively, compared with those under in passive suspension. This reduction improves the ride comfort and stability of the heavy rescue vehicles on unstructured pavement.

Recursive optimal linear attitude estimator based on star sensor and gyro

Recursive optimal linear attitude estimator based on star sensor and gyro

Visual Sorting of Express Parcels Based on Multi-Task Deep Learning.

Visual sorting of express parcels in complex scenes has always been a key issue in intelligent logistics sorting systems. With existing methods, it is still difficult to achieve fast and accurate sorting of disorderly stacked parcels. In order to achieve accurate detection and efficient sorting of disorderly stacked express parcels, we propose a robot sorting method based on multi-task deep learning. Firstly, a lightweight object detection network model is proposed to improve the real-time performance of the system. A scale variable and the joint weights of the network are used to sparsify the model and automatically identify unimportant channels. Pruning strategies are used to reduce the model size and increase the speed of detection without losing accuracy. Then, an optimal sorting position and pose estimation network model based on multi-task deep learning is proposed. Using an end-to-end network structure, the optimal sorting positions and poses of express parcels are estimated in real time by combining pose and position information for joint training. It is proved that this model can further improve the sorting accuracy. Finally, the accuracy and real-time performance of this method are verified by robotic sorting experiments.

Attitude Determination and Control System Design of Sub-Arcsecond Pointing Spacecraft

Spacecraft pointing accuracies with sub-arcsec to milli-arcsec levels are becoming a norm for the future space missions, which is mainly achieved by employing mission-specific fine guidance sensor (FGS). European Space Agency’s Herschel is the only spacecraft to date that has achieved an accuracy between 0.8 and 0.9 arcsec without employing FGS and by using only precise commercial-off-the-shelf (COTS) sensors. This paper improves upon Herschel’s pointing accuracy by at least [314, 925, 925]% for German Aerospace Center’s future mission named “Infrared Astronomy Satellite Swarm Interferometer (IRASSI).” IRASSI’s closed-loop attitude determination and control system (ADCS) is carefully developed by selecting high-precision COTS sensors and actuators, implementing two optimal attitude estimation algorithms for the sensor data fusion, three robust control algorithms for the attitude control, and a pseudoinverse distribution algorithm for spacecraft momenta allocation among the redundant reaction wheels in three different configurations. Monte Carlo simulations of IRASSI’s ADCS demonstrate that an unprecedented three-axis absolute pointing error of [0.193, 0.078, 0.078] arcsec is achieved. Furthermore, performance comparison between the rate-integrating and rate-gyroscope-based multiplicative extended Kalman filter for this mission is demonstrated. Finally, performance comparison of three attitude controllers establishes their feasibility for this mission.

In-Motion Initial Alignment Using State-Dependent Extended Kalman Filter for Strapdown Inertial Navigation System

The in-motion alignment of the strapdown inertial navigation system (SINS) is still a challenging problem due to the complex environmental changes that occur during carrier movement. This article proposes a novel initial alignment method by integrating the advantages of the Special Orthogonal Group of order 3 [SO(3)] representation and the optimal attitude estimation alignment idea. In this method, the SO(3) is used to represent the initial attitude matrix, and the optimal attitude estimation alignment model is established by analyzing the influence of the sensor error during the calculation process. Next, state-dependent extended Kalman filter is investigated by mapping the SO(3) equations to the Lie algebra space, and the Lagrange formula is used to separate the state-dependent errors in the Lie algebraic filtering equation. The simulation and experimental results indicate that the proposed initial alignment method can achieve better alignment accuracy and shorter alignment time than existing methods and can fulfill the in-motion alignment tasks for SINSs in various environments.

A New In-Flight Alignment Method with an Application to the Low-Cost SINS/GPS Integrated Navigation System.

The optimization-based alignment (OBA) methods, which are implemented by the optimal attitude estimation using vector observations—also called double-vectors—have proven to be effective at solving the in-flight alignment (IFA) problem. However, the traditional OBA methods are not applicable for the low-cost strap-down inertial navigation system (SINS) since the error of double-vectors will be accumulated over time due to the substantial drift of micro-electronic- mechanical system (MEMS) gyroscope. Moreover, the existing optimal estimation method is subject to a large computation burden, which results in a low alignment speed. To address these issues, in this article we propose a new fast IFA method based on modified double-vectors construction and the gradient descent method. To be specific, the modified construction method is implemented by reducing the integration interval and identifying the gyroscope bias during the construction procedure, which improves the accuracy of double-vectors and IFA; the gradient descent scheme is adopted to estimate the optimal attitude of alignment without complex matrix operation, which results in the improvement of alignment speed. The effect of different sizes of mini-batch on the performance of the gradient descent method is also discussed. Extensive simulations and vehicle experiments demonstrate that the proposed method has better accuracy and faster alignment speed than the related traditional methods for the low-cost SINS/global positioning system (GPS) integrated navigation system

Optimal Geometry for Ultra-wideband Localization using Bayesian Optimization

Abstract This paper introduces a novel algorithm to find a geometric configuration of ultra-wideband sources in order to provide optimal position estimation performance with Time-Difference-of-Arrival measurements. Different from existing works, we aim to achieve the best localization performance for a user-defined region of interest instead of a single target point. We employ an analysis based on the Cramer-Rao lower bound and dilution of precision to formulate an optimization problem. A Bayesian optimization-based algorithm is proposed to find an optimal geometry that achieves the smallest estimation variance upper bound while ensuring source placement constraints. The approach is validated through simulation and experimental results in 2D scenarios, showing an improvement over a naive source placement.

Variational Bayesian adaptive Kalman filter for asynchronous multirate multi-sensor integrated navigation system

This study considers an asynchronous multirate data integration problem in the linear state space model with unknown and time-varying statistical parameters of the measurement noises. To improve performance of the multirate adaptive Kalman filter algorithm, a multi-sensor adaptive Kalman filtering algorithm based on variational Bayesian approximations has been developed in an asynchronous multirate multi-sensor integrated navigation system. The proposed filtering algorithm estimates measurement noise variances of the sensors adaptively and also it is robust to anomalous measurements of sensors and however, multirate adaptive Kalman filter is required to use an appropriate algorithm for outlier rejection to achieve a reliable and optimal estimation of position, velocity, and orientation. A navigation system composed of a strapdown inertial navigation system along with Doppler velocity log, inclinometer and depth meter with different sampling rates is designed to evaluate performance of multirate error state Kalman filter (MESKF) and multirate adaptive error state Kalman filter (MAESKF) algorithms and the proposed algorithm. Results of two experimental tests show that the average relative root mean square error (RMSE) of the position estimated by the proposed filtering algorithm can be decreased approximately 57% and 36% when compared to that of MESKF and MAESKF algorithms, respectively.

Uncertainty Characterisation of Mobile Robot Localisation Techniques using Optical Surveying Grade Instruments.

Recent developments in localisation systems for autonomous robotic technology have been a driving factor in the deployment of robots in a wide variety of environments. Estimating sensor measurement noise is an essential factor when producing uncertainty models for state-of-the-art robotic positioning systems. In this paper, a surveying grade optical instrument in the form of a Trimble S7 Robotic Total Station is utilised to dynamically characterise the error of positioning sensors of a ground based unmanned robot. The error characteristics are used as inputs into the construction of a Localisation Extended Kalman Filter which fuses Pozyx Ultra-wideband range measurements with odometry to obtain an optimal position estimation, all whilst using the path generated from the remote tracking feature of the Robotic Total Station as a ground truth metric. Experiments show that the proposed method yields an improved positional estimation compared to the Pozyx systems’ native firmware algorithm as well as producing a smoother trajectory.

Optimal Position and Velocity Estimation for Multi-USV Positioning Systems with Range Measurements

This paper investigates the problem on simultaneously estimating the velocity and position of the target for range-based multi-USV positioning systems. According to the range measurement and kinematics model of the target, we formulate this problem in a mixed linear/nonlinear discrete-time system. In this system, the input and state represent the velocity and position of the target, respectively. We divide the system into two components and propose a three-step minimum variance unbiased simultaneous input and state estimation (SISE) algorithm. First, we estimate the velocity in the local level plane and predict the corresponding position. Then, we estimate the velocity in the heave direction. Finally, we estimate the 3-dimensional (3D) velocity and position. We establish the unbiased conditions of the input and state estimation for the MLBL system. Simulation results illustrate the effectiveness of the problem formulation and demonstrate the performance of the proposed algorithm.

Enhance accuracy of kinematic GPS positioning with Kalman filtering

Abstract: The article discusses the Kalman filter application for temporal random motion of the GPS receiver location. The motion of the GPS receiver is a space state model with time-varying. The spatial state model is usually represented by linear differential equations with white noise. When the state of space fluctuates over time, it is represented by Riccati equations, ie nonlinear differential equations.Kalman filter for optimal estimation reliable, even unstable system, respectively random moves of the GPS receiver. The mobile GPS coordinates over time are compared to the coordinates in a previous static test, confirming that the Kalman filter can apply an optimal estimate of the mobile GPS position. This reduces the investment cost and increases the efficiency of using a common GPS receiver.

Closed-Form Position and Orientation Estimation for a Three-Axis Electromagnetic Tracking System

Electromagnetic tracking systems are a practical and cost-effective alternative to vision-based systems for virtual reality applications, providing a large working range without suffering from the line-of-sight problem. We present closed-form formulas for the optimal least-squares position and orientation estimates of an electromagnetic tracking system. A generic system consisting of three-axis sensor and generator coils—the coils need not be orthogonal—is considered, and a least-squares objective function for tracking is formulated. The optimal solution is then derived in closed form. Experimental validation via numerical simulations and hardware experiments confirm that our least-squares tracking algorithm can run in real time, and that tracking performance is more robust to measurement errors than existing methods.

Semidefinite programming‐based localisation and tracking algorithm using Gaussian mixture modelling

In this study, the authors propose a semidefinite programming (SDP)-based localisation and tracking algorithm, which mitigates the non-line-of-sight (NLOS) error of range measurement and calibrates the accumulative error within the inertial sensing data. Both the range measurement in a mixed line-of-sight/NLOS environment and the step length estimated from inertial sensing information are approximated parametrically using Gaussian mixture modelling, and a maximum-likelihood estimator (MLE) is formulated to obtain the optimal position estimation. Since the Gaussian mixture models are non-linear functions of positions, the MLE is a non-convex problem, which global optimum is difficult to attain. Then, the non-convex MLE is transformed into an SDP-based localisation and tracking problem, relying on Jensen's inequality and semidefinite relaxation. Thus, a sub-optimal solution to the original MLE can be achieved. Moreover, the Cramer-Rao lower bound is also derived to serve as a performance indicator for localisation errors. The simulation and experimental results demonstrate the performance of the proposed algorithm. Compared with the existing algorithms, the proposed algorithm owns the best localisation accuracy, and can achieve a sub-metre level accuracy to a root mean square error of 0.46 m in the real deployments.

A new optimal fusion algorithm for spacecraft attitude determination and estimation algorithms

The principal objective of the paper at hand is to introduce the idea of a new optimal spacecraft attitude estimation algorithm. The proposed optimal attitude estimation algorithm depends mainly on the optimal fusion of the outputs of spacecraft attitude determination and/or estimation algorithms. This proposed optimal fusion algorithm is able to generate attitude estimates with better standard deviation than the determination and/or estimation algorithms alone. The proposed optimal attitude estimation algorithm is not standalone because it needs at least another hardware measurement sensor in addition to determination and/or estimation algorithms.

LS-SVM Based WSN Location Algorithm in NLOS Environments

Location methods based on learning theory perform well in wireless cellular networks. These methods may be further improved since range measurements among all nodes are not taken into consideration, while these range measurements in the WSN location system are generally available. In this paper, we propose an improved LS-SVM based location algorithm to solve mobile location problem in a NLOS environment. We extend LS-SVM method from wireless cellular networks to WSN location system. Compared with LSSVM in wireless cellular networks only using the range measurements between anchor nodes and blind nodes, the proposed method can improve the positioning accuracy by using all the range measurements among the nodes. Moreover, steepest descent method is used in the proposed method to iterative search the optimal position estimation of blind nodes. The simulations results in different cases illustrate that the proposed algorithm outperforms the kernel method and LS-SVM method on location accuracy.