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This paper proposes a novel quaternion-based attitude estimation method for land-vehicle applications by fusing the low-cost magnetic, angular rate, and gravity (MARG) sensors and global navigation satellite systems measured velocity (GNSS-V). A structure of three-layer cascaded indirect Kalman filter (IKF) is devised to minimize the interactions of heterogeneous error sources on attitude quaternion solutions. It sequentially fuses the Earth's gravity vector, magnetic vector, and GNSS-V vector pairs with quaternion state constraints from Euler angles in each local filter. To further ensure the robustness of quaternion-based attitude solution, the external acceleration term is adaptively compensated within a sliding window of GNSS-V information. Meanwhile, independent and cross check procedures for observation vectors are also established for excluding individual sensor fault by taking land-vehicle dynamics into account. It is of significant importance that, in this contribution, the GNSS measured velocity is fully utilized in all potential aspects of aiding attitude determination with MARG sensors. Real-world vehicular experiments are carried out to evaluate the performance of our proposed method. The presented results verify the validity and efficiency thus the developed method may be promising for implemention in land-vehicle applications. [ABSTRACT FROM AUTHOR]

Focusing on generalized sensor combinations, this paper deals with the attitude estimation problem using a linear complementary filter (CF). The quaternion observation model is obtained via a gradient descent algorithm. An additive measurement model is then established according to derived results. The filter is named as the generalized CF where the observation model is simplified as a linear one that is quite different from previous-reported brute-force nonlinear results. Moreover, we prove that representative derivative-based optimization algorithms are essentially equivalent to each other. Derivations are given to establish the state model based on the quaternion kinematic equation. The proposed algorithm is validated under several experimental conditions involving the free-living environment, harsh external field disturbances, and aerial flight test aided by robotic vision. Using the specially designed experimental devices, data acquisition and algorithm computations are performed to give comparisons on accuracy, robustness, time-consumption, and so on with representative methods. The results show that not only the proposed filter can give fast, accurate, and stable estimates in terms of various sensor combinations but also produces robust attitude estimation in the scenario of harsh situations, e.g., irregular magnetic distortion. Note to Practitioners—Multisensor attitude estimation is a crucial technique in robotic devices. Many existing methods focus on the orientation fusion of specific sensor combinations. In this paper, we make the problem more concise. The results given in this paper are very general and can significantly decrease the space consumption and computation burden without losing the original estimation accuracy. Such performance will be of benefit to robotic platforms requiring flexible and easy-to-tune attitude estimation in the future. [ABSTRACT FROM AUTHOR]

Asynchronous multisensor systems have been widely equipped on various host platforms to meet the requirements of modern navigation campaigns. However, the existing asynchronous fusion algorithms are not efficient in many challenged environments, due to the limitations of communication condition, out-of-sequence observation, and computation affordance. To solve these problems, this paper proposes a batch state asynchronous fusion algorithm with feedback for distributed architecture systems. It is optimal in the sense of minimum mean-squared estimation and its fusion solution is rigorously derived by fully considering the correlations of sequential/cross channels and one-step prediction information. The final fusion solution is straightforward expressed with the combinations of multiple local Kalman filtering estimates outputs during one fusion period. Moreover, no additional interpolation, extrapolation or synchronization procedures are required. Furthermore, to alleviate the computational burden of our proposed algorithm, its approximation form is also given by replacing the weighting matrix by the weighting scalar. Simulations are carried out to illustrate the efficiency and the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

A super fast attitude solution is obtained for consumer electronics accelerometer-magnetometer combination. The quaternion parameterizing the orientation is analytically derived from a least-square optimization that maintains very simple form. Like previously developed approaches, this algorithm does not require predetermined magnetometer reference vector. It has been proven in the paper that the proposed algorithm is equivalent to two recent representative methods. Computational complexity analysis shows that the proposed algorithm has the least floating-number operations. Comparisons with recent and classical methods indicate the definite superiority of the proposed algorithm on execution time in real embedded applications. [ABSTRACT FROM AUTHOR]

The integration of the Accelerometer and Magnetometer (AM) provides continuous, stable and accurate attitude information for land-vehicle navigation without magnetic distortion and external acceleration. However, magnetic disturbance and linear acceleration strongly degrade the overall system performance. As an important complement, the Global Navigation Satellite System (GNSS) produces the heading estimates, thus it can potentially benefit the AM system. Such a GNSS/AM system for attitude estimation is mathematically converted to a multi-observation vector pairs matching problem in this paper. The optimal and sub-optimal attitude determination and their time-varying recursive variants are all comprehensively investigated and discussed. The developed methods are named as the Optimal Linear Estimator of Quaternion (OLEQ), Suboptimal-OLEQ (SOLEQ) and Recursive-OLEQ (ROLEQ) for different application scenarios. The theory is established based on our previous contributions, and the multi-vector matrix multiplications are decomposed with the eigenvalue factorization. Some analytical results are proven and given, which provides the reader with a brand new viewpoint of the attitude determination and its evolution. With the derivations of the two-vector case, the n-vector case is then naturally formed. Simulations are carried out showing the advantages of the accuracy, robustness and time consumption of the proposed OLEQs, compared with representative methods. The algorithms are then implemented using the C++ programming language on the designed hardware with a GNSS module, three-axis accelerometer and three-axis magnetometer, giving an effective validation of them in real-world applications. The designed schemes have proven their fast speed and good accuracy in these verification scenarios. [ABSTRACT FROM AUTHOR]

As a key problem for multisensor attitude determination, Wahba’s problem has been studied for almost 50 years. Different from existing methods, this paper presents a novel linear approach to solve this problem. We name the proposed method the fast linear attitude estimator (FLAE) because it is faster than known representative algorithms. The original Wahba’s problem is extracted to several 1-D equations based on quaternions. They are then investigated with pseudoinverse matrices establishing a linear solution to $n$ -D equations, which are equivalent to the conventional Wahba’s problem. To obtain the attitude quaternion in a robust manner, an eigenvalue-based solution is proposed. Symbolic solutions to the corresponding characteristic polynomial are derived, showing higher computation speed. Simulations are designed and conducted using test cases evaluated by several classical methods, e.g., Shuster’s quaternion estimator, Markley’s singular value decomposition method, Mortari’s second estimator of the optimal quaternion, and some recent representative methods, e.g., Yang’s analytical method and Riemannian manifold method. The results show that FLAE generates attitude estimates as accurate as that of several existing methods, but consumes much less computation time (about 50% of the known fastest algorithm). Also, to verify the feasibility in embedded application, an experiment on the accelerometer–magnetometer combination is carried out where the algorithms are compared via C++ programming language. An extreme case is finally studied, revealing a minor improvement that adds robustness to FLAE, inspired by Cheng et al.

Note to Practitioners—Attitude determination using vector observations can be applied in many areas. The most frequently involved are the accelerometer–magnetometer combination and star tracker array. Based on the proposed efficient fast linear attitude estimator algorithm, the time consumption of the sensor fusion can be significantly reduced, saving the execution time for fault detection, fail safe, and so on. [ABSTRACT FROM AUTHOR]

This study solves the attitude determination problem based on a single sensor observation. The rotation equation is transformed into a quadratic quaternion form and is then derived to a linear matrix equation with pseudoinverse matrices. The analytic solutions to the equation are computed via elementary row operations. The solutions show that the attitude determination from a single sensor observation has infinite solutions and the general one is governed by two limiting quaternions. Accordingly, the variance analysis is given in view of probabilistic characters. The authors explore the experimental results via the accelerometer attitude determination system. The properties of the two limiting quaternions are investigated in the experiment. The results show that the gravity‐determination abilities of the two limiting quaternions are quite different. Using the rotation vector and eigenvalue decomposition of the attitude matrix, the authors prove that one limiting quaternion is better than another one geometrically. The singularity analysis is also performed revealing the non‐existence of singularities for limiting quaternions. The above findings are novel, which are quite different from the conclusions made in a previously published study. [ABSTRACT FROM AUTHOR]

The objective of this paper is to propose an energy-aware and gait corrected pedestrian dead reckoning (PDR) approach using foot-mounted magnetic, angular rate and gravity (MARG) sensors. Compared with existing algorithms of PDR, the proposed method aims to solve three main problems for real pedestrian applications. First, to avoid limitations of off-line calibration for personal step length parameters, we utilize the zero-velocity-update (ZUPT) aided pedestrian MARG performance to continuously compute one's pose information. Meanwhile, it accumulates the moving distance for further estimation of one's step length during the initialization process. Secondly, due to different pedestrian gaits implicating the heading deviation angle between one's moving direction and heading, there are non-negligible impacts on pedestrian dead reckoning accuracy. The linear Kalman filter (KF) is used to recursively estimate the deviated heading during aforementioned initialization process. The third problem is related to the energy consumption. Following three aspects of adaptive energy saving work are devised: (i) energy-aware strategy for gyroscopes measurements acquisition is adopted to guarantee lower energy consumption. (ii) Modes switching mechanism of navigation computation is applied to the initialization and dead reckoning processes. (iii) De-sampling after initialization process has been invoked. Finally, real-world experiments are carried out to evaluate the performances of developed PDR system. The results show the efficiency of the suggested approach. [Display omitted] • A joint ZUPT/dead reckoning based pedestrian navigation method. It is free of off-line calibration for personal PDR parameters. The ZUPT-aided Pedestrian MARG Navigation is utilized to continuously compute one's pose information meanwhile it accumulates the moving distance during the initialization process for further estimating one's step length in the way of dead reckoning. • A gait related heading deviation angle compensation. Due to different pedestrian gaits implicating the heading deviation angle between one's moving direction and heading, there are non-negligible impacts on PDR accuracy. To solve such problem, a linear KF is proposed to recursively estimate the deviated heading for adapting one's different behavior modes. • An adaptive and efficient energy management strategy. Three aspects of adaptive energy saving work are devised: (a) Energy-aware strategy for gyroscope measurements acquisition is adopted to ensure the lower energy consumption. (b) Modes switching mechanism of navigation computation is applied to the initialization and dead reckoning processes. (c) Adaptive de- sampling during pedestrian dead reckoning process. [ABSTRACT FROM AUTHOR]

In the Kalman filtering applications, the conventional dynamic model which connects the states information of two consecutive epochs by state transition matrix is usually predefined and assumed to be invariant. Aiming to improve the adaptability and accuracy of dynamic model, we propose multiple historical states involved filtering algorithm. An autoregressive model is used as the dynamic model which is subsequently combined with observation model for deriving the optimal window-recursive filter formulae in the sense of minimum mean square error principle. The corresponding test statistics characteristics of system residuals are discussed in details. The test statistics of regional predicted residuals are then constructed in a time-window for model bias testing with two hypotheses, that is, the null and alternative hypotheses. Based on the innovations test statistics, we develop a model bias processing procedure including bias detection, location identification, and state correction. Finally, the minimum detectable bias and bias-to-noise ratio are both computed for evaluating the internal and external reliability of overall system, respectively. [ABSTRACT FROM AUTHOR]

Constraints can provide additional aids to a multi-sensor integrated navigation system and hence can increase accuracy of the solution and enhance reliability of the system. To integrate the constraints with the data from the sensors, the traditional integration Kalman filter (IKF) needs to be reconstructed. A new algorithm, the so-called constrained adaptive robust integration Kalman filter (CARIKF) is presented, which implements adaptive integration upon the robust direct fusion solution. In the algorithm the raw observations from all heterogeneous sensors are corrected by the pseudoobservations derived from state equality constraint. The posterior covariances of the corrected observations are subsequently estimated upon the robust maximum-likelihood-type estimation (M-estimation) theory. The fusion state and its covariance are solved for all sensors further in the least squares (LS) sense. The pseudoobservations are constructed according to the estimated state and its covariance. They are further combined with the dynamic model of the host platform in an adaptive Kalman filter (AKF), from which a reliable and accurate navigation solution can be then obtained. A state constraint model is proposed upon Newton's forward differential extrapolation numerical method. To demonstrate performance of the CARIKF algorithm, simulations have been conducted in different dynamic and observation scenarios. Several algorithms are compared to evaluate the validity and efficiency of the CARIKF. The results show that the CARIKF is superior to other algorithms and can significantly improve the precision and reliability of the integrated solution. [ABSTRACT FROM AUTHOR]

In kinematic Global Navigation Satellite Systems (GNSS) navigation, the Kalman Filter (KF) solution relies, to a great extent, on the quality of the dynamic model that describes the moving object's motion behaviour. However, it is rather difficult to establish a precise dynamic model that only connects the previous state and the current state, since these high-order quantities are usually unavailable in GNSS navigation receivers. To overcome such limitations, the Window-Recursive Approach (WRA) that employs the previous multiple states to predict the current one was developed in Zhou et al., (2010). Its essence is to adaptively fit the moving object's motion behaviour using the multiple historical states in a short time span. Up to now, the WRA method has been performed only using GNSS pseudorange measurements. However, in GNSS navigation fields, the strength of pseudorange observation model is usually weak due to various reasons, e.g., multi-path delay, outliers, insufficient visible satellites. As an important complementary measurement, Doppler can be used to aid Position and Velocity (PV) estimation. In this contribution, implementation of WRA will be developed using the pseudorange and Doppler measurements. Its corresponding state transition matrix is constructed based on the Newton's Forward Difference Extrapolation (NFDE) and Definite Integral (DI) methods for the efficient computation. The new implementation of WRA is evaluated using the real kinematic vehicular GNSS data with two sampling rates. The results show that: (i)aided by GNSS Doppler measurement, the new implementation of WRA significantly improves the accuracy compared with the pseudorange-only WRA.(ii)In high sampling rate, the WRA works best in the case of 2 epochs in time window, while in the low sampling rate, it obtains better solutions if more epochs involved in time window.(iii)Compared with KF with constant velocity dynamic model, the WRA demonstrates better in the self-adaptation and validity.(iv)As a benefit of WRA itself, the NFDE/DI-based state transition matrix for WRA can be previously computed offline without increasing the computation burdens. [ABSTRACT FROM PUBLISHER]

3-D registration has always been performed invoking singular value decomposition (SVD) or eigenvalue decomposition (EIG) in real engineering practices. However, these numerical algorithms suffer from uncertainty of convergence in many cases. A novel fast symbolic solution is proposed in this article by following our recent publication in this journal. The equivalence analysis shows that our previous solver can be converted to deal with the 3-D registration problem. Rather, the computation procedure is studied for further simplification of computing without complex-number support. Experimental results show that the proposed solver does not loose accuracy and robustness but improves the execution speed to a large extent by almost 50%–80%, on both a personal computer (PC) and an embedded processor. Note to Practitioners—3-D registration usually has a large computational burden in engineering tasks. The proposed symbolic solution can directly solve the eigenvalue and its associated eigenvector. A lot of computation resources can then be saved for better overall system performance. The deterministic behavior of the proposed solver also ensures long-endurance stability and can help an engineer better design thread timing logic. [ABSTRACT FROM AUTHOR]

Attitude determination using the accelerometer–magnetometer combination is basically an applied mathematical problem. Commonly, such attitude determination tasks should be accomplished with reference information of sensors, e.g. the magnetometer's reference vector, from calibration processes. However, this piece of important information cannot be accurately acquired or would differ with the change of body's position. In this paper, to solve such problem, the conventional accelerometer–magnetometer combination fusion equations are transformed into a brand new set of equations, which are free of reference information. Quaternion solutions to the novel equations are obtained via analytic computation techniques. According to the unique design, the proposed attitude estimator owns very fast computation speed compared with representative methods including iterative ones and algebraic ones. Experiments and simulations are carried out to give demonstrations and comparisons, which verify the correctness and effectiveness of the proposed method. The results also show that using the proposed quaternion solution, fusion with gyroscope can be more efficiently obtained. [ABSTRACT FROM AUTHOR]

Purpose: Autonomous orbit determination using geomagnetic measurements is an important backup technique for safe spacecraft navigation with a mere magnetometer. The geomagnetic model is used for the state estimation of orbit elements, but this model is highly nonlinear. Therefore, many efforts have been paid to developing nonlinear filters based on extended Kalman filter (EKF) and unscented Kalman filter (UKF). This paper aims to analyze whether to use UKF or EKF in solving the geomagnetic orbit determination problem and try to give a general conclusion. Design/methodology/approach: This paper revisits the problem and from both the theoretical and engineering results, the authors show that the EKF and UKF show identical estimation performances in the presence of nonlinearity in the geomagnetic model. Findings: While EKF consumes less computational time, the UKF is computationally inefficient but owns better accuracy for most nonlinear models. It is also noted that some other navigation techniques are also very similar with the geomagnetic orbit determination. Practical implications: The intrinsic reason of such equivalence is because of the orthogonality of the spherical harmonics which has not been discovered in previous studies. Thus, the applicability of the presented findings are not limited only to the major problem in this paper but can be extended to all those schemes with spherical harmonic models. Originality/value: The results of this paper provide a fact that there is no need to choose UKF as a preferred candidate in orbit determination. As UKF achieves almost the same accuracy as that of EKF, its loss in computational efficiency will be a significant obstacle in real-time implementation. [ABSTRACT FROM AUTHOR]

The rotary INS (inertial navigation system) has been applied to compensate the navigation errors of the MEMS (micro-electro-mechanical-systems) INS recently. In such system, the PVA (position, velocity, and attitude) errors can be compensated through IMU (inertial measurement unit) carouseling. However, the navigation errors are only partially compensated due to the intrinsic property of the inertial system and the randomness of the IMU errors. In this paper, we present an integrated rotary MEMS INS/GNSS (global navigation satellite systems) system based on the ANN (artificial neural networks) technique. The ANFIS (adaptive neuro-fuzzy inference system) is applied to eliminate the residual PV (position and velocity) errors of the rotary MEMS INS during GNSS outages. A cascaded velocity-position structure is designed to recognize the pattern of the rotary MEMS INS PV errors and to reduce them of the rotary inertial system in standalone mode. The road tests are conducted with artificial GNSS outages to evaluate the ability of the integrated system to predict the PV errors. Compared to the position errors of the integrated rotary INS/GNSS system based on an EKF (extended Kalman filtering), they are reduced by 79.98% in the proposed system. [ABSTRACT FROM AUTHOR]

Wireless sensor networks (WSNs) have become one of the core technologies of the internet of things (IoT) system. They are information generation and acquisition systems used by the IoT to sense and identify the surrounding environment. They are also sensor technology, embedding computing technology, communication technology and important product in the development of Internet technology, which have made the whole society more intelligent and humanized. WSNs are multi-hop self-organizing networks consisting of a large number of micro-sensor nodes deployed in the monitoring area. They can collaboratively sense, collect and process the monitored objects and transmit them to the observers. In this paper, we use the cascade failure method to find the key nodes in the WSNs. First, a complex network cascade failure model based on load redistribution is proposed. Differences from the existing model are as follows: (1) for each node, an overload function is defined; (2) the evolution of the network topology is replaced by node weight evolution. Based on the cascade failure model, a method for evaluating the importance of complex load network nodes is proposed and a new definition of node importance is given. This method helps to discover some potential "critical nodes" in the network. The final experimental analysis verifies the effectiveness and feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

For visually aided industrial robots, the transformation between the mounted visual information system and the end-effector must be calibrated prior to the practical use. However, during the data acquisition stage, measurement uncertainties will lead to inevitable mismatched data. This article proposes a novel correspondence matching method for the hand-eye calibration system of the type $\boldsymbol {AX} = \boldsymbol {XB}$. The correspondence matching refers to the problem of finding out the well-matched $\boldsymbol {A}$ and $\boldsymbol {B}$ and the relative time delay between them, from a series of measurements. A neat Lie algebra formulation has been obtained to cast the original problem into a high-dimensional point-cloud registration problem. This solution allows for the simultaneous solution of the hand-eye calibration, correspondence matching, and time-delay estimation as well as the uncertainty description of the obtained results. Synthetic simulations verify the correctness of the proposed method. Experimental studies have also confirmed its practical feasibility on an automatic welding platform. [ABSTRACT FROM AUTHOR]