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For nonlinear systems with continuous dynamic and discrete measurements, a Log-Euclidean metric (LEM) based novel scheme is proposed to refine the covariance integration steps of continuous–discrete Extended Kalman filter (CDEKF). In CDEKF, the covariance differential equation is usually integrated with regular Euclidean matrix operations, which actually ignores the Riemannian structure of underlying space and poses a limit on the further improvement of estimation accuracy. To overcome this drawback, this work proposes to define the covariance variable on the manifold of symmetric positive definite (SPD) matrices and propagate it using the Log-Euclidean metric. To embed the LEM based novel propagation scheme, the manifold integration of the covariance for LEMCDEKF is proposed together with the details of efficient realization, which can integrate the covariance on SPD manifold and avoid the drawback of Euclidean scheme. Numerical simulations certify the new method's superior accuracy than conventional methods. • A Log-Euclidean metric based continuous–discrete Extended Kalman filter is elaborated for nonlinear continuous–discrete systems. • The covariance variable is propagated on the manifold of symmetric positive definite matrices according to the Log-Euclidean metric. • Efficient realization of the LEMCDEKF is proposed by combining the LEM based scheme with the Runge–Kutta method. [ABSTRACT FROM AUTHOR]

Celestial navigation using time delay measurement is an innovative autonomous navigation method. To calculate the equivalent measurement, the numerical method needs to be applied, which is time-consuming. The event-triggered mechanism intermittently and aperiodically processes measurements by judging if the update error has changed drastically. However, its performance is greatly affected by the constant threshold. To solve this problem, a parameter-independent event-triggered implicit unscented Kalman filter (UKF) is proposed and applied to the celestial navigation using time delay measurement. The innovation at the current moment and the updated estimate covariance at the last moment are compared with the previous value instead of the constant threshold. The event is automatically triggered when the accuracy of the state estimate is low. Simulation results indicate that the proposed parameter-independent event-triggered implicit UKF can reduce the running time by reducing unnecessary measurement updates, whose performance will not be affected by any parameter or window size. In a word, the proposed method substitutes the dynamic threshold for the constant threshold, ensuring that its performance will not be affected by any parameter or window size. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper mainly studies the longitudinal and lateral deck motion compensation technology. In order to ensure the safe landing of the carrier-based aircrafts on the flight decks of carriers during the landing process, it is necessary to introduce deck motion information into the guidance law information of the automatic landing guidance system when the aircraft is about to land so that the aircraft can track the deck motion. To compensate the influence of the height change in the ideal landing point on the landing process, the compensation effects of the deck motion compensators with different design parameters are verified by simulation. For further phase-lead compensation for the longitudinal automatic landing guidance system, a deck motion predictor is designed based on the particle filter optimal prediction theory and the AR model time series analysis method. Because the influence of up and down motions on the vertical motion of the ideal landing point is the largest, the compensation effects of the designed predictor and compensator are simulated and verified based on the up and down motion of the power spectrum. For the compensation for the lateral motion, a tracking strategy of the horizontal measurement axis of the inertial stability coordinate system to the horizontal axis of the hull coordinate system (center line of the deck) is proposed. The tracking effects of the horizontal measurement axis of the designed integral and inertial tracking strategies are simulated and compared. Secondly, the lateral deck motion compensation commands are designed, and the compensation effects of different forms of compensation commands are verified by simulations. Finally, the compensation effects for the lateral deck motion under integral and inertial tracking strategies are simulated and analyzed. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to propose a high-precision attitude solution to solve the attitude drift problem caused by the dispersion of low-cost micro-electro-mechanical system devices in strap-down inertial navigation attitude solution of micro-quadrotor. Design/methodology/approach: In this study, a three-stage attitude estimation scheme that combines data preprocessing, gyro drifts prediction and enhanced unscented Kalman filtering (UKF) is proposed. By introducing a preprocessing model, the quaternion orientation is calculated as the composition of two algebraic quaternions, and the decoupling feature of the two quaternions makes the roll and pitch components independent of magnetic interference. A novel real-time based on differential value (DV) estimation algorithm is proposed for gyro drift. This novel solution prevents the impact of quartic characteristics and uses the iterative method to meet the requirement of real-time applications. A novel attitude determination algorithm, the pre-process DV-UKF algorithm, is proposed in combination with UKF based on the above solution and its characteristics. Findings: Compared to UKF, both simulation and experimental results demonstrate that the pre-process DV-UKF algorithm has higher reliability in attitude determination. The dynamic errors in the three directions of the attitude are below 2.0°, the static errors are all less than 0.2° and the absolute attitude errors tailored by average are about 47.98% compared to the UKF. Originality/value: This paper fulfils an identified need to achieve high-precision attitude estimation when using low-cost inertial devices in micro-quadrotor. The accuracy of the pre-process DV-UKF algorithm is superior to other products in the market. [ABSTRACT FROM AUTHOR]

The problem of simultaneous estimation of states and uncertainties by using limited information is investigated in this article. A sampled‐data learning observer (SLO) is presented for linear time‐invariant continuous systems, which can achieve successful estimation while only needs intermittent sampled‐data, saves computing resources, and does not require persistent excitation signals. The observer's demand for continuous measurement is reduced, that is, limited‐information is sufficient. Notably, the uncertainty estimation is performed by a learning equation with only simple addition operations, which is particularly suitable for actual digital system scenarios. Simulation results illustrate the effectiveness of the proposed SLO. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to propose a general and rigorous study on the propagation property of invariant errors for the model conversion of state estimation problems with discrete group affine systems. Design/methodology/approach: The evolution and operation properties of error propagation model of discrete group affine physical systems are investigated in detail. The general expressions of the propagation properties are proposed together with the rigorous proof and analysis which provide a deeper insight and are beneficial to the control and estimation of discrete group affine systems. Findings: The investigation on the state independency and log-linearity of invariant errors for discrete group affine systems are presented in this work, and it is pivotal for the convergence and stability of estimation and control of physical systems in engineering practice. The general expressions of the propagation properties are proposed together with the rigorous proof and analysis. Practical implications: An example application to the attitude dynamics of a rigid body together with the attitude estimation problem is used to illustrate the theoretical results. Originality/value: The mathematical proof and analysis of the state independency and log-linearity property are the unique and original contributions of this work. [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]

For linear time-invariant systems, this paper develops a new kind of adaptive Kalman filter to deal with Kalman filtering problems troubled by unknown/inaccurate process noise covariance. The limitation of Kalman filter is that its performance would deteriorate or even degrade if the accurate noise statistics could not be obtained in advance. To reduce or mitigate the negative influence caused by unknown/mismatched process noise covariance, this work elaborates a novel covariance control scheme in which the prior error covariance is recursively regulated with the proportional form of feedback information: the posterior sequence is first evaluated as online feedback to constitute a closed-loop structure for covariance propagation process, and then a proportional gain is employed to amplify the feedback term and fasten the converging of the estimated covariance parameter; note that, the new approach is relatively more independent of the parameter of process noise covariance and, therefore, the Kalman theory's rigorous dependency on accurate process noise covariance could be relaxed significantly. The mathematical properties and sub-optimality of the new covariance control scheme are discussed in detail as well as some practical considerations. The advantage of this newly developed method in filtering accuracy, adaptability and simplicity are illustrated with an object tracking scenario. • To reduce the influence of unknown noise covariance, this work elaborates a new adaptive Kalman filter using novel covariance control. • The posterior sequence is evaluated as feedback to constitute closed-loop structure for covariance propagation and a proportional gain is employed to fasten convergence. • In the new approach, the Kalman theory's constraint on a prior accurate knowledge about process noise covariance is relaxed significantly. [ABSTRACT FROM AUTHOR]

Attitude estimation is a basic task for most spacecraft missions in aerospace engineering and many Kalman type attitude estimators have been applied to the guidance and navigation of spacecraft systems. By building the attitude dynamics on matrix Lie groups, the invariant Kalman filter (IKF) was developed according to the invariance properties of symmetry groups. However, the Gaussian noise assumption of Kalman theory may be violated when a spacecraft maneuvers severely and the process noise might be heavy-tailed, which is prone to degrade IKF's performance for attitude estimation. To address the attitude estimation problem with heavy-tailed process noise, this paper proposes a hierarchical Gaussian state-space model for invariant Kalman filtering: The probability density function of state prediction is defined based on student's t distribution, while the conjugate prior distributions of the scale matrix and degrees of freedom (dofs) parameter are respectively formulated as the inverse Wishart and Gamma distribution. For the constructed hierarchical Gaussian attitude estimation state-space model, the Lie groups rotation matrix of spacecraft attitude is inferred together with the scale matrix and dof parameter using the variational Bayesian iteration. Numerical simulation results illustrate that the proposed approach can significantly improve the filtering robustness of invariant Kalman filter for Lie groups spacecraft attitude estimation problems with heavy-tailed process uncertainty. [ABSTRACT FROM AUTHOR]