Robust and reliable estimation via recursive nonlinear dynamic data reconciliation based on cubature Kalman filter

Constrained nonlinear state estimation based on the UKF approach

Modified unscented recursive nonlinear dynamic data reconciliation for constrained state estimation

Performance evaluation of Cubature Kalman filter in a GPS/IMU tightly-coupled navigation system

This paper presents a Cubature Kalman Filter (CKF) based speed and position observer for a Permanent Magnet Synchronous Motor (PMSM). CKF is a new variety of Kalman filter which uses a third degree spherical-radial cubature rule to numerically compute multivariate moment integrals. Unlike in an Extended Kalman Filter(EKF), mean and covariance are propagated through the non-linear system, which minimizes the errors due to linearization. The proposed observer is incorporated in the sensorless control of an IPMSM of 1.5kW, 3000rpm rating. For the CKF algorithm, PMSM is modeled in stationary αβ reference frame. To get comparatively better transient performance and convergence of the CKF for a non-zero initial rotor position, system covariance matrix Q is chosen adaptively. Simulation results for a VSI fed IPMSM are presented and the convergence of CKF is shown for a variation of stator resistance. Performance of the proposed observer is compared with that of an EKF observer.

In this paper, vision-based relative navigation of two spacecraft is addressed using the sparse Gauss-Hermite quadrature filter. The relative navigation provides the estimation of the relative attitude and relative orbit between spacecraft, which is a challenging filtering problem since it is a highly nonlinear and high dimensional estimation problem. Many filters have been used to solve this problem, such as, the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). However, these filters are not accurate enough when the initial uncertainty is large or the nonlinearity is significant. Moreover, although the conventional Gauss-Hermite quadrature filter is more accurate than the UKF, it cannot be used since a huge number of points is required. It is shown in this paper that the sparse Gauss-Hermite quadrature filter can achieve better estimation accuracy than the EKF, the UKF, and the cubature Kalman filter without excessive computation load.

According to the problem on tracking planning of mobility assistance robot, a tracking planning method was presented using the kalman filter (KF). Based on known nonholonomic dynamic model of mobility assistance robot, the cubature kalman filter (CKF) was used to improve the influence of nonlinear system, and the autonomous navigation and control of mobility assistance robot was realized. The experimental results indicate that the method presented in this paper was excellent than extended kalman filter (EKF) and unscented kalman filter (UKF) in the stability, precision and computational complexity.

In this paper, the state trajectories of a hypersonic vehicle is estimated using a new generalized cubature Kalman filter. This new nonlinear estimation technique is based on a class of arbitrary-degree cubature rules to compute the multivariate integrals in the Bayesian filtering algorithm and can achieve higher degree of estimation accuracy. The performance of this new cubature Kalman filter is compared with the Extended Kalman filter, the unscented Kalman filter and the conventional third-degree cubature Kalman filter. The simulation results demonstrate that the proposed filter outperforms those three filters in estimation accuracy and convergence rate. It is also computationally more efficient than many other point-based estimation techniques.

A novel sparse Gauss―Hermite quadrature filter is proposed using a sparse-grid method for multidimensional numerical integration in the Bayesian estimation framework. The conventional Gauss―Hermite quadrature filter is computationally expensive for multidimensional problems, because the number of Gauss―Hermite quadrature points increases exponentially with the dimension. The number of sparse-grid points of the computationally efficient sparse Gauss―Hermite quadrature filter, however, increases only polynomially with the dimension. In addition, it is proven in this paper that the unscented Kalman filter using the suggested optimal parameter is a subset of the sparse Gauss―Hermite quadrature filter. The sparse Gauss-Hermite quadrature filter is therefore more flexible to use than the unscented Kalman filter in terms of the number of points and accuracy level, and it is more efficient than the conventional Gauss―Hermite quadrature filter. The application to the spacecraft attitude estimation problem demonstrates better performance of the sparse Gauss―Hermite quadrature filter in comparison with the extended Kalman filter, the cubature Kalman filter, and the unscented Kalman filter.

The trajectory estimation of a highly maneuvering target is a challenging problem and has practical applications. The interacting multiple model (IMM) filter is a well-established filtering algorithm for the trajectory estimation of maneuvering targets. In this study, we present an overview of IMM filtering algorithms for tracking a highly-maneuverable fighter aircraft using an air moving target indicator (AMTI) radar on another aircraft. This problem is a nonlinear filtering problem due to nonlinearities in the dynamic and measurement models. We first describe single-model nonlinear filtering algorithms: the extended Kalman filter (EKF), unscented Kalman filter (UKF), and cubature Kalman filter (CKF). Then, we summarize the IMM-based EKF (IMM-EKF), IMM-based UKF (IMM-UKF), and IMM-based CKF (CKF). In order to compare the state estimation accuracies of the IMM-based filters, we present a derivation of the posterior Cramér-Rao lower bound (PCRLB). We consider fighter aircraft traveling with accelerations 3g, 4g, 5g, and 6g and present numerical results for state estimation accuracy and computational cost under various operating conditions. Our results show that under normal operating conditions, the three IMM-based filters have nearly the same accuracy. This is due to the accuracy of the measurements of the AMTI radar and the high data rate.

An introduction of a new observer for estimating speed and flux of induction motor drive is done in this paper. The main tool of designing the observer is cubature Kalman filter (CKF). In order to compute multivariate integrals for moment estimation the CKF uses spherical-radial transformation followed by a third degree spherical-radial rule. The utmost advantage of CKF lies on capturing the system nonlinearity using the spherical-radial transformation giving it and edge over Extended Kalman Filter (EKF), as the errors is in it are minimized by linearizing the state model of the system. In this paper square root form of CKF (SRCKF) is used to eliminate the most hazardous situation of the loss of positive definiteness of error covariance matrix in each update which can stop the CKF from running continuously. The sensor less direct torque control is used for an Induction motor of 0.75Kw, 1475 rpm, for conducting performance test of the proposed observer. For simpler design of SRCKF, state space model of IM in stationary reference frame has been used. Effectiveness of the proposed observer is validated using simulation result for a VSI fed IM drive and compared with that of an EKF observer.

The Kalman-filter-based algorithms as the mainstream algorithms of dynamic state estimation of power systems have been extensively used to provide accurate data for power system applications. However, few comparisons are made to show their advantages and disadvantages. In this paper, four Kalman-filter-based algorithms (i.e., extended Kalman filter, unscented Kalman filter, cubature Kalman filter, and ensemble Kalman filter) are compared to show their differences from implementation complexity, estimation accuracy and calculation efficiency, the resistance to measurement errors, and the sensitivity to system scales. Finally, the simulation results on the 3-machine, 10-machine, and 48-machine power systems show their advantages and disadvantages.

Firstly, the problems and common methods of power system dynamic state estimation are briefly introduced, and then the basic principles of Kalman filtering are introduced. Based on this principle, the common methods of power system dynamic state estimation problems are derived: extended Kalman filter, unscented Kalman filter and cubature Kalman filter, which are introduced respectively. The advantages and disadvantages of these methods and their applications in power system dynamic state estimation are compared and analyzed. Finally, the development trend of Kalman filter in dynamic state estimation is prospected.

Simultaneous state and parameter estimation is essential for control system design and dynamic modeling of physical systems. This capability provides critical real-time insight into system behavior, supports the discovery of underlying mechanisms, and facilitates adaptive control strategies. Surveyed in this review paper are two classes of state and parameter estimation methods: Kalman Filters and Luenberger Observers. The Kalman Filter framework, including its major variants such as the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), Cubature Kalman Filter (CKF), and Ensemble Kalman Filter (EnKF), has been widely applied for joint and dual estimation in linear and nonlinear systems under uncertainty. In parallel, Luenberger observers, typically used in deterministic settings, offer alternative approaches through high-gain, sliding mode, and adaptive observer structures. This review focuses on the theoretical foundations, algorithmic developments, and application domains of these methods and provides a comparative analysis of their advantages, limitations, and practical relevance across diverse engineering scenarios.

This paper presents an approach to test and validate a number of power system dynamic state estimation (PSDSE) algorithms, utilizing Real Time Digital Simulator (RTDS), a real-time simulation tool. WSCC 9-bus and IEEE 30-bus systems have been utilized to demonstrate the proposed approach. The test systems are developed on the RSCAD software of the RTDS. The conventional remote terminal unit (RTU) measurements and the phasor measurement unit (PMU) measurements are sent from the RTDS runtime environment to the MATLAB based PSDSE application at regular intervals for the estimation of the states, using software-in-the-loop (SIL) configuration. The PSDSE is solved by utilizing the extended Kalman filter (EKF), the unscented Kalman filter (UKF), and the cubature Kalman filter (CKF) approaches, and their relative performances are studied with the help of the simulation results on the two test systems.

As a new type of guidance technology, the strapdown imaging guidance technology, which helps improve the system reliability and reduce costs efficiently, has been paid great attention and developed quickly. However, the detecting information of strapdown seeker can’t be used to proportional navigation directly because it is coupled with missile attitude. A method to estimate the inertial Line-of-Sight (LOS) rate of strapdown imaging seeker based on Cubature Kalman filter (CKF) and Tracking-Differentiator (TD) was presented. As there were high nonlinearity in both state and measurement equations and more serious non-Gaussian noise in the measurements, the Extended Kalman filter (EKF) could not completely meet the requirements of filtering. Compared with EKF and Unscented Particle filter (UKF), CKF was a congruent method for states estimating in the conditions of nonlinearity and non-Gaussian noise. CKF was applied to estimate the LOS rate of strapdown imaging seeker. Because measurement noise of missile attitude will be reflected in estimation result, TD was used to decrease noise of the missile attitude measurements for improving the estimation precision. Monte Carlo simulation results show that the proposed method can improve the precision of guidance.