External force estimation for robot manipulator based on a LuGre-linear-hybrid friction model and an improved square root cubature Kalman filter

State of charge (SOC) is a key parameter for lithium-ion battery management systems. The square root cubature Kalman filter (SRCKF) algorithm has been developed to estimate the SOC of batteries. SRCKF calculates 2n points that have the same weights according to cubature transform to approximate the mean of state variables. After these points are propagated by nonlinear functions, the mean and the variance of the capture can achieve third-order precision of the real values of the nonlinear functions. SRCKF directly propagates and updates the square root of the state covariance matrix in the form of Cholesky decomposition, guarantees the nonnegative quality of the covariance matrix, and avoids the divergence of the filter. Simulink models and the test bench of extended Kalman filter (EKF), Unscented Kalman filter (UKF), cubature Kalman filter (CKF) and SRCKF are built. Three experiments have been carried out to evaluate the performances of the proposed methods. The results of the comparison of accuracy, robustness, and convergence rate with EKF, UKF, CKF and SRCKF are presented. Compared with the traditional EKF, UKF and CKF algorithms, the SRCKF algorithm is found to yield better SOC estimation accuracy, higher robustness and better convergence rate.

Kalman filters are very popular in turbofan engine community for health monitoring purposes. In this study, in order to get better performance in terms of filtering accuracy and noise adaptability, an Adaptive Square Root Cubature Kalman Filter (ASRCKF) was proposed to estimate health parameters of the turbofan engine gas path components. In the ASRCKF algorithm, the mean value and covariance of the engine nonlinear function were calculated by cubature rule-based numerical integration method and used as a substitute for nonlinear model in nonlinear Kalman filter. The latest information of measurement parameters in the recursion and filtering process was used to estimate and self-adjust the noises cross-covariance by removable window method to get higher filtering accuracy. Compared with the Extended Kalman Filter (EKF) and Square Root Cubature Kalman Filter (SRCKF), the simulation results in the gradual and rapid deterioration process of turbofan engine gas path components indicate that the higher accuracy and faster convergence can be obtained through ASRUKF, which can be used in health parameters estimation and condition monitoring of turbofan engine gas path.1

An iterated filtering method is presented to improve the update stage of nonlinear filtering. First, we develop a generalized iterative framework for sigma point kalman filter by utilizing Gauss-Newton algorithm. A simplified iterated square root cubature kalman filter (SCKF) is proposed with application to tightly coupled GNSS/INS, where the linear combination of innovations is used in measurement update. Numerical experiment and field test results indicate that SCKF has similar performance with extended kalman filter. Compared with the non-iterated methods, iterated SCKF improves the heading by 23.6% with two iterations, and get a faster convergence rate regarding heading and velocity.

Aiming at the problem that the ultra wide band (UWB) wireless signal is easy to be interfered, a robust adaptive square root cubature Kalman filter (RA-SRCKF) is proposed to be used in UWB/PDR integrated indoor positioning. RA-SRCKF is based on square root cubature Kalman filter (SRCKF) and its statistical characteristic of measurement noise is updated with the method of first estimating and then modifying. The experimental results show that the proposed RA-SRCKF can effectively improve the accuracy and stability of UWB/PDR integrated positioning.

To account for the impulsive non-Gaussian noises, a minimum error entropy square root cubature Kalman filter (MEE-SRCKF) is proposed to estimate the state of charge (SOC) of lithium-ion batteries. It adopts the robust minimum error entropy (MEE) criterion as the optimization criterion, instead of the MMSE or maximum correntropy criterion (MCC). And then the square root cubature Kalman filter (SRCKF) is used to deal with the nonlinearity. The performance of the proposed algorithm is validated by a pulsed discharge test and an urban dynamometer driving schedule (UDDS) test. Experimental results demonstrate that the proposed approach has significantly improved the SOC estimation accuracy of the lithium-ion battery under non-Gaussian measurement noise compared with the SRCKF algorithm. In addition, given different initial SOC values, MEE-SRCKF algorithm also converges rapidly to its true value.

This paper proposes two novel methods for fault detection in non-linear processes. These methods apply a Gaussian process (GP) to model the underlying process, and then the extended Kalman filter (EKF) and square root cubature Kalman filter (SCKF) are used to detect faults. Accordingly, two approaches called the Gaussian process–extended Kalman filter (GP-EKF) and Gaussian process–square root cubature Kalman filter (GP-SCKF) are proposed. The most important characteristic of these proposed methods is that there is no need for an accurate model of the system. Therefore, these methods are considered non-parametric approaches of fault detection in non-linear systems. To illustrate the performance of these algorithms in fault detection, they have been used in a continuous stirred-tank reactor system (CSTR). Both proposed methods are able to detect sensor faults at an early stage.

To improve the low state estimation accuracy of nonlinear state estimation due to large initial estimation error and nonlinearity of measurement equation, we obtain Levenberg-Marquardt (abbr. L-M) method based iteration square root cubature Kalman filter (ISRCKFLM) combining the measurement update of square root cubature Kalman filter (SRCKF) with nonlinear least square error, so the ISRCKFLM algorithm has the virtues of global convergence and numerical stability. We apply the ISRCKFLM algorithm to state estimation for re-entry ballistic target; the simulation results demonstrate the ISRCKFLM algorithm has better accuracy of state estimation.

An accurate state of charge (SOC) estimation is vital for safe operation and efficient management of lithium-ion batteries. To improve the accuracy and robustness, an adaptive and robust square root cubature Kalman filter based on variational Bayesian approximation and Huber’s M-estimation (VB-HASRCKF) is proposed. The variational Bayesian (VB) approximation is used to improve the adaptivity by simultaneously estimating the measurement noise covariance and the SOC, while Huber’s M-estimation is employed to enhance the robustness with respect to the outliers in current and voltage measurements caused by adverse operating conditions. A constant-current discharge test and an urban dynamometer driving schedule (UDDS) test are performed to verify the effectiveness and superiority of the proposed algorithm by comparison with the square root cubature Kalman filter (SRCKF), the VB-based SRCKF, and the Huber-based SRCKF. The experimental results show that the proposed VB-HASRCKF algorithm outperforms the other three filters in terms of SOC estimation accuracy and robustness, with a little higher computation complexity.

The distance of deep space exploration is far away from earth, the communication delay is not conducive to the handling of emergencies and detector failures, and the survival of spacecraft faces a huge risk. Therefore, in the deep space, the spacecraft must rely on its own sensors to achieve positioning and environmental perception. The key problem of autonomous navigation in deep space is the nonlinear state estimation of the spacecraft in a dynamic 3D environment. However, the use of a single sensor in deep space usually has a big error, and to overcome this limitation, the state can be corrected using observations of multiple known objects in the world. This is referred to as multi-sensor fusion, since the information of multiple sensors needs to be combined in order to obtain an estimation of the state. In this paper, we combine the observations of stars in the deep space with the dynamics of celestial objects to analyze the state of spacecraft. We proposed a multi-sensor fusion method based on the square root cubature kalman filter (SRCKF) to solve the multi-sensor fusion problem of spacecraft. Specifically, we perform the improved cubature kalman filter on sensor data obtained from interferometer, star tracker, planet sensor, sun sensor, and earth sensor. In order to solve the problem of high computational complexity when SRCKF is used in nonlinear filtering problems, the QR decomposition is used to pass the covariance array square root factor, which reduces the amount of computation, avoids negative matrix determination, and improves the filtering accuracy. Then we incorporate the idea of extended information filter, according to the nature of statistical linear error propagation, the update process of the cubature kalman filter is embedded into the extended information filter framework. Specifically, the information contribution vector and information contribution matrix are proposed as the evaluation of each sensor's contribution in the filter estimation composition. And the square root of the covariance in the SRCKF process is implemented by updating the square root of the information contribution matrix. The results show that the proposed multi-sensor fusion algorithm outperforms the SRCKF and EKF algorithms in terms of position and velocity estimation.

In order to balance filtering accuracy and time cost, this paper introduces an improved square root cubature particle filter algorithm (ISRCPF) navigation method. For the lack of measurement information of the PF, it combines square root cubature Kalman filter (SRCKF) with strong tracking filter (STF), and proposes an improved square root cubature Kalman filter (ISRCKF). The ISRCPF adopting the ISRCKF to develop the proposal distribution and incorporates the latest measurement into updating phase is proposed by introducing the ISRCKF into the particle filter framework. The results show that considering both time cost and filtering accuracy, the ISRCPF is a good choice to improve the particle filter algorithm.

The development of a novel method to estimate the state of charge (SOC) with low read-only memory (ROM) occupancy, high stability, and high anti-interference capability is very important for the battery management system (BMS) in actual electric vehicles. This paper proposes the square root cubature Kalman filter (SRCKF) with a temperature correction rule, based on the BMS of a common on-board embedded micro control unit (MCU), to achieve smooth estimation of SOC. The temperature correction rule is able to reduce the testing effort and ROM space used for data table storage (189.3 kilobytes is much smaller than the storage of the MPC5604B, with 1000 kilobytes), while the SRCKF is adopted to achieve highly robust real-time SOC estimation with high resistance to interference and moderate computing cost (68.3% of the load rate of the MPC5604B). The results of multiple experiments show that the proposed method with less computational complexity converges rapidly (in approximately 2.5 s) and estimates the SOC of the battery accurately under dynamic temperature condition. Moreover, the SRCKF algorithm is not sensitive to the high measuring interference and highly nonlinear working conditions (even with 1% current and voltage measurement disturbances, the root mean square error of the proposed method can be as high as 0.679%).

A deconvolution scheme for the stochastic metabolic/hemodynamic model (sMHM) based on the square root cubature Kalman filter and maximum likelihood estimation

In order to improve the deficiency of range information unmeasurable in passive location and high computational complexity in distributed fusion estimation, an improved range parameterized square root cubature information filter (RP-SRCIF) algorithm is proposed. The proposed algorithm adopts fully distributed fusion estimation structure, integrates square root cubature Kalman filter (SRCKF) algorithm, range parameterized method and information filter (IF) algorithm. SRCKF can ensure better numerical stability and higher estimation accuracy; the improved range parameterized method can provide good robustness for initial estimation range and better real-time performance than traditional range parameterized method; IF with fully distributed fusion estimation structure makes fusion estimation computation more simple and convenient. Simulation results indicate the RP-SRCIF algorithm is feasible and more effective when compared with other algorithms for multi-UAV cooperative passive location.

With the development of unmanned driving technology, the demand for tracking accuracy is increasing. To rely on a single sensor to obtain detection results in complex environments is limited in accuracy, and multi-sensor fusion is an effective method. Therefore, the environmental sensing technology based on multi-sensor fusion is one of the present research hotspots. This paper proposes a multi-sensor fusion tracking algorithm based on the square root Cubature Kalman filter (SRCKF) for the purpose of nonlinearity of the vehicle target tracking system. This method establishes the equation of state and the measurement equation using the dynamic model, and utilizes the multi sensor measurement signal. A data fusion method based on cubature Kalman filter (CKF) with nonlinear system to avoid errors caused by linearization of nonlinear systems by extended Kalman filter (EKF). In the filtering process, the covariance square root matrix is used in place of the covariance matrix participating in the iterative operation. It effectively avoids the divergence of the filter and improves the convergence speed and stability of the filtering algorithm.

Wind energy conversion systems (WECSs) based networked microgrids has been widely used in recent years. The mean square error (MSE) metric can yield imprecise outcomes if measurement data is polluted by non‐Gaussian disturbances or extreme values. To address this problem, we propose a new robust square root cubature Kalman filter (SRCKF) method called maximum correlation criterion (MCC)‐SRCKF, which incorporates MCC into the SRCKF framework of dynamic state estimation. In MCC, by considering the high‐order moments of the error distribution, it demonstrates anti‐interference ability against non‐Gaussian noise, thus serving as an ideal alternative in the MSE cost function field of SRCKF. Furthermore, within the framework of SRCKF, this study introduces statistical linear regression models and non‐moving point iteration strategies to solve the optimal state estimation under MCC conditions. Therefore, a historical measurement triggered DoS attack model is proposed from the attacker's perspective, aiming to destabilise the WECS‐based networked microgrids. The security conditions of the power system under such attacks are obtained. The proposed method is validated numerically using an IEEE 39‐bus system, and the results demonstrate its effectiveness and superiority.