Adaptive Square-root Unscented Kalman Filter Research Articles

Attitude Calculation Method of Drilling Tools Based on Cross-Correlation Extraction and ASRUKF

As a key component of the measurement while drilling technology, the accuracy of attitude calculation is directly related to the efficiency of resource exploration. To reduce the influence of vibration, rotation, and other disturbances on the attitude sensor during drilling, a method based on cross-correlation extraction and the adaptive square-root unscented Kalman filter (ASRUKF) is proposed to solve the attitude of the drilling tool in this paper. Firstly, the error of the signal collected by the attitude sensor is compensated, and the unscented Kalman filter (UKF) is used for filtering. Then, the effective gravitational acceleration signal is extracted by the cross-correlation method. Finally, an experimental platform for simulating the fully rotating attitude measurement system is established, and the application effects of the UKF and ASRUKF in the attitude calculation are compared. Compared with the UKF, the root mean square error of the inclination angle calculated by the ASRUKF is reduced by 12.9%, and the variance is reduced by 27.3%; the root mean square error of the azimuth angle is reduced by 29.5%, and the variance is reduced by 39.9%. The experimental results show that the attitude calculation method proposed in this paper can stably and effectively improve the accuracy of the attitude calculation of drilling tools.

Online Adaptive Model Identification and State of Charge Estimation for Vehicle-Level Battery Packs

Accurate state of charge (SOC) estimation of traction batteries plays a crucial role in energy and safety management for electric vehicles. Existing studies focus primarily on cell battery SOC estimation. However, numerical instability and divergence problems might occur for a large-size lithium-ion battery pack consisting of many cells. This paper proposes a high-performance online model identification and SOC estimation method based on an adaptive square root unscented Kalman filter (ASRUKF) and an improved forgetting factor recursive least squares (IFFRLS) for vehicle-level traction battery packs. The model parameters are identified online through the IFFRLS, where the conventional method might encounter numerical stability problems. By updating the square root of the covariance matrix, the divergence problem in the traditional unscented Kalman filter is solved in the ASRUKF algorithm, where the positive semi-definiteness of the covariance matrix is guaranteed. Combined with the adaptive noise covariance matched filtering algorithm and real-time compensation of system error, the proposed method solves the problem of ever-degrading estimation accuracy in the presence of time-varying noise with unknown statistical characteristics. Using a 66.2-kWh vehicle battery pack, we experimentally verified that the proposed algorithm could achieve high estimation accuracy with guaranteed numerical stability. The maximum error of SOC estimation can be bounded by 1%, and the root-mean-square error is as low as 0.47% under real-world vehicle operating conditions.

Open circuit voltage - state of charge curve calibration by redefining max–min bounds for lithium-ion batteries

The relationship between open circuit voltage (OCV) and state of charge (SoC) is essential for SoC estimation of lithium-ion batteries, which can be secured by either low-current OCV test or incremental OCV test, with incremental OCV test demonstrating better results. Nevertheless, low current always leads to a discharge capacity that is inconsistent with maximum available capacity, which is a key parameter in SoC estimation. Therefore, the resultant OCV-SoC curve fails to provide a consistent SoC range and thus affects SoC estimation. In this paper, OCV-SoC curves obtained from low-current OCV tests are calibrated by redefining max–min bounds to improve SoC estimation accuracy. Max–min bounds of SoC are redefined by measuring, calculating and resetting upper and lower cut-off voltages of the OCV-SoC curve. Based on second-order RC model, model parameters are identified online and adaptive square-root unscented Kalman filter (ASRUKF) algorithm is introduced to perform SoC estimation, which is proved to be precise and adaptive. The calibrated OCV-SoC curve achieves an overall better SoC estimation performance than that obtained from the low-current OCV test and incremental OCV test, which is validated by experiments of LiNiMnCoO2 (NMC) batteries at 0°C and 25°C.

State of charge estimation for lithium-ion battery based on improved online parameters identification and adaptive square root unscented Kalman filter

Accurate state of charge estimation is crucial for the safe and efficient operation of lithium-ion batteries. The Kalman filtering algorithm has been widely used in state-of-charge (SOC) estimation. To solve the problem of filter divergence and sensitivity to noise, the joint SOC estimation method is proposed to achieve accurate and robust estimation of SOC, which is composed of improved variable forgetting factor recursive least square (VFFRLS) and adaptive square root unscented Kalman filter (ASRUKF). The improved VFFRLS method uses the mean square value of the multi-step voltage residual instead of the traditional one-step voltage residual to correct the forgetting factor, and the ASRUKF improves the accuracy and stability of estimation by introducing the square root method and the adaptive method. Estimations under three typical working conditions are quantitatively studied, the experimental results show that the proposed method has good accuracy and stability. The maximum mean absolute error (MAE) is 0.0061, and the corresponding root mean square error (RMSE) is 0.0090. Furthermore, the experimental verification after adding offset errors to measured data shows that the proposed method can still track the reference SOC with satisfactory accuracy in the range of voltage offset error less than ±0.5 % and current offset error less than ±3 %, both for the constant offset error and the random error, and the SOC error is less than 2.5 %.

An experimental comparative study of adaptive sigma-point Kalman filters: Case study of a rigid–flexible four-bar linkage mechanism and a servo-hydraulic actuator

This paper investigates the application, design, and implementation of different adaptive sigma-point Kalman filters for nonlinear dynamic systems. It is a well-known fact that the performance of nonlinear Kalman filters depends on a prior knowledge of system noise statistics. In real-time applications, this knowledge is difficult and in some cases impossible to predefine. Therefore, an adaptation mechanism based on the random weighting method is proposed in this work to estimate, simultaneously, noise covariance and the state of the system. On the other hand, for real time execution, the computational efficiency of such filters should also be considered to minimize the burden on computational resources. Based on these two factors, in this paper, four different variants of the adaptive sigma-point Kalman filter are studied in detail: (I) an Adaptive Unscented Kalman filter (AUKF), (II) an Adaptive Square-root Unscented Kalman filter (ASr-UKF) with an Unscented Transformation sigma-point selection strategy, (III) an Adaptive Scaled Spherical Simplex Unscented Kalman filter (AS3UKF), and (IV) an Adaptive Square-root Scaled Spherical Simplex Unscented Kalman filter (ASr-S3UKF) with scaled spherical simplex sigma-point selection strategy. The performance of these adaptive sigma-point Kalman filters is analyzed here in depth and discussed for application to a simulated rigid–flexible four-bar linkage mechanism and a practical servo-hydraulic actuator setup under different scenarios. The simulation and the experimental results indicated that, for the cases studied in this article, the filters are competitive and present advantages and disadvantages that should be dealt with according to the requirements of the problem.

Adaptive Square-Root Unscented Kalman Filter Phase Unwrapping with Modified Phase Gradient Estimation

Phase unwrapping (PU) is a key program in data processing in the interferometric synthetic aperture radar (InSAR) technique, and its accuracy directly affects the quality of final SAR data products. However, PU in regions with large gradient changes and high noise has always been a difficult problem. To overcome the limitation, this article proposes an adaptive square-root unscented Kalman filter PU method. Specifically, a modified phase gradient estimation (PGE) algorithm is proposed, in which a Butterworth low-pass filter is embedded, and the PGE window can be adaptively adjusted according to phase root-mean-square errors of pixels. Furthermore, the outliers of the PGE results are detected and revised to obtain high-precision vertical and horizontal phase gradients. Finally, the unwrapped phase is calculated by the adaptive square-root unscented Kalman filter method. To the best of our knowledge, this article is the first to combine the modified PGE with an adaptive square-root unscented Kalman filter for PU. Two sets of simulated data and a set of TerraSAR-X/TanDEM-X real data were used for experimental verification. The experimental results demonstrated that the various improvement measures proposed in this article were effective. Additionally, compared with the minimum-cost flow algorithm (MCF), statistical-cost network-flow algorithm (SNAPHU) and unscented Kalman filter PU (UKFPU), the proposed method had better accuracy and model robustness.

A reliable estimation method for mining lithium-ion battery

Power battery SOC (state of charge, SOC) is one of the important decision-making factors of energy management. Accurate estimation plays an important role in optimizing vehicle energy management and improving the utilization of power battery energy. The key to accurate estimation of SOC is to determine circuit model parameters and estimation methods. The research object of this article is lithium manganese oxide battery for mining (LiMn2O4). The experiments of multiplying power, temperature and HPPC (hybrid pulse power characteristic, HPPC) are carried out. A self-tuning calculation method of dynamic system is proposed, and the dynamic self-tuning model based on second-order RC is established. At the same time, in view of the shortcoming that the UKF (Unscented Kalman Filter, UKF) algorithm cannot estimate the noise in real time, In order to improve the accuracy of battery SOC estimation, an adaptive square root unscented Kalman filter (ASR-UKF) algorithm is proposed, which can make the noise statistical characteristics follow the estimation results for adaptive adjustment. Finally, the constant current and dynamic conditions are tested. The results show that the maximum change rate of model parameters with magnification is 76%, and the maximum change rate with temperature is 73.7%. The analysis of dynamic characteristics is a key factor to improve the accuracy of SOC estimation; ASR-UKF Compared with the UKF algorithm, the error is reduced by 78% under constant current conditions and 85.7% under dynamic conditions. The reliability and real-time performance of the algorithm can be obtained by comparing the simulation data with the actual data. The conclusions of this paper can be used as a theoretical basis, which can be used for model analysis of lithium batteries for mining and estimation of internal state variables.

Model-Free and Uncalibrated Eye-in-Hand Visual Servoing Approach for Concentric-Tube Robots

This article proposes a model-free and uncalibrated eye-in-hand visual servoing (EiH-VS) approach for controlling concentric-tube robots (CTRs) in minimally invasive surgery (MIS). Traditionally, a closed-loop EiH-VS controller requires an accurate robot kinematic model and hand–eye calibration. However, it is difficult to model CTR accurately when considering torsion, shear, friction, interactive force, and nonlinear constitutive behavior. In this article, we map image deviations to robot actuation variables with numerically calculated image Jacobian. The estimation of dynamic image Jacobian is based on a modified adaptive square-root unscented Kalman filter (MASR-UKF). A customized measurement matrix is constructed to describe the transformation between state and observation vectors. Moreover, an adaptive gain controller is designed to accelerate convergence. As a result, no prior knowledge of the CTR kinematic model and hand–eye calibration is needed in visual servoing tasks. Simulations and experiments have been conducted. The results validated the efficacy and efficiency of the proposed methods.

Adaptive Square-Root Unscented Kalman Filter-Based State-of-Charge Estimation for Lithium-Ion Batteries with Model Parameter Online Identification

The state-of-charge (SOC) is a fundamental indicator representing the remaining capacity of lithium-ion batteries, which plays an important role in the battery’s optimized operation. In this paper, the model-based SOC estimation strategy is studied for batteries. However, the battery’s model parameters need to be extracted through cumbersome prior experiments. To remedy such deficiency, a recursive least squares (RLS) algorithm is utilized for model parameter online identification, and an adaptive square-root unscented Kalman filter (SRUKF) is designed to estimate the battery’s SOC. As demonstrated in extensive experimental results, the designed adaptive SRUKF combined with RLS-based model identification is a promising SOC estimation approach. Compared with other commonly used Kalman filter-based methods, the proposed algorithm has higher precision in the SOC estimation.

Parallelized and adaptive square-root unscented Kalman filter for carrier recovery in satellite-to-ground coherent optical communications

An adaptive square-root unscented Kalman filter with a parallelized architecture for carrier recovery is proposed in QPSK based satellite-to-ground coherent optical communication systems. A new observation model is raised in the proposed scheme to make the state estimation more accurate. The process noise covariance (Q) and the measurement noise covariance (R) are adaptively estimated to make them consistent with their theoretical covariance. For verification of the feasibility of the proposed scheme, corresponding simulations of carrier recovery in satellite-to-ground laser links are carried out and compared with the scheme that is based on linear Kalman filter (LKF). The simulation results demonstrate that, compared with parallelized LKF, the proposed scheme has a wider range of block size and laser linewidth options, and it can relax the required transmit power by up to 0.5-3 dB under different zenith angle at the same BER. Moreover, the proposed scheme can achieve high estimation accuracy and fast tracking capability simultaneously in the case of dynamic frequency offset with better tolerance against the initial errors in Q and R.

Adaptive square-root unscented Kalman filter: An experimental study of hydraulic actuator state estimation

Abstract This paper introduces a new adaptive Kalman filter for nonlinear systems. The proposed method is an adaptive version of the square-root unscented Kalman filter (Sr-UKF). The presented adaptive square-root unscented Kalman filter (ASr-UKF) is developed to estimate/detect the states of a nonlinear system while noise statistics that affect system measurement and states are unknown. The filter attempts to adaptively estimate means and covariances of both process and measurement noises and also the states of the system simultaneously. This evaluation of the value of covariances helps the filter to modify itself in order to have more precise estimation. To test the efficiency of the investigated filter, it is applied to different approaches, including state estimation and fault detection. First, the proposed filter is used to predict states of two different nonlinear systems: a robot manipulator and a servo-hydraulic system. Second, the filter is employed to detect a leakage fault in a hydraulic system. All applications are tested under three assumptions: noises with known constant statistics, noises with unknown constant statistics and noises with unknown time-varying statistics. Simulation and experimental results prove the efficiency of the presented filter in comparison with the previous version.

Adaptive square-root unscented Kalman filter for position and pose prediction of UAV

Adaptive square-root unscented Kalman filter for position and pose prediction of UAV

An Adaptive Square Root Unscented Kalman Filter Approach for State of Charge Estimation of Lithium-Ion Batteries

An accurate state of charge (SOC) estimation is of great importance for the battery management systems of electric vehicles. To improve the accuracy and robustness of SOC estimation, lithium-ion battery SOC is estimated using an adaptive square root unscented Kalman filter (ASRUKF) method. The square roots of the variance matrices of the SOC and noise can be calculated directly by the ASRUKF algorithm, which ensures the symmetry and nonnegative definiteness of the matrices. The process values and measurement noise covariance can be adaptively adjusted, which greatly improves the accuracy, stability, and self-adaptability of the filter. The effectiveness of the proposed method has been verified through experiments under different operating conditions. The obtained results were compared with those of extended Kalman filter (EKF) and unscented Kalman filter (UKF) , which indicates that the ASRUKF method provides better accuracy, robustness and convergence in the estimation of battery SOC for electric vehicles. The proposed method has a mean SOC estimation error of 0.5% and a maximum SOC estimation error of 0.8%. These errors are lower than those of other methods.

A New Adaptive Square-Root Unscented Kalman Filter for Nonlinear Systems with Additive Noise

The Kalman filter (KF), extended KF, and unscented KF all lack a self-adaptive capacity to deal with system noise. This paper describes a new adaptive filtering approach for nonlinear systems with additive noise. Based on the square-root unscented KF (SRUKF), traditional Maybeck’s estimator is modified and extended to nonlinear systems. The square root of the process noise covariance matrixQor that of the measurement noise covariance matrixRis estimated straightforwardly. Because positive semidefiniteness ofQorRis guaranteed, several shortcomings of traditional Maybeck’s algorithm are overcome. Thus, the stability and accuracy of the filter are greatly improved. In addition, based on three different nonlinear systems, a new adaptive filtering technique is described in detail. Specifically, simulation results are presented, where the new filter was applied to a highly nonlinear model (i.e., the univariate nonstationary growth model (UNGM)). The UNGM is compared with the standard SRUKF to demonstrate its superior filtering performance. The adaptive SRUKF (ASRUKF) algorithm can complete direct recursion and calculate the square roots of the variance matrixes of the system state and noise, which ensures the symmetry and nonnegative definiteness of the matrixes and greatly improves the accuracy, stability, and self-adaptability of the filter.