Improved Cubature Kalman Filter Research Articles

Disturbance-observer-based finite time sliding mode controller with unmatched uncertainties utilizing improved cubature Kalman filter

Complex reactions are difficult to control as the reactants not only produce desired product but may also further undergo unwanted reactions or the original reactants may degrade through alternate paths. This can be improved by selecting proper measurement and control. In this paper, a robust augmented derivative-free Kalman filter (augmented cubature Kalman filter, ACKF) is propounded for the continuous stirred tank reactor (CSTR) carrying out Van-de-Vusse type complex reactions where the intermediate is the desired product in the midst of consecutive and parallel reactions. Non-isothermal CSTR shows strong non-linearity with inherent challenges as the reaction kinetics depends on process temperature through Arrhenius laws and accompanies non-ideal flow behaviour and unmeasurable disturbances. First, the process exhibits inverse or non-minimum phase behaviour. Second, to control product temperature and concentration, a finite time sliding mode controller (FSMC) is suggested which effectively tracks servo response to the desired set point. Third, a disturbance filter has been proposed in association with FSMC, which constructively eliminates the input disturbances. Realistic simulations for servo-regulatory compliance, elimination of measurement noise, impact on large perturbation, and parametric uncertainty with a state-of-the-art simulator ensure the efficacy of the proposed controller. The results are analysed further with a derivative-free FSMC control approach, considering various performance indices (root mean square error (RMSE), total variation (TV), mean square deviation (MSD)) to assess the goodness of the newly developed control strategy. It has been found that improved control law (improved augmented cubature Kalman filter (IACKF)-FSMC) yields better RMSE (7.2645e–05) than ACKF-FSMC (7.5814e–05).

An improved GNSS/INS navigation method based on cubature Kalman filter for occluded environment

Global navigation satellite systems and inertial navigation systems (GNSSs/INSs) based on the cubature Kalman filter (CKF) can provide an effective land vehicle navigation and positioning solution. The accuracy of CKF depends mainly on the prior probability density function (PDF), which is inaccurate when the GNSS signal is temporarily blocked in an urban environment. Although the improved CKF (ICKF) can reduce cubature point errors by using the historical information obtained iteratively, the generation of cubature points is still related to measurement noise. To obtain a more accurate PDF, adjustment off the sensor measurement noise is necessary. In this paper, an adaptive ICKF for GNSS/INS system based on the Mahalanobis distance called MD-ICKF is proposed, which expands the usability of the micro-electronic mechanical system based integrated navigation system in an urban environment. Two lower triangular matrices obtained by Cholesky decomposition are used to adjust the cubature point errors during each iteration. Furthermore, the measurement noise will be inflated to obtain a more accurate PDF when it exceeds the threshold calculated by the MD and chi-square test. The field experiment results show that the proposed method has better positioning accuracy and performance than CKF and ICKF in an occluded environment

Employing NMPC scheme utilizing improved cubature Kalman filter for an AUV system

This paper deals with the diving-plane controller design problem for a class of torpedo-type Autonomous Underwater Vehicles (AUVs). Complex hydrodynamic characteristics of AUVs are truly onerous to model and control. AUVs exhibit peculiar nonlinear behaviour and have a high degree of coupling. As a result, they suffer from many practical limitations, such as a lack of hovering capability, limited payload-carrying capacity, poor pitch and roll motion stability, etc. To design an effective and reliable diving-plane control scheme for AUVs, this paper develops a new Stochastic Nonlinear Model Predictive Control (SNMPC) scheme relying on an improved Cubature Kalman Filtering (ICKF) algorithm. This scheme enables an AUV to reach the desired depth underwater and keep hovering at that depth. The ICKF algorithm estimates both the states and plant parameters to update the control law, which helps to reducethe effect of measurement noise and input disturbances. An in-depth simulation case study has been conducted in the presence of external disturbances, noises and plant-parameter variations to demonstrate the usefulness of the proposed ICKF-based NMPC scheme. The results are further analysed based on 'root mean square error' to show the controller's performance.

A novel improved cubature Kalman filter with adaptive generation of cubature points and weights for target tracking

In nonlinear state estimation, the generation method of cubature points and weights of the classical cubature Kalman filter (CKF) limits its estimation accuracy. Inspired by this, in this paper, a novel improved CKF with adaptive generation of the cubature points and weights is proposed. Firstly, to improve the accuracy of the classical CKF while considering the calculation efficiency, we introduce a new high-degree cubature rule combining the third-order spherical rule and the sixth-degree radial rule. Next, in the new cubature rule, a novel method that can adaptively generate cubature points and weights based on the distance between the points and center point in the sense of the inner product is designed. We use the cosine similarity to quantify the distance. Then, based on that, a novel high-degree CKF (HCKF) is derived that uses much fewer points than other HCKFs. In the proposed filter, based on the actual dynamic filtering process, the simultaneous adaptive generation of cubature points and weight can make the filter reasonably distribute the cubature points and allocate the corresponding weights, which can obviously improve the approximate accuracy of the one-step state and measurement prediction. Finally, the superior performance of the proposed filter is demonstrated in a benchmark target-tracking model.

Innovative method for state of energy estimation based on improved Cubature Kalman filter

As the increasing concern of driving ranges for electric vehicles, the precision of state of energy (SOE) estimation contributes to the better performance of battery management. In this article, an innovative method based on 5th-order simplex square-radius cubature Kalman filter is developed to achieve the precise and robust estimation for SOE on electric vehicles. Based on second-order equivalent circuit model and particle-swarm-optimization algorithm, the implementation helps the validation of SOE estimation. The max error of SOE estimation under stable condition is less than 3%, and that for dynamic stress test condition is under 4%. Moreover, the robustness is investigated based on diverse deviations on initialization, delivering the future potential applications on embedded system on cloud-controlling.

Stage of Charge Estimation of Lithium-Ion Battery Packs Based on Improved Cubature Kalman Filter With Long Short-Term Memory Model

Accurate estimation of the state of charge (SOC) of lithium-ion battery packs remains challenging due to inconsistencies among battery cells. To achieve precise SOC estimation of battery packs, first, a long short-term memory (LSTM) recurrent neural network (RNN)-based model is constructed to characterize the battery electrical performance, and a rolling learning method is proposed to update the model parameters for improving the model accuracy. Then, an improved square root-cubature Kalman filter (SRCKF) is designed together with the multi-innovation technique to estimate the battery cell's SOC. Next, to cope with inconsistencies among battery cells, the SOC estimation values from the maximum and minimum cells are combined with a smoothing method to estimate the pack SOC. The robustness and accuracy of the proposed battery model and the cell SOC estimation method are verified by exerting the experimental validation under time-varying temperature conditions. Finally, real operation data are collected from an electric-scooter (ES) monitoring platform to further validate the generalization of the designed pack SOC estimation algorithm. The experimental results manifest that the SOC estimation error can be limited to 2% after convergence.

Improved Cubature Kalman Filter for Spacecraft Attitude Estimation

One of the critical challenges in spacecraft attitude estimation is the handling nonlinear non-Gaussian noisy conditions originating from measurement errors, model drifts, and incorrect models. In this article, we propose a new, adaptive and robust nonlinear Kalman filter to address this issue. The proposed filter is derived by casting the problem as a nonlinear regression problem and then realized by building on the robust filter, based on multiple strong tracking with multiple fading factors. In particular, the optimal filter gain is achieved by minimizing the constrained cost function that combines the minimum mean square error and the norm constraint. The resulting algorithm, referred to as the adaptive Huber filter based on the multiple strong tracking (AHFMST), shows promising results. Several simulation scenarios considering the realistic initial errors for a low-orbiting spacecraft attitude estimation are studied to compare the performance of the new algorithm and the state-of-the-art algorithms. The proposed algorithm has demonstrated better performance in terms of robustness and estimation accuracy.

State estimation based on improved cubature Kalman filter algorithm

During the recursive calculate process of the cubature Kalman filter (CKF), the covariance matrix tends to lose positive definiteness and noise statistical characteristics are inaccurate, which results in inaccurate filtering or even filter divergence. This study presents an improved algorithm based on the CKF. The algorithm combines the square root filter algorithm and the Sage–Husa maximum a posterior noise estimator, which can ensure the non-negative determination and symmetry of the covariance matrix and has the ability to deal with unknown and time-varying noise statistical characteristics in the filtering process adaptively. In the multi-dimension system, the noise covariance matrix may dissatisfy non-negative definiteness and result in filter divergence, and then the noise covariance matrix estimator is improved. The analysis is verified by state estimation example of the non-linear system, compared with the standard CKF, the accuracy of the adaptive square root CKF (ASRCKF) state estimation is increased by 63.13, 63.88, and 42.71%, respectively. Finally, the effectiveness of the ASRCKF is verified by the state estimation of the permanent magnet linear synchronous motor.

Improved Cubature Kalman Filter for High-Dimensional Systems with Multiplicative Noises

It is a challenging mission to estimate accurately the state of a non-cooperative spacecraft with multiplicative noises. In this paper, an improved cubature Kalman filter for nonlinear systems with multiplicative noises (ICKF_M) is proposed. First, based on the assumption that multiplicative noise satisfies the Gaussian distribution, the conditional mean variance of multiplicative noise is considered in the prediction and updating process. According to the Bayesian estimation theory, the conditional probability density distribution of multiplicative noise is added to the prediction and update functions to adapt the multiplicative noise. Then, to solve the defect of cubature Kalman filter (CKF), a new method for generating sigma points is designed instead of the classical methods, which has transformed the posterior sigma-points error matrix from prediction phase to the posterior domain of update. Finally, a binocular visual method is used to measure the state of the spacecraft. Compared with the previous methods, the simulation results indicate that the average norm of estimation error has nearly decreased by 20% in comparison with the similar filters in the reference. Moreover, the convergence rate of the proposed algorithm is obviously faster than that of the previous algorithm.

Maximum correntropy generalized high-degree cubature Kalman filter with application to the attitude determination system of missile

For SINS/CNS integrated navigation system, the CKF can perform well for state estimation in Gaussian noise. However, its performances are likely to degrade significantly under non-Gaussian noise conditions. To improve the robustness of the CKF against non-Gaussian noise, we propose an improved cubature Kalman filter, called the maximum correntropy generalized high-degree CKF (MCGHCKF). In the MCGHCKF, the generalized high-degree cubature rule is used to improve the filtering performance, and the maximum correntropy criterion is utilized to reduce the influence of non-Gaussian noise on state estimation. Simulation experiments illustrate the effectiveness and robustness of our algorithm.

A novel model-based state of charge estimation for lithium-ion battery using adaptive robust iterative cubature Kalman filter

Accurate and robust state of charge (SOC) estimation is the key evaluation index for battery management system (BMS) in electric vehicles (EVs). To improve the SOC estimation precision and reliability, a novel model-based estimation approach has been proposed. Firstly, the dynamic property of lithium-ion battery (LIB) is approximated by the auto-regressive and moving average (ARMA) model which compensates the measurement errors of terminal voltage and discharge current. Secondly, a variant of the Kalman filter (KF), namely improved cubature Kalman filter (CKF) based on the combination of singular value decomposition (SVD) and Gauss–Newton iterative technology is employed to develop a reliable estimator for SOC. Furthermore, an adaptive robust strategy is used to improve anti-interference performance by accounting for bidirectional adjustment of observation covariance and gain matrix. Finally, the Dynamic Stress Test (DST) and Federal Urban Driving Schedule (FUDS) are loaded on LIB to test the validity of the improved approach. The experiment results demonstrate the effectiveness of the combination of ARMA model and filtering method in terms of SOC estimation. Besides, simulated measurement noise is added to the test data to prove the robustness of the proposed method.

Online parameters identification and state of charge estimation for lithium-ion capacitor based on improved Cubature Kalman filter

Abstract Lithium-ion capacitor is a hybrid electrochemical energy storage device which combines the merits of lithium-ion battery and electric double-layer capacitor. The precise state of charge estimation is essential to utilize lithium-ion capacitor efficiently. In this paper, the electrical characteristics of lithium-ion capacitor have been studied and the corresponding equivalent circuit model is established. Then, an adaptive square root cubature Kalman filter with variable forgetting factor recursive least square has been proposed to achieve state of charge estimation at each sampling step. The proposed method identifies the model parameters and noise statistics in real time, leading to obtain accurate SOC estimation even if the method is initialized with inaccurate parameters. Estimations under four working conditions are quantitatively studied, the experimental results show that the proposed method has better performance and the corresponding maximum root mean square error is controlled within 1%. Furthermore, the verification of robustness illustrates that the proposed method remains stability and acceptable accuracy when external interference and inaccurate initial SOC are included.

Integrated Velocity Measurement Algorithm Based on Optical Flow and Scale-Invariant Feature Transform

The pyramid Lucas-Kanade (LK) optical flow algorithm has been widely used in velocity measurement applications. However, these applications are limited by some shortcomings of the algorithm, such as its slow calculation speed and susceptibility to illumination changes. To solve these problems, a data fusion scheme based on the scale-invariant feature transform (SIFT) and optical flow is proposed to alleviate the dependence of the optical flow on the illumination conditions. In addition, an improved cubature Kalman filter (CKF) based on multi-rate residual correction (CKF-MRC) is proposed to solve the problem of inconsistency between the sampling frequencies of the SIFT and the optical flow, and takes full advantage of the high sampling frequency of SIFT. The experimental results demonstrate that the proposed CKF-MRC method can effectively improve the accuracy of velocity measurement under variable illumination conditions with a high sampling frequency.

Robust cubature Kalman filter for GNSS/INS with missing observations and colored measurement noise

In order to improve the accuracy of GNSS/INS working in GNSS-denied environment, a robust cubature Kalman filter (RCKF) is developed by considering colored measurement noise and missing observations. First, an improved cubature Kalman filter (CKF) is derived by considering colored measurement noise, where the time-differencing approach is applied to yield new observations. Then, after analyzing the disadvantages of existing methods, the measurement augment in processing colored noise is translated into processing the uncertainties of CKF, and new sigma point update framework is utilized to account for the bounded model uncertainties. By reusing the diffused sigma points and approximation residual in the prediction stage of CKF, the RCKF is developed and its error performance is analyzed theoretically. Results of numerical experiment and field test reveal that RCKF is more robust than CKF and extended Kalman filter (EKF), and compared with EKF, the heading error of land vehicle is reduced by about 72.4%.

Improved Cubature Kalman Filter for GNSS/INS Based on Transformation of Posterior Sigma-Points Error

Tightly coupled GNSS/INS has been widely approved as a promising substitute for standalone GNSS in urban areas navigation. However, due to the frequent GNSS signal outages, the filter used in GNSS/INS should be insensitive to the less informative observations. In this paper, a novel sigma-points update method is proposed to enhance the robustness of cubature Kalman filter (CKF) under the circumstance of unavailable observations. First, the problems of existing sampling-based filters are analyzed. Then, by transforming the posterior sigma-points error matrix from prediction phase of filtering to the posterior domain of update, the updated sigma-points are expected to capture the covariance more precisely than traditional sigma-points. Finally, an improved CKF (ICKF) is developed by embedding these points into the Bayesian estimation framework, and the upper bounds of error covariance matrices are analyzed theoretically. Signal outages with different durations are simulated and results demonstrate that ICKF outperforms state-of-the-art methods.

Strap-down Inertial Navigation System Initial Alignment Based on Iterative Square-Root Cubature Kalman Filter

This paper presents an improved Cubature Kalman filter (CKF) for strap-down inertial navigation system (SINS) initial alignment. In order to enhance the stability and precision of the filter, Newton iteration algorithm and square-root strategy are blended into CKF. Iterative Square-root Cubature Kalman Filter (ISRCKF)makes full use of latest measurement information and directly employs the square root of covariance matrix for recursive update in the iterative process. ISRCKF can effectively avoid non-positive covariance matrix and improve the estimation accuracy. Simulation results show that ISRCKF performs well for SINS initial alignment with large azimuth misalignment.

SINS/GPS Carrier Phase Rate Integrated Navigation System based on Square-root CKF

The integration of Strap-down Inertial Navigation System (SINS) and Global Positioning System(GPS)can not merely reduce the error of navigation system, which would enhance the system dynamic performance. GPS Carrier phase rate is a high-precision measurement without integer ambiguity problem. Moreover, only one GPS receiver is needed for SINS/GPS carrier phase rate integrated navigation system. The measurement of GPS carrier phase rate is derived and a integrated scheme of SINS and GPS carrier phase rate is proposed. Common used nonlinear filter, extended Kalman filter (EKF) has high-order truncation errors which affects the system accuracy. An improved cubature Kalman filter(CKF) used square root is introduced. The square-root CKF calculate avoids calculating the Jacobian matrix and has better estimate precision.

Gaussian filter for nonlinear systems with one-step randomly delayed measurements

This paper is motivated by the filtering estimation for a class of nonlinear stochastic systems in the case that the measurements are randomly delayed by one sampling time. Through presenting Gaussian approximation about the one-step posterior predictive probability density functions (PDFs) of the state and delayed measurement, a novel Gaussian approximation (GA) filter is derived, which recursively operates by analytical computation and Gaussian weighted integrals. The proposed GA filter gives a general and common framework since: (1) it is applicable for both linear and nonlinear systems, (2) by setting the delay probability as zero, it automatically reduces to the standard Gaussian filter without the randomly delayed measurements, and (3) many variations of the proposed GA filter can be developed through utilizing different numerical technologies for computing such Gaussian weighted integrals, including the previously existing EKF and UKF methods, as well as the improved cubature Kalman filter (CKF) in our paper using the spherical–radial cubature rule. The performance of the new method is demonstrated with a simulation example of the high-dimensional GPS/INS integrated navigation.