A robust unscented Kalman filter and its application in estimating dynamic positioning ship motion states

Accurate remaining useful life (RUL) prediction under the noisy environment is a big challenge for the health management of modern industrial systems since the extraction of the accurate data structure from heavily corrupted data is difficult. In recent years, the kernel adaptive filter (KAF) has been widely adopted to solve the robust regression problem due to its low-complexity and high-approximation capability and robustness while the applications in battery RUL prediction are still few and far between. Thus, this paper is concerned with long-term RUL prediction using the KAF method. At first, concretely speaking, a robust KAF algorithm is derived based on the double-Gaussian-mixture (DGM) cost function, which is used to learn the capacity degradation mechanism from contaminated capacity data and so as to build the long-term prediction model. Second, a robust unscented Kalman filter (UKF) algorithm employing the DGM-based cost function is developed, which is then combined with the KAF-based prediction model to realize a more accurate and reliable prediction. Under the hybrid prognostic framework, the proposed UKF algorithm is applied to filter the noisy observations. When the observation data are inaccessible, the predicted data from the off-line trained KAF-based prediction model are adopted as the approximated value of the real observations for the UKF algorithm to optimize the prediction results and to provide the uncertainty representation. The experimental results reveal that the proposed method has great robustness when the measurements contain noise and large outliers, which makes it possible to get satisfactory prediction performance without preprocessing the data manually.

The accurate estimation of battery state of charge (SOC) enables the reliable and safe operation of lithium‐ion batteries. Data‐driven SOC estimation is considered an emerging and effective solution. However, existing data‐driven SOC estimation methods typically involve direct estimation and lack effective feedback correction. Moreover, battery degradation poses additional challenges to accurate SOC estimation. Therefore, this study proposes an adaptive combined method for battery SOC estimation based on a long short‐term memory (LSTM) network and unscented Kalman filter (UKF) algorithm considering battery aging status. First, an LSTM model is constructed to characterize the battery's dynamic performance instead of traditional battery models. Then, the UKF algorithm is employed to perform SOC estimation through the feedback of terminal voltage prediction. To enhance estimation accuracy under different aging statuses, a proportional‐integral‐derivative controller is employed to correct the capacity fading during the SOC estimation process. Validation results indicate that the terminal voltage prediction model demonstrates exceptional robustness against interference from current and voltage noise. Compared to the traditional estimation method combining the deep learning model and Kalman filter algorithm, the proposed method demonstrates superior estimation accuracy under various complex operating conditions. Furthermore, the proposed method outperforms the traditional method in estimation performance during battery aging.

GPS disciplined crystal oscillator technology has been widely used to obtain high-precision and low-cost frequency standards. But there are two factors that would affect the accuracy of the frequency correction. The first is the random error and outliers contained in the one pulse per second (PPS) outputted by the GPS. The second factor is the frequency nonlinear drift of crystal oscillator because of the aging and the temperature. To solve these problems, a mathematical model of the frequency difference between IPPS signal and crystal oscillator signal is established in this paper. And then a novel high-precision method based on the sequence weighted adaptive Unscented Kalman filter (UKF) algorithm is proposed on the basis of the mathematical model. To be more specific, the UKF is used to address the problem of random error and frequency nonlinear drift. And the effect of outliers is eliminated by weighing sequence in the UKF algorithm. The adaptive filtering technology can reduce the impact of the variable and random system noise. Numerical simulation and verification are described. The results show that the proposed method can make frequency standards higher stability and precision.

Numerical simulation of a new early gas kick detection method using UKF estimation and GLRT

Wireless Sensor Network (WSN) is a new technology integrated with communications, embedded technology, and network functions; having capability of real-time collecting, communicating, and sensing, for which dynamic target locating and tracking is its critical task, as well as a basic element in its commercial and military application such as battlefield information accessing and traffic monitoring. Sensor target tracking is the technology of target location estimate based on measurements from corresponding sensors. An inaccurate estimated location may very easily lead to target tracking failure which reduces the reliability and stability of the target tracking [1]. Experts and scholars have done a lot of researches to solve problems exited in wireless sensor target tracking, and many new tracking algorithms have been proposed, among which tracking algorithms such as target contrail-fitting, linear prediction, Kalman filter, unscented Kalman filter(UKF) and particle filter[2] are most common applied. Sikdar, with his partners, has proposed target location tracking algorithm based on linear sensor which is proved better than conventional contrail fitting algorithm in its effects. Zhang Xiaoping , with his partners, has proposed WSN target tracking algorithm through modeling for quadratic polynomial motions which has improved target tracking accuracy[3]. However, there is a problem in common: all the algorithms above assume the tracking target contrail-fittings being in linear motion, while the actual contrail fitting is of uncertainty and variability, and the estimated accuracy can hardly be improved after being to a certain level. In this condition, the tracking error of the above algorithms can be greater [4]. Kalman filter algorithm can be applied for weakly nonlinear models, but for strongly nonlinear models, Unscented Kalman Filter algorithm can be better. Kalman filter work well in cases based on model-linear and Gaussian noise, thus its estimated accuracy is not that ideal [5, 6]. Particle filter algorithm is based on optimal regression Bayesian filtering algorithm in Monte Carlo simulation, which can accurately estimate the any distribution state with only a small amount of mobile anchor nodes. PF algorithm has distinguished advantages in processing non-linear, non-Gaussian cases [7]. However, in PF application process after several iterations, diversified degradation of the particles will occur, which is likely to lead a target tracking loss, thus further affect WSN target tracking accuracy [8]. In order to solve the diversified degradation of the particles in Particle Filter algorithm, this paper Research on the Target Tracking Algorithm for Wireless Sensor Network Based on Improved Particle Filter Liang Peng,Xinhan Huang, Li He

In view of abnormal situations, such as multimodal noise, bad measurement data, and sudden load changes in a ship integrated electric propulsion system, this article proposes an unscented Kalman filter with enhanced mixture minimum error entropy (EnMMEE-UKF) to estimate the dynamic state of a ship integrated electric propulsion system. The new algorithm mixture includes two Gaussian functions, defines them as kernel functions, and uses quantization operators to lighten the weight of the mixture minimum error entropy (MMEE). This not only reduces the calculation burden of the MMEE but also effectively improves the system’s ability to handle strongly nonlinear models. In addition, in the lightweight MMEE (LMMEE)-unscented Kalman filter (UKF) algorithm, a fading factor is introduced, based on the strong tracking filter (STF) theory, to modify the error covariance matrix. The enhanced MMEE replaces the mean square error loss of the traditional UKF algorithm. This enhances the robustness of the algorithm estimation, in which a statistical linearization method is adopted to merge the state and measurement errors into the cost function of the enhanced MMEE. Finally, a fixed-point iteration method is applied to recursively update the posterior estimate and covariance matrix. To verify the effectiveness of the proposed method, numerical simulation experiments of various scenarios are conducted on the simulation system and the prototype system. The results demonstrate that the proposed algorithm not only has high estimation accuracy under various abnormal conditions but also effectively reduces the computational complexity of the algorithm, making its application in engineering possible.

X-ray pulsars navigation is a newly developed celestial navigation method, but the filter cycle time is long, and it cannot provide continuous navigation information. COMPASS can provide all-weather and continuous navigation information, but it has poor dynamic performance, and is susceptible to electromagnetic interference and the satellite signal is easy to be blocked. A X-ray pulsars/COMPASS integrated navigation method was proposed in order to improve the autonomous navigation capability of spacecraft. In this case, an autonomous orbit determination method of spacecraft is proposed through federal filtering that combines COMPASS navigation with X-ray pulsar navigation system. The extended Kalman filter (EKF), unscented Kalman filter (UKF) and the square root unscented Kalman filter (SR_UKF) algorithm are applied as the sub-filter. Simulation shows that the integration of the two systems can provide a higher accuracy of orbit determination, and SR_UKF performs better than EKF and UKF in filtering precision and stability.

In this paper, a scale-corrected minimal skew simplex sampling unscented Kalman filter (UKF) algorithm for the permanent magnet (PM) brushless DC motors (BLDCM) sensorless control has been studied to cancel the position sensor by the use of a systematical and analytical approach. Compared with the general UKF, the sampling method with the least Sigma points called minimal skew simplex sampling is adopted to reduce amount of computation and increase the estimation precision. Moreover, the scale-corrected strategy is introduced into the minimal skew simplex sampling UKF to overcome the nonlocal effects. On the other hand, for more easily calculating the value of back-EMF, the shape function of counter electromotive force is approximated by a series of sine and cosine functions based on the law of Fourier series. The purpose of the problem addressed is, by the method of scale-corrected minimal skew simplex sampling UKF, to properly estimate the rotor speed and position without installing encoders. Finally, the effectiveness of the proposed sensorless control technique is verified by simulation in MATLAB/Simulink.

This paper studies the relay selection in wireless cooperative communication systems. Since the high mobility of Unmanned Aerial Vehicles (UAVs) will lead to the change of link state, a relay selection algorithm based on position prediction is proposed in this paper to better study this problem. First, the Unscented Kalman Filter (UKF) algorithm is used to predict the real-time location information of each UAV, and based on the location information, it is determined whether the current UAV relay node needs to be replaced. The real-time location information of each UAV is predicted by UKF algorithm, which is the basis for determining whether the current UAV relay node needs to be replaced. Then, the outage probability of each standby UAV relay node is calculated, and the standby UAV relay node is sorted according to the link outage probability. Finally, the greedy algorithm is used to find the node with the smallest interruption probability among the backup UAV relay nodes as the next UAV relay node. The simulation results show that in terms of position prediction, the UKF algorithm is more accurate than the Kalman Filtering (KF) algorithm, and the error is smaller. In terms of interruption probability, the relay selection algorithm proposed in this paper reduces the interruption probability of the link, and the interruption probability of the link is more stable.

Yao, W.; Zhang, J.; Liu, Y.; Zhou, M.; Sun, M., and Zhang G., 2015. Improved vector control for marine podded propulsion control system based on wavelet analysis. In this paper, the rotor speed and the position of the marine SSP propulsion motor were estimated for building sensorless vector control system with speed and current double closed loops, based on a wavelet square-root unscented Kalman filter (Wavelet-SRUKF) algorithm. The observed data were pretreated by wavelet analysis and the high frequency noise was filtered, thus offering further smooth observed data for the UKF (Unscented Kalman Filter). This Wavelet-SRUKF algorithm can not only filter the spike point but also showed a better dynamic tracing property of the marine SSP podded propulsion system. Simulation results showed that the improved UKF algorithm was more accurate and demonstrated a higher rate of convergence compared with UKF speed controller.

Conditioned measurement fused estimate Unscented Kalman filter for underwater target tracking using acoustic signals captured by Towed array

High dynamic aircraft is a very attractive new generation vehicles, in which provides near space aviation with large flight envelope both speed and altitude, for example the hypersonic vehicles. The complex flight environments for high dynamic vehicles require high accuracy and stability navigation scheme. Since the conventional Strapdown Inertial Navigation System (SINS) and Global Position System (GPS) federal integrated scheme based on EKF (Extended Kalman Filter) is invalidation in GPS single blackout situation because of high speed flight, a new high precision and stability integrated navigation approach is presented in this paper, in which the SINS, GPS and Celestial Navigation System (CNS) is combined as a federal information fusion configuration based on nonlinear Unscented Kalman Filter (UKF) algorithm. Firstly, the new integrated system state error is modeled. According to this error model, the SINS system is used as the navigation solution mathematic platform. The SINS combine with GPS constitute one error estimation filter subsystem based on UKF to obtain local optimal estimation, and the SINS combine with CNS constitute another error estimation subsystem. A non-reset federated configuration filter based on partial information is proposed to fuse two local optimal estimations to get global optimal error estimation, and the global optimal estimation is used to correct the SINS navigation solution. The χ 2 fault detection method is used to detect the subsystem fault, and the fault subsystem is isolation through fault interval to protect system away from the divergence. The integrated system takes advantages of SINS, GPS and CNS to an immense improvement for high accuracy and reliably high dynamic navigation application. Simulation result shows that federated fusion of using GPS and CNS to revise SINS solution is reasonable and availably with good estimation performance, which are satisfied with the demands of high dynamic flight navigation. The UKF is superior than EKF based integrated scheme, in which has smaller estimation error and quickly convergence rate.

Accurate and real-time estimation of pack system-level chips is essential for the performance and reliability of future electric vehicles. Firstly, this study constructed a model of a nickel manganese cobalt cell on the ground of the electrochemical process of the packs. Then, it used methods on the grounds of the unscented Kalman filter and unscented Kalman particle filter for system-level chip estimation and algorithm construction. Both algorithms are on the ground of Kalman filters and can handle nonlinear and uncertain system states. In comparative testing, it can be seen that the unscented Kalman filter algorithm can accurately evaluate the system-level chip of the nickel manganese cobalt cell under intermittent discharge conditions. The system-level chip was 0.53 at 1000 s and was reduced to 0.45 at 1500 s. These results demonstrate that the evaluation of the ternary lithium battery pack’s performance is time-dependent and indicate the accuracy of the algorithm used during this time period. These data should be considered in the broader context of the study for a comprehensive understanding of their meaning. In the later stage, the estimation error of the recursive least-squares unscented Kalman particle filter method for system-level chips began to significantly increase, gradually exceeding 1%, with a corresponding root-mean-square error of 0.002171. This indicates that the recursive least-squares optimization algorithm, the unscented Kalman particle filter algorithm, diminished its root mean square error by 27.59%. The unscented Kalman filter and unscented Kalman particle filter are effective in estimating the system-level chip of nickel manganese cobalt cells. However, UPF performs more robustly in handling complex situations, such as pack aging and temperature changes. This study provides a new perspective and method that has a high reference value for pack management systems. This helps to achieve more effective energy management and improve pack life, thereby enhancing the reliability and practicality of electric vehicles.

Underwater target tracking system can be kept covert using the bearing-only or the bearing-Doppler measurements (passive measurements), which will reduce the risk of been detected. According to the characteristics of underwater target tracking, the square root unscented Kalman filter (SRUKF) algorithm, which is based on the Bayesian theory, was applied to the underwater bearing-only and bearing-Doppler non-maneuverable target tracking problem. Aiming at the shortcomings of the unscented Kalman filter (UKF), the SRUKF uses the QR decomposition and the Cholesky factor updating, in order to avoid that the process noise covariance matrix loses its positive definiteness during the target tracking period. The SRUKF uses sigma sampling to avoid the linearization of the nonlinear bearing-only and the bearing-Doppler measurements. To ensure the target state observability in underwater target tracking, the paper uses single maneuvering observer to track the single non-maneuverable target. The simulation results show that the SRUKF has better tracking performance than the extended Kalman filter (EKF) and the UKF in tracking accuracy and stability, and the computational complexity of the SRUKF algorithm is low.

In this paper, a state estimation method of distributed electric drive articulated vehicle dynamics parameters based on the forgetting factor unscented Kalman filter with singular value decomposition (SVD-UKF) is proposed. The 7DOF nonlinear dynamics model of a distributed electric drive articulated vehicle is established. The unscented Kalman filter algorithm is the foundation, with singular value decomposition replacing the Cholesky decomposition. A forgetting factor is introduced to dynamically adapt the observation noise covariance matrix in real time, resulting in a centralized parameter state estimator for the articulated vehicle. The proposed parameter state estimation method based on the forgetting factor SVD-UKF is simulated and compared with the unscented Kalman filter (UKF) estimation method. Key dynamic parameters are estimated, such as the lateral and longitudinal velocities and accelerations, angular velocity, articulated angle, wheel speeds, and longitudinal and lateral tire forces of both the front and rear vehicle bodies. The results show that the proposed forgetting factor SVD-UKF method outperforms the traditional UKF method. Furthermore, a prototype vehicle test is conducted to compare the estimated values of various dynamic parameters with the actual values, demonstrating minimal errors. This verifies the effectiveness of the proposed dynamic parameter estimation method for articulated vehicles.