RKHS Based Dynamic State Estimator for Non-Gaussian Radar Measurements

Global Navigation Satellite Systems (GNSSs) observables, such as those of the Global Positioning System (GPS), are frequently affected by multipath effects that cause unpredictable signal interference at the receiver, posing significant challenges for accurate state estimation in complex environments with non-Gaussian noise or outliers. The traditional extended Kalman filter (EKF), based on the minimum mean square error (MMSE) criterion, assumes Gaussian noise distributions and exhibits degraded performance under non-Gaussian conditions. To overcome this limitation, the minimum error entropy (MEE) criterion was proposed to reduce random uncertainty in estimation error distributions; however, due to its translation invariance property, MEE may inadvertently increase bias when errors contain systematic offsets, leading to poor convergence. In contrast, the maximum correntropy criterion (MCC) concentrates the error probability density function (PDF) around zero, enabling effective entropy adjustment even in the presence of bias and achieving superior error convergence. This paper presents the centered error entropy (CEE) extended Kalman filter (CEE-EKF) that integrates the complementary merits of both MEE and MCC approaches to overcome their individual limitations. Experimental validation in complex nonlinear GPS environments with non-Gaussian noise demonstrates that the CEE-EKF significantly outperforms individual algorithms in noise suppression, particularly exhibiting enhanced robustness and accuracy when handling outliers. These results offer an effective approach to enhancing the reliability of GPS navigation in challenging real-world environments, and the algorithm can be readily extended to other GNSS applications.

This brief reports single degrees of freedom nonlinear dynamic model-based state estimators for the navigation of remotely operated vehicles (ROVs)-unmanned, tethered robots commonly used for underwater commercial and scientific tasks. These methods exploit knowledge of the vehicle's nonlinear dynamics, the forces and moments acting on the vehicle, and disparate position and velocity measurements. The position and velocity of the ROV are estimated using two methods: 1) a nonlinear observer (NLO) and 2) an extended Kalman filter (EKF). The NLO is derived and its stability proven using Lyapunov techniques. A high-precision 300-kHz acoustic positioning system provided a ground truth for the laboratory experiments and our results show that both the NLO and EKF position estimates possess lower standard deviations than the measurements from conventional 12-kHz long-baseline systems. A dynamic model sensitivity analysis is included for the laboratory experiments. Field experiments obtained with the Jason2 ROV at 2300-m depth demonstrate that the NLO and EKF work in the field. These experiments are, to the best of our knowledge, the first reported experiments of an NLO and EKF using a nonlinear model of ROV dynamics. The performance of the NLO and EKF are compared using the criteria of convergence, accuracy, precision, parameter sensitivity, and robustness to velocity measurement outages, and our results show that the NLO provides superior performance. The impact of these results includes more robust state estimation for underwater robots and an increased operating range that will provide new capabilities.

For enhancing the robustness of the Kalman filter in the presence of non-Gaussian noise or measurement outliers within a nonlinear state-space model, a robust filter based on mixed correlation entropy is proposed in this paper. The mixed correlation entropy cost function is utilized as a replacement for the second-order function used in the Kalman filter for measurement fitting errors in the Global Positioning System (GPS). Leveraging entropy theory with kernel functions, a novel robust filtering algorithm is designed by using the maximum correntropy criterion (MCC). While it has been demonstrated, the MCC-based robust filters are feasible for handling non-Gaussian noise and the default kernel in the original MCC, such as the Gaussian kernel, which may not be sufficient for dealing with more complex data encountered in many practical problems. The selection of kernel parameters for MCC-based filters becomes challenging when an adaptive kernel is not used. Therefore, there is a need to design algorithms, which are insensitive to kernel parameters for handling the measurement outliers. In this paper, the robust filters based on double-Gaussian mixture correntropy are proposed and combined with the nonlinear filtering algorithms, replacing filtering methods that rely solely on the minimum mean square criterion. Finally, the algorithm’s robustness is validated through simulation experiments under a certain degree of accuracy. The solutions suggested may outperform the current robust approaches, according to simulation findings, which can achieve better performance for GPS navigation applications.

The process and measurement noise covariance matrices significantly impact the Extended Kalman Filter (EKF) performance and are often hand-tuned in practice, which usually entails a tedious task. Q-learning, a well-known method in reinforcement learning, has been applied recently to better adapt the noise covariance matrices for the EKF, thanks to its simplicity and capability in handling uncertain environments. Typically, some heuristics are involved in designing the Q-learning-based EKF (QLEKF), such as tuning grid size and covariance matrices values of each state, which inevitably degrades the estimation performance when the heuristics are not suitable. We propose a dynamic grid-based Q-learning EKF (DG-QLEKF) to overcome that drawback, which brings two novelties, an updated ϵ-greedy algorithm and a dynamic grid strategy. The proposed algorithm and strategy can thoroughly exploit arbitrary search scope and find appropriate values of noise covariance matrices. The effectiveness of DGQLEKF, applied in navigation for attitude and bias estimation, is validated through the Monte Carlo method and real flight data from an unmanned aerial vehicle. The DG-QLEKF leads to much more improved state estimation than the QLEKF and traditional EKF.

Nowadays, magnetic and inertial measurement units (MIMUs) have become useful tools for determining the attitude of moving objects. An attitude calculation algorithm (ACA) is programed into an MIMU, which determines the attitude by fusing three built-in sensors, namely, gyroscope, accelerometer, and magnetometer. Attitude is often represented by Euler angles, quaternion, or rotation matrix. Despite that great development has been achieved, how to eliminate the negative effect of magnetic disturbance on the pitch and roll estimation is still difficult for an ACA. This article aims to propose an Extended Kalman Filter (EKF)-based approach for problem solving. Inspired by the fact that the Euler angles are computed by using some elements of the rotation matrix, a diagonalizable regulation matrix (DRM) is multiplied to the right half part of the gain matrix (which is multiplied to the residual of the magnetometer measurement in the update stage of EKF). The determination of DRM is based on the principle that these elements can be appropriately regulated by the DRM so as to make the magnetometer measurement only participate in the computation of azimuth. No further revision to EKF is made except the Kalman gain matrix, hence the proposed EKF behaves similar as traditional EKF, except its ability of eliminating the negative effect of magnetic disturbance on the pitch and roll estimation. The superiority of the proposed EKF is validated by comparing it with four other competing algorithms through simulation and experimental experiments.

Effect of Noises on the Performance of Nonlinear State Estimator for Semi Batch Autocatalytic Esterification Reactor

Robust adaptive smooth variable structure Kalman filter for spacecraft attitude estimation

For vehicle state estimation, conventional Kalman filters work well under Gaussian assumptions. Still, they are likely to degrade dramatically in the practical non-Gaussian situation (especially the noise is heavy-tailed), showing poor accuracy and robustness. This article presents an estimation technique based on the maximum correntropy criterion (MCC) combined with an adaptive extended Kalman filter (AEKF), and an extended Kalman filter (EKF) based on the MCC has also been studied. A lateral-longitudinal coupled vehicle model is developed, while an observer containing the state vectors such as yaw rate, sideslip angle, vehicle velocity and tire cornering stiffness is designed using easily available in-vehicle sensors and low-cost GPS. After analyzing the algorithmic complexity, the proposed algorithm is validated by sine steering input and double lane change driving scenarios. Finally, it is found that MCC combined with AEKF/EKF has stronger robustness and better estimation accuracy than AEKF/EKF in dealing with non-Gaussian noise for vehicle state estimation.

A major challenge in ensuring the reliability of battery systems is the uncertainty surrounding their service life. An accurate prediction of the remaining useful life (RUL) is essential for effective maintenance and operation. Traditional extended Kalman filter (EKF) algorithms, which rely heavily on historical data, often have limited long-term prediction accuracy. To overcome this problem, this study proposes a multi-observation fusion approach to enhance the performance of the EKF for battery life prediction. To improve the practical applicability, we replaced the conventional aging capacity test values with operational capacity data obtained under real-world conditions. This modification refined the trajectory of the battery aging state space, thereby reducing the dependency on the quantity and quality of historical data while simultaneously boosting the long-term prediction accuracy and stability. Furthermore, a semi-empirical aging model was introduced to extract prior knowledge from offline data. This provided valuable insights into the life degradation trends and guided the filtering process. The resulting framework forms the basis for a novel RUL prediction method that utilizes a multi-observation fusion EKF. Validation experiments showed that the proposed method enhanced the prediction accuracy by over 60% compared with traditional EKF and particle filter algorithms throughout the lifecycle of lithium-ion batteries. Additionally, the technique exhibited robust stability (with no divergence observed over the full battery life) and demonstrated notable improvements in early stage RUL prediction.

This paper investigates the kernel entropy based extended Kalman filter (EKF) as the navigation processor for the Global Navigation Satellite Systems (GNSS), such as the Global Positioning System (GPS). The algorithm is effective for dealing with non-Gaussian errors or heavy-tailed (or impulsive) interference errors, such as the multipath. The kernel minimum error entropy (MEE) and maximum correntropy criterion (MCC) based filtering for satellite navigation system is involved for dealing with non-Gaussian errors or heavy-tailed interference errors or outliers of the GPS. The standard EKF method is derived based on minimization of mean square error (MSE) and is optimal only under Gaussian assumption in case the system models are precisely established. The GPS navigation algorithm based on kernel entropy related principles, including the MEE criterion and the MCC will be performed, which is utilized not only for the time-varying adaptation but the outlier type of interference errors. The kernel entropy based design is a new approach using information from higher-order signal statistics. In information theoretic learning (ITL), the entropy principle based measure uses information from higher-order signal statistics and captures more statistical information as compared to MSE. To improve the performance under non-Gaussian environments, the proposed filter which adopts the MEE/MCC as the optimization criterion instead of using the minimum mean square error (MMSE) is utilized for mitigation of the heavy-tailed type of multipath errors. Performance assessment will be carried out to show the effectiveness of the proposed approach for positioning improvement in GPS navigation processing.

Single ended primary inductance converter (SEPIC) is a type of DC–DC converter whose industrial applications include maximum power point tracking and Active power factor correction. Owing to present nonlinear circuit components, SEPIC has discontinuous nonlinearity and for the mathematical model determination, state space averaging or more advanced modeling techniques are required. Once the approximated nonlinear model is obtained, the states of the plant can be estimated using a nonlinear state estimator. Nonlinear estimators are preferred mostly when the real trajectory of the states cannot be estimated accurately by a linear state estimator and the deviation from the linear behavior and nonlinear one is above what is tolerable for the applications. Extended Kalman filter (EKF), being such a state estimator is widely employed in control and fault monitoring applications where a complete or an approximated nonlinear model of the plant is available. EKF especially operates well for the plants where the nonlinearity does not cause the assumptions behind EKF to be violated. In this study, first an approximated nonlinear model for SEPIC is determined. Using the model, EKF is designed to estimate the states of the plant. The efficacy of the designed EKF is demonstrated in a series of numerical MATLAB based simulations where the both open loop and closed loop performances are analyzed, and the results are detailed in the paper.

The Kalman filter has earned its fame through its elegance, its compatibility with digital simulation, and its reasonable performance even when the somewhat restrictive assumptions on which it is based are not all met. Extensions of the Kalman filter are varied, and not all estimators dubbed Extended Kalman Filter (EKF) are equivalent. This chapter develops some filter extensions appropriate to target tracking, classification, and command architectures. These include estimation of essentially nonlinear and non-Gaussian motion models for targets, nonlinear conversion of range-bearing measurements into position measurements, and lack of true independence between target state and observation system errors. In target tracking, using models of target motion and a stream of measurements or observations, the Kalman filter provides the conditional distribution of the location of a target following an unpredictable path. From distribution we can not only accurately estimate the location of the target, but we can also place a capture region about the estimate that will contain the target with any pre-specified probability. The Kalman algorithm is based upon a linear-Gauss–Markov (LGM) model of the engagement. Even when there are nonlinearities in the engagement model, an expanded version of the Kalman filter (the EKF) generates plausible position estimates and capture regions. We will contrast realized performance with that predicted by the EKF. The shortcomings of the Kalman filter when used in command architectures are important, but in many cases they can be mitigated. In others alternative approaches like the GWE, explored in later chapters, are much more effective.

The basic requirement of mobile robot localization is to know the information about its position and direction. The extended Kalman filter is an excellent tool to estimate the robot's posture in its work environment. Traditional extended Kalman filter uses fixed error covariance matrices Q and R, which does not conform the real situation. In this paper, GA-fuzzy logic controller is developed to adjust the error covariance matrices on-line. To improve the accuracy of fuzzy logic controller, a genetic algorithm is developed to tune the membership functions. The simulation results show that the proposed approach has good performance.

In servo systems, encoders are usually used to measure the position and speed signals of electric machines. But in a low speed range, the traditional M/T method has a larger time delay, which will cause an increase of the speed loop order and degradation of the speed loop performance. A method employed to reduce the delay of speed feedback by using a reduced-order Extended Kalman Filter (EKF) is introduced in this paper. The speed of the permanent magnet synchronous motor is estimated by the reduced-order EKF in a low speed range, which reduces the delay of speed feedback and extends the cutoff frequency of the speed loop to improve the dynamic performance of the servo system. In order to solve the issues that the traditional full-order EKF is sensitive to the inertia of the system and computationally complex, a composite load torque observer (CLTO) is proposed in this paper. The load torque and the friction torque are simultaneously observed by the CLTO. Additionally, the CLTO is used to reduce the order of the EKF, which reduces the sensitivity of EKF on inertia to enhance the robustness of the algorithm and simplifies the computational complexity. The feasibility and effectivity of the above method are verified by simulations and experiments.

: This paper represents orbit propagation and determination of Low Earth Orbit(LEO) satellites, which is immediate orbit satellite positioning. Beiseds, satellite global positioning system (GPS) configured satellite receiver provides position and velocity measures by navigating the filter to get the coordinates of the orbit propagation (OP), while the satellite orbit coordinates is an important basis for the task operation. The main contradictions in real time orbit which is determined by the problem are: orbit positioning accuracy and the amount of calculating two indicators; how to balance these two indicators. This article is dedicated to solving the problem of tradeoffs. To plan to use a non-linear filtering method for immediate orbit tasks requires more precise satellite orbit state parameters in a short time. Although the traditional extended Kalman filter (Extended Kalman Filter, EKF) method is widely used, its linear approximation of the drawbacks in dealing with nonlinear problems was especially evident, without compromising Kalman filter (Unsented Kalman Filter, UKF). As a new non-linear estimation method, it is measured at the estimated measurements on more and more applications. This paper will be the first study to UKF microsatellites in LEO orbit in real time, trying to explore the real-time precision orbit determination techniques.