Several methods of radar data fusion

SummaryThis paper considers the state estimation problem of bilinear systems in the presence of disturbances. The standard Kalman filter is recognized as the best state estimator for linear systems, but it is not applicable for bilinear systems. It is well known that the extended Kalman filter (EKF) is proposed based on the Taylor expansion to linearize the nonlinear model. In this paper, we show that the EKF method is not suitable for bilinear systems because the linearization method for bilinear systems cannot describe the behavior of the considered system. Therefore, this paper proposes a state filtering method for the single‐input–single‐output bilinear systems by minimizing the covariance matrix of the state estimation errors. Moreover, the state estimation algorithm is extended to multiple‐input–multiple‐output bilinear systems. The performance analysis indicates that the state estimates can track the true states. Finally, the numerical examples illustrate the specific performance of the proposed method.

For Time-varying, Time-invariant, and steady-state systems, Kalman Filter can be implemented as a prediction algorithm, since it produces the state prediction and the corresponding prediction error covariance matrix via the state estimation and the corresponding estimation error covariance matrix. Lainiotis Filter is equivalent to Kalman Filter and can be used to compute the prediction. In this paper, for Time-varying, Time-invariant and steady state systems, estimation-free Prediction Algorithms are derived via Kalman and Lainiotis filters; they are equivalent and compute iteratively the prediction and the corresponding prediction error covariance matrix. The estimation and the corresponding estimation error covariance matrix are not needed and are not computed. The proposed estimation-free prediction algorithms are faster than the Kalman filter.

Simultaneous localization and mapping (SLAM) is a central and complex problem in robot research community. In SLAM, extended Kalman filter (EKF) implementation is widely used to localize the robot and build the environment map incrementally. In this paper, we propose a strong tracking filter (STF) SLAM algorithm. This algorithm applies STF to deal with the non-linear estimated problem in SLAM instead of EKF. It can make the performance of the nonlinear filter approximate to that of optimal linear Kalman Filter (KF), so it can construct high accuracy maps and locate the robot more accurately than EKF SLAM. Simulation experiments illustrate the superior performance of our approach compared to EKF SLAM algorithm.

Object-Oriented Environment for Assessing Tracking Algorithms

Data fusion algorithms are inevitable in improving the accuracy and reliability of radar target tracking. Considering the shortcomings of target tracking in Cartesian coordinates, all the fusion process are carried out in spherical coordinate system. To fuse data from bidimensional radar and Infrared Search and Track (IRST), five data fusion methods, Bayesian fusion, Signal variance based fusion, Optimal fusion, Error variance based fusion and Extended Kalman Filter (EKF) based fusion are proposed and analyzed. The performances of the methods are analyzed in terms of Root Mean Square Error in Position (RMSPE) and Mean Absolute Error in Position (MAPE) for a wide range of measurement noise variances. It is concluded that EKF based fusion has the best error performance. Kalman Filter State-Vector Fusion (KF-SVF) which is a hierarchical fusion architecture, having first level of fusion with Kalman filter and second level with error variance based fusion method, is available in the literature. In this work it has been expanded to Extended Kalman Filter—State-Vector Fusion (EKF-SVF) with either error variance based fusion, signal variance based fusion or optimal information fusion as second level. All the three EKF-SVF methods have similar error characteristics, but EKF-SVF with signal variance based fusion, unlike the other two, provides less computational cost since it does not involve matrix inversion. While comparing EKF based fusion and EKF-SVF, EKF-SVF offers increased error minimization.

When the extended strong tracking filter (ESTF) is used to improve the carrier tracking estimation instead of the extended Kalman filter (EKF), it is found to be difficult to effectively and consistently evaluate superiority of the ESTF than the EKF. The primary cause is that the basic properties of the traditional Kalman filter are broken due to the subjective fading factor. The superiority of the ESTF is customarily shown by simulations and experiments in previous work only and the corresponding mechanism analysis is very lacking. Motivated by this, we study the performance comparison of the ESTF and EKF. First, the statistical parameters such as the prediction mean-squared error (MSE), the MSE, and the gain matrix are analytically and systematically compared in theory. Second, the inconsistency of estimation performances is explicitly revealed based on the comparison results. Third, mismatching analysis of estimation performance expressions, which are the root-mean-squared error and MSE, is briefly presented for the ESTF. The presented results state clearly that the usability of the conventional Kalman filtering theory is seriously limited and its structure is easy to be destroyed. It is a challenge and a good chance to study new performance evaluation methods on the class of strong tracking filters for engineering application.

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.

Low-cost adaptive square-root cubature Kalman filter for systems with process model uncertainty

Efficient implementation of positioning algorithm plays a crucial role in modern Global Positioning System (GPS). Conventional non-linear Least Squares (LS) method is applied iteratively by Taylor expansion, which doesn't combine different epoch-time for mutual restraint. While with respect to generally used extended Kalman filter (EKF), it requires an accurate system model estimation and exact stochastic Gaussian white noise, resulting in non-uniformly convergence with an unknown bias or model error. To solve this problem, this paper proposes a Strong Tracking Filter (STF) modeling. To achieve robustness about model uncertainty and tracking capability on the mutation status, the STF adjusts the real-time state prediction error covariance matrix and the corresponding gain matrix. It also makes use of Time-varying Fading Factor (TVFF) to deal with the past data, which weakens the stale data to the impact of current filtered value. Simulation shows that the proposed STF is capable of enhancing more than half precision than traditional EKF and LS.

This paper designs a fixed-wing UAV postural reference system, which uses magnetometer, accelerometer and gyroscope (MARG) to perform the attitude measurement of high precision. A quaternion is calculated using Gyroscope sensor by means of quaternion algorithm, and we can get another quaternion using Magnetometer and Accelerometer sensor in the same way. The postural data are calculated using both two quaternions by two data fusion methods, adaptive complementary filter and extended Kalman filter, respectively. We compared data precision from the two filter methods in experiments. The results show that both this two fusion methods can meet the required precision of attitude data, in which Kalman filter method is more accurate than adaptive complementary filter although the latter is simpler and more practical than the former.

A switched SDRE filter for state of charge estimation of lithium-ion batteries

В работе рассматривается математическая модель комплекса обнаружения воздушных целей с комплексированием данных от различных источников информации - средств обнаружения. В составе комплекса обнаружения рассматриваются средства обнаружения трех типов: радиолокационная станция, радиопеленгатор и оптико-электронная система. Приводятся математические модели каждого средства обнаружения и динамики цели, заданной в виде материальной точки. Обработка информации строится с использованием селективного метода комплексирования на основе федеративного фильтра Калмана. При использовании которого на каждом такте моделирования работы комплекса обнаружения выбирается наиболее достоверный источник информации о координатах цели (между всеми средствами обнаружения) с наименьшим следом ковариационной матрицы ошибок оценивания. Результаты моделирования показывают принципиальную применимость предложенной математической модели комплекса обнаружения воздушных целей. The paper considers a mathematical model of an air target detection system with data integration from various information sources - detection means. The detection system includes three types of detection means: a radar station, a radio direction finder, and an optical-electronic system. Mathematical models of each detection means and the dynamics of a target specified as a material point are given. Information processing is built using a selective integration method based on the federated Kalman filter. When using it, at each simulation cycle of the detection system operation, the most reliable source of information on the target coordinates (between all detection means) with the smallest trace of the covariance matrix of estimation errors is selected. The modeling results show the fundamental applicability of the proposed mathematical model of the air target detection system.

The stochastic nature of noise signals affects the vehicle’s internal states and the outputs, resulting in the difficulty in estimation. The unknown or time-varying nature of noise signals if not taken into account for estimation, the results will diverge and be highly deteriorated. In this paper, a maximum likelihood principle (MLP) based adaptive robust extended kalman filter for estimating the states of the adopted non-linear vehicle model is proposed. An observability test is done for the purpose of estimation. A covariance matching (CM) based robust adaptive high forgetting factor based fault tolerant technique is also employed on the robust adaptive extended and unscented kalman filters for comparison purpose. The Robustness of the filter is analyzed by varying the parameter of the vehicle through a local sensitivity analysis. The results show that the MLP based approach to the extended kalman filter performs well in three simulations for sinusoidal steering, Double Lance Change, J-Turn, Fishhook, Slalom maneuver in comparison to robust adaptive unscented kalman filter. Friction coefficient of 0.8 (dry road) and 0.4 (wet road) is chosen for the simulation. The sideslip angle RMSE value for MLP based estimation is obtained as 2.62e-05, 4.545e-06 for Sine and DLC maneuver.

State of Charge (SOC) estimation plays a crucial role in managing the performance and longevity of electric vehicle (EV) batteries. Various estimation techniques, including various Kalman Filters (KF), have been employed for this purpose. The mathematical process and limits of different KF family algorithms are analysed. In this study, an impact of nonlinear KF parameters on SOC estimation accuracy for EV batteries is analyzed. Specifically, the performance of Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Particle Filter (PF) is examined. EKF is most preferred for SOC estimation whereas introducing sigma points in UKF is the basic difference between EKF and UKF. In comparison to EKF and UKF, PF is more flexible since it applies to nonlinear systems with non-Gaussian distributions. Utilising a sequence of noisy measurements, KF is a recursive method that approximates the state of a dynamic system. It requires accurate parameters such as process noise covariance (Q) and measurement noise covariance (R) to work effectively. In this work, the effect of these parameters on state of charge estimation using nonlinear KFs has been analysed under different settings of noise covariance matrices. Tuning these parameters is essential for optimizing the performance of the KF and ensuring accurate and reliable state estimation in real-world applications. To find parameter values that provide the best balance between accuracy, robustness, and computational efficiency, the tuning process involves experimentation, simulation, and validation using real-world data. According to the results observed, the filter parameters such as three diagonal elements of Q are selected as 2e-8, 0.005, 0.003 and R as 2e-6. By evaluating the state estimation accuracy under different driving scenarios, robustness and sensitivity of filtering technique in estimating SOC for EV batteries has been studied. This analysis contributes to the optimization of SOC estimation algorithms, enhancing the reliability and efficiency of EV battery management systems.

Covariance intersection fusion steady-state Kalman estimator for discrete time stochastic linear systems with system errors and sensor errors is presented in this paper. Gevers-Wouters (G-W) algorithm is used in this paper. Steady-state Kalman estimator is presented in this paper avoids the complex Diophantine equation, and it is based on the ARMA model to compute the steady-state Kalman estimators gain, further the Lyapunov equation is used to estimate the variance matrix and covariance matrix of estimation error. So this algorithm can obviously reduce the computational burden. The information fusion algorithm presented in this paper is covariance intersection fusion. Compared with the single sensor case, the accuracy of the fused filter is greatly improved. A simulation example of the target tracking controllable system with two sensors shows its effectiveness and correctness.