Coordinate Conversion and Tracking for Very Long Range Radars

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.

Traffic state estimation problems must deal with imperfect information. Imperfect information may occur as a result of misalignments between reality and the assumptions or simplifications made when developing the models as well as incomplete or corrupted data. One of the well-known methods of handling imperfect information is the Kalman filter algorithm and its variations, such as the extended Kalman filter and the unscented Kalman filter. While the standard Kalman filter and the extended Kalman filter have been widely applied to the state estimation of linear systems, the unscented Kalman filter has been reported the better choice in the multiclass traffic state estimation. In many applications of Kalman filters to traffic estimation problems, the model and measurement noise covariance matrices are normally estimated. When there is a mismatch between the true and the assumed noise distribution, however, the filter often suffers from performance degradation and even divergence in certain situations. To this end, this paper presents a more efficient and accurate algorithm embedded in the unscented Kalman filter to simultaneously estimate the traffic state and the model noise distribution statistics. The proposed method is facilitated through a simultaneous update of the model noise covariance matrix in the predicted covariance equations of the unscented Kalman filter algorithm. It is found through simulation that the proposed algorithm may improve the model performance over the standard algorithm.

In the extended Kalman filter (EKF) and the unscented Kalman filter (UKF) of non-linear system, the mathematical model and the noise statistics are essential; this limitation was settled by adaptive algorithm. The adaptive extended Kalman filter (AEKF) and adaptive unscented filter (AUKF) were proposed to solve the filtering problem of the system with unknown mathematical model or noise statistics in information fusion. The simulation result shows that the adaptive algorithm in EKF and UKF can improve the performance of filter and decrease the computing time.

A new filtering method is proposed to accurately estimate target state via decreasing the nonlinearity between radar polar measurements (or spherical measurements in three-dimensional (3D) radar) and target position in Cartesian coordinate. The degree of linearity is quantified here by utilizing correlation coefficient and Taylor series expansion. With the proposed method, the original measurements are converted from polar or spherical coordinate to a carefully chosen Cartesian coordinate system that is obtained by coordinate rotation transformation to maximize the linearity degree of the conversion function from polar/spherical to Cartesian coordinate. Then the target state is filtered along each axis of the chosen Cartesian coordinate. This method is compared with extended Kalman filter (EKF), Converted Measurement Kalman filter (CMKF), unscented Kalman filter (UKF) as well as Decoupled Converted Measurement Kalman filter (DECMKF). This new method provides highly accurate position and velocity with consistent estimation.

In a multi-sensor system, sensors often provide data at different rates with different communication delays. To the asynchronous fusion for target tracking with infrared and laser sensors, that provide range and bearing information respectively, there mainly exist two problems need to be solved. One is temporal registration of different sensors since infrared sensor has a shorter sample time than laser sensor. The measurements are dealt with least square method, which makes full use of the high frequency characteristic of infrared sensor. The other is the choice of filtering algorithm because of the correlation of coordinate transformation when measurement equation is described in Cartesian coordinate. Converted measurement Kalman filter (CMKF) is a popular solution to the nonlinear estimation problem expect nonlinear filtering algorithm. Simulations of the algorithms adopted in the paper were carried out to track the target and the performance of different algorithms was compared. The results show that the algorithm based on CMKF yields better track performance than the fusion algorithm based on standard Kalman filter (KF) and a little worse than the algorithm based on unscented Kalman filter (UKF).

Over the last 20-30 years, the extended Kalman filter (EKF) has become the algorithm of choice in numerous nonlinear estimation and machine learning applications. These include estimating the state of a nonlinear dynamic system as well estimating parameters for nonlinear system identification (eg, learning the weights of a neural network). The EKF applies the standard linear Kalman filter methodology to a linearization of the true nonlinear system. This approach is sub-optimal, and can easily lead to divergence. Julier et al. (1997), proposed the unscented Kalman filter (UKF) as a derivative-free alternative to the extended Kalman filter in the framework of state estimation. This was extended to parameter estimation by Wan and Van der Merwe et al., (2000). The UKF consistently outperforms the EKF in terms of prediction and estimation error, at an equal computational complexity of (OL/sup 3/)/sup l/ for general state-space problems. When the EKF is applied to parameter estimation, the special form of the state-space equations allows for an O(L/sup 2/) implementation. This paper introduces the square-root unscented Kalman filter (SR-UKF) which is also O(L/sup 3/) for general state estimation and O(L/sup 2/) for parameter estimation (note the original formulation of the UKF for parameter-estimation was O(L/sup 3/)). In addition, the square-root forms have the added benefit of numerical stability and guaranteed positive semi-definiteness of the state covariances.

In this paper, an adaptive unscented Kalman filter (AUKF) is developed for state estimation on a tractor-trailer system. For nonlinear systems, the unscented Kalman filter (UKF) is a well-known approach for observer design. Some research has shown the UKF can be more accurate than extended Kalman filter (EKF) with similar computation burden. However, the performance of traditional Kalman filter may deteriorate when process noise changes or sudden disturbance occurs due to the fixed process noise covariance (Q matrix) in the filter. An adaptive gain is calculated to compensate for the mismatch between the actual residual covariance and the deduced value from the filter, ensuring that the sequence of residual is uncorrelated. An estimated Q matrix is referred in the adaptive gain calculation at each sample. Simulation is done in various situations. The positions of trailer are used as measurements. Compared with the standard UKF (SUKF) and another adaptive UKF, the proposed algorithm has better result.

This study represents a method for estimating the state of charge (SOC) of lithium‐ion batteries using radial basis function (RBF) networks and square‐root unscented Kalman filter (KF). The RBF network is trained offline by sampled data from the battery in the charging process. This type of neural network finds the non‐linear relation which is required in the state‐space equations. The state variables include the battery terminal voltage and the SOC, at the previous sample and the present sample, respectively. The proposed method is tested experimentally on a lithium‐ion battery with 1.2 Ah capacity to estimate the actual SOC of the battery. The experimental results of the proposed method show some advantages, which include: (i) it is not very sensitive to determine, precisely, the measurement and process noise covariance matrices such as Kalman filter and (ii). It contains lower noise on the output, in comparison with Adaptive extended Kalman filter (EKF).

In this work, the problem of battery state of charge estimation is investigated using a model based approach. An experimentally validated model of a battery developed by AllCell Technologies, specific for light electric vehicles (electric scooter or bicycles) is used. Two state of charge estimation algorithms are developed: an extended Kalman filter and an adaptive extended Kalman filter. The adaptive version of Kalman filter is designed in order to adaptively set a proper value of the model noise covariance, using the information coming from the on-line innovation analysis. A comparison between the two approaches is conducted that shows that the adaptive Kalman filter can deal with the problem of incorrect value of the model noise covariance matrix producing lower estimation error.

Fast non-intrusive estimation of liquid-phase interface and boundary heat flux in participating media by the Kalman filtering methods

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.

Combined Kalman and sliding innovation filtering: An adaptive estimation strategy

The unscented Kalman filter (UKF) has become a popular alternative to the extended Kalman filter (EKF) during the last decade. UKF propagates the so called sigma points by function evaluations using the unscented transformation (UT), and this is at first glance very different from the standard EKF algorithm which is based on a linearized model. The claimed advantages with UKF are that it propagates the first two moments of the posterior distribution and that it does not require gradients of the system model. We point out several less known links between EKF and UKF in terms of two conceptually different implementations of the Kalman filter: the standard one based on the discrete Riccati equation, and one based on a formula on conditional expectations that does not involve an explicit Riccati equation. First, it is shown that the sigma point function evaluations can be used in the classical EKF rather than an explicitly linearized model. Second, a less cited version of the EKF based on a second-order Taylor expansion is shown to be quite closely related to UKF. The different algorithms and results are illustrated with examples inspired by core observation models in target tracking and sensor network applications.

Inherent flaws in the extended Kalman filter (EKF) algorithm were pointed out and unscented Kalman filter (UKF) was put forward as an alternative. Furthermore, a novel adaptive unscented Kalman filter (AUKF) based on innovation was developed. The three data-fusing approaches were analyzed and evaluated in a mathematically rigorous way. Field experiments conducted in lake further demonstrate that AUKF reduces the position error approximately by 65% compared with EKF and by 35% UKF and improves the robust performance.

This paper presents the efficient Unscented Kalman filter (UKF) based estimation and control of a 3-DOF Omni bundle robot. The angular trajectory tracking becomes more difficult under highly non-linear measurement noise and process noise. A rapidly converging Unscented Kalman Filter (UKF) is presented in the paper. The extended Kalman filter (EKF) provides less accurate results in the highly non-linear system and sometime may become unstable because of convergence related issues, whereas in UKF the results in the non-linear system are better than EKF. UKF is more accurate in state and noise estimation. The computed torque technique is taken as a model to apply UKF. After, estimation the noise is removed. The experiment is conducted on Omni bundle with process and measurement noise. The results prove the superiority of presented UKF over conventional UKF and EKF.