Unscented Filter Research Articles

Maximum correntropy unscented filter based on unbiased minimum-variance estimation for a class of nonlinear systems

Introduction: The unscented Kalman filter based on unbiased minimum-variance (UKF-UMV) estimation is usually used to handle the state estimation problem of nonlinear systems with an unknown input. When the nonlinear system is disturbed by non-Gaussian noise, the performance of UKF-UMV will seriously deteriorate.Methods: A maximum correntropy unscented filter based on the unbiased minimum variance (MCUF-UMV) estimation method is proposed on the basis of the UKF-UMV without the need for estimation of an unknown input and uses the maximum correntropy criterion (MCC) and fixed-point iterative algorithm for state estimation.Results: When the measurement noise of the nonlinear system is non-Gaussian noise, the algorithm performs well.Discussion: Our proposed algorithm also does not require estimation of an unknown input, and there is no prior knowledge available about the unknown input or any prior assumptions. The unknown input can be any signal. Finally, a simulation example is used to demonstrate the effectiveness and reliability of the algorithm.

Improved Jacobian matrix estimation applied to snake robots.

Two manipulator Jacobian matrix estimators for constrained planar snake robots are developed and tested, which enables the implementation of Jacobian-based obstacle-aided locomotion (OAL) control schemes. These schemes use obstacles in the robot's vicinity to obtain propulsion. The devised estimators infer manipulator Jacobians for constrained planar snake robots in situations where the positions and number of surrounding obstacle constraints might change or are not precisely known. The first proposed estimator is an adaptation of contemporary research in soft robots and builds on convex optimization. The second estimator builds on the unscented Kalman filter. By simulations, we evaluate and compare the two devised algorithms in terms of their statistical performance, execution times, and robustness to measurement noise. We find that both algorithms lead to Jacobian matrix estimates that are similarly useful to predict end-effector movements. However, the unscented filter approach requires significantly lower computing resources and is not poised by convergence issues displayed by the convex optimization-based method. We foresee that the estimators may have use in other fields of research, such as soft robotics and visual servoing. The estimators may also be adapted for use in general non-planar snake robots.

An Iterative Guidance and Navigation Algorithm for Orbit Rendezvous of Cooperating CubeSats

Modern space missions often require satellites to perform guidance, navigation, and control tasks autonomously. Despite their limited resources, small satellites are also involved in this trend, as in-orbit rendezvous and docking maneuvers and formation flying have become common requirements in their operational scenarios. A critical aspect of these tasks is that these algorithms are very much intertwined with each other, although they are often designed completely independently of one another. This paper describes the design and simulation of a guidance and relative navigation architecture for the rendezvous of two cooperating CubeSats. The integration of the two algorithms provides robustness to the solution, by simulating realistic levels of noise and uncertainty in the guidance law implementation. The proposed guidance law is derived based on the linearized equations of orbital motion, written in terms of spherical coordinates. The trajectory is iteratively corrected at a fixed time step, so that errors from the navigation and the initial orbital condition can be recovered. The navigation algorithm processes the bearing and range measurements from a camera and an intersatellite link through an unscented filter to provide the information required from the guidance law. A Monte Carlo campaign based on a 3-DOF simulation demonstrates the effectiveness of the proposed solution.

Wrapped Particle Filtering for Angular Data

Particle filtering is probably the most widely accepted methodology for general nonlinear filtering applications. The performance of a particle filter critically depends on the choice of proposal distribution. In this paper, we propose using a wrapped normal distribution as a proposal distribution for angular data, <i>i.e</i>. data within finite range (-&#x03C0;,&#x03C0;]. We then use the same method to derive the proposal density for a particle filter, in place of a standard assumed Gaussian density filter such as the unscented Kalman filter. The numerical integrals with respect to wrapped normal distribution are evaluated using Rogers-Szeg&#x0151; quadrature. Compared to using the unscented filter and similar approximate Gaussian filters to produce proposal densities, we show through examples that wrapped normal distribution gives a far better filtering performance when working with angular data. In addition, we demonstrate the trade-off involved in particle filters with local sampling and global sampling (<i>i.e</i>. by running a bank of approximate Gaussian filters vs running a single approximate Gaussian filter) with the former yielding a better filtering performance than the latter at the cost of increased computational load.

The effect of population size for pathogen transmission on prediction of COVID-19 spread

Extreme public health interventions play a critical role in mitigating the local and global prevalence and pandemic potential. Here, we use population size for pathogen transmission to measure the intensity of public health interventions, which is a key characteristic variable for nowcasting and forecasting of COVID-19. By formulating a hidden Markov dynamic system and using nonlinear filtering theory, we have developed a stochastic epidemic dynamic model under public health interventions. The model parameters and states are estimated in time from internationally available public data by combining an unscented filter and an interacting multiple model filter. Moreover, we consider the computability of the population size and provide its selection criterion. With applications to COVID-19, we estimate the mean of the effective reproductive number of China and the rest of the globe except China (GEC) to be 2.4626 (95% CI: 2.4142–2.5111) and 3.0979 (95% CI: 3.0968–3.0990), respectively. The prediction results show the effectiveness of the stochastic epidemic dynamic model with nonlinear filtering. The hidden Markov dynamic system with nonlinear filtering can be used to make analysis, nowcasting and forecasting for other contagious diseases in the future since it helps to understand the mechanism of disease transmission and to estimate the population size for pathogen transmission and the number of hidden infections, which is a valid tool for decision-making by policy makers for epidemic control.

Receding horizon directional unscented filter for heavy-duty vehicles incorporating sensor modeling constraints

This paper proposes a new wheelbase and mass estimation algorithm called the receding horizon-based directional unscented filter (RHDUF) algorithm, which is developed based on the lateral dynamics model. The unscented Kalman filter (UKF), which is widely used for estimating nonlinear systems, has an infinite impulse response structure. However, the UKF is vulnerable to uncertainty and accumulates errors gradually. To address this problem, filters with a receding horizon structure can be introduced, but they may lead to a heavy computational burden, which is not desirable for fast estimation. To overcome this problem, we propose a new sigma-point distribution method combined with the receding horizon structure in this paper. The formula is derived through the measured sensor value and the modeling equation of the sensor, and the direction of the sigma points is determined using this equation. This formula can improve performance and reduce the increase in the computation time caused by the receding horizon structure by reducing the number of sigma points simultaneously. The accuracy of the new estimation algorithm is verified through an experiment for heavy-duty vehicles.

State of Charge Estimation for Li-Ion Batteries Based on an Unscented H-Infinity Filter

The state of charge (SOC) of lithium-ion batteries reflects their remaining capacity. Accurate estimation of SOC helps battery safety and is beneficial to the efficient management of batteries. The charging and discharging processes of lithium-Ion batteries are very complicated, and it is difficult to obtain accurate SOC estimation results. Therefore, it is important to study improved algorithms for SOC estimation for this nonlinear non-Gaussian battery system. In this paper, we propose an unscented H-infinity filter (UHF) based SOC estimation method, which combines the advantages of both the unscented Kalman filter (UKF) and the H-infinity filter (HF). The UKF propagates the sigma points through the nonlinear system and does not need the first-order linear approximation of the system equation, while the HF can suppress the non-Gaussian noise in the system to the greatest extent. The proposed UHF based SOC estimation algorithm is verified and evaluated in the battery management system, and further optimized in practical problems. Experimental results show that the proposed UHF based algorithm can perform accurate SOC estimation for lithium-ion batteries, and is superior to the UKF based SOC estimation.

Force control of an uncertain series elastic actuator system via a fuzzy sliding mode controller and a nonlinear state estimator

Nowadays, series elastic actuators play an important role in actuation technology, especially for mechatronics and robotic applications. In this article, the accurate tracking of output force for a series elastic actuator is investigated. In order to achieve this aim, a novel robust control scheme is developed to overcome friction effects, backlash in the drivetrain, measurement noises (sensor inaccuracy) and uncertainties in the dynamic model. The control scheme consists of a fuzzy sliding mode controller and a nonlinear state estimator. The theory of Lyapunov stability is used for the formulation of the proposed controller and also the fuzzy logic strategy is used for tuning the sliding surface parameter in order to achieve accurate and chattering-free performance. Furthermore, a powerful estimator algorithm, unscented H-infinity filter, is added to the control scheme to improve the robustness of the system. Simulation results, as well as experimental analysis, approved the efficiency of the proposed approach in the presence of uncertainties and disturbances.

Improved Student’s t-Based Unscented Filter and its Application to Trajectory Estimation for Maneuvering Target

To estimate the systems with one-step randomly delayed measurement and time-correlated heavy-tailed measurement noises, on the basis of robust Student’s t based unscented filter (RSTUF), an improved Student’s t based unscented filter (ISTUF) is proposed. Referring to the measurement differencing method, a reformed measurement model was built. Then, by augmenting the system state vector, the conditional probability distribution of the measurement noise with respect to delayed measurement was taken into consideration. Based on the reformed measurement model and the augment state vector, a novel estimator was designed to solve the one-step randomly delayed problem. Maneuvering target tracking systems were used for simulation. Compared with unscented Kalman filter (UKF) or RSTUF, ISTUF had higher accuracy.

Robust dynamic state estimation of power systems with model uncertainties based on adaptive unscented filter

This study considers the dynamic state estimation of power systems with model uncertainties that might be caused by the unknown noise statistics or unpredicted changes to the model parameters. To deal with these issues, an innovation-based estimator that is able to dynamically revise the statistics of system and measurement noise is proposed firstly. Then, based on the H ∞ criteria for bounding the adverse influences on the estimation error of model uncertainties and unscented transform technique, an adaptive strategy is developed to adjust the estimation error covariance matrix under various conditions. Finally, by incorporating the proposed approaches and H ∞ filter theory, a novel adaptive unscented H ∞ filter is established to realise dynamic state estimation of power system against model uncertainties. Extensive simulation results obtained from the IEEE-39 bus test system are presented to illustrate the effectiveness and robustness of the proposed method.

Switching Multiple Model Filter for Boost-Phase Missile Tracking

This paper introduces a filter for tracking a ballistic missile during its boost phase. This filter includes a new switching algorithm and a modified interacting multiple model unscented filter (IMMUF), where the Markov transition matrix is time variable. Position, velocity, and all unknown parameters of a medium-range ballistic missile model are reconstructed. Simulations demonstrate that the new filter is able to consistently estimate a missile's trajectory and all unknown parameters and to outperform the previous forms of the IMMUF.

A New Method for Generating Sigma Points and Weights for Nonlinear Filtering

In this letter, a new method termed as new sigma point Kalman filter, is proposed for generating sigma points and weights for estimating the states of a stochastic nonlinear dynamic system. The sigma points and their corresponding weights are generated such that the points nearer to the mean (in inner product sense) have a higher probability of occurrence, and the mean vector and covariance matrix are matched exactly. Performance of the new algorithm is compared with the existing unscented Kalman filter (UKF), the cubature Kalman filter (CKF), the cubature quadrature Kalman filter (CQKF) and higher order unscented filter (HOUF) for two different problems. Comparison is done by calculating the root mean square error, relative computational time and track-loss. From simulation results, it can be concluded that the proposed algorithm performs with superior estimation accuracy when compared to the UKF, CKF, CQKF and HOUF.

Model aided airborne integrated navigation system based on an improved square-root unscented H∞ filter

An inertial navigation system (INS) aided with an aircraft dynamic model (ADM) is developed as a novel airborne integrated navigation system, coping with the absence of a global navigation satellite system. To overcome the shortcomings of the conventional linear integration of INS/ADM based on an extended Kalman filter, a nonlinear integration method is proposed. Fast-update ADM makes it possible to utilize a direct filtering method, which employs nonlinear INS mechanics as system equations and a nonlinear ADM as observation equations, substituting the indirect filtering based on linear error equations. The strong nonlinearity generally calls for an unscented Kalman filter to accomplish the fusion process. Dealing with the model uncertainty, the inaccurate statistical characteristics of the noise and the potential nonpositive definiteness of the covariance matrix, an improved square-root unscented H∞ filter (ISRUHF) is derived in the paper, in which the robust factor [Formula: see text] is further expanded into a diagonal matrix [Formula: see text], to improve the accuracy and robustness of the integrated navigation system. Corresponding simulations as well as real flight tests based on a small-scale fixed-wing aircraft are operated and ISRUHF shows superiority compared with the commonly used fusion algorithm.

Maximum correntropy unscented filter

ABSTRACTThe unscented transformation (UT) is an efficient method to solve the state estimation problem for a non-linear dynamic system, utilising a derivative-free higher-order approximation by approximating a Gaussian distribution rather than approximating a non-linear function. Applying the UT to a Kalman filter type estimator leads to the well-known unscented Kalman filter (UKF). Although the UKF works very well in Gaussian noises, its performance may deteriorate significantly when the noises are non-Gaussian, especially when the system is disturbed by some heavy-tailed impulsive noises. To improve the robustness of the UKF against impulsive noises, a new filter for non-linear systems is proposed in this work, namely the maximum correntropy unscented filter (MCUF). In MCUF, the UT is applied to obtain the prior estimates of the state and covariance matrix, and a robust statistical linearisation regression based on the maximum correntropy criterion is then used to obtain the posterior estimates of the state and covariance matrix. The satisfying performance of the new algorithm is confirmed by two illustrative examples.

Mining of electricity prices in energy markets using a hybrid linear ARMA and nonlinear functional link neural network trained by evolutionary unscented H-infinity filter

This paper presents a hybrid autoregressive moving average (ARMA) and a nonlinear functional link neural network for electricity price forecasting in an Energy market. The functional neural block helps to introduce nonlinearity by expanding the input space to higher dimensional space through a basis function without using any hidden layers like MLP structure. Unlike the conventional functional link artificial neural network (FLANN), the input layer comprises the inputs and tangent hyperbolic functions of the linear combination of the inputs known as the basis functions. The proposed hybrid neural network is trained by an unscented H-infinity filter to provide an accurate forecasting of day ahead electricity prices. The noise covariance parameters of the unscented H-infinity filter are further optimised with an adaptive differential evolution strategy. The studies on PJM, Spanish and Australian energy markets exhibit excellent forecasting results over different seasonal horizons for one day ahead of time.

Mining of electricity prices in energy markets using a hybrid linear ARMA and nonlinear functional link neural network trained by evolutionary unscented H-infinity filter

Mining of electricity prices in energy markets using a hybrid linear ARMA and nonlinear functional link neural network trained by evolutionary unscented H-infinity filter

Improved Underwater Integrated Navigation System using Unscented Filtering Approach

In underwater navigation, the conventional Error State Kalman Filter (ESKF) is used for combining navigation data where due to first order linearization of the nonlinear equations of the dynamics and measurements, considerable error is induced in estimated error state and covariance matrices. This paper presents an underwater integrated inertial navigation system using the unscented filter as an improved nonlinear version of the Kalman filter family. The designed system consists of a strap-down inertial navigation system accompanying Doppler velocity log and depth meter. In the proposed approach, to use the nonlinear capabilities of the unscented filtering approach the integrated navigation system is implemented in a direct approach where the nonlinear total state dynamic and and measurement models are utilised without any linearization. To our knowledge, no results have been reported in the literature on the experimental evaluation of the unscented-based integrated navigation system for underwater vehicles. The performance of the designed system is studied using real measurements. The results of the lake test show that the proposed system estimates the vehicle's position more accurately compared with the conventional ESKF structure.

Evaluation of nonlinear filtering for radar data tracking

Abstract Radar tracking plays an important role in the area of early warning and detection system, whose precision is closely connected with filtering algorithm. With the development of noise jamming technology in radar echo signal, linear filtering becomes more and more difficult to satisfy the demands of radar tracking, while nonlinear filtering can solve problems such as non-Gaussian noises. There exist a lot of nonlinear filtering algorithms at present, owning their particular characteristics. With this in mind, we provide a comprehensive overview of different nonlinear filtering algorithms in radar tracking, including basic ideas and concrete steps of them. For a more clear presentation, we also make comparisons of them from all sides. Through the analyses of different nonlinear data filters, we find that the unscented Kalman data filter (UKF) can achieve better performance than others. Therefore, we will simulate and show the performance of UKF, and performance of the extended Kalman data filter (EKF) under the same condition will be taken as comparison, whose accuracy was not ideal for radar tracking data filtering.

Dual Station Based Bearings-Only Tracking Using Unscented Filter

This paper investigated the bearings-only tracking approach based on dual station detection. In order to solve the problem of strong nonlinearity in bearings –only measurement system, we introduced the unscented filter which is based on the idea of unscented transformation. Compared with traditional extended Kalman filter, unscented filter has shown better convergence and stabiltiy, especially in stabiltiy of tracking waveform. Matlab simulation scenario is taken for illustrating the effectiveness and validity of the unscented filtering algorithm.

Quadrature Kalman filter–based state of charge estimation for lithium-ion battery

This article presents an approach to lithium-ion battery state of charge estimation based on the quadrature Kalman filter. Among the existing state of charge estimation approaches, the extended Kalman filter–based state of charge and unscented filter–based state of charge algorithms are influenced by the linearization or the solution of sigma points. The proposed quadrature Kalman filter–based state of charge algorithm avoids these problems. Specifically, the battery system equations are built based on the second-order resistance–capacitance equivalent circuit model, and the parameters are identified according to the hybrid pulse power characterization discharging test. Then, the quadrature points and corresponding weights are defined by the Gauss–Hermite quadrature rule, and the Kronecker tensor product is adopted to solve the points of multivariate. In addition, the stability of quadrature Kalman filter–based state of charge is verified. Finally, the simulation is carried out under the discharging and urban dynamometer driving schedule condition, which demonstrates that the quadrature Kalman filter–based state of charge algorithm has a better performance compared with extended Kalman filter–based state of charge and unscented filter–based state of charge.