Standard Unscented Kalman Filter Research Articles

LIF-M: A Manifold-Based Approach for 3D Robot Localization in Unstructured Environments

Accurate localization of robots in unstructured environments poses challenges due to low localization accuracy and local trajectory oscillation caused by complex feature points when using Euclidean-based filtering methods. In this study, we propose a novel 3D robot localization method named LIF-M that leverages a manifold-based approach in conjunction with an unscented Kalman filter (UKF-M). Additionally, a relocalization algorithm is designed to ensure localization stability. The proposed method addresses the limitations of conventional Euclidean-based filtering methods by incorporating manifold-based techniques, providing a more comprehensive representation of the complex geometric features. We introduce the manifold concept, where the relevant definition is defined and utilized within the LIF-M framework. By combining left and right invariants, we effectively reduce noise uncertainty, resulting in improved localization accuracy. Moreover, we employ sigma points as a matrix representation of the state points’ space in order to seamlessly transition between the matrix space and the vector representation of the tangent space. Experimental tests and error calculations were conducted to evaluate the performance of various algorithm frameworks, and the results demonstrated the importance of the manifold-based approach for accurate attitude estimation. Compared to the standard UKF, the manifold space equips LIF-M with better robustness and stability in unstructured environments.

Active disturbance rejection control strategy for PEMFC oxygen excess ratio based on adaptive internal state estimation using unscented Kalman filter

The effectiveness of gas flow control will significantly affect the output performance of the PEMFC, however, the gas state inside the cathode is difficult to observe due to the tightness and safety requirements. To achieve effective control of PEMFC in the presence of parameter bias, an improved active disturbance rejection control (IADRC) strategy based on the adaptive unscented Kalman filter (AUKF) is proposed in this paper. A dynamic model of the air supply system with seven state variables was developed, capable of describing the non-linear characteristics of the system, and a semi-empirical air compressor model was designed to match the actual operating characteristics based on the experimental data set. Based on the standard UKF algorithm, an adaptive process was designed using the moving window method to dynamically adjust the noise characteristics to reduce the state estimation bias caused by changes in system structural parameters during service. Finally, the algorithmic structure of the ADRC was optimized to achieve an accurate estimation of the total system perturbation using cascaded extended state observers (ESO), thus achieving a control effect with the advantages of less overshoot and response speed based on fewer tuning parameters. Simulation results show that the proposed strategy can effectively improve the system response and robustness to structural parameters, and has great control effects under real road conditions.

Strong Tracking UKF-Based Hybrid Algorithm and Its Application to Initial Alignment of Rotating SINS With Large Misalignment Angles

In this paper, the fast and precise initial alignment of the low-cost rotary strapdown inertial navigation system under mooring conditions is investigated. The unscented Kalman filter (UKF) is used to address model nonlinearity and to achieve fast alignment for large misalignment angles. A generalized multi-fading strong tracking UKF (GSTUKF) is proposed to effectively compensate for the kinematic model errors caused by mooring and rotary motions. The performance of the standard strong tracking UKF cannot be optimal because only a portion of the fading factors associated with the directly observable state variables can be obtained approximately using the analytical method. By contrast, using the iteration method to calculate the full-dimension fading factors precisely, the GSTUKF has greater robustness and adaptability. To find out the optimal fading factors in real time, the multivariate nonlinear optimization model is first designed, and then the iteration approach based on a hybrid algorithm consisting of particle swarm optimization and beetle antennae search is developed, which has no risk of falling into a local minimum. Simulations and experiments are conducted to validate the GSTUKF's effectiveness. The experiments demonstrate that the proposed method reduces the yaw error by 47.2% compared with the standard strong tracking UKF.

Combined Kalman and sliding innovation filtering: An adaptive estimation strategy

This paper proposes a new adaptive estimation strategy for a nonlinear system with modeling uncertainties. The extended Kalman filter (EKF) and unscented Kalman filter (UKF) are optimal estimators which have been used extensively for state estimation in literature and industry. While the EKF uses a first order Taylor series expansion to approximate nonlinearities, the UKF uses sigma points from the projected probability distribution of states. The sliding innovation filter (SIF) is a suboptimal, yet robust estimation strategy which has recently been proposed. For nonlinear systems, the extended SIF (ESIF) is formulated by using a first order Taylor series expansion like the EKF. This work proposes a novel adaptive estimation strategy which combines and balances the optimality of the EKF and UKF with the robustness of the ESIF. These new methods are referred to as the EKF-ESIF and UKF-ESIF, respectively. A time-varying sliding boundary layer is used as a means of detecting the presence of faults or uncertainties and as a criterion for switching between the EKF or UKF and the ESIF. In normal operating conditions the algorithm computes estimates using an optimal KF-based gain, and an SIF-based gain when a fault is detected. The system examined in this study consists of a magnetorheological (MR) damper with a constant current. Faults or uncertainties are introduced as unwanted behavior in the power supply in the form of undercurrent and overcurrent. The robustness of the EKF-ESIF and UKF-ESIF was validated for force estimation exerted by the MR damper and the results were compared with the standard EKF and UKF.

A tracking method for GEO space targets based on adaptive memory attenuation UKF

Aiming at the problem that the nonlinearity of the tracking state equation and the problem of strong noise in the measurement process in the process of tracking the target, a non-cooperative target tracking method in geostationary earth orbit based on adaptive memory attenuation UKF is proposed. Firstly, the relative motion model of the non-cooperative target is constructed, and the state equation and measurement equation are established. Use the memory attenuation adjustment factor to enhance the correction effect of the new measurement on the state estimation, improve the adaptability of the filtering method to nonlinearity and noise, and finally the relative motion trajectory of the space non-cooperative target is obtained. Finally, the standard UKF algorithm and improved UKF algorithm are applied to target tracking and compared by simulation. The deviation of the three coordinate axis components of the actual motion trajectory and the predicted trajectory of the space target is used as the evaluation index. The simulation results show that the filtering accuracy of the improved UKF algorithm is significantly improved, while taking into account the real-time performance of on-orbit tracking.

State Parameter Estimation of Intelligent Vehicles Based on an Adaptive Unscented Kalman Filter

The premise of vehicle intelligent decision making is to obtain vehicle motion state parameters accurately and in real-time. Several state parameters cannot be measured directly by vehicle sensors, so estimation algorithms based on filtering are effective solutions. The most representative algorithm is the Kalman filter, especially the standard unscented Kalman filter (UKF) that has been widely used in vehicle state estimation because of its superiority in dealing with nonlinear filtering problems. However, although the UKF assumes that the noise statistics of the system are known, due to the complex and changeable operating conditions, sensor aging and other factors, these noises vary. In order to realize high-precision vehicle state estimation, a noise-adaptive UKF algorithm is proposed in this article. The maximum a posteriori (MAP) algorithm is used to dynamically update the noise of the vehicle system, and it is embedded into the update step of the UKF to form an adaptive unscented Kalman filter (AUKF). The system will dynamically update the noise when noise statistics are unknown and prevent filter divergence by adjusting the mean and covariance of the estimated noise to improve accuracy. On this basis, the proposed method is verified by the joint simulation of CarSim and Matlab/Simulink, confirming that the AUKF performs better than the standard UKF in estimation accuracy and stability under different degrees of noise disturbance, and the estimation accuracy for the yaw rate, side slip angle and longitudinal velocity is improved by 20.08%, 40.98% and 89.91%, respectively.

The Simple Solution for Nonlinear State Estimation of Ill-Conditioned Systems: The Normalized Unscented Kalman Filter

An easy-to-implement method for nonlinear state estimation for ill-conditioned systems is proposed. By propagating standard deviations and correlations instead of the covariance in the unscented Kalman filter (UKF), the condition numbers of relevant matrices are reduced. The reduction in the condition number is related to the scaling of the problem. Hence, what we propose is a normalization method that acts as an “auto-scaler”. Compared to other methods in state estimation for ill-conditioned systems, our proposed method factors the covariance matrix into physically meaningful statistics which can be used to check for filter divergence online. The method is compared to a standard UKF in a case study and shows a significant reduction in the condition number.

Unscented Kalman filter with stable embedding for simple, accurate, and computationally efficient state estimation of systems on manifolds in Euclidean space

AbstractThis article proposes a simple, accurate, and computationally efficient method to apply the ordinary unscented Kalman filter (UKF) developed in Euclidean space to systems whose dynamics evolve on manifolds. We use the mathematical theory called stable embedding to make a variant of UKF that keeps state estimates in close proximity to the manifold while exhibiting excellent estimation performance. We confirm the performance of our devised filter by applying it to the satellite system model and comparing the performance with other UKFs devised specifically for systems on manifolds. Our devised filter has a low estimation error, keeps the state estimates in close proximity to the manifold as expected, and consumes a minor amount of computation time. Also our devised filter is simple and easy to use because our filter directly employs the off‐the‐shelf standard UKF devised in Euclidean space without any particular manifold‐structure‐preserving discretization method or coordinate transformation.

Control-Oriented Physics-Based Modeling and Observer Design for State-of-Charge Estimation of Lithium-Ion Cells for High Current Applications

This article proposes a physics-based control-oriented model and observer design for the state-of-charge (SoC) estimation of lithium-ion cells for applications involving high magnitude fluctuating current profiles. The physics-based single-particle model (SPM) provides enhanced accuracy due to the inclusion of electrolyte dynamics and addresses the issue of nonobservability associated with it. The computationally efficient physics-based model is utilized to design a robust observer-based SoC estimator in the framework of linear matrix inequality to guarantee fast convergence despite parametric uncertainty in the state and output equations, and unknown initial conditions. The observer performance is validated using FTP75 and US06 dynamic tests at different temperatures, and the results are compared with the standard unscented Kalman filter (UKF). The mean SoC estimation error and the integral square error of the estimated SoC for the proposed observer are at least one order of magnitude smaller than that of UKF. Furthermore, robustness to ±30% parametric uncertainty, measurement noise, and unknown initial conditions is demonstrated through Monte Carlo simulations at different temperatures.

On accurate estimation of vehicle lateral states based on an improved adaptive unscented Kalman filter

This paper proposes an improved adaptive unscented Kalman filter (iAUKF)-based vehicle lateral state estimation method. A three-degree-of-freedom vehicle dynamics model is first established. Second, the influence of process noise and measurement noise on vehicle lateral state estimation using standard UKF is analyzed, and a new type of normalized innovation square-based adaptive noise covariance adjustment strategy is designed and incorporated into the standard UKF to form the iAUKF algorithm with the purpose of achieving accurate estimation of vehicle lateral states. Finally, a comparative simulation investigation using CarSim and MATLAB/Simulink is conducted to validate the effectiveness of the proposed method, and the results show that the proposed iAUKF-based estimation method has higher accuracy and stronger robustness against the standard UKF algorithm.

Reliability Assessment of an Unscented Kalman Filter by Using Ellipsoidal Enclosure Techniques

The Unscented Kalman Filter (UKF) is widely used for the state, disturbance, and parameter estimation of nonlinear dynamic systems, for which both process and measurement uncertainties are represented in a probabilistic form. Although the UKF can often be shown to be more reliable for nonlinear processes than the linearization-based Extended Kalman Filter (EKF) due to the enhanced approximation capabilities of its underlying probability distribution, it is not a priori obvious whether its strategy for selecting sigma points is sufficiently accurate to handle nonlinearities in the system dynamics and output equations. Such inaccuracies may arise for sufficiently strong nonlinearities in combination with large state, disturbance, and parameter covariances. Then, computationally more demanding approaches such as particle filters or the representation of (multi-modal) probability densities with the help of (Gaussian) mixture representations are possible ways to resolve this issue. To detect cases in a systematic manner that are not reliably handled by a standard EKF or UKF, this paper proposes the computation of outer bounds for state domains that are compatible with a certain percentage of confidence under the assumption of normally distributed states with the help of a set-based ellipsoidal calculus. The practical applicability of this approach is demonstrated for the estimation of state variables and parameters for the nonlinear dynamics of an unmanned surface vessel (USV).

A Robust Algorithm for State-of-Charge Estimation under Model Uncertainty and Voltage Sensor Bias

Accurate estimation of the state of charge (SOC) of zinc–nickel single-flow batteries (ZNBs) is an important problem in battery management systems (BMSs). A nonideal electromagnetic environment will usually cause the measured signal to contain nonnegligible noise and bias. At the same time, due to the influence of battery ageing, environmental temperature changes, and a complex reaction mechanism, it is difficult to establish a very accurate system model that can be applied to various complex working conditions. The unscented Kalman filter (UKF) is a widely used SOC estimation algorithm, but the UKF will reduce the estimation accuracy and divergence under the influence of inaccurate model and sensor errors. To improve the performance of the UKF, a robust desensitized unscented Kalman filter (RDUKF) is proposed to realize an accurate SOC estimation of batteries in the context of different disturbances. Then, the proposed method is applied to cases of error interference, such as Gaussian noise, voltage sensor drift, an unknown initial state, and inaccurate model parameters. The simulation and experimental results show that compared with the standard UKF algorithm, the proposed estimation algorithm can effectively suppress the influence of various errors and disturbances and achieve higher accuracy and robustness.

A Comparison of Two Sigma Point Kalman Filters for Adaptive Cross-phase Cavity Pressure Control in Injection Molding

Injection molding is a discontinuous manufacturing process used for the automated production of plastic parts. An adaptive model-based predictive controller (MPC) for cross-phase cavity pressure control has been proposed in prior work showing good reference tracking capabilities for different processing conditions. The adaptive control topology is complemented by an Unscented Kalman Filter (UKF) estimating the system states along with a lumped model parameter mapping the system's time-variant dynamics. Previous experiments with a deterministic MPC have shown that the closed-loop performance is significantly improved when reducing the sample time. Thereby, a lower bound is given by the limited computing capacity of the controller hardware. Additionally, the closed-loop control performance correlates with the convergence rate of the parameter estimate. Both convergence behavior and computational effort are influenced by the sigma points (SP) selected within the UKF algorithm. Therefore, two different SP selection procedures, namely the standard UKF as well as the spherical simplex UKF (ssUKF) are evaluated for accuracy, computational effort and closed-loop performance. Both variations of the UKF are implemented in context of the adaptive control scheme and experimentally validated. It is shown that for both UKF designs the adaptive controller ensures good tracking of a given cross-phase cavity pressure reference. Similar closed-loop control performance is obtained if an individual tuning for each filter is performed. However, the averaged computation time of the ssUKF is approximately 34.2 (%) less compared to the UKF, which enables a significant reduction of the sampling time.

Constrained unscented Kalman filter for parameter identification of structural systems

The unscented Kalman filter (UKF) can be used to identify model parameters of structural systems from the measurement data. However, the standard UKF may provide unreliable and nonphysical estimates, since no parameter constraints are incorporated in the identification process. This paper discusses and compares several constrained UKF (CUKF) methods for parameter identification of structural systems. The effectiveness and robustness of the methods are evaluated through numerical simulation on a Bouc–Wen hysteretic system. The results demonstrate that with properly handling of the constraints, the identification accuracy can be improved. The proposed CUKF method is further validated using experimental data collected from a full-scale reinforced concrete structure. Based on the identified model parameters, the updated models can achieve more accurate simulation responses than the initial model.

A new multi-sensor hierarchical data fusion algorithm based on unscented Kalman filter for the attitude observation of the wave glider

In order to improve the accuracy of a single low-cost attitude observation sensor of the wave glider (WG), a new multi-sensor hierarchical data fusion algorithm is proposed. The bottom-level fusion strategy is the complementary data fusion of the accelerometer and the magnetometer, and the global optimal estimation of the bottom-level fusion result and the gyroscope based on the unscented Kalman filter (UKF) algorithm in the top-level fusion strategy. However, the estimation accuracy of the standard UKF algorithm depends on the accuracy of the noise model. Inaccurate estimation of the covariance matrix of the state noise and the measurement noise will cause the accuracy of the UKF algorithm to decrease or even diverge. By introducing the covariance matching technology, the innovation sequence and the residual sequence are used to realize the real-time estimation of the covariance matrix of state noise and measurement noise. At the same time, in view of the characteristic that the measurement equation is a strongly nonlinear equation, an improved covariance matching adaptive UKF algorithm is proposed. It effectively overcomes the limitations of the standard UKF and improves the adaptability of the multi-sensor hierarchical data fusion algorithm. Numerical simulation and experiment are carried out and the results demonstrate that the multi-sensor hierarchical data fusion algorithm is effective in solving the precision problem of the WG low-cost attitude observation unit.

Design of unscented Kalman filter based on the adjustments of the number and placements of the sampling points

This paper addresses a general sampling method of the unscented Kalman filter (UKF) for nonlinear state estimation. The sampling method for standard UKF is analyzed, and we propose a theorem to address the conditions that UKF provides a third order accuracy in terms of Taylor series expansion for expectation estimation by changing the number and placements of the sampling points. This theorem can be used to develop new UKF. Based on this theorem, we propose a method to design the placements of the sampling points, including the directions and lengths by optimization strategies. Simulation studies demonstrate that the proposed UKF is effective and can significantly improve the filter performance.

Unscented kalman filter with process noise covariance estimation for vehicular ins/gps integration system

The unscented Kalman filter (UKF) has proved to be a promising methodology to integrate INS and GPS for vehicular navigation. Nevertheless, the disturbance suppression of system noise uncertainty on the UKF performance is still an open issue. In this paper, based on the maximum likelihood (ML) principle, a new adaptive UKF with process noise covariance estimation is proposed to enhance the UKF robustness against process noise uncertainty for vehicular INS/GPS integration. The proposed method extends the concept of ML estimation from the linear Kalman filter to the nonlinear UKF to estimate the process noise covariance. Meanwhile, an estimation window for fixed-length memory is introduced to emphasize the use of the new observations and gradually discard the old ones. Since it has the capability to estimate and update the process noise covariance online, the proposed method improves the standard UKF by restraining the disturbance of process noise uncertainty on the filtering solution. The effectiveness and superiority of the proposed method have been verified through Monte Carlo simulations and practical experiment in vehicular INS/GPS integration system.

A correlational inference-based unscented total Kalman filter for integrated navigation

An unscented total Kalman filter (UTKF) estimator with nonlinear dynamic errors-in-variables (DEIV) model is derived based on correlational inference. The proposed UTKF considers all random errors in both system and observation equations and is a Jacobian matrix free alternative to the existing TKF estimators. In particular, this estimator is applied to the inertial navigation system (INS)/ultra-wideband (UWB) integration, in which the marginalised unscented transformation (MUT) as well as the use of generalised Rodrigues parameter (GRP) for attitude updates are embedded into the UTKF to improve the computational efficiency and deal with the dimensional mismatching problems. Furthermore, a theoretical analysis to the effects of DEIV model on total Kalman filter is given. Simulation test has been conducted to compare the performance of UTKF and standard unscented Kalman filter (UKF) in terms of attitude, velocity and position errors. The results demonstrate the feasibility and effectiveness of the proposed estimator.

Slip-Aware Motion Estimation for Off-Road Mobile Robots via Multi-Innovation Unscented Kalman Filter

Benefiting from high mobility and robust mechanical structure, ground mobile robots are widely adopted in the outdoor environment. The mobility of skid-steered mobile robots highly depends on the nonlinear and uncertain interaction between the tire and terrain. This paper introduces an approach to estimate the position, orientation, velocity, and wheel slip for the skid-steered mobile robots navigating on off-road terrains. More specifically, a Multi-Innovation Unscented Kalman Filter (MI-UKF) is developed to fusing different sensors' data. Historical innovations generated along the time sequence are merged into the update process of standard UKF to improve the accuracy of motion estimation. In the proposed estimator, an asymmetric ICR kinematic indicating wheel slip is taken into localization process. A four-wheeled prototype is introduced and three challenging test scenarios are designed. The improvements in orientation and velocity estimation are achieved according to results comparison. In the turning maneuver, the ICRs-based model operates more steady than the traditional wheel slip/skid model.

Reliable Indoor Pseudolite Positioning Based on a Robust Estimation and Partial Ambiguity Resolution Method

The unscented Kalman filter (UKF) can effectively reduce the linearized model error and the dependence on initial coordinate values for indoor pseudolite (PL) positioning unlike the extended Kalman filter (EKF). However, PL observations are prone to various abnormalities because the indoor environment is usually complex. Standard UKF (SUKF) lacks resistance to frequent abnormal observations. This inadequacy brings difficulty in guaranteeing the accuracy and reliability of indoor PL positioning, especially for phase-based high-precision positioning. In this type of positioning, the ambiguity resolution (AR) will be difficult to achieve in the presence of abnormal observations. In this study, a robust UKF (RUKF) and partial AR (PAR) algorithm are introduced and applied in indoor PL positioning. First, the UKF is used for parameter estimation. Then, the anomaly recognition statistics and optimal ambiguity subset of PAR are constructed on the basis of the posterior residuals. The IGGIII scheme is adopted to weaken the influence of abnormal observation, and the PAR strategy is conducted in case of failure of the conventional PL-AR. The superiority of our proposed algorithm is validated using the measured indoor PL data for code-based differential PL (DPL) and phase-based real-time kinematic (RTK) positioning modes. Numerical results indicate that the positioning accuracy of RUKF-based indoor DPL is higher with a decimeter-level improvement compared that of the SUKF, especially in the presence of large gross errors. In terms of high-precision RTK positioning, RUKF can correctly identify centimeter-level anomalous observations and obtain a corresponding positioning accuracy improvement compared with the SUKF. When relatively large gross errors exist, the conventional method cannot easily realize PL-AR. By contrast, the combination of RUKF and the PAR algorithm can achieve PL-AR for the selected ambiguity subset successfully and can improve the positioning accuracy and reliability significantly. In summary, our proposed algorithm has certain resistance ability for abnormal observations. The indoor PL positioning of this algorithm outperforms that of the conventional method. Thus, the algorithm has some practical application value, especially for kinematic positioning.