Iterated Unscented Kalman Filter Research Articles

Identification of amplitude-dependent aerodynamic damping from free vibration data using iterative unscented kalman filter

This study presents an innovative approach employing an iterative Unscented Kalman Filter (IUKF) for the identification of amplitude-dependent nonlinear aerodynamic damping using wind tunnel free vibration data. The wind-structure interaction system is represented as a single-degree-of-freedom system, with the amplitude-dependent aerodynamic damping modeled as a polynomial function of structural displacement and velocity. The augmented state variables, encompassing structural vibration frequency and polynomial coefficients for aerodynamic damping, are concurrently estimated from free vibration data using the UKF technique. To enhance the robustness of the identification results against variations in initial conditions, the UKF is applied iteratively by assigning the estimated polynomial coefficients as new initial values for the state variables. Validation of the IUKF-based method is performed through a numerical example featuring a typical bridge deck sectional model, as well as experimental data from two spring-suspended sectional models experiencing vertical vortex-induced vibration (VIV) and torsional post-flutter limit cycle oscillation. The feasibility of identifying amplitude-dependent aerodynamic damping for amplitude range not covered by the displacement signal is examined.

A Novel Tightly Coupled Solution for SINS/Polarized Navigation System/Odometer Integration Using Polarized and Installed Angle Errors Model

Precise and reliable autonomous navigation in a GPS-denied environment is critical to unmanned systems. The idea of combining SINS, the polarized navigation system (PNS), and the odometer (OD) inspired by desert ants has been proven to be effective for autonomous navigation. However, there are two major challenges for polarization navigation nowadays: inaccurate modeling and obtaining reliable heading information when some sensor channels are blocked. Aiming at these two problems, a tightly-coupled solution for SINS/PNS is proposed in this paper. To obtain a refined integrated navigation system model, the installation errors between the inertial units and PNS, and polarization angle calculation errors are analyzed and modeled for SINS/PNS. Then, to quickly gain the accurate state estimation, an improved iterative unscented filtering method is devised. In particular, the sigma-point updating step with the conditional distribution of high-dimensional Gaussian distribution random variables is developed, which employs partial states to sample in each iteration to reduce the calculation burden. Finally, a detection and elimination mechanism for the abnormal light channels is provided to enhance the reliability of the integration in the presence of a light blockage. The optical channels for navigation are chosen using this mechanism depending on the difference between the predicted and measured incident light intensities. The results in both simulations and outdoor experiments show that the proposed method provides a higher heading estimation accuracy than the traditional SINS/PNS navigation method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article is motivated by the inaccurate modeling and obtaining reliable heading in the presence of light occlusion for the polarization navigation. Various integrated navigation algorithms based on polarized skylight have been widely developed. However, the complex environment and inaccurate modeling limit the application of the polarization navigation. This article gives a novel accurate modeling method and reliable navigation algorithm. Tightly-coupled model with installation errors and the polarization angle error aims to improve the accuracy of the polarization navigation model. The improved iterative unscented Kalman filter is utilized to quickly obtain accurate state estimation. And the light detection and elimination mechanism is used to select normal light channels to navigate in the presence of light blockage. This navigation method can also extend the application of the polarization navigation.

Underwater Doppler-bearing maneuvering target motion analysis based on joint estimated adaptive unscented Kalman filter

Noncooperative maneuvering target motion analysis is one of the challenging tasks in the field of underwater target localization and tracking for passive sonar. Underwater noncooperative targets often perform various maneuvers, and the targets are commonly modeled as a combination of constant-velocity models and coordinate-turn models with unknown turning rates. Traditional algorithms for Doppler-bearing target motion analysis are incapable of processing noncooperative maneuvering targets because the algorithms rely on a priori information of the turning rate and the center frequency. To address these shortcomings, this paper proposes the joint estimated adaptive unscented Kalman filter (JE-AUKF) algorithm. The JE-AUKF places the center frequency and turning rate into the state vector and constructs a time-varying state model that self-adapts to a maneuvering target. The JE-AUKF also introduces a time-varying fading factor into the process noise covariance matrix to improve the tracking performance. Simulations and sea trials are conducted to compare the performance of the JE-AUKF with the iterative unscented Kalman filter, the interacting multiple model-unscented Kalman filter, the interacting multiple model-iterative unscented Kalman filter, and the interacting multiple model-joint estimated unscented Kalman filter. The result shows that the JE-AUKF achieves better tracking performance for noncooperative maneuvering targets.

Optimization-based iterative and robust strategy for spacecraft relative navigation in elliptical orbit

The nonlinear relative dynamics in elliptical orbits and heavy-tailed observation noise can induce a noticeable degradation in navigation accuracy. Although the extensively applied Huber-based M-estimation can cope with non-Gaussian noise, the iterative strategy employed fails to re-linearize the observation model using posterior estimate, and this can induce degradation in filtering efficiency. Considering the inadequate research on iterative and robust strategies, we combine iterated unscented Kalman filter (IUKF) with generalized M-estimation, thereby uniformly and strictly deriving an optimization-based iterative and robust strategy. To approximate the nonlinear observation model more exactly, statistical linearization regression is introduced in the Gauss-newton method, by which the uncertainty induced by approximation errors is compensated in observation noise covariance. Further, we improve the IUKF-based iterative and robust strategy by presenting a novel cost function, where the modified covariance matrix from the previous iteration is incorporated again in the next iteration loop. Comparative studies under non-Gaussian noise show that the novel strategy can facilitate the estimator to achieve higher filtering accuracy, stronger robustness and better consistency. Therefore, the proposed strategy is more suitable for the robust filtering framework.

Robust stable iterated unscented Kalman filter based on maximum correntropy criterion

The Unscented Kalman filter (UKF) based on maximum correntropy criterion (MCC) is robust to heavy-tailed non-Gaussian noise. However, the approximate linear measurement equation obtained by statistical linearization technique may be not accurate enough since it only uses prior information. In this paper, a robust stable iterative maximum correntropy criterion UKF (RS-IMCC-UKF) is proposed by using nonlinear measurement function directly and numerical stability methods. Different from the existing UKF algorithms, we only need to perform one-time unscented transformation in each filtering cycle, reducing the execution time of algorithm. Then a nonlinear enhancement model is constructed to handle predictions and observations simultaneously, which will be included in the cost function of robust MCC. In the process of iterative solution, thanks to the latest iteration values which are used to update the measurement information, RS-IMCC-UKF has more accurate results compared with traditional filters. In order to avoid non-positive definite characteristic in covariance matrix and the inverse operation in ill-conditioned matrix, the hyperbolic QR decomposition and Moore–Penrose pseudo-inversion are introduced to improve the numerical stability of the algorithm. Finally, a target tracking is modeled to verify the effectiveness of the algorithm.

Visual object tracking via iterative ant particle filtering

Visual object tracking remains a challenging task in computer vision although important progress has been made in the past decades. Particle filter (PF) is now a standard framework for solving non-linear/non-Gaussian problems, especially in visual object tracking. This study proposes an ant colony optimisation (ACO)-based iterative PF for object tracking. In the proposed method, the basic idea of ACO is used to simulate the behaviour of a particle moving toward the posterior distribution. Such idea is incorporated into the particle filtering framework in order to overcome the well-known particle impoverishment problem. An iterative unscented Kalman filter is used to design a proposal distribution for particle generation in order to generate better predicted sample states. For the likelihood model, the authors adopt the locality sensitive histogram to model the appearance of the target object, which can better handle the illumination variation during tracking. The experimental results demonstrate that the proposed tracker shows better performance than the other tracking methods.

Iterative Truncated Unscented Particle Filter

The particle filter method is a basic tool for inference on nonlinear partially observed Markov process models. Recently, it has been applied to solve constrained nonlinear filtering problems. Incorporating constraints could improve the state estimation performance compared to unconstrained state estimation. This paper introduces an iterative truncated unscented particle filter, which provides a state estimation method with inequality constraints. In this method, the proposal distribution is generated by an iterative unscented Kalman filter that is supplemented with a designed truncation method to satisfy the constraints. The detailed iterative unscented Kalman filter and truncation method is provided and incorporated into the particle filter framework. Experimental results show that the proposed algorithm is superior to other similar algorithms.

Model based fault diagnosis for drillstring washout using iterated unscented Kalman filter

In this study, a model based fault diagnosis method for drillstring washout is proposed, which uses iterated unscented Kalman filter (IUKF) to detect the emergence of drillstring washout and to estimate washout depth and washout rate. To quantify the changes in pressure-loss and annulus outlet flow rate resulting from drillstring washout, pressure-loss factors and flow rate factor are introduced into the governing equations of circulating drilling fluid under normal drilling condition. Pressure-loss factors and flow rate factor are estimated by IUKF with updated measurements, and the emergence of drillstring washout is automatically detected by confirming the changes in pressure-loss factors and flow rate factor using generalized likelihood ratio test (GLRT). After drillstring washout is detected, continuously updated pressure and flow rate measurements are sent to the identification model of drillstring washout to estimate washout depth and washout rate by IUKF. In addition, the performances of fault diagnosis method for drillstring washout using IUKF and unscented Kalman filter (UKF) are contrasted.Numerical simulation indicates that IUKF and UKF have equivalent performance in drillstring washout detection, while IUKF shows a better performance in washout depth estimation. When using IUKF, the average relative errors of estimated washout depth and washout rate are 2.1% and 1.5% respectively. The errors of estimated washout depth and washout rate are 2.8% and 1.49% when using UKF. Robustness analysis indicates that IUKF is more robust than UKF to measurement noise. IUKF and UKF both have the ability to estimate washout depth and washout rate within the noise scope of 0%–0.8%, while IUKF is more accurate than UKF for washout depth estimation.

Dynamic Illustration of Stranded Wire Helical Springs Using a Modified Bouc–Wen Model

Stranded wire helical spring exhibits a particular dynamic behavior of nonlinear asymmetry hysteretic characteristic due to its special structure. The hysteresis loops with hardening overlap phenomenon are observed through the cycle loading experiments. In recognizing the incapacity of the existing model, a phenomenology-modified Bouc–Wen model, which combines a nonlinear elastic component, a nonlinear amplifier and the pure hysteretic variable of the normalized Bouc–Wen model, is proposed to capture the dynamic behavior. A two-stage identification method is developed to obtain all the parameters of the mode: The parameters of the nonlinear elastic component and the nonlinear amplifier are identified firstly using linear least squares method, and then the IUKF (Iterated Unscented Kalman Filter) algorithm is applied to identify the parameters of the pure hysteretic component. The experiment results corroborate the validity and effectiveness of the proposed model and the identification method.

Constrained Iterated Unscented Kalman Filter for Dynamic State and Parameter Estimation

This paper presents a robust dynamic state estimator for the synchronous generators with unknown parameters. The estimator uses a constrained iterated unscented Kalman filter to estimate the state variables and unknown parameters of a two-axis model of a synchronous generator. The developed estimator's performance is validated using simulations, where the estimator is subjected to arbitrary initialization and large parameter errors. The developed dynamic estimator can potentially be used not only to track the dynamic states but also to detect and identify changes in model parameters with little a priori knowledge about the parameters other than a broad range which can be specified via appropriate constraints.

Application of Kalman Filtering Methods to Online Real-Time Structural Identification: A Comparison Study

System identification refers to the process of building or improving mathematical models of dynamical systems from the observed experimental input–output data. In the area of civil engineering, the estimation of the integrity of a structure under dynamic loadings and during service condition has become a challenge for the engineering community. Therefore, there has been a great deal of attention paid to online and real-time structural identification, especially when input–output measurement data are contaminated by high-level noise. Among real-time identification methods, one of the most successful and widely used algorithms for estimation of system states and parameters is the Kalman filter and its various nonlinear extensions such as extended Kalman filter (EKF), Iterated EKF (IEKF), the recently developed unscented Kalman filter (UKF) and Iterated UKF (IUKF). In this paper, an investigation has been carried out on the aforementioned techniques for their effectiveness and efficiencies through a highly nonlinear single degree of freedom (SDOF) structure as well as a two-storey linear structure. Although IEKF is an improved version of EKF, results show that IUKF generally produces better results in terms of structural parameters and state estimation than UKF and IEKF. Also IUKF is more robust to noise levels compared to the other approaches.

Enhanced particle filter for states and parameters estimation in structural health monitoring applications

In this paper, an iterated square-root central difference Kalman particle filter method (ISRCDKF-PF) is used for the estimation of the state variables and model parameters of nonlinear structural systems. In the current work, we propose to extend our previous work (Mansouri et al. in J Civil Struct Health Monit 5(4):493–508, 2015) to deal with non-parametric Monte Carlo sampling-based method and propose to use an enhanced PF technique which incorporates the latest observations into a prior updating scheme using the ISRCDKF algorithm. Various conventional and state-of-the-art state estimation methods are compared for the estimation performance, namely the unscented Kalman filter (UKF), the square-root central difference Kalman filter (SRCDKF), the iterated unscented Kalman filter (IUKF), the iterated square-root central difference Kalman filter (SRCDKF), the conventional particle filter (PF), the unscented Kalman particle filter (UKF-PF), the SRCDKF-PF, the iterated unscented Kalman particle filter (IUKF-PF) and the developed ISRCDKF-PF, in two comparative studies through two examples, one using synthetic data and the other using simulated three DOF damped system data. In the first comparative study, the state variables are estimated from noisy measurements of these variables, and the comparison of the different estimation techniques is performed by computing the root mean square error (RMSE) of the state with respect to the noise-free data. In the second comparative study, both the state variables and the model parameters are simultaneously estimated, and the impact of the used measurement noise, and number of estimated states/parameters on the performances of the estimation techniques are investigated. The ISRCDKF-PF algorithm consists of a PF based on ISRCDKF to obtain a better importance proposal distribution. This proposal is able to integrate the latest observation into the state density, then it can improve the posteriori density. The results of both comparative study show that PF, UKF-PF, SRCDKF-PF, IUKF-PF and ISRCDKF-PF provide improved estimation performance over the UKF, SRCDKF, IUKF, ISRCDKF. The results also show that ISRCDKF-PF provides improved estimation performance over IUKF-PF, even with abrupt changes in estimated states, and both of them provide better accuracy than the conventional PF, UKF-PF and SRCDKF-PF. These advantages of the ISRCDKF-PF are due to the fact that it uses an optimal proposal distribution which make efficient use of the latest observation by using the ISRCDKF algorithm.

Iterated square root unscented Kalman filter for nonlinear states and parameters estimation: three DOF damped system

Structural health monitoring of civil engineering infrastructure involves uncertainties for damage detection, damage identification, damage classification, sensor optimization, safety, durability, reliability, serviceability, performance based engineering, life-cycle performance, risk management, decision making and so on. For incorporating such uncertainties, several filtering techniques accounting for stochasticity can be implemented utilizing collected data from the structures. In this paper, an iterated square root unscented Kalman filter method is proposed for the estimation of the nonlinear state variables of nonlinear structural systems. Various conventional and state-of-the-art state estimation methods are compared for the estimation performance, namely the unscented Kalman filter (UKF), the square-root unscented Kalman filter (SRUKF), the iterated unscented Kalman filter (IUKF) and the iterated square root unscented Kalman filter (ISRUKF), in two comparative studies. In the first study, UKF, IUKF, SRUKF and ISRUKF methods are utilized at a simple non-linear second order LTI system with the aim to predict a two state variables, and to estimate two model parameters. In the second study, UKF, IUKF, SRUKF and ISRUKF techniques are utilized to a complex three degree of freedom spring-mass-dashpot system to predict the displacements and the velocities state variables. They are also used to estimate the model’s hysteretic parameters. Furthermore, the effect of practical challenges (e.g., measurement noise, number of states and parameters to be estimated) on the performances of UKF, IUKF, SRUKF and ISRUKF were investigated. The results of both comparative studies reveal that the ISRUKF method provides a better estimation accuracy than the IUKF method; while both methods provide improved accuracy over the UKF and SRUKF methods. The benefit of the ISRUKF method lies in its ability to provide accuracy related advantages over other estimation methods since it re-linearizes the measurement equation by iterating an approximate maximum a posteriori (MAP) estimate around the updated state, instead of relying on the predicted state. The results of the comparative studies show also that, for all the techniques, estimating more model parameters affects the estimation accuracy as well as the convergence of the estimated states and parameters. The ISRUKF, however, still provides advantages over other methods in terms of the estimation accuracy and convergence.

IUKF neural network modeling for FOG temperature drift

A novel neural network based on iterated unscented Kalman filter (IUKF) algorithm is established to model and compensate for the fiber optic gyro (FOG) bias drift caused by temperature. In the network, FOG temperature and its gradient are set as input and the FOG bias drift is set as the expected output. A 2-5-1 network trained with IUKF algorithm is established. The IUKF algorithm is developed on the basis of the unscented Kalman filter (UKF). The weight and bias vectors of the hidden layer are set as the state of the UKF and its process and measurement equations are deduced according to the network architecture. To solve the unavoidable estimation deviation of the mean and covariance of the states in the UKF algorithm, iterative computation is introduced into the UKF after the measurement update. While the measurement noise R is extended into the state vectors before iteration in order to meet the statistic orthogonality of estimate and measurement noise. The IUKF algorithm can provide the optimized estimation for the neural network because of its state expansion and iteration. Temperature rise (-20-20°C) and drop (70-20°C) tests for FOG are carried out in an attemperator. The temperature drift model is built with neural network, and it is trained respectively with BP, UKF and IUKF algorithms. The results prove that the proposed model has higher precision compared with the back-propagation (BP) and UKF network models.

Nonorthogonal problem in iterated unscented Kalman filter for passive tracking

AbstractThe iterated unscented Kalman filter (IUKF) is a promising nonlinear tracking algorithm. However, we find that the IUKF has poor performance in tracking accuracy and will diverge easily when the variance of observation noise is large, because the iterated state prediction is nonorthogonal to the current observation after the first iteration. This will increase the proportion of current observation in state estimate and lead to the tendency for the final iteration result to be closer to the observation compared with the optimal solution, which is a phenomenon termed the nonorthogonal problem here. We solve this problem by augmenting the state vector with the process and observation noise vectors and slightly reconstructing the IUKF formula. Simulation results show that the proposed algorithm has better tracking performance than IUKF. © 2013 Institute of Electrical Engineers of Japan. Published by John Wiley &amp; Sons, Inc.

Parameter Estimation of Biological Phenomena: An Unscented Kalman Filter Approach

Recent advances in high-throughput technologies for biological data acquisition have spurred a broad interest in the construction of mathematical models for biological phenomena. The development of such mathematical models relies on the estimation of unknown parameters of the system using the time-course profiles of different metabolites in the system. One of the main challenges in the parameter estimation of biological phenomena is the fact that the number of unknown parameters is much more than the number of metabolites in the system. Moreover, the available metabolite measurements are corrupted by noise. In this paper, a new parameter estimation algorithm is developed based on the stochastic estimation framework for nonlinear systems, namely the unscented Kalman filter (UKF). A new iterative UKF algorithm with covariance resetting is developed in which the UKF algorithm is applied iteratively to the available noisy time profiles of the metabolites. The proposed estimation algorithm is applied to noisy time-course data synthetically produced from a generic branched pathway as well as real time-course profile for the Cad system of E. coli. The simulation results demonstrate the effectiveness of the proposed scheme.

Maximum Likelihood-Based Iterated Divided Difference Filter for Nonlinear Systems from Discrete Noisy Measurements

A new filter named the maximum likelihood-based iterated divided difference filter (MLIDDF) is developed to improve the low state estimation accuracy of nonlinear state estimation due to large initial estimation errors and nonlinearity of measurement equations. The MLIDDF algorithm is derivative-free and implemented only by calculating the functional evaluations. The MLIDDF algorithm involves the use of the iteration measurement update and the current measurement, and the iteration termination criterion based on maximum likelihood is introduced in the measurement update step, so the MLIDDF is guaranteed to produce a sequence estimate that moves up the maximum likelihood surface. In a simulation, its performance is compared against that of the unscented Kalman filter (UKF), divided difference filter (DDF), iterated unscented Kalman filter (IUKF) and iterated divided difference filter (IDDF) both using a traditional iteration strategy. Simulation results demonstrate that the accumulated mean-square root error for the MLIDDF algorithm in position is reduced by 63% compared to that of UKF and DDF algorithms, and by 7% compared to that of IUKF and IDDF algorithms. The new algorithm thus has better state estimation accuracy and a fast convergence rate.

Marginalised iterated unscented Kalman filter

In this study, the authors investigate the role of iteration in the unscented Kalman filter (UKF) with additive measurement noise and propose a novel filter referred to as the marginalised iterated unscented Kalman filter (MIUKF). In each iteration of the MIUKF, the new sigma points are regenerated and propagated through the same measurement update strategy as the UKF. In order to guarantee the state to be statistically independent with the measurement noise, the state variables are augmented with the measurement noise. Since the measurement noise is additive, the measurement function is conditionally linear of the augmented state, then the marginalised unscented transformation is investigated to reduce the computational burden. Compared with the traditional iterated UKF, the MIUKF is more rigorous in terms of efficiency and accuracy. The simulation results agree well with the theoretical analyses.

In Vitro Identification of Four-Element Windkessel Models Based on Iterated Unscented Kalman Filter

Mock circulatory loops (MCLs) have been widely used to test left ventricular assist devices. The hydraulic properties of the mock systemic arterial system are usually described by two alternative four-element windkessel (W4) models. Compared with three-element windkessel model, their parameters, especially the inertial term, are much more difficult to estimate. In this paper, an estimator based on the iterated unscented Kalman filter (IUKF) algorithm is proposed to identify model parameters. Identifiability of these parameters for different measurements is described. Performance of the estimator for different model structures is first evaluated using numerical simulation data contaminated with artificial noise. An MCL is developed to test the proposed algorithm. Parameter estimates for different models are compared with the calculated values derived from the mechanical and hydraulic properties of the MCL to validate model structures. In conclusion, the W4 model with an inertance and an aortic characteristic resistance arranged in series is proposed to represent the mock systemic arterial system. Once model structure is appropriately selected, IUKF can provide reasonable estimation accuracy in a limited time and may be helpful for future clinical applications.

Real-time nonlinear structural system identification via iterated unscented Kalman filter

Structural system identification has attracted much attention in the structural dynamics field over the past decades. The unscented Kalman filter (UKF) is often used to deal with nonlinear system identification in civil engineering field. In practices, applying a UKF to highly nonlinear structural systems is not a trivial task, particularly those subject to severe loading. Recently, a new technique, the iterated unscented Kalman filter (IUKF) is applicable to highly nonlinear systems. In this paper, the IUKF is applied for nonlinear structural system identification (NSSI). Experimental results show that the IUKF produces better state estimation and parameter identification than the UKF, and the IUKF is also more robust to measurement noise levels.