• Journal of Institute of Control, Robotics and Systems
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• v.20 no.3
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• pp.277-288
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• 2014

This article reviews various state estimation methods for nonlinear systems, particularly with a perspective of a process control engineer. Nonlinear state estimation methods can be classified into the following two categories: stochastic approaches and deterministic approaches. The current review compares the Bayesian approach, which is mainly a stochastic approach, and the MHE (Moving Horizon Estimation) approach, which is mainly a deterministic approach. Though both methods are reviewed, emphasis is given to the latter as it is particularly well-suited to highly nonlinear systems with slow sampling rates, which are common in chemical process applications. Recent developments in underlying theories and supporting numerical algorithms for MHE are reviewed. Thanks to these developments, applications to large-scale and complex chemical processes are beginning to show up but they are still limited at this point owing to the high numerical complexity of the method.

• Advances in aircraft and spacecraft science
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• v.7 no.6
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• pp.495-516
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• 2020

Nonlinear state estimation is a desirable and required technique for many situations in engineering (e.g., aircraft/spacecraft tracking, space situational awareness, collision warning, radar tracking, etc.). Due to high standards on performance in these applications, in the last few decades, there was an increasing demand for methods that are able to provide more accurate results. However, because of the mathematical complexity introduced by the nonlinearities of the models, the nonlinear state estimation uses techniques that, in practice, are not so well-established which, leads to sub-optimal results. It is important to take into account that each method will have advantages and limitations when facing specific environments. The main objective of this paper is to provide a comprehensive overview and interpretation of the most well-known methods for nonlinear state estimation with Gaussian priors. In particular, the Kalman filtering methods: EKF (Extended Kalman Filter), UKF (Unscented Kalman Filter), CKF (Cubature Kalman Filter) and EnKF (Ensemble Kalman Filter) with an aerospace perspective.

• Journal of the Korean Statistical Society
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• v.32 no.4
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• pp.385-399
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• 2003

We first introduce the quasi-score estimating function and applied the quasi-score estimating function to nonlinear time series models. We proposed the M quasi-score estimating functions bounded functions for the quasi-score estimating functions. Also, we investigated the asymptotic properties of quasi-likelihood estimators and M quasi-likelihood estimators. Simulation results show that the M quasi-likelihood estimators work better than the least squares estimators under the heavy-tailed distributions

• East Asian mathematical journal
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• v.14 no.2
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• pp.421-427
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• 1998

In this paper we provide sufficient conditions which ensure the strong consistency of $L_p$-norm estimation in nonlinear regression model when the probability distribution of the errors term is symmetric about zero. The least absolute deviation and least square estimation are discussed as special cases of the proposed estimation.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.42 no.10
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• pp.816-822
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• 2014

The estimation of the angular rate of a satellite has been discussed. A nonlinear observer has been proposed based on the state-dependent Riccati equation method. A sufficient stability condition for the convergence of estimation error has been presented. This condition is related to a state-dependent algebraic Riccati equation. It has been derived by transforming nonlinear error dynamics into a Lipschitz nonlinearity. An observer gain is obtained from this condition. Numerical simulations are presented to verify the proposed method.

• International Journal of Control, Automation, and Systems
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• v.4 no.2
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• pp.165-171
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• 2006

This paper proposes a data fusion algorithm of nonlinear multi sensor dynamic systems of synchronous sampling based on filtering step by step. Firstly, the object state variable at the next time index can be predicted by the previous global information with the systems, then the predicted estimation can be updated in turn by use of the extended Kalman filter when all of the observations aiming at the target state variable arrive. Finally a fusion estimation of the object state variable is obtained based on the system global information. Synchronously, we formulate the new algorithm and compare its performances with those of the traditional nonlinear centralized and distributed data fusion algorithms by the indexes that include the computational complexity, data communicational burden, time delay and estimation accuracy, etc.. These compared results indicate that the performance from the new algorithm is superior to the performances from the two traditional nonlinear data fusion algorithms.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.2
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• pp.276-283
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• 2012

In this paper, a practical quasi-optimal DOA(direction of arrival) estimator is proposed in order to develop a one-axis gimbaled ultrasonic source tracker for mobile robot applications. With help of the gimbal structure, the ultrasonic moving source tracking problem can be simply reduced to the DOA estimation. The DOA estimation is known as one of the representative long-pending nonlinear filtering problems, but the conventional nonlinear filters might be restrictive in many actual situations because it cannot guarantee the reliable performance due to the use of nonlinear signal model. This motivates us to reformulate the DOA estimation problem in the linear robust state estimation setting. Based on the assumption that the received ultrasonic signals are noisy sinusoids satisfying linear prediction property, a linear uncertain measurement model is newly derived. To avoid the DOA estimation performance degradation caused by the stochastic parameter uncertainty contained in the linear measurement model, the recently developed NCRKF (non-conservative robust Kalman filter) scheme [1] is utilized. The proposed linear DOA estimator provides excellent DOA estimation performance and it is suitable for real-time implementation for its linear recursive filter structure. The effectiveness of the suggested DOA estimation scheme is demonstrated through simulations and experiments.

• Proceedings of the KSME Conference
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• 2001.06b
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• pp.565-570
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• 2001

Vehicle dynamics control (VDC) system requires more information on driving conditions compared with ABS and/or TCS. In order to develop the VDC system, tire slip angles, vehicle side-slip angle, and vehicle lateral velocity as well as road friction coefficient are needed. Since there are not any cheap and reliable sensors, recent researches on parameter estimation have given rise to a number of parameter estimation techniques. This paper presents new vehicle model to estimate vehicle's yaw rate. This model is improved from the conventional 2 degrees of freedom vehicle model, so-called bicycle model, taking nonlinear effects into account. These nonlinear effects are: (i) tyre nonlinearity; (ii) lateral load transfer during cornering; (iii) variable gear ratio with respect to vehicle velocity. Estimation results are validated with the experimental results.

• Journal of Institute of Control, Robotics and Systems
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• v.12 no.2
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• pp.93-100
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• 2006

In this paper, a new-type Extended Kalman Filter (EKF) is proposed as a robust nonlinear filter for a stochastic nonlinear system. The original EKF is widely used for various nonlinear system applications. But it is fragile to its estimation errors because they give rise to linearization errors that affect the system mode1 as the modeling errors. The linearization errors are nonlinear functions of the estimation errors therefore it is very difficult to obtain the accurate error covariance of the EKF using the linear form. The inaccurately estimated error covariance hinders the EKF from being a sub-optimal estimator. The proposed filter tries to obtain the upper bound of the error covariance tolerating the uncertainty of the error covariance instead of trying to obtain the accurate one. It treats the linearization errors as uncertain modeling errors that can be handled by the robust linear filtering. In order to be more robust to the estimation errors than the original EKF, the proposed filter minimizes the upper bound like the robust linear filter that is applied to the linear model with uncertainty. The in-flight alignment problem of the inertial navigation system with GPS position measurements is a good example that the proposed robust filter is applicable to. The simulation results show the efficiency of the proposed filter in the robustness to initial estimation errors of the filter.

• Smart Structures and Systems
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• v.24 no.2
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• pp.209-221
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• 2019

The classical Kalman filter (KF) provides a practical and efficient way for state estimation. It is, however, not applicable when the external excitations applied to the structures are unknown. Moreover, it is known the classical KF is only suitable for linear systems and can't handle the nonlinear cases. The aim of this paper is to extend the classical KF approach to circumvent the aforementioned limitations for the joint estimation of structural states and the unknown inputs. On the basis of the scheme of the classical KF, analytical recursive solution of an improved KF approach is derived and presented. A revised form of observation equation is obtained basing on a projection matrix. The structural states and the unknown inputs are then simultaneously estimated with limited measurements in linear or nonlinear systems. The efficiency and accuracy of the proposed approach is verified via a five-story shear building, a simply supported beam, and three sorts of nonlinear hysteretic structures. The shaking table tests of a five-story building structure are also employed for the validation of the robustness of the proposed approach. Numerical and experimental results show that the proposed approach can not only satisfactorily estimate structural states, but also identify unknown loadings with acceptable accuracy for both linear and nonlinear systems.