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Journal articles on the topic 'Nonlinear Estimation'

Author: Grafiati

Published: 4 June 2021

Last updated: 16 June 2025

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1

Liu, Bing, Zhen Chen, Xiangdong Liu, and Fan Yang. "An Efficient Nonlinear Filter for Spacecraft Attitude Estimation." International Journal of Aerospace Engineering 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/540235.

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Increasing the computational efficiency of attitude estimation is a critical problem related to modern spacecraft, especially for those with limited computing resources. In this paper, a computationally efficient nonlinear attitude estimation strategy based on the vector observations is proposed. The Rodrigues parameter is chosen as the local error attitude parameter, to maintain the normalization constraint for the quaternion in the global estimator. The proposed attitude estimator is performed in four stages. First, the local attitude estimation error system is described by a polytopic linear model. Then the local error attitude estimator is designed with constant coefficients based on the robustH2filtering algorithm. Subsequently, the attitude predictions and the local error attitude estimations are calculated by a gyro based model and the local error attitude estimator. Finally, the attitude estimations are updated by the predicted attitude with the local error attitude estimations. Since the local error attitude estimator is with constant coefficients, it does not need to calculate the matrix inversion for the filter gain matrix or update the Jacobian matrixes online to obtain the local error attitude estimations. As a result, the computational complexity of the proposed attitude estimator reduces significantly. Simulation results demonstrate the efficiency of the proposed attitude estimation strategy.

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2

Shadmehr, Reza, and David Z. D'Argenio. "A Neural Network for Nonlinear Bayesian Estimation in Drug Therapy." Neural Computation 2, no. 2 (1990): 216–25. http://dx.doi.org/10.1162/neco.1990.2.2.216.

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The feasibility of developing a neural network to perform nonlinear Bayesian estimation from sparse data is explored using an example from clinical pharmacology. The problem involves estimating parameters of a dynamic model describing the pharmacokinetics of the bronchodilator theophylline from limited plasma concentration measurements of the drug obtained in a patient. The estimation performance of a backpropagation trained network is compared to that of the maximum likelihood estimator as well as the maximum a posteriori probability estimator. In the example considered, the estimator prediction errors (model parameters and outputs) obtained from the trained neural network were similar to those obtained using the nonlinear Bayesian estimator.

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3

Haigh, John, and Gavin J. S. Ross. "Nonlinear Estimation." Mathematical Gazette 75, no. 473 (1991): 393. http://dx.doi.org/10.2307/3619550.

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4

Kushary, Debashis, and Gavin J. S. Ross. "Nonlinear Estimation." Technometrics 34, no. 1 (1992): 108. http://dx.doi.org/10.2307/1269572.

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5

Sandry, Thomas D., and Gavin J. S. Ross. "Nonlinear Estimation." Technometrics 34, no. 3 (1992): 356. http://dx.doi.org/10.2307/1270045.

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6

Weisberg, Sanford, and Gavin J. S. Ross. "Nonlinear Estimation." Journal of the American Statistical Association 86, no. 416 (1991): 1142. http://dx.doi.org/10.2307/2290540.

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7

Liese, F., and G. J. S. Ross. "Nonlinear Estimation." Biometrics 47, no. 3 (1991): 1202. http://dx.doi.org/10.2307/2532680.

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8

Shimizu, Chihiro, Koji Karato, and Kiyohiko Nishimura. "Nonlinearity of housing price structure." International Journal of Housing Markets and Analysis 7, no. 4 (2014): 459–88. http://dx.doi.org/10.1108/ijhma-10-2013-0055.

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Purpose – The purpose of this article, starting from linear regression, was to estimate a switching regression model, nonparametric model and generalized additive model as a semi-parametric model, perform function estimation with multiple nonlinear estimation methods and conduct comparative analysis of their predictive accuracy. The theoretical importance of estimating hedonic functions using a nonlinear function form has been pointed out in ample previous research (e.g. Heckman et al. (2010). Design/methodology/approach – The distinctive features of this study include not only our estimation of multiple nonlinear model function forms but also the method of verifying predictive accuracy. Using out-of-sample testing, we predicted and verified predictive accuracy by performing random sampling 500 times without replacement for 9,682 data items (the same number used in model estimation), based on data for the years before and after the year used for model estimation. Findings – As a result of estimating multiple models, we believe that when it comes to hedonic function estimation, nonlinear models are superior based on the strength of predictive accuracy viewed in statistical terms and on graphic comparisons. However, when we examined predictive accuracy using out-of-sample testing, we found that the predictive accuracy was inferior to linear models for all nonlinear models. Research limitations/implications – In terms of the reason why the predictive accuracy was inferior, it is possible that there was an overfitting in the function estimation. Because this research was conducted for a specific period of time, it needs to be developed by expanding it to multiple periods over which the market fluctuates dynamically and conducting further analysis. Practical implications – Many studies compare predictive accuracy by separating the estimation model and verification model using data at the same point in time. However, when attempting practical application for auto-appraisal systems and the like, it is necessary to estimate a model using past data and make predictions with respect to current transactions. It is possible to apply this study to auto-appraisal systems. Social implications – It is recognized that housing price fluctuations caused by the subprime crisis had a massive impact on the financial system. The findings of this study are expected to serve as a tool for measuring housing price fluctuation risks in the financial system. Originality/value – While the importance of nonlinear estimation when estimating hedonic functions has been pointed out in theoretical terms, there is a noticeable lag when it comes to testing based on actual data. Given this, we believe that our verification of nonlinear estimation’s validity using multiple nonlinear models is significant not just from an academic perspective – it may also have practical applications.

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9

Siriopoulos, Costas, and Alexandros Leontitsis. "Nonlinear Noise Estimation in International Capital Markets." Multinational Finance Journal 6, no. 1 (2002): 43–63. http://dx.doi.org/10.17578/6-1-3.

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10

Eglit, Y. Y., К. Y. Eglite, A. R. Balybin, and A. S. Gramatskiy. "ALGORITHM FOR ESTIMATING PARAMETERS OF THE NONLINEAR SYSTEM." System analysis and logistics 2, no. 28 (2021): 52–57. http://dx.doi.org/10.31799/2077-5687-2021-2-52-57.

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The article presents an algorithm for estimating the parameters of nonlinear systems, which is one of the main tasks of classical statistical analysis. The parametric estimation of the coefficients of models that are based on experimental data is the basis. The basis for evaluating parameters. Key words: estimation algorithm, nonlinear systems, statistical analysis, nonlinear function, experiment, models.

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11

Note, Yuya, Masahito Watanabe, Hiroaki Yoshimura, Takaharu Yaguchi, and Toshiaki Omori. "Sparse Estimation for Hamiltonian Mechanics." Mathematics 12, no. 7 (2024): 974. http://dx.doi.org/10.3390/math12070974.

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Estimating governing equations from observed time-series data is crucial for understanding dynamical systems. From the perspective of system comprehension, the demand for accurate estimation and interpretable results has been particularly emphasized. Herein, we propose a novel data-driven method for estimating the governing equations of dynamical systems based on machine learning with high accuracy and interpretability. The proposed method enhances the estimation accuracy for dynamical systems using sparse modeling by incorporating physical constraints derived from Hamiltonian mechanics. Unlike conventional approaches used for estimating governing equations for dynamical systems, we employ a sparse representation of Hamiltonian, allowing for the estimation. Using noisy observational data, the proposed method demonstrates a capability to achieve accurate parameter estimation and extraction of essential nonlinear terms. In addition, it is shown that estimations based on energy conservation principles exhibit superior accuracy in long-term predictions. These results collectively indicate that the proposed method accurately estimates dynamical systems while maintaining interpretability.

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12

Sun, Yanxiu, and Hong Li. "An estimation method for sensor faults based on observer in interconnected systems." PLOS ONE 19, no. 3 (2024): e0296848. http://dx.doi.org/10.1371/journal.pone.0296848.

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In this research, a class of nonlinear interconnected systems with sensor faults were investigated and an estimation method was proposed for system sensor faults based on the theory of system state reconstruction. Considering sensor fault vectors in nonlinear interconnected systems, this method constructed a generalized nonlinear interconnected system, whose state was designed by augmenting the original system state and fault vectors, which provides a foundation for fault estimation of nonlinear interconnected systems. An augmented observer was developed by equivalent transformation of generalized interconnected system, so as to realize robust estimations of sensor faults in interconnected systems. This estimation method took into account the effect of external disturbance of the system on fault estimation and estimated the convergence speed of error system; the developed method also considered the convenience of solving the gain matrix of the augmented observer, which was beneficial to the realization of sensor fault estimation in interconnected system. The sensor estimation method proposed in the paper has the advantages of robustness in fault estimation,rapidity in error convergence, and convenience in solving the gain matrix. Finally, the state and sensor fault estimation errors of two interconnected systems can both approach 0 within 10 seconds, thus achieving the purpose of fault estimation. Two simulation experiments verified the effectiveness of the proposed fault estimation method and provided a reference for the fault estimation method of nonlinear interconnected systems with disturbance.

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13

Wasim, Muhammad, Ahsan Ali, Muhammad Mateen Afzal Awan, and Inam ul Hasan Shaikh. "Estimation of airship states and model uncertainties using nonlinear estimators." Mehran University Research Journal of Engineering and Technology 43, no. 1 (2024): 55. http://dx.doi.org/10.22581/muet1982.2401.1613.

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This Airships are lighter than air vehicles and due to their growing number of applications, they are becoming attractive for the research community. Most of the applications require an airship autonomous flight controller which needs an accurate model and state information. Usually, airship states are affected by noise and states information can be lost in the case of sensor's faults, while airship model is affected by model inaccuracies and model uncertainties. This paper presents the application of nonlinear and Bayesian estimators for estimating the states and model uncertainties of neutrally buoyant airship. It is considered that minimum sensor measurements are available, and data is corrupted with process and measurement noise. A novel lumped model uncertainty estimation approach is formulated where airship model is augmented with six extra state variables capturing the model uncertainty of the airship. The designed estimator estimates the airship model uncertainty along with its states. Nonlinear estimators, Extended Kalman Filter and Unscented Kalman Filter are designed for estimating airship attitude, linear velocities, angular velocities and model uncertainties. While Particle filter is designed for the estimation of airship attitude, linear velocities and angular velocities. Simulations have been performed using nonlinear 6-DOF simulation model of experimental airship for assessing the estimator performances. 1−𝜎 uncertainty bound and error analysis have been performed for the validation. A comparative study of the estimator's performances is also carried out.

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Liu, Yu-Sun, Shingchern You, and Yu-Chun Lai. "Machine Learning-Based Channel Estimation Techniques for ATSC 3.0." Information 15, no. 6 (2024): 350. http://dx.doi.org/10.3390/info15060350.

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Channel estimation accuracy significantly affects the performance of orthogonal frequency-division multiplexing (OFDM) systems. In the literature, there are quite a few channel estimation methods. However, the performances of these methods deteriorate considerably when the wireless channels suffer from nonlinear distortions and interferences. Machine learning (ML) shows great potential for solving nonparametric problems. This paper proposes ML-based channel estimation methods for systems with comb-type pilot patterns and random pilot symbols, such as ATSC 3.0. We compare their performances with conventional channel estimations in ATSC 3.0 systems for linear and nonlinear channel models. We also evaluate the robustness of the ML-based methods against channel model mismatch and signal-to-noise ratio (SNR) mismatch. The results show that the ML-based channel estimations achieve good mean squared error (MSE) performance for linear and nonlinear channels if the channel statistics used for the training stage match those of the deployment stage. Otherwise, the ML estimation models may overfit the training channel, leading to poor deployment performance. Furthermore, the deep neural network (DNN)-based method does not outperform the linear channel estimation methods in nonlinear channels.

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15

Hawkes, R. M. "Optimal Nonlinear Estimation." IFAC Proceedings Volumes 18, no. 5 (1985): 903–8. http://dx.doi.org/10.1016/s1474-6670(17)60676-1.

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16

Liu, Yingjie, and Dawei Cui. "Vehicle State Estimation Based on Adaptive Fading Unscented Kalman Filter." Mathematical Problems in Engineering 2022 (April 26, 2022): 1–11. http://dx.doi.org/10.1155/2022/7355110.

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Aiming at solving problem of vehicle state estimation, an adaptive fading unscented Kalman filter(AFUKF) algorithm was proposed. Based on this purpose, a 7-DOF nonlinear vehicle model with the Pacejka nonlinear tire model was established firstly. Then, the vehicle state estimator based on Kalman filter was designed to solve the problem of vehicle state estimation. The simulation verification shows the effectiveness and reliability of the designed estimator for vehicle state estimation. Compared with other traditional methods, the calculation accuracy is higher for the AFUKF algorithm to solve the problem of vehicle state estimation. The study can help drivers easily identify key state estimation in safe driving area.

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Liu, Yingjie, and Dawei Cui. "Vehicle State Estimation Based on Adaptive Fading Unscented Kalman Filter." Mathematical Problems in Engineering 2022 (April 26, 2022): 1–11. http://dx.doi.org/10.1155/2022/7355110.

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Aiming at solving problem of vehicle state estimation, an adaptive fading unscented Kalman filter(AFUKF) algorithm was proposed. Based on this purpose, a 7-DOF nonlinear vehicle model with the Pacejka nonlinear tire model was established firstly. Then, the vehicle state estimator based on Kalman filter was designed to solve the problem of vehicle state estimation. The simulation verification shows the effectiveness and reliability of the designed estimator for vehicle state estimation. Compared with other traditional methods, the calculation accuracy is higher for the AFUKF algorithm to solve the problem of vehicle state estimation. The study can help drivers easily identify key state estimation in safe driving area.

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18

Dermanis, Athanasios, and Fernando Sansó. "Nonlinear estimation problems for nonlinear models." manuscripta geodaetica 20, no. 2 (1995): 110–22. http://dx.doi.org/10.1007/bf03655360.

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19

Nguyễn, Thành, Mai Thanh Hai, Nguyen Huu Tho, Nguyen Thi Thao, and Nguyen Tat Nam. "Expectation maximization channel estimation for nonlinear OFDM systems." Journal of Military Science and Technology, no. 81 (August 26, 2022): 31–43. http://dx.doi.org/10.54939/1859-1043.j.mst.81.2022.31-43.

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This paper introduces the expectation maximization (EM)-based channel estimation for the high power amplifier (HPA)-incurred nonlinear orthogonal frequency division multiplexing (OFDM) systems based on the linearization using extended Bussgang decomposition. Analyses and numerical simulations show that the proposed algorithm only requires reasonable computation complexity with relatively small number of iterations while vastly improves the estimation performance compared to the other conventional estimation methods such as least square error (LSE) or minimum mean square error (MMSE) applied to such system. Moreover, the EM-LSE estimator could give almost the same performance as the EM-MMSE counterpart while does not require channel statistics, forming a robust estimator for both fading and nonlinear channels with reduced computation complexity. This makes the estimator more applicable.

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20

Cheng, Guorui, Jingang Liu, and Shenmin Song. "Event-Triggered State Filter Estimation for Nonlinear Systems with Packet Dropout and Correlated Noise." Sensors 24, no. 3 (2024): 769. http://dx.doi.org/10.3390/s24030769.

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This paper begins by exploring the challenge of event-triggered state estimations in nonlinear systems, grappling with packet dropout and correlated noise. A communication mechanism is introduced that determines whether to transmit measurement values based on whether event-triggered conditions are violated, thereby minimizing redundant communication data. In designing the filter, noise decorrelation is initially conducted, followed by the integration of the event-triggered mechanism and the unreliable network transmission system for state estimator development. Subsequently, by combining the three-degree spherical–radial cubature rule, the numerical implementation steps of the proposed state estimation framework are outlined. The performance estimation analysis highlights that by adjusting the event-triggered threshold appropriately, the estimation performance and transmission rate can be effectively balanced. It is established that when there is a lower bound on the packet dropout rate, the covariance matrix of the state estimation error remains bounded, and the stochastic stability of the state estimation error is also confirmed. Ultimately, the algorithm and conclusions that are proposed in this paper are validated through a simulation example of a target tracking system.

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21

Morimoto, Jun, and Kenji Doya. "Reinforcement Learning State Estimator." Neural Computation 19, no. 3 (2007): 730–56. http://dx.doi.org/10.1162/neco.2007.19.3.730.

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In this study, we propose a novel use of reinforcement learning for estimating hidden variables and parameters of nonlinear dynamical systems. A critical issue in hidden-state estimation is that we cannot directly observe estimation errors. However, by defining errors of observable variables as a delayed penalty, we can apply a reinforcement learning frame-work to state estimation problems. Specifically, we derive a method to construct a nonlinear state estimator by finding an appropriate feedback input gain using the policy gradient method. We tested the proposed method on single pendulum dynamics and show that the joint angle variable could be successfully estimated by observing only the angular velocity, and vice versa. In addition, we show that we could acquire a state estimator for the pendulum swing-up task in which a swing-up controller is also acquired by reinforcement learning simultaneously. Furthermore, we demonstrate that it is possible to estimate the dynamics of the pendulum itself while the hidden variables are estimated in the pendulum swing-up task. Application of the proposed method to a two-linked biped model is also presented.

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22

Chen, Lijuan, Zihao Zhang, Yapeng Zhang, Xiaoshuang Xiong, Fei Fan, and Shuangbao Ma. "Research on Projection Filtering Method Based on Projection Symmetric Interval and Its Application in Underwater Navigation." Symmetry 13, no. 9 (2021): 1715. http://dx.doi.org/10.3390/sym13091715.

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For non-linear systems (NLSs), the state estimation problem is an essential and important problem. This paper deals with the nonlinear state estimation problems in nonlinear and non-Gaussian systems. Recently, the Bayesian filter designer based on the Bayesian principle has been widely applied to the state estimation problem in NLSs. However, we assume that the state estimation models are nonlinear and non-Gaussian, applying traditional, typical nonlinear filtering methods, and there is no precise result for the system state estimation problem. Therefore, the larger the estimation error, the lower the estimation accuracy. To perfect the imperfections, a projection filtering method (PFM) based on the Bayesian estimation approach is applied to estimate the state. First, this paper constructs its projection symmetric interval to select the basis function. Second, the prior probability density of NLSs can be projected into the basis function space, and the prior probability density solution can be solved by using the Fokker–Planck Equation (FPE). According to the Bayes formula, the proposed estimator utilizes the basis function in projected space to iteratively calculate the posterior probability density; thus, it avoids calculating the partial differential equation. By taking two illustrative examples, it is also compared with the traditional UKF and PF algorithm, and the numerical experiment results show the feasibility and effectiveness of the novel nonlinear state estimation filter algorithm.

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23

Zhang, Yuexin, and Lihui Wang. "Real-Time Disturbances Estimating and Compensating of Nonlinear Dynamic Model for Underwater Vehicles." Mathematical Problems in Engineering 2018 (September 24, 2018): 1–16. http://dx.doi.org/10.1155/2018/3073072.

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To reduce the deviation caused by the stochastic environmental disturbances, estimating these disturbances is required to compensate the navigation system. Based on the idea of Kalman filter using least-squares algorithm for optimal estimation, a nonlinear disturbances estimator which can be perfectly integrated with cubature Kalman filter (CKF) is proposed. For the nonlinear disturbances estimator, the disturbances are estimated by gain matrix, innovation sequences, and innovation covariance generated by CKF. The disturbances estimating and compensating algorithm consists of three parts. Firstly, the navigation system state space model is established based on nonlinear dynamic model of six degrees of freedom. Secondly, the external disturbances are estimated by using CKF and a nonlinear estimator. Finally, the disturbances compensation is carried out by improving the system state equation. In view of the uncertainty of the dynamic model and the randomness of external disturbances, numerical simulation experiments are conducted in the circumstances of sinusoidal disturbances, random disturbances, and uncertain model parameters. The results demonstrate that the proposed method can estimate disturbances effectively and improves navigation accuracy significantly.

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24

Li, Rui, and Youming Liu. "Wavelet Optimal Estimations for Density Functions under Severely Ill-Posed Noises." Abstract and Applied Analysis 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/260573.

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Motivated by Lounici and Nickl's work (2011), this paper considers the problem of estimation of a densityfbased on an independent and identically distributed sampleY1,…,Ynfromg=f*φ. We show a wavelet optimal estimation for a density (function) over Besov ballBr,qs(L)andLprisk (1≤p<∞) in the presence of severely ill-posed noises. A wavelet linear estimation is firstly presented. Then, we prove a lower bound, which shows our wavelet estimator optimal. In other words, nonlinear wavelet estimations are not needed in that case. It turns out that our results extend some theorems of Pensky and Vidakovic (1999), as well as Fan and Koo (2002).

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25

Ghahramani, M., and A. Thavaneswaran. "Nonlinear recursive estimation of volatility via estimating functions." Journal of Statistical Planning and Inference 142, no. 1 (2012): 171–80. http://dx.doi.org/10.1016/j.jspi.2011.07.006.

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26

Schilhabel, T. E., and C. J. Harris. "Nonlinear Estimation of Population Coded Nonlinear Dynamics." IFAC Proceedings Volumes 31, no. 29 (1998): 70. http://dx.doi.org/10.1016/s1474-6670(17)38357-x.

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27

Zhang, Zhenglei, Jirong Wang, Junwei Gao, and Huabo Liu. "Robust State Estimation for T–S Fuzzy Markov Jump Systems." Mathematics 11, no. 2 (2023): 487. http://dx.doi.org/10.3390/math11020487.

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The problem of robust state estimation for a class of uncertain nonlinear systems with Markov jump is investigated. The uncertain nonlinear system under consideration is represented by the Takagi–Sugeno (T–S) fuzzy model because it is difficult to describe. Firstly, different from the traditional T–S fuzzy modeling method, the deviation of the linear system approaching a nonlinear system is considered, which is represented as a model error in system modeling. Secondly, through a robust state estimation method based on the sensitivity penalty, we develop a robust state estimator for linear subsystems, and the fuzzy robust state estimator is obtained by fuzzy rules. Thirdly, the stability and boundedness of the fuzzy robust state estimator are proved under the assumption conditions to ensure the reliability of the obtained estimator. Finally, some numerical examples are given to verify the effectiveness of the fuzzy robust state estimator.

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28

Nabati, Parisa, and Arezoo Hajrajabi. "Three-factor mean reverting Ornstein-Uhlenbeck process with stochastic drift term innovations: Nonlinear autoregressive approach with dependent error." Filomat 36, no. 7 (2022): 2345–55. http://dx.doi.org/10.2298/fil2207345n.

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This paper introduces a novel approach, withen the context of energy market, by employing a three-factor mean reverting Ornstein-Uhlenbeck process with a stochastic nonlinear autoregressive drift term having a dependent error. Initially the unique solvability for the given nonlinear system is investigated. Then, to estimate the nonlinear regression function, a semiparametric method, based on the conditional least square estimator for the parametric approach, and the nonparametric kernel method for autoregressive modification estimation have been presented . A maximum likelihood estimator has been used for parameter estimation of the Ornstein-Uhlenbeck process. Finally, some numerical simulations and real data studies have been provided to support the main conclusions of the study.

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Choi, Chan Kyu, and Hong Hee Yoo. "1C23 Performance Uncertainty Estimation of a Nonlinear Vibration System." Proceedings of the Symposium on the Motion and Vibration Control 2010 (2010): _1C23–1_—_1C23–7_. http://dx.doi.org/10.1299/jsmemovic.2010._1c23-1_.

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30

Mahaboob, B., B. Venkateswarlu, J. Ravi Sankar, J. Peter Praveen, and C. Narayana. "A Discourse on the Estimation of Nonlinear Regression Model." International Journal of Engineering & Technology 7, no. 4.10 (2018): 992. http://dx.doi.org/10.14419/ijet.v7i4.10.26642.

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The present study evaluates an estimation for regression model which are nonlinear with Goldfeld, Quandt and exponential structure for heteroscedastic errors. An IENLGLS (Iterative Estimated Nonlinear Generalised Least Squares) estimator based on Goldfeld and Quandt for parametric vector has been derived in this research article. Volkan Soner Ozsoy e.t.al [1], in their paper, proposed an effective approach based on the particle Swarm Optimisation (PSO) algorithm in order to enhance the accuracy in the estimation of parameters of nonlinear regression model. Ting Zhang et.al [2], in their article, established an asymptotic theory for estimates of the time-varying regression functions. Felix Chan et.al [3], in their paper, proposed some principals which are sufficient for asymptotic normality and consistency of the MLH estimator

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Gao, Zhaohui, Dejun Mu, Yongmin Zhong, Chengfan Gu, and Chengcai Ren. "Adaptively Random Weighted Cubature Kalman Filter for Nonlinear Systems." Mathematical Problems in Engineering 2019 (January 17, 2019): 1–13. http://dx.doi.org/10.1155/2019/4160847.

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This paper presents a new adaptive random weighting cubature Kalman filtering method for nonlinear state estimation. This method adopts the concept of random weighting to address the problem that the cubature Kalman filter (CKF) performance is sensitive to system noise. It establishes random weighting theories to estimate system noise statistics and predicted state and measurement together with their associated covariances. Subsequently, it adaptively adjusts the weights of cubature points based on the random weighting estimations to improve the prediction accuracy, thus restraining the disturbances of system noises on state estimation. Simulations and comparison analysis demonstrate the improved performance of the proposed method for nonlinear state estimation.

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Meitz, Mika, and Pentti Saikkonen. "PARAMETER ESTIMATION IN NONLINEAR AR–GARCH MODELS." Econometric Theory 27, no. 6 (2011): 1236–78. http://dx.doi.org/10.1017/s0266466611000041.

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This paper develops an asymptotic estimation theory for nonlinear autoregressive models with conditionally heteroskedastic errors. We consider a general nonlinear autoregression of order p (AR(p)) with the conditional variance specified as a general nonlinear first-order generalized autoregressive conditional heteroskedasticity (GARCH(1,1)) model. We do not require the rescaled errors to be independent, but instead only to form a stationary and ergodic martingale difference sequence. Strong consistency and asymptotic normality of the global Gaussian quasi-maximum likelihood (QML) estimator are established under conditions comparable to those recently used in the corresponding linear case. To the best of our knowledge, this paper provides the first results on consistency and asymptotic normality of the QML estimator in nonlinear autoregressive models with GARCH errors.

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33

Lagrange, S., L. Jaulin, V. Vigneron, and C. Jutten. "Nonlinear Blind Parameter Estimation." IEEE Transactions on Automatic Control 53, no. 3 (2008): 834–38. http://dx.doi.org/10.1109/tac.2008.919573.

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Yang, Yuhong. "Nonlinear Estimation and Classification." Journal of the American Statistical Association 99, no. 466 (2004): 561. http://dx.doi.org/10.1198/jasa.2004.s330.

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35

Sposito, Vince A. "Nonlinear Lp,-Norm Estimation." Technometrics 32, no. 4 (1990): 450–51. http://dx.doi.org/10.1080/00401706.1990.10484734.

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36

Pollard, David, and Peter Radchenko. "Nonlinear least-squares estimation." Journal of Multivariate Analysis 97, no. 2 (2006): 548–62. http://dx.doi.org/10.1016/j.jmva.2005.04.002.

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37

Inzerillo, Santo, and Michael J. Grimble. "H∞ Robust Nonlinear Estimation." IFAC Proceedings Volumes 44, no. 1 (2011): 6634–39. http://dx.doi.org/10.3182/20110828-6-it-1002.03491.

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Amicarelli, Adriana, Lucía Quintero Montoya, and Fernando di Sciascio. "Substrate Feeding Strategy Integrated with a Biomass Bayesian Estimator for a Biotechnological Process." International Journal of Chemical Reactor Engineering 14, no. 6 (2016): 1187–200. http://dx.doi.org/10.1515/ijcre-2015-0182.

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Abstract This work proposes a substrate feeding strategy for a bioprocess integrated with a biomass estimator based in nonlinear filtering techniques. The performance of the proposed estimator and the substrate strategy are illustrated for the δ-endotoxin production of Bacillus thuringiensis (Bt) in batch and fed batch cultures. Nonlinear filtering techniques constitutes an adequate option as estimation tool because of the strongly nonlinear dynamics of this bioprocess and also due to nature of the uncertainties and perturbations that cannot be supposed Gaussians distributed. Biomass estimation is performed from substrate and dissolved oxygen. Substrate feeding strategy is intended to obtain high product concentration. Simulations results along with their experimental verifications demonstrate the acceptable performance of the proposed biomass estimator and the substrate feeding strategy.

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39

Kou, Junke, Qinmei Huang, and Huijun Guo. "Pointwise Wavelet Estimations for a Regression Model in Local Hölder Space." Axioms 11, no. 9 (2022): 466. http://dx.doi.org/10.3390/axioms11090466.

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This paper considers an unknown functional estimation problem in a regression model with multiplicative and additive noise. A linear wavelet estimator is first constructed by a wavelet projection operator. The convergence rate under the pointwise error of linear wavelet estimators is studied in local Hölder space. A nonlinear wavelet estimator is provided by the hard thresholding method in order to obtain an adaptive estimator. The convergence rate of the nonlinear estimator is the same as the linear estimator up to a logarithmic term. Finally, it should be pointed out that the convergence rates of two wavelet estimators are consistent with the optimal convergence rate on pointwise nonparametric estimation.

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40

Xu, Junlian. "Wavelet thresholding estimation of density derivatives from a negatively associated size-biased sample." International Journal of Wavelets, Multiresolution and Information Processing 18, no. 03 (2020): 2050016. http://dx.doi.org/10.1142/s0219691320500162.

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This paper considers wavelet estimation for density derivatives based on negatively associated and size-biased data. We provide upper bounds of nonlinear wavelet estimator on [Formula: see text] risk. It turns out that the convergence rate of the nonlinear estimator is better than that of the linear one.

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41

Li, Zhengbin, Lijun Ma, and Yongqiang Wang. "Parameter estimation for nonlinear sandwich system using instantaneous performance principle." PLOS ONE 17, no. 12 (2022): e0271160. http://dx.doi.org/10.1371/journal.pone.0271160.

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The vast majority of reports mainly focus on the steady-state performance of parameter estimation. Few findings are reported for the instantaneous performance of parameter estimation because the instantaneous performance is difficult to quantify by using the design algorithm, for example, in the initial stage of parameter estimation, the error of parameter estimation varies in a specific region on the basis of the user’s request. With that in mind, we design an identification algorithm to address the transient performance of the parameter estimations. In this study, the parameter estimation of nonlinear sandwich system is studied by using the predefined constraint technology and high-effective filter. To achieve the above purpose, the estimation error information reflecting the transient performance of parameter estimation is procured using the developed some intermediate variables. Then, a predefined constraint function is used to prescribe the error convergence boundary, in which the convergence rate is lifted. An error equivalent conversion technique is then employed to obtain the transformed error data for establishing an parameter adaptive update law, in which the estimation error convergence and the predefined domain can be achieved. In comparison with the available estimation schemes, the good instantaneous performance is obtained on the basis of the numerical example and practical process results.

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42

Orłowski, Przemysław. "Estimation of the Output Deviation Norm for Uncertain, Discrete-Time Nonlinear Systems in a State Dependent Form." International Journal of Applied Mathematics and Computer Science 17, no. 4 (2007): 505–13. http://dx.doi.org/10.2478/v10006-007-0042-z.

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Estimation of the Output Deviation Norm for Uncertain, Discrete-Time Nonlinear Systems in a State Dependent FormNumerical evaluation of the optimal nonlinear robust control requires estimating the impact of parameter uncertainties on the system output. The main goal of the paper is to propose a method for estimating the norm of an output trajectory deviation from the nominal trajectory for nonlinear uncertain, discrete-time systems. The measure of the deviation allows us to evaluate the robustness of any designed controller. The first part of the paper concerns uncertainty modelling for nonlinear systems given in the state space dependent form. The method for numerical estimation of the maximal norm of the output trajectory deviation with applications to robust control synthesis is proposed based on the introduced three-term additive uncertainty model. Theoretical deliberations are complemented with a numerical, water-tank system example.

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43

Annaswamy, A. M., C. Thanomsat, N. Mehta, and Ai-Poh Loh. "Applications of Adaptive Controllers to Systems With Nonlinear Parametrization." Journal of Dynamic Systems, Measurement, and Control 120, no. 4 (1998): 477–87. http://dx.doi.org/10.1115/1.2801489.

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Nonlinear parametrizations occur in dynamic models of several complex engineering problems. The theory of adaptive estimation and control has been applicable, by and large, to problems where parameters appear linearly. We have recently developed an adaptive controller that is capable of estimating parameters that appear nonlinearly in dynamic systems in a stable manner. In this paper, we present this algorithm and its applicability to two problems, temperature regulation in chemical reactors and precise positioning using magnetic bearings both of which contain nonlinear parametrizations. It is shown in both problems that the proposed controller leads to a significantly better performance than those based on linear parametrizations or linearized dynamics.

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44

Alvarado-Méndez, Pedro Eusebio, Carlos M. Astorga-Zaragoza, Gloria L. Osorio-Gordillo, Adriana Aguilera-González, Rodolfo Vargas-Méndez, and Juan Reyes-Reyes. "H∞ State and Parameter Estimation for Lipschitz Nonlinear Systems." Mathematical and Computational Applications 29, no. 4 (2024): 51. http://dx.doi.org/10.3390/mca29040051.

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A H∞ robust adaptive nonlinear observer for state and parameter estimation of a class of Lipschitz nonlinear systems with disturbances is presented in this work. The objective is to estimate parameters and monitor the performance of nonlinear processes with model uncertainties. The behavior of the observer in the presence of disturbances is analyzed using Lyapunov stability theory and by considering an H∞ performance criterion. Numerical simulations were carried out to demonstrate the applicability of this observer for a semi-active car suspension. The adaptive observer performed well in estimating the tire rigidity (as an unknown parameter) and induced disturbances representing damage to the damper. The main contribution is the proposal of an alternative methodology for simultaneous parameter and actuator disturbance estimation for a more general class of nonlinear systems.

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45

Zhang, Shuo, Dongqing Wang, and Feng Liu. "Separate block-based parameter estimation method for Hammerstein systems." Royal Society Open Science 5, no. 6 (2018): 172194. http://dx.doi.org/10.1098/rsos.172194.

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Different from the output–input representation-based identification methods of two-block Hammerstein systems, this paper concerns a separate block-based parameter estimation method for each block of a two-block Hammerstein CARMA system, without combining the parameters of two parts together. The idea is to consider each block as a subsystem and to estimate the parameters of the nonlinear block and the linear block separately (interactively), by using two least-squares algorithms in one recursive step. The internal variable between the two blocks (the output of the nonlinear block, and also the input of the linear block) is replaced by different estimates: when estimating the parameters of the nonlinear part, the internal variable between the two blocks is computed by the linear function; when estimating the parameters of the linear part, the internal variable is computed by the nonlinear function. The proposed parameter estimation method possesses property of the higher computational efficiency compared with the previous over-parametrization method in which many redundant parameters need to be computed. The simulation results show the effectiveness of the proposed algorithm.

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Musunuri, Yogendra Rao, and Oh-Seol Kwon. "State Estimation Using a Randomized Unscented Kalman Filter for 3D Skeleton Posture." Electronics 10, no. 8 (2021): 971. http://dx.doi.org/10.3390/electronics10080971.

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In this study, we propose a method for minimizing the noise of Kinect sensors for 3D skeleton estimation. Notably, it is difficult to effectively remove nonlinear noise when estimating 3D skeleton posture; however, the proposed randomized unscented Kalman filter reduces the nonlinear temporal noise effectively through the state estimation process. The 3D skeleton data can then be estimated at each step by iteratively passing the posterior state during the propagation and updating process. Ultimately, the performance of the proposed method for 3D skeleton estimation is observed to be superior to that of conventional methods based on experimental results.

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Kosmatopoulos, E. B., A. W. Smyth, S. F. Masri, and A. G. Chassiakos. "Robust Adaptive Neural Estimation of Restoring Forces in Nonlinear Structures." Journal of Applied Mechanics 68, no. 6 (2001): 880–93. http://dx.doi.org/10.1115/1.1408614.

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The availability of methods for on-line estimation and identification of structures is crucial for the monitoring and active control of time-varying nonlinear structural systems. Adaptive estimation approaches that have recently appeared in the literature for on-line estimation and identification of hysteretic systems under arbitrary dynamic environments are in general model based. In these approaches, it is assumed that the unknown restoring forces are modeled by nonlinear differential equations (which can represent general nonlinear characteristics, including hysteretic phenomena). The adaptive methods estimate the parameters of the nonlinear differential equations on line. Adaptation of the parameters is done by comparing the prediction of the assumed model to the response measurement, and using the prediction error to change the system parameters. In this paper, a new methodology is presented which is not model based. The new approach solves the problem of estimating/identifying the restoring forces without assuming any model of the restoring forces dynamics, and without postulating any structure on the form of the underlying nonlinear dynamics. The new approach uses the Volterra/Wiener neural networks (VWNN) which are capable of learning input/output nonlinear dynamics, in combination with adaptive filtering and estimation techniques. Simulations and experimental results from a steel structure and from a reinforced-concrete structure illustrate the power and efficiency of the proposed method.

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48

Kontio, Juho A. J., Marko J. Rinta-aho, and Mikko J. Sillanpää. "Estimating Linear and Nonlinear Gene Coexpression Networks by Semiparametric Neighborhood Selection." Genetics 215, no. 3 (2020): 597–607. http://dx.doi.org/10.1534/genetics.120.303186.

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Whereas nonlinear relationships between genes are acknowledged, there exist only a few methods for estimating nonlinear gene coexpression networks or gene regulatory networks (GCNs/GRNs) with common deficiencies. These methods often consider only pairwise associations between genes, and are, therefore, poorly capable of identifying higher-order regulatory patterns when multiple genes should be considered simultaneously. Another critical issue in current nonlinear GCN/GRN estimation approaches is that they consider linear and nonlinear dependencies at the same time in confounded form nonparametrically. This severely undermines the possibilities for nonlinear associations to be found, since the power of detecting nonlinear dependencies is lower compared to linear dependencies, and the sparsity-inducing procedures might favor linear relationships over nonlinear ones only due to small sample sizes. In this paper, we propose a method to estimate undirected nonlinear GCNs independently from the linear associations between genes based on a novel semiparametric neighborhood selection procedure capable of identifying complex nonlinear associations between genes. Simulation studies using the common DREAM3 and DREAM9 datasets show that the proposed method compares superiorly to the current nonlinear GCN/GRN estimation methods.

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49

Deller, J. R., Hayder Radha, J. Justin McCormick, and Huiyan Wang. "Nonlinear Dependence in the Discovery of Differentially Expressed Genes." ISRN Bioinformatics 2012 (April 12, 2012): 1–18. http://dx.doi.org/10.5402/2012/564715.

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Microarray data are used to determine which genes are active in response to a changing cell environment. Genes are “discovered” when they are significantly differentially expressed in the microarray data collected under the differing conditions. In one prevalent approach, all genes are assumed to satisfy a null hypothesis, ℍ0, of no difference in expression. A false discovery (type 1 error) occurs when ℍ0 is incorrectly rejected. The quality of a detection algorithm is assessed by estimating its number of false discoveries, F. Work involving the second-moment modeling of the z-value histogram (representing gene expression differentials) has shown significantly deleterious effects of intergene expression correlation on the estimate of F. This paper suggests that nonlinear dependencies could likewise be important. With an applied emphasis, this paper extends the “moment framework” by including third-moment skewness corrections in an estimator of F. This estimator combines observed correlation (corrected for sampling fluctuations) with the information from easily identifiable null cases. Nonlinear-dependence modeling reduces the estimation error relative to that of linear estimation. Third-moment calculations involve empirical densities of 3×3 covariance matrices estimated using very few samples. The principle of entropy maximization is employed to connect estimated moments to F inference. Model results are tested with BRCA and HIV data sets and with carefully constructed simulations.

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50

Zhu, Jiang, Yajuan Yu, and Vasile Postolica. "Initial value problems for first order impulsive integro-differential equations of Volterra type in Banach spaces." Journal of Function Spaces and Applications 5, no. 1 (2007): 9–26. http://dx.doi.org/10.1155/2007/968435.

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In this paper, we use a new method and combining the partial ordering method to study the existence of the solutions for the first order nonlinear impulsive integro-differential equations of Volterra type on finite interval in Banach spaces and for the first order nonlinear impulsive integro-differential equations of Volterra type on infinite interval with infinite number impulsive times in Banach spaces. By introducing an interim space and using progressive estimation method, some restrictive conditions on impulsive terms, used before, such as, prior estimation, noncompactness measure estimations are deleted.

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