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Journal articles on the topic 'Guaranteed estimation'

Author: Grafiati

Published: 3 June 2025

Last updated: 22 June 2025

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1

Ananyev, Boris. "About control of guaranteed estimation." Cybernetics and Physics, Volume 7, 2018, Number 1 (June 18, 2018): 18–25. http://dx.doi.org/10.35470/2226-4116-2018-7-1-18-25.

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The control problem by parameters in the course of the guaranteed state estimation of linear non-stationary systems is considered. It is supposed that unknown disturbances in the system and the observation channel are limited by norm in the space of square integrable functions and the initial state of the system is also unknown. The process of guaranteed state estimation includes the solution of a matrix Riccati equation that contains some parameters, which may be chosen at any instant of time by the first player (an observer) and the second player (an opponent of the observer). The purposes of players are diametrically opposite: the observer aims to minimize diameter of information set at the end of observation process, and the second player on the contrary aims to maximize it. This problem is interpreted as a differential game with two players for the Riccati equation. All the choosing parameters are limited to compact sets in appropriate spaces of matrices. The payoff of the game is interpreted through the Euclidean norm of the inverse Riccati matrix at the end of the process. A specific case of the problem with constant matrices is considered. Methods of minimax optimization, the theory of optimal control, and the theory of differential games are used. Examples are also given.

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2

Jaulin, L., and E. Walter. "Guaranteed robust nonlinear minimax estimation." IEEE Transactions on Automatic Control 47, no. 11 (2002): 1857–64. http://dx.doi.org/10.1109/tac.2002.804479.

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Pelevin, Alexander E. "GUARANTEED ESTIMATION OF SHIPS� DOMAINS." Vestnik Gosudarstvennogo universiteta morskogo i rechnogo flota imeni admirala S. O. Makarova 11, no. 5 (2019): 823–30. http://dx.doi.org/10.21821/2309-5180-2019-11-5-823-830.

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4

Artzová, Petra, and Radoslav Paulen. "Moving-horizon Guaranteed Parameter Estimation." IFAC-PapersOnLine 52, no. 1 (2019): 112–17. http://dx.doi.org/10.1016/j.ifacol.2019.06.046.

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Alamo, T., J. M. Bravo, and E. F. Camacho. "Guaranteed state estimation by zonotopes." Automatica 41, no. 6 (2005): 1035–43. http://dx.doi.org/10.1016/j.automatica.2004.12.008.

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6

Nakonechnyi, O. G., P. M. Zinko, and T. P. Zinko. "Estimates of solutions for ambiguously solvable linear matrix equations." Mathematical Modeling and Computing 12, no. 1 (2025): 10–21. https://doi.org/10.23939/mmc2025.01.010.

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The article examines the problem of estimating solutions of operator equations under conditions of uncertainty. We obtain the expressions for guaranteed errors of solutions of indefinite linear equations in the spaces of rectangular matrices in the presence of additional data with deterministic errors belonging to special sets. In a particular case, explicit formulas are obtained for guaranteed linear vector estimates and guaranteed vector estimation errors and for guaranteed posterior estimates and measurement errors. These estimation results are illustrated by a test example in the case of operators that act in the space of 2×2 matrices with a non-zero kernel.

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7

Lin, Xiaogong, Heng Li, Kun Liang, Jun Nie, and Juan Li. "Fault-Tolerant Supervisory Control for Dynamic Positioning of Ships." Mathematical Problems in Engineering 2019 (January 3, 2019): 1–11. http://dx.doi.org/10.1155/2019/9134952.

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A fault-tolerant supervisory control method for dynamic positioning of ships with actuator failures and sensor failures is presented in this paper. Unlike the traditional fault detection and control, fault detection and fault-tolerant controller are designed as a unit in this paper through a supervisor. By introducing a nonlinear estimation error and virtual controller, the sensor failures are separated from the actuator failures in the supervisory control system. It guarantees that the detectability property and matching property of the switched system are satisfied. Firstly, a new extended state observer is designed to match the models of different actuator failures. Secondly, by introducing a virtual controller, the detectability property of the switched system is guaranteed. Finally, a nonlinear estimation error operator is used in the designing of switching logic to guarantee stability of the closed-loop system with sensor failures. When sensor failures and actuator failures occur, we show that all the states of the closed-loop system are guaranteed to be bounded. The effectiveness of the fault-tolerant control is verified by simulation experiments.

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8

Gusev, M. I. "On Stability of Guaranteed Estimation Problems." IFAC Proceedings Volumes 33, no. 16 (2000): 125–30. http://dx.doi.org/10.1016/s1474-6670(17)39615-5.

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9

Kolessa, A. E., and I. S. Sokolov. "SPACE OBJECT ORBIT ESTIMATION AT LIMITED ANGLE MEASUREMENTS ERRORS." Issues of radio electronics, no. 3 (March 20, 2018): 69–75. http://dx.doi.org/10.21778/2218-5453-2018-3-69-75.

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The problem of a space object orbit estimation and determination of region with minimum volume, which contains with guarantee orbit state vector, is considered. Measurements are provided by the telescope and estimation of angle measurements errors are limited in absolute value. The significant dependence of the guaranteed area size on the choice of coordinate system for observations is found, the algorithm for determination of the minimum volume area is suggested based on the simplex-method. In addition the comparison analysis of results of created algorithm with known ones based on various methods (guaranteed and probabilistic) is presented. The developed algorithm is able to give more precise results in several cases in comparison with other known algorithms.

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10

Xu, Ke-Li. "REWEIGHTED FUNCTIONAL ESTIMATION OF DIFFUSION MODELS." Econometric Theory 26, no. 2 (2009): 541–63. http://dx.doi.org/10.1017/s0266466609100087.

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The local linear method is popular in estimating nonparametric continuous-time diffusion models, but it may produce negative results for the diffusion (or volatility) functions and thus lead to insensible inference. We demonstrate this using U.S. interest rate data. We propose a new functional estimation method of the diffusion coefficient based on reweighting the conventional Nadaraya–Watson estimator. It preserves the appealing bias properties of the local linear estimator and is guaranteed to be nonnegative in finite samples. A limit theory is developed under mild requirements (recurrence) of the data generating mechanism without assuming stationarity or ergodicity.

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11

Jian-hong, Wang. "One Improvement on Zonotope Guaranteed Parameter Estimation." Science Journal of Circuits, Systems and Signal Processing 6, no. 5 (2017): 44. http://dx.doi.org/10.11648/j.cssp.20170605.11.

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12

Walter, Eric, and Michel Kieffer. "Interval analysis for guaranteed nonlinear parameter estimation." IFAC Proceedings Volumes 36, no. 16 (2003): 249–60. http://dx.doi.org/10.1016/s1474-6670(17)34770-5.

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13

Le, Vu Tuan Hieu, Cristina Stoica, Teodoro Alamo, Eduardo F. Camacho, and Didier Dumur. "Zonotopic guaranteed state estimation for uncertain systems." Automatica 49, no. 11 (2013): 3418–24. http://dx.doi.org/10.1016/j.automatica.2013.08.014.

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14

Vasiliev, Vyacheslav A. "A truncated estimation method with guaranteed accuracy." Annals of the Institute of Statistical Mathematics 66, no. 1 (2013): 141–63. http://dx.doi.org/10.1007/s10463-013-0409-x.

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15

Khadanovich, Dina V., and Vladimir I. Shiryaev. "To the Problem of Adaptive Guaranteed Estimation." IFAC-PapersOnLine 51, no. 32 (2018): 717–22. http://dx.doi.org/10.1016/j.ifacol.2018.11.462.

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16

Su, Junyan, Yanlin Zha, Kai Wang, Mario E. Villanueva, Radoslav Paulen, and Boris Houska. "Interval Superposition Arithmetic for Guaranteed Parameter Estimation." IFAC-PapersOnLine 52, no. 1 (2019): 574–79. http://dx.doi.org/10.1016/j.ifacol.2019.06.124.

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17

Ananyev, B. I., and P. A. Yurovskikh. "Guaranteed Estimation Problem for Multi-Step Systems." Bulletin of Irkutsk State University. Series Mathematics 45 (2023): 37–53. http://dx.doi.org/10.26516/1997-7670.2023.45.37.

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Questions of the guaranteed estimation of nonlinear multistep systems are considered, for which part of coordinates is not observable. For disturbances we set a priori restrictions with non-negative semi-continuous functions that includes geometrical restrictions as well. As the general formulas for creation of information sets and their specification in special cases are provided. Two-dimensional logistics systems and the equations of Lotka-Volterra are considered as examples. The case of the linear equations where basic functions of convex sets are used is separately considered. Under geometrical restrictions on disturbances the rough procedure of estimation with possible use of functions of distance to the set is given.

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18

Hirose, Kei, and Hiroki Masuda. "Robust Relative Error Estimation." Entropy 20, no. 9 (2018): 632. http://dx.doi.org/10.3390/e20090632.

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Relative error estimation has been recently used in regression analysis. A crucial issue of the existing relative error estimation procedures is that they are sensitive to outliers. To address this issue, we employ the γ -likelihood function, which is constructed through γ -cross entropy with keeping the original statistical model in use. The estimating equation has a redescending property, a desirable property in robust statistics, for a broad class of noise distributions. To find a minimizer of the negative γ -likelihood function, a majorize-minimization (MM) algorithm is constructed. The proposed algorithm is guaranteed to decrease the negative γ -likelihood function at each iteration. We also derive asymptotic normality of the corresponding estimator together with a simple consistent estimator of the asymptotic covariance matrix, so that we can readily construct approximate confidence sets. Monte Carlo simulation is conducted to investigate the effectiveness of the proposed procedure. Real data analysis illustrates the usefulness of our proposed procedure.

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19

Mahmoud, Magdi S., and Peng Shi. "Optimal guaranteed cost filtering for Markovian jump discrete-time systems." Mathematical Problems in Engineering 2004, no. 1 (2004): 33–48. http://dx.doi.org/10.1155/s1024123x04108016.

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This paper develops a result on the design of robust steady-state estimator for a class of uncertain discrete-time systems with Markovian jump parameters. This result extends the steady-state Kalman filter to the case of norm-bounded time-varying uncertainties in the state and measurement equations as well as jumping parameters. We derive a linear state estimator such that the estimation-error covariance is guaranteed to lie within a certain bound for all admissible uncertainties. The solution is given in terms of a family of linear matrix inequalities (LMIs). A numerical example is included to illustrate the theory.

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20

LIU, Xuefeng, and Shin'ichi OISHI. "Guaranteed high precision estimation for interpolation error constant." IEICE Proceeding Series 2 (March 17, 2014): 439–40. http://dx.doi.org/10.15248/proc.2.439.

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21

Benavoli, Alessio, Luigi Chisci, and Alfonso Farina. "Estimation of Constrained Parameters With Guaranteed MSE Improvement." IEEE Transactions on Signal Processing 55, no. 4 (2007): 1264–74. http://dx.doi.org/10.1109/tsp.2006.888094.

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22

Polyak, Boris T., Sergey A. Nazin, Cécile Durieu, and Éric Walter. "Guaranteed ellipsoidal state estimation for uncertain MIMO models." IFAC Proceedings Volumes 36, no. 16 (2003): 1017–22. http://dx.doi.org/10.1016/s1474-6670(17)34892-9.

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23

Chernousko, F. L., A. I. Ovseevich, and V. L. Trushchenkov. "Method for Guaranteed State Estimation of Dynamic Systems." IFAC Proceedings Volumes 20, no. 5 (1987): 17–23. http://dx.doi.org/10.1016/s1474-6670(17)55059-4.

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24

Reshetnyak, Yu N. "Summation of ellipsoids in the guaranteed estimation problem." Journal of Applied Mathematics and Mechanics 53, no. 2 (1989): 193–97. http://dx.doi.org/10.1016/0021-8928(89)90008-7.

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25

Walter, Éric, and Michel Kieffer. "Guaranteed nonlinear parameter estimation in knowledge-based models." Journal of Computational and Applied Mathematics 199, no. 2 (2007): 277–85. http://dx.doi.org/10.1016/j.cam.2005.07.039.

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26

Pokotilo, V. G. "Optimal-experiment designs in guaranteed-estimation problems. III." Cybernetics and Systems Analysis 29, no. 4 (1994): 514–21. http://dx.doi.org/10.1007/bf01125865.

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27

Chabane, S. Ben, C. Stoica Maniu, T. Alamo, E. F. Camacho, and D. Dumur. "A New Approach for Guaranteed Ellipsoidal State Estimation." IFAC Proceedings Volumes 47, no. 3 (2014): 6533–38. http://dx.doi.org/10.3182/20140824-6-za-1003.01629.

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28

García, R. A., L. Orihuela, P. Millán, F. R. Rubio, and M. G. Ortega. "Guaranteed estimation and distributed control of vehicle formations." International Journal of Control 93, no. 11 (2020): 2729–42. http://dx.doi.org/10.1080/00207179.2020.1714074.

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29

Li, Jing, Tao Yang, and Jingyi Yu. "Random sampling and model competition for guaranteed multiple consensus sets estimation." International Journal of Advanced Robotic Systems 14, no. 1 (2017): 172988141668567. http://dx.doi.org/10.1177/1729881416685673.

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Robust extraction of consensus sets from noisy data is a fundamental problem in robot vision. Existing multimodel estimation algorithms have shown success on large consensus sets estimations. One remaining challenge is to extract small consensus sets in cluttered multimodel data set. In this article, we present an effective multimodel extraction method to solve this challenge. Our technique is based on smallest consensus set random sampling, which we prove can guarantee to extract all consensus sets larger than the smallest set from input data. We then develop an efficient model competition scheme that iteratively removes redundant and incorrect model samplings. Extensive experiments on both synthetic data and real data with high percentage of outliers and multimodel intersections demonstrate the superiority of our method.

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30

Sainudiin, Raazesh, and Gloria Teng. "Minimum distance histograms with universal performance guarantees." Japanese Journal of Statistics and Data Science 2, no. 2 (2019): 507–27. http://dx.doi.org/10.1007/s42081-019-00054-y.

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AbstractWe present a data-adaptive multivariate histogram estimator of an unknown density f based on n independent samples from it. Such histograms are based on binary trees called regular pavings (RPs). RPs represent a computationally convenient class of simple functions that remain closed under addition and scalar multiplication. Unlike other density estimation methods, including various regularization and Bayesian methods based on the likelihood, the minimum distance estimate (MDE) is guaranteed to be within an $$L_1$$ L 1 distance bound from f for a given n, no matter what the underlying f happens to be, and is thus said to have universal performance guarantees (Devroye and Lugosi, Combinatorial methods in density estimation. Springer, New York, 2001). Using a form of tree matrix arithmetic with RPs, we obtain the first generic constructions of an MDE, prove that it has universal performance guarantees and demonstrate its performance with simulated and real-world data. Our main contribution is a constructive implementation of an MDE histogram that can handle large multivariate data bursts using a tree-based partition that is computationally conducive to subsequent statistical operations.

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31

Khadanovich, D. V., and V. I. Shiryaev. "ADAPTIVE GUARANTEED ESTIMATION OF A CONSTANT SIGNAL UNDER UNCERTAINTY OF MEASUREMENT ERRORS." Bulletin of the South Ural State University. Ser. Computer Technologies, Automatic Control & Radioelectronics 20, no. 4 (2020): 22–36. http://dx.doi.org/10.14529/ctcr200403.

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In the guaranteed estimation problems under uncertainty relative to disturbances and meas-urement errors, the admissible sets of their possible values are determined. The solution is chosen due to conditions of guaranteed bounded estimates optimization corresponding to the worst realiza-tion of disturbances and measurement errors. The result of the guaranteed estimation is an unim-provable bounded estimate (information set), which turns to be overly pessimistic (reinsurance) if a prior admissible set of measurement errors is too large compared to their realized values. The admis-sible sets of disturbances and measurement errors can turn to be only rough upper estimates on a short observation interval. The goal of research is the accuracy enhancement problem of guaran-teed estimation when measurement errors are not realized in the worst way, i.e. the environment in which the object operates does not behave as aggressively as it is built in a priori data on the permis-sible set of error values. Research design. The problem of adaptive guaranteed estimation of a con-stant signal from noisy measurements is considered. The adaptive filtering problem is, according to the results of measurement processing, from the whole set of possible realizations of errors, to choose the one that would generate the measurement sequence. Results. An adaptive guaranteed estimation algorithm is presented. The adaptive algorithm construction is based on a multi-alternative method based on the Kalman filter bank. The method uses a set of filters, each of which is tuned to a specific hypoth-esis about the measurement error model. Filter residuals are used to compute estimates of realized measurement errors. The choice of the realization of possible errors is performed using a function that has the meaning of the residual variance over a short time interval. Conclusion. The computa-tional scheme of the adaptive algorithm, the numerical example, and comparative analysis of ob-tained estimates are presented.

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32

Zhao, Pan, Ziyao Guo, Yikun Cheng, Aditya Gahlawat, Hyungsoo Kang, and Naira Hovakimyan. "Guaranteed Trajectory Tracking under Learned Dynamics with Contraction Metrics and Disturbance Estimation." Robotics 13, no. 7 (2024): 99. http://dx.doi.org/10.3390/robotics13070099.

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This paper presents a contraction-based learning control architecture that allows for using model learning tools to learn matched model uncertainties while guaranteeing trajectory tracking performance during the learning transients. The architecture relies on a disturbance estimator to estimate the pointwise value of the uncertainty, i.e., the discrepancy between a nominal model and the true dynamics, with pre-computable estimation error bounds, and a robust Riemannian energy condition for computing the control signal. Under certain conditions, the controller guarantees exponential trajectory convergence during the learning transients, while learning can improve robustness and facilitate better trajectory planning. Simulation results validate the efficacy of the proposed control architecture.

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33

You, Fuqiang, Hualu Zhang, and Fuli Wang. "Improved set-membership guaranteed state estimation for uncertain non-linear systems." Transactions of the Institute of Measurement and Control 40, no. 5 (2017): 1471–80. http://dx.doi.org/10.1177/0142331216686158.

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This paper presents a new improved set-membership algorithm for guaranteed state estimation for non-linear discrete-time systems with an unknown but bounded description of disturbance and noise. In this paper, the non-linear model is linearized first and the difference of convex (DC) programming method is used to outer-bound the linearization error, which is regarded as a disturbance of the system, and the improved set-membership algorithm guaranteed state estimation for the linearization system. An example is given to illustrate the proposed algorithm.

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34

Nakonechnyi, O. G., G. I. Kudin, P. M. Zinko, and T. P. Zinko. "GUARANTEED ROOT MEAN SQUARE ESTIMATES OF OBSERVATIONS WITH UNKNOWN MATRICES." Journal of Numerical and Applied Mathematics, no. 2 (2022): 98–115. http://dx.doi.org/10.17721/2706-9699.2022.2.12.

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The problems of guaranteed mean square estimation of unknown rectangular matrices based on observations of linear functions from random matrices with random errors are considered in the paper. Asymptotic distributions of guaranteed errors and guaranteed estimates are obtained in the case of small perturbations of the matrices. A test example of the asymptotic distribution is given.

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35

Li, Yajun, Feiqi Deng, and Jingzhao Li. "Improved Results on State Estimation for Uncertain Takagi-Sugeno Fuzzy Stochastic Neural Networks with Time-Varying Delays." International Journal of Nonlinear Sciences and Numerical Simulation 18, no. 6 (2017): 495–505. http://dx.doi.org/10.1515/ijnsns-2016-0125.

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AbstractThe delay-dependent state estimation problem for Takagi-Sugeno fuzzy stochastic neural networks with time-varying delays is considered in this paper. We aim to design state estimators to estimate the network states such that the dynamics of the estimation error systems are guaranteed to be exponentially stable in the mean square. Both fuzzy-rule-independent and the fuzzy-rule-dependent state estimators are designed. Delay-dependent sufficient conditions are presented to guarantee the existence of the desired state estimators for the fuzzy stochastic neural networks. Finally, two numerical examples demonstrate that the proposed approaches are effective.

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36

Kieffer, Michel, Eric Walter, and Ivan Simeonov. "GUARANTEED NONLINEAR PARAMETER ESTIMATION FOR CONTINUOUS-TIME DYNAMICAL MODELS." IFAC Proceedings Volumes 39, no. 1 (2006): 843–48. http://dx.doi.org/10.3182/20060329-3-au-2901.00133.

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37

Kulakova, V. I., and A. V. Nebylov. "Guaranteed estimation of signals with bounded variances of derivatives." Automation and Remote Control 69, no. 1 (2008): 76–88. http://dx.doi.org/10.1134/s0005117908010086.

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38

Kameda, Yusuke, Ichiro Matsuda, and Susumu Itoh. "A Scene-Flow Estimation Method with Guaranteed Numerical Stability." Journal of The Institute of Image Information and Television Engineers 68, no. 7 (2014): J292—J298. http://dx.doi.org/10.3169/itej.68.j292.

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39

Luc Jaulin, M. Kieffer, E. Walter, and D. Meizel. "Guaranteed robust nonlinear estimation with application to robot localization." IEEE Transactions on Systems, Man and Cybernetics, Part C (Applications and Reviews) 32, no. 4 (2002): 374–81. http://dx.doi.org/10.1109/tsmcc.2002.806747.

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40

Jaulin, L., M. Kieffer, I. Braems, and E. Walter. "Guaranteed non-linear estimation using constraint propagation on sets." International Journal of Control 74, no. 18 (2001): 1772–82. http://dx.doi.org/10.1080/00207170110090642.

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41

Kurzhanski, Α., and I. Vályi. "Guaranteed State Estimation for Dynamic Systems: Beyond the Overviews." IFAC Proceedings Volumes 25, no. 15 (1992): 255–59. http://dx.doi.org/10.1016/s1474-6670(17)50642-4.

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42

Vakulov, N. V., А. V. Myshlyavtsev, and V. I. Malyutin. "Estimation of in-use Guaranteed Rubber Lifetime test methods." Procedia Engineering 113 (2015): 479–83. http://dx.doi.org/10.1016/j.proeng.2015.07.339.

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43

Golovan, A., and A. Matasov. "The Kalman-Bucy filter in the guaranteed estimation problem." IEEE Transactions on Automatic Control 39, no. 6 (1994): 1282–86. http://dx.doi.org/10.1109/9.293197.

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44

Le, V. T. H., T. Alamo, E. F. Camacho, C. Stoica, and D. Dumur. "A New Approach for Guaranteed State Estimation by Zonotopes." IFAC Proceedings Volumes 44, no. 1 (2011): 9242–47. http://dx.doi.org/10.3182/20110828-6-it-1002.02496.

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45

Vukovich, G., and Y. Kim. "Guaranteed ellipsoidal estimation for satellite formation flying collision avoidance." International Journal of Space Science and Engineering 4, no. 2 (2016): 77. http://dx.doi.org/10.1504/ijspacese.2016.081560.

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46

Thangavel, Sakthi, Mohamed Aboelnour, Sergio Lucia, Radoslav Paulen, and Sebastian Engell. "Robust Dual Multi-stage NMPC using Guaranteed Parameter Estimation." IFAC-PapersOnLine 51, no. 20 (2018): 72–77. http://dx.doi.org/10.1016/j.ifacol.2018.10.177.

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47

Wang, Andong, Guoxu Zhou, and Qibin Zhao. "Guaranteed Robust Tensor Completion via ∗L-SVD with Applications to Remote Sensing Data." Remote Sensing 13, no. 18 (2021): 3671. http://dx.doi.org/10.3390/rs13183671.

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This paper conducts a rigorous analysis for the problem of robust tensor completion, which aims at recovering an unknown three-way tensor from incomplete observations corrupted by gross sparse outliers and small dense noises simultaneously due to various reasons such as sensor dead pixels, communication loss, electromagnetic interferences, cloud shadows, etc. To estimate the underlying tensor, a new penalized least squares estimator is first formulated by exploiting the low rankness of the signal tensor within the framework of tensor ∗L-Singular Value Decomposition (∗L-SVD) and leveraging the sparse structure of the outlier tensor. Then, an algorithm based on the Alternating Direction Method of Multipliers (ADMM) is designed to compute the estimator in an efficient way. Statistically, the non-asymptotic upper bound on the estimation error is established and further proved to be optimal (up to a log factor) in a minimax sense. Simulation studies on synthetic data demonstrate that the proposed error bound can predict the scaling behavior of the estimation error with problem parameters (i.e., tubal rank of the underlying tensor, sparsity of the outliers, and the number of uncorrupted observations). Both the effectiveness and efficiency of the proposed algorithm are evaluated through experiments for robust completion on seven different types of remote sensing data.

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48

Xu, Yu, Wenda Sun, and Ping Li. "A Miniature Integrated Navigation System for Rotary-Wing Unmanned Aerial Vehicles." International Journal of Aerospace Engineering 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/748940.

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This paper presents the development of a low cost miniature navigation system for autonomous flying rotary-wing unmanned aerial vehicles (UAVs). The system incorporates measurements from a low cost single point GPS and a triaxial solid state inertial/magnetic sensor unit. The navigation algorithm is composed of three modules running on a microcontroller: the sensor calibration module, the attitude estimator, and the velocity and position estimator. The sensor calibration module relies on a recursive least square based ellipsoid hypothesis calibration algorithm to estimate biases and scale factors of accelerometers and magnetometers without any additional calibration equipment. The attitude estimator is a low computational linear attitude fusion algorithm that effectively incorporates high frequency components of gyros and low frequency components of accelerometers and magnetometers to guarantee both accuracy and bandwidth of attitude estimation. The velocity and position estimator uses two cascaded complementary filters which fuse translational acceleration, GPS velocity, and position to improve the bandwidth of velocity and position. The designed navigation system is feasible for miniature UAVs due to its low cost, simplicity, miniaturization, and guaranteed estimation errors. Both ground tests and autonomous flight tests of miniature unmanned helicopter and quadrotor have shown the effectiveness of the proposed system, demonstrating its promise in UAV systems.

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49

Mahmoud, Magdi S. "Robust stability and ℋ∞-estimation for uncertain discrete systems with state-delay". Mathematical Problems in Engineering 7, № 5 (2001): 393–412. http://dx.doi.org/10.1155/s1024123x01001703.

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Abstract:

In this paper, we investigate the problems of robust stability and ℋ∞-estimation for a class of linear discrete-time systems with time-varying norm-bounded parameter uncertainty and unknown state-delay. We provide complete results for robust stability with prescribed performance measure and establish a version of the discrete Bounded Real Lemma. Then, we design a linear estimator such that the estimation error dynamics is robustly stable with a guaranteed ℋ∞-performance irrespective of the parameteric uncertainties and unknown state delays. A numerical example is worked out to illustrate the developed theory.

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Nakonechnyi, Alexander G., Petr N. Zinko, and Yulia M. Shevchuk. "Guaranteed Estimation of Nonstationary Parameters of Difference Equations under Uncertainty." Journal of Automation and Information Sciences 50, no. 11 (2018): 1–18. http://dx.doi.org/10.1615/jautomatinfscien.v50.i11.10.

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