Robust Finite-Horizon Kalman Filtering for Uncertain Discrete-Time Systems

Mohamed, Shady; Nahavandi, Saeid

doi:10.1109/tac.2011.2174697

Cited by 59 publications

(30 citation statements)

References 18 publications

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“…While a full-scale review over the field is clearly out of the scope of this paper, interested readers are referred to (an incomplete list of) [3][4][5][6][7][8][9][10][11][12][13][14][15][16], for the development of this subject in several directions over the past 10 years. The multiplier approach to robust estimation has been considered in [17][18][19][20][21]; none of these allows the use of dynamic IQCs.…”

Section: Introductionmentioning

confidence: 99%

Robust estimation with dynamic integral quadratic constraints: the discrete‐time case

Kao¹,

Chen²

2013

IET Control Theory & Applications

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The authors consider the problem of robust output estimation in the discrete-time setting. The uncertainty in the system is characterised by integral quadratic constraints with dynamic multipliers. The main technical contribution of this study is to derive two different synthesis conditions in terms of linear matrix inequalities (LMI) by two different approaches. The LMI condition derived by the first approach allows one to find the robust estimator and the performance certificate simultaneously, whereas the condition by the second approach has a smaller size but requires an additional step for recovering the estimator. The synthesis conditions are validated by numerical examples. The results verify the equivalence of the two approaches and show that the two-step approach is in fact computationally favourable when the system has large number of state variables. NomenclatureSymbols R, R n , R n×m and Z + are used to denote the sets of real numbers, n-dimensional real vectors, n × m real matrices and non-negative integers, respectively. Symbols I n and 0 n×m are used to denote n-dimensional identity matrix and n × m zero matrix, respectively. The subscripts are dropped when the dimension is evident from the text. Given a matrix M , the transposition and the conjugate transposition are denoted by M and M * , respectively. Given matrix M and N , we use diag(M , N ) to denote the block-diagonal matrix with M and N being the (1,1) block and the (2,2) block, respectively.

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Section: Introductionmentioning

confidence: 99%

Robust estimation with dynamic integral quadratic constraints: the discrete‐time case

Kao¹,

Chen²

2013

IET Control Theory & Applications

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“…3) Unlike the Measurement extrapolation, the optimality of estimation is assured to a certain extent. In this paper, a novel algorithm is proposed based on the norm-bound scheme which is a popular and useful tool in robust control theory (25)- (27) . Thanks to the norm-bound scheme, it is possible to obtain the upper-bound of the estimation error covariance considering the delayed measurement.…”

Section: ) Inter-sample Observermentioning

confidence: 99%

Upper-Bound-Based State Estimation with Large-Time-Delay Measurement and Its Applications to Motion Control

2016

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In many motion control applications, it is essential to handle a delayed measurement to estimate the unknown states correctly. However, a literature review shows that difficulties still remain if the delay time is quite large in comparison with the period of the control input. For instance, some methods need to increase the size of the original system considerably. This paper describes a novel filter for a linear system with a large-time-delay measurement. By utilizing the norm-bound scheme based on a matrix inequality, the upper-bound of the estimation error covariance is obtained, and the filter gain can be computed easily. The proposed algorithm is almost similar to the standard Kalman filter without any increase in the dimension of the system. The algorithm is developed for two cases: Case 1: considering only a delayed measurement and Case 2: considering the fusion of delayed and nondelayed measurements. Two motion control applications are performed to verify the algorithm: sideslip angle estimation for vehicle motion control and target position estimation for visual servo control.

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“…The method minimizes a multi-objective optimization criterion which represents the compromise between the size of the zonotopic part and the covariance of the Gaussian distribution. Regarding to parameter uncertainties, several results have been derived on the design of optimal robust Kalman filters for discrete timevarying systems subject to norm-bounded uncertainties, for instance Zhe and Zheng [2006], Mohamed and Nahavandi [2012]. The optimality of these methods is based on finding an upper bound on the estimation error covariance for any acceptable modeling uncertainties and then to minimize the proposed upper bound.…”

Section: Introductionmentioning

confidence: 99%

Interval Kalman filter enhanced by positive definite upper bounds

et al. 2017

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A method based on the interval Kalman filter for discrete uncertain linear systems is presented. The system under consideration is subject to bounded parameter uncertainties not only in the state and observation matrices, but also in the covariance matrices of Gaussian noises. The gain matrix provided by the filter is optimized to give a minimal upper bound on the state estimation error covariance for all admissible uncertainties. The state estimation is then determined by using interval analysis in order to enclose the set of all possible solutions with respect to the classical Kalman filtering structure.

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Robust Finite-Horizon Kalman Filtering for Uncertain Discrete-Time Systems

Cited by 59 publications

References 18 publications

Robust estimation with dynamic integral quadratic constraints: the discrete‐time case

Robust estimation with dynamic integral quadratic constraints: the discrete‐time case

Upper-Bound-Based State Estimation with Large-Time-Delay Measurement and Its Applications to Motion Control

Interval Kalman filter enhanced by positive definite upper bounds

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