American Institute of Mathematical Sciences

October  2005, 1(4): 499-512. doi: 10.3934/jimo.2005.1.499

Branch and bound method for sensor scheduling in discrete time

 1 Department of Mathematics, Zhongshan University, Guangzhou 510275 P.R.C., China, China 2 Department of Mathematics and Statistics, Curtin University of Technology, Perth W.A. 6102, Australia

Received  May 2005 Revised  September 2005 Published  October 2005

In this paper we consider the question of sensor scheduling in discrete time. The basic problem is to design a linear filter whose output provides an unbiased minimum variance estimate of a signal process whose noisy measurements from multiple sensors are available for input to the filter. The problem is to select one source (sensor data) dynamically so as to minimize estimation errors. We formulate the problem as an optimal control problem. By analyzing the positive semi-definite property of the error covariance matrix, we develop a branch and bound method to calculate the optimal scheduling strategy and give a numerical result for interpretation.
Citation: Z.G. Feng, K.L. Teo, Y. Zhao. Branch and bound method for sensor scheduling in discrete time. Journal of Industrial & Management Optimization, 2005, 1 (4) : 499-512. doi: 10.3934/jimo.2005.1.499
 [1] Yi Xu, Jinjie Liu, Liqun Qi. A new class of positive semi-definite tensors. Journal of Industrial & Management Optimization, 2020, 16 (2) : 933-943. doi: 10.3934/jimo.2018186 [2] Lipu Zhang, Yinghong Xu, Zhengjing Jin. An efficient algorithm for convex quadratic semi-definite optimization. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 129-144. doi: 10.3934/naco.2012.2.129 [3] Stephane Chretien, Paul Clarkson. A fast algorithm for the semi-definite relaxation of the state estimation problem in power grids. Journal of Industrial & Management Optimization, 2020, 16 (1) : 431-443. doi: 10.3934/jimo.2018161 [4] Monika Eisenmann, Etienne Emmrich, Volker Mehrmann. Convergence of the backward Euler scheme for the operator-valued Riccati differential equation with semi-definite data. Evolution Equations & Control Theory, 2019, 8 (2) : 315-342. doi: 10.3934/eect.2019017 [5] Yue Lu, Ying-En Ge, Li-Wei Zhang. An alternating direction method for solving a class of inverse semi-definite quadratic programming problems. Journal of Industrial & Management Optimization, 2016, 12 (1) : 317-336. doi: 10.3934/jimo.2016.12.317 [6] Xiantao Xiao, Liwei Zhang, Jianzhong Zhang. On convergence of augmented Lagrangian method for inverse semi-definite quadratic programming problems. Journal of Industrial & Management Optimization, 2009, 5 (2) : 319-339. doi: 10.3934/jimo.2009.5.319 [7] Wei Huang, Ka-Fai Cedric Yiu, Henry Y. K. Lau. Semi-definite programming based approaches for real-time tractor localization in port container terminals. Numerical Algebra, Control & Optimization, 2013, 3 (4) : 665-680. doi: 10.3934/naco.2013.3.665 [8] Wenxiong Chen, Congming Li. A priori estimate for the Nirenberg problem. Discrete & Continuous Dynamical Systems - S, 2008, 1 (2) : 225-233. doi: 10.3934/dcdss.2008.1.225 [9] Yuhong Dai, Nobuo Yamashita. Convergence analysis of sparse quasi-Newton updates with positive definite matrix completion for two-dimensional functions. Numerical Algebra, Control & Optimization, 2011, 1 (1) : 61-69. doi: 10.3934/naco.2011.1.61 [10] Sihem Guerarra. Positive and negative definite submatrices in an Hermitian least rank solution of the matrix equation AXA*=B. Numerical Algebra, Control & Optimization, 2019, 9 (1) : 15-22. doi: 10.3934/naco.2019002 [11] Nguyen Van Thoai. Decomposition branch and bound algorithm for optimization problems over efficient sets. Journal of Industrial & Management Optimization, 2008, 4 (4) : 647-660. doi: 10.3934/jimo.2008.4.647 [12] Zongming Guo, Xuefei Bai. On the global branch of positive radial solutions of an elliptic problem with singular nonlinearity. Communications on Pure & Applied Analysis, 2008, 7 (5) : 1091-1107. doi: 10.3934/cpaa.2008.7.1091 [13] Jing Zhou, Zhibin Deng. A low-dimensional SDP relaxation based spatial branch and bound method for nonconvex quadratic programs. Journal of Industrial & Management Optimization, 2020, 16 (5) : 2087-2102. doi: 10.3934/jimo.2019044 [14] Jing Zhou, Cheng Lu, Ye Tian, Xiaoying Tang. A SOCP relaxation based branch-and-bound method for generalized trust-region subproblem. Journal of Industrial & Management Optimization, 2021, 17 (1) : 151-168. doi: 10.3934/jimo.2019104 [15] Yang Cao, Wei- Wei Tan, Mei-Qun Jiang. A generalization of the positive-definite and skew-Hermitian splitting iteration. Numerical Algebra, Control & Optimization, 2012, 2 (4) : 811-821. doi: 10.3934/naco.2012.2.811 [16] Sofian De Clercq, Koen De Turck, Bart Steyaert, Herwig Bruneel. Frame-bound priority scheduling in discrete-time queueing systems. Journal of Industrial & Management Optimization, 2011, 7 (3) : 767-788. doi: 10.3934/jimo.2011.7.767 [17] Lishan Lin. A priori bounds and existence result of positive solutions for fractional Laplacian systems. Discrete & Continuous Dynamical Systems, 2019, 39 (3) : 1517-1531. doi: 10.3934/dcds.2019065 [18] Kun-Peng Jin, Jin Liang, Ti-Jun Xiao. Uniform polynomial stability of second order integro-differential equations in Hilbert spaces with positive definite kernels. Discrete & Continuous Dynamical Systems - S, 2021, 14 (9) : 3141-3166. doi: 10.3934/dcdss.2021077 [19] Guofeng Che, Haibo Chen, Tsung-fang Wu. Bound state positive solutions for a class of elliptic system with Hartree nonlinearity. Communications on Pure & Applied Analysis, 2020, 19 (7) : 3697-3722. doi: 10.3934/cpaa.2020163 [20] S. E. Kuznetsov. An upper bound for positive solutions of the equation \Delta u=u^\alpha. Electronic Research Announcements, 2004, 10: 103-112.

2020 Impact Factor: 1.801