TY - JOUR

T1 - Sensor placement for optimal estimation of vector-valued diffusion processes

AU - Belabbas, Mohamed Ali

AU - Chen, Xudong

N1 - Funding Information:
M.-A. Belabbas was supported in part by National Science Foundation (NSF) , United States, grant CAREER ECCS-1351586 .
Publisher Copyright:
© 2018 Elsevier B.V.

PY - 2018/11

Y1 - 2018/11

N2 - Diffusion processes are commonplace in many scientific disciplines, as they describe a broad range of physical phenomenon. Consider a diffusion process observed through linear sensors with additive white noise. We derive the optimal placement of these sensors for estimating this process, where optimality is defined in terms of the mean squared estimation error (MSE) of the state given past observations. We consider two cases. First, we assume the sensors to be orthogonal. We show in this case that the minimum MSE is related to the nuclear norm of the system matrix of the process. Second, we remove the orthogonality constraint and show that the MSE is related to the Schatten p-norm of the system matrix of the process and the optimal sensors are proportional its matrix cube root. We present simulation results illustrating the fact that the gain afforded by optimizing the choice of sensors depends on the ratio p∕n, where n is the dimension of the system and p the dimension of the Wiener processes driving it, and this gain is in general large, especially when p∕n is small.

AB - Diffusion processes are commonplace in many scientific disciplines, as they describe a broad range of physical phenomenon. Consider a diffusion process observed through linear sensors with additive white noise. We derive the optimal placement of these sensors for estimating this process, where optimality is defined in terms of the mean squared estimation error (MSE) of the state given past observations. We consider two cases. First, we assume the sensors to be orthogonal. We show in this case that the minimum MSE is related to the nuclear norm of the system matrix of the process. Second, we remove the orthogonality constraint and show that the MSE is related to the Schatten p-norm of the system matrix of the process and the optimal sensors are proportional its matrix cube root. We present simulation results illustrating the fact that the gain afforded by optimizing the choice of sensors depends on the ratio p∕n, where n is the dimension of the system and p the dimension of the Wiener processes driving it, and this gain is in general large, especially when p∕n is small.

KW - Estimation

KW - Sensor design

KW - Wiener process

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U2 - 10.1016/j.sysconle.2018.09.004

DO - 10.1016/j.sysconle.2018.09.004

M3 - Article

AN - SCOPUS:85054337250

VL - 121

SP - 24

EP - 30

JO - Systems and Control Letters

JF - Systems and Control Letters

SN - 0167-6911

ER -