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In both cases the unknown parameter multiplies the measured output of the system, which is obtained with a boundary sensor located on the "opposite side" of the domain from the actuator.
where B n (k) is non-zero if n is a boundary sensor, i.e. (n in mathcal {S}_{partial Omega }), or if it is one of the two nearest sensors to a boundary sensor, (n in mathcal {N}_{partial Omega }).
Specifically, we find the regression function U x n )=α n x 1,n +β n x 2,n +γ n by estimating (α n,β n,γ n ) for each boundary sensor n=1,…,I using measurements of the nearest neighbors to the point x n.
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There have been a number of works to determine the location of boundary sensors for an event [33,34].
Thus, unlike many hole-bypassing algorithms [15, 31 33], using routing directions may alleviate the excess energy consumption of the boundary sensors.
Let (mathcal {S}_{partial Omega } = {1, ldots, n, ldots, I}) denote the cyclically ordered set of the boundary sensors; these coincide with the vertices of the convex hull.
The algorithm works with various limited sensing models, such as depth-limited boundary distance sensor, quadridirectional depth sensor, depth-limited gap sensor, and depth-limited radially-bounded depth senor.
The proposed platform provides nanometric resolution with respect to the distance from the boundary wall sensor's surface.
In order to stabilize the system with boundary input, sensor influence functions are assumed to be located at interior of the domain.
In particular, potentiometric, bulk and boundary conductometric sensors are considered with emphasis on the role of transport and rate coefficients with respect to thermodynamics and kinetics of the sensor signal.
The top figures show the simulation result by means of Matlab, and the bottom figures represent the signal boundary of each sensor and removable sensors (bold circle).
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