Tag Counting and Monitoring in Large-Scale RFID Systems by Jihong Yu & Lin Chen

Author:Jihong Yu & Lin Chen
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(3.72)

Next, we show the boundedness of the estimation error in Theorem 3.2.

Theorem 3.2

Under the conditions of Theorem 1 , consider the discrete-time stochastic system given by (3.28) and (3.25) and Algorithm 2 , if there exist time-varying positive real number λ k , σ k  > 0 such that

(3.73)

(3.74)

then the estimation error e k|k−1 defined by (3.10) is exponentially bounded in mean square and bounded w.p.o..

Remark

Note that the condition E[w k ] ≤ λ k always holds for E[w k ] < 0, we thus focus on the case that E[w k ] ≥ 0. In the proof, the explicit formulas of λ k and σ k are derived. As in the static case, the conditions may be too stringent such that the results still hold even if the conditions are not satisfied, as illustrated in the simulations.

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