Fig. 9
From: Collision-aware distributed detection with population-splitting algorithms
A comparison between the estimated number of sensor nodes \({\hat{n}}_m\) and the actual number of sensor nodes \(n_m\) in the mth frame for 50 trials when \(M=2\), \(T=60\), \(K=30\), and \(N=500\). We assume that the event \(H_1\) is happening. The range of the observation is divided into a censored region \({\mathcal {C}}_1 = \{x: -1 < x \le 2\}\) and two uncensored regions \({\mathcal {U}}_1 = \{x: -\infty < x \le -1\}\) and \({\mathcal {U}}_2 = \{x: 2< x < \infty \}\). As a result, we have \(q_{m|0} P_0 + q_{m|1} P_1\), for \(1 \le m \le 2\), are identical. The approximations of the optimal transmission probabilities \(\varvec{\rho ^{\star }} = (\rho _1^{\star }, \rho _2^{\star })\) are obtained from Proposition 4, where we have \(\rho _1^{\star } = \rho _2^{\star } = 0.28\)