From: Social learning for resilient data fusion against data falsification attacks
Network properties | ||
N | \(\triangleq\) | Size of the sensor network |
\(N^*\) | \(\triangleq\) | Number of Byzantine nodes |
\(p_{\text{b}}\) | \(\triangleq\) | Probability of a given node being compromised |
Sensor and social signals | ||
\(S_n\) | \(\triangleq\) | Signal measured by the n-th node |
\(\mathcal {S}\) | \(\triangleq\) | Set of values that \(S_n\) can take |
\(\mu _w\) | \(\triangleq\) | Distribution of \(S_n\) given \(W=w\) |
\(\Lambda _S(s)\) | \(\triangleq\) | Log-likelihood of \(S_n\) with respect to W |
\(F_w^\Lambda (s)\) | \(\triangleq\) | c.d.f. of \(\Lambda _S(s)\) conditioned on \(W=w\) |
\(\varvec{G}_n\) | \(\triangleq\) | Social observations of the n-th node |
\(\mathcal {G}_n\) | \(\triangleq\) | Set of values that \(\varvec{G}_n\) can take |
\(\Lambda _{\varvec{G}_n}(\varvec{g})\) | \(\triangleq\) | Log-likelihood of \(\varvec{G}_n\) with respect to W |
\(\beta _w^n(\varvec{g} | x_n,\varvec{g'})\) | \(\triangleq\) | Transition probabilities from \(\varvec{G}_{n-1}\) to \(\varvec{G}_{n}\) given \(X_n\) and W |
Data fusion variables | ||
W | \(\triangleq\) | Target of the networked inference |
\(u(\pi _n,w)\) | \(\triangleq\) | Node’s utility function for deciding \(\pi _n\) when \(W=w\) |
\(\tau _n\) | \(\triangleq\) | Decision threshold used by the n-th node |
\(\pi _n(s,\varvec{g})\) | \(\triangleq\) | Data fusion strategy of the n-th node given \(S_n\) and \(\varvec{G}_n\) |
\(X_n\) | \(\triangleq\) | Signal broadcasted by the n-th node |
\(C(\pi _n), c_{0|0}, c_{0|1}\) | \(\triangleq\) | Corruption function, which links \(\pi _n\) and \(X_n\) |
\(\mathbb {P}\{\text {MD};p_b\}\) | \(\triangleq\) | Network miss-detection rate |
\(\mathbb {P}\{\text {FA};p_b\}\) | \(\triangleq\) | Network false alarm rate |
Simulation parameters | ||
r | \(\triangleq\) | Ratio of the area of interest within the sensing range of a single node |
m | \(\triangleq\) | Number of quantization levels of a node’s sensor |
k | \(\triangleq\) | Node’s memory size |