SCIENTIA SINICA Informationis, Volume 49 , Issue 7 : 868-885(2019) https://doi.org/10.1360/N112018-00030

WLAN indoor target intrusion detection algorithm based on adaptive-depth ray tree

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  • ReceivedFeb 7, 2018
  • AcceptedMay 18, 2018
  • PublishedMay 10, 2019


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  • Table 1   The calculation process of each layer of PNN neurons
    Functional layer Number of neurons Calculation process
    Input layer Signal feature dimension $d$ (1) Compute ${z_k}~=~{\boldsymbol~x}_k^{\rm{T}}{\boldsymbol~x}~(k~=~1,{\rm{~}}~\ldots~,~n)$, in which ${\boldsymbol~x}~=~({{{x_1}}~/~{\sqrt~{\sum\nolimits_{j~=~1}^d~{x_j^2}~}~}},~\ldots~,$ ${{{x_d}}~/~{\sqrt~{\sum\nolimits_{j~=~1}^d~{x_j^2}~}~}})$ and ${{\boldsymbol~x}_k}~=~({{{x_{k1}}}~/~{\sqrt~{\sum\nolimits_{j~=~1}^d~{x_{kj}^2}~}~}},{\rm{~}}~\ldots~,{\rm{~}}{{{x_d}}~/~{\sqrt~{\sum\nolimits_{j~=~1}^d~{x_{kj}^2}~}~}})$ are normalization vectors of test sample and $k$-th training sample, respectively, $n$ is the size of training samples. (2) Assign the connection weights $\omega_{jk}$ of the $j$-th neuron in the input layer and the $k$-th neuron in the model layer, and the assignment process is described in Algorithm 3.
    Model layer $n$ (1) Compute kernel density function $\varphi~({z_k})~=~\exp~(\frac{{{z_k}~-~1}}{{{\delta~^2}}})$, in which $\delta$ is the smoothing factor. (2) Assign the connection weights ${a_{ki}}~(i~=~1,{\rm{~}}~\ldots~,{\rm{~}}c)$ of the $k$-th neuron in the model layer and the $i$-th neuron in the summation layer, in which $c$ is the number of states. If ${\boldsymbol~x}_k$ belongs to $i$-th state, then $a_{ki}=1$, otherwise $a_{ki}=0$, as described in Algorithm 3.
    Summation layer $c$ Compute the conditional probability of ${\boldsymbol~x}$ belonging to the $i$-th state ${g_i}({\boldsymbol{x)}}~=~\frac{{{P_i}}}{{{N_i}}}\sum\nolimits_{k~\in~\{~1,{\rm{~}}~\ldots~,{\rm{~}}n\}~~\cup~{a_{ki}}~=~1}~{\varphi~({z_k})}$, in which $P_i$ is the priori probability of the $i$-th state and, $N_i$ is the number of training samples that belong to the $i$-th state.
    Output layer $1$ Compute$\max~\{~{g_i}({\boldsymbol~x}),{\rm{~}}i~\in~\{~1,{\rm{~}}~\ldots~,{\rm{~}}c\}~\}$, in which the $i$ that corresponds to the maximum value of $g_i({\boldsymbol~x})$ is the output state of PNN.
  • Table 2   Average time cost for ray modeling between each pair of AP and MP
    Performance index Ref. [18] Ref. [12] The proposed method
    Time overhead (s) 6.03 7.25 3.41
  • Table 3   Performance comparison of different intrusion detection methods
    Performance index MA MV Radio tomographic imaging Neural network The proposed method
    Missed detection probability (%) 14.46 14.26 7.08 5.23 3.42
    False detection probability (%) 13.85 10.40 12.47 9.01 7.96
    Successful detection probability (%) 95.8 94.5 97.40
    Average time overhead 2.35 2.46 9.77 6.57 6.62
    for single detection (s)