Real-Time Vehicle Motion Detection and Motion Altering for Connected Vehicle: Algorithm Design and Practical Applications

. 2019 Sep 23;19(19):4108. doi: 10.3390/s19194108

Algorithm 1: Fast Optimal Wavelet Basis (OWB) Extraction

Step 1. Select as the largest levels No. for wavelet packet (WP) dissolution
Step 2. If the current level (

d

) of dissolution is smaller than

L

. Execute 2.1–2.4 to every existent parent-node (sub-band)

S_{d}^{i} (0 \leq i \leq 4^{d} - 1)

.
Step 2.1 Calculate Shannon entropy

S E (S_{d}^{i})

of sub-band as the cost function.
Step 2.2 Divide

S_{d}^{i}

into 4 sub-bands (children-nodes:

L L_{d + 1}^{4 i}

L L H_{d + 1}^{4 i + 1}

H L_{d + 1}^{4 i + 2}

and

H H_{d + 1}^{4 i + 3}

). Calculate their Shannon entropy:

{S E (L L}_{d + 1}^{4 i})

S E (L H_{d + 1}^{4 i + 1})

S E (H L_{d + 1}^{4 i + 2})

and

S E (H H_{d + 1}^{4 i + 3})

.
Step 2.3 If

{S E (S}_{d}^{i} {) < (S E (L L}_{d + 1}^{4 i} {) + S E (L H}_{d + 1}^{4 i + 1} {) + S E (H L}_{d + 1}^{4 i + 2} {) + S E (H H}_{d + 1}^{4 i + 3}))

is true, keep the parent node and delete the children-nodes. If it is false, keep both the parent- nodes and children-nodes.
Step 2.4 If no nodes are available to divide, end for extracting the OWB.