## 3 Wireless Sensor Network Model for the Internet of Things
### Establishment of the LE-LPCCA Positioning Algorithm Model Based on the Sensor Grid  
In wireless sensor networks, the signal space data and physical space data collected by known sensors can be expressed as two sets of datasets [21], with X = [x1, x2,..., xn]\({}^{\mathrm{p}\times\mathrm{N}}\) representing the signal strength received by n known nodes, where the dimension of each signal vector \(x_{i}\) (I = 1, 2,..., n) is p, p is the number of Access Points (AP nodes), and Y = [y1, y2,..., yn]\({}^{\mathrm{p}\times\mathrm{N}}\) represents the physical coordinate of the corresponding node. The direct neighbor q represents the direct neighbor of the sample data p, and the direct neighbor relationship is irreversible. If the direct neighbor of data point p is data point q, then the direct neighbor of data point q is not data point p, so q = 2 or 3. The primary task of building a positioning model is to establish the mapping between two datasets. The CCA data mapping method based on a wireless sensor grid is a classical method used to construct the mapping between two groups of data. Its goal is to find two groups of basis vectors \(w_{x}\in\mathrm{RP}\) and \(w_{y}\in\mathrm{Rq}\) for X and Y, respectively, so that the correlation between the transformed data \(w_{x}\mathrm{{}^{T}}\) (\(x_{i}-x\)) and \(w_{y}\mathrm{{}^{T}}\) (\(y_{i}-y\)) can reach the maximum. Through the definition of correlation and several steps of mathematical derivation, the CCA can be expressed as the solution to the optimization problem:  
\[\max_{w_{x},w_{y}}\mathbf{w}_{x}^{\mathrm{T}}\sum_{i=1}^{n}\sum_{j=1}^{n}\bigl{(}x_ {i}-x_{j}\bigr{)}\bigl{(}\mathbf{y}_{i}-\mathbf{y}_{j}\bigr{)}^{\mathrm{T}}\mathbf{w}_{y} \tag{1}\]  
\[\mathrm{s}\cdot\mathrm{t}\cdot\mathbf{w}_{x}^{\mathrm{T}}\sum_{i=1}^{n}\sum_{j=1}^ {n}\bigl{(}\mathbf{x}_{i}-\mathbf{x}_{j}\bigr{)}\bigl{(}\mathbf{x}_{i}-\mathbf{x}_{j}\bigr{)} ^{\mathrm{T}}\mathbf{w}_{x}=1 \tag{2}\]  
\[\mathbf{w}_{y}^{\mathrm{T}}\sum_{i=1}^{n}\sum_{j=1}^{n}\bigl{(}\mathbf{y}_{i}-\mathbf{y}_{ j}\bigr{)}\bigl{(}\mathbf{y}_{i}-\mathbf{y}_{j}\bigr{)}^{\mathrm{T}}\mathbf{w}_{y}=1. \tag{3}\]  
By solving the optimization problem (1), (2), and (3), we can obtain \(w_{x}\) and \(w_{y}\) and then transform the IoT data to the forms \(w_{x}\mathrm{{}^{T}}\) (\(x_{i}-x\)) and \(w_{y}\mathrm{{}^{T}}\) (\(y_{i}-y\)). After transformation, the correlation between the two datasets is the largest; however, if the mapping of the signal space to the physical space in the WSN is established based on the CCA, and the positioning model is built, only the linear correlation between two groups of data can be mined, and the local structure information of the network is not used. The wireless sensor algorithm model can measure the static strain of the structure, and the measurement data are better after the data fusion processing. Therefore, some scholars have used the algorithm model to collect the swing data of the large lifting pipe-laying vessel hook model and effectively verified the feasibility of the anti-swing control model. In the signal space of wireless sensor networks, the ne (_i_) represents a set of node labels similar to the signal strength received by node \(i\), that is, the subscript set of \(x_{i}\)'s local nearest neighbor samples. In the physical space, the ne (_i_) represents the subscript set of nodes adjacent to the location of node \(i\), where the local nearest neighbor is divided by the k-nearest neighbor method: if \(x_{j}\) (\(y_{j}\)) is the k-nearest neighbor sample of \(x_{i}\) (\(y_{i}\)), then \(x_{j}\) (\(y_{j}\)) is said to be the local nearest neighbor of \(x_{i}\) (\(y_{i}\)).