## 4 Edge Prediction Algorithm Based on ARMA
### EP-ARMA Implementation  
The sensor nodes will collect monitoring data sets as \(\{\mathrm{collect_{i}}\}\) in the monitoring period T. Additionally, then, based on the ARIMA\((\mathrm{p},\mathrm{d},\mathrm{q})\) model and historical data, the forecast data sets \(\{\mathrm{forecast_{i}}\}\) can also be generated, where \(\mathrm{i}\) is the time point of data collection. When the underwater monitoring data acquisition accuracy is \(\{\mathrm{accuracy}\}\), the following requirements should be met to ensure the result of edge prediction is suitable for underwater monitoring:  
\[\forall\,\mathrm{i}\in\{1,\cdots,\mathrm{T}\}|\mathrm{forecast_{i}}-\mathrm{ collect_{i}}|\leq\mathrm{accuracy}, \tag{6}\]  
However, due to the randomness and abruptness of time series changes, it is not possible to ensure that all prediction data can fulfil Formula (6). Therefore, a certain amount of collected data should be used as the correction data. When there is a large deviation between the predicted data and the collected data at a certain time point, the collected data at that time point are used to replace the prediction data, and the corrected prediction data set \(\{\mathrm{forecast^{\prime}_{i}}\}\) and the correction data set \(\{\mathrm{n},\mathrm{i},\mathrm{\ correct_{j}}\}\) are generated, where \(\mathrm{n}\) is the number of correction data, \(\mathrm{i}\) is the correction time point, and \(j\) is the identification of correction data. By transmitting the prediction parameters and the correction data set, the corrected prediction data set \(\{\mathrm{forecast^{\prime}_{i}}\}\) that meets the accuracy requirements of Formula (6) can be recovered at the remote end. The underwater monitoring data acquisition accuracy is dynamically adjusted within the range of \(\{\mathrm{accuracy_{high}},\cdots,\mathrm{\ accuracy_{low}}\}\). When the number of correction data sets \(\mathrm{n}\) is equal to \(n_{min}\), the corrected forecast data set \(\{\mathrm{forecast^{\prime}_{i}}\}\) can meet the accuracy\({}_{\mathrm{low}}\). When the number of correction data sets is equal to \(\mathrm{n_{max}}\), the corrected forecast data set \(\{\mathrm{forecast^{\prime}_{i}}\}\) can meet the accuracy\({}_{\mathrm{high}}\). Therefore, \(\mathrm{n}\) will change in \(\{\mathrm{n_{min}},\cdots,\mathrm{\ n_{max}}\}\). The prediction parameters (\(\mathrm{p}\), \(\mathrm{d}\), \(\mathrm{q}\)) and correction time points \(\mathrm{i}\) are also transmitted when the correction data are transmitted. If the number of correction data sets is taken as \(\mathrm{n_{min}}\), the amount of data to be transmitted is still greater than the amount of data to be collected directly, and the algorithm will not be applicable. Assume that \(\mathrm{p}\), \(\mathrm{d}\), \(\mathrm{q}\) and \(\mathrm{i}\) are expressed as integer data, and the collected and correction data are expressed as float data. Then, \(\mathrm{1}\) byte represents the integer data, \(\mathrm{4}\) bytes represent the float data, and when \(\mathrm{n_{min}}\) cannot meet:  
\[\mathrm{n_{min}}<\frac{4\times\mathrm{T}-3}{5}, \tag{7}\]  
EP-ARMA will not be suitable for underwater monitoring applications with such accuracy. It is more efficient to directly transmit the collected data or adjust the prediction model. When \(\mathrm{n_{min}}\) fulfils Formula (7), the number of correction data sets can be adjusted to reduce the amount of data actually transmitted in the underwater network and improve the efficiency of underwater monitoring data transmission. \(\mathrm{n_{min}}\) is set as the threshold value. Each node needs to ensure that the number of transmission correction nodes is not less than the threshold value. The value of accuracy\({}_{\mathrm{low}}\) is generally given by the application program, which is an insurmountable threshold for data transmission. The accuracy\({}_{\mathrm{low}}\) is constant in the whole communication process.