# An Approach to Dynamic Sensing Data Fusion
## 2 Dynamic Acquisition and Fusion  
### Data Change Decision  
In data change decision, we make decisions based on the data currently collected. It determines a collection window in advance and then fits the data in the collection window and predicts the data of the next collection point. After collecting the data of the next collection point, the predicted data and the practical data are compared. If the compared result exceeds the specified threshold, the data is regarded to be changing remarkably; otherwise, the data is considered to be changing slowly. During the whole movement process, due to the interference of external factors, the change in sensor data appears irregular. However, in a relatively small range, this change can be approximated by a function [14]. In order to facilitate calculation, the data in the acquisition window are processed by regression. Suppose \(m\) to be the size of the collection window. For \(x_{i}\), which is one of the components of \(X\), we continuously conduct the collection process \(m\) times, i.e., collect \(m\) times the values of \(x_{i,1}\), \(x_{i,2}\),..., \(x_{i,m}\) and then predict the value of \(x_{i,m+1}\) based on the collected data. If the predicted value of \(x_{i}\) is \(x_{i}\)', then the absolute value of the degree of change will be \(|x_{i}-x_{i}\)'. Let \(\overline{D}_{i}^{m}\) denote the variance of \(m\) collection points related with \(x_{i}\). Then, \(|x_{i}-x_{i}|/\overline{D}_{i}^{m}\) denotes the relative changing degree related with \(x_{i}\). Obviously, the relative changing degree is a numeric number greater than 0, and in most cases, the number is less than 1. For the method of data change decision, we give a data changing degree threshold [\(\varepsilon^{-}\), \(\varepsilon^{+}\)] in advance and then compare the value of actual change and the threshold. If the value of actual change is greater than the given threshold \(\varepsilon^{+}\), we regard the data change as exceeding the maximum linear errors permitted by the system, and the acquisition time intervals will be shortened to improve the fitting precision. If the actual change is less than the given threshold \(\varepsilon^{-}\), we regard the data change as lower than the minimum linear errors permitted by the system and then adopt the method that increases the acquisition timeintervals to decrease the bandwidth. If the actual change is within the interval [\(\varepsilon^{-}\), \(\varepsilon^{+}\)], we regard the current acquisition timeintervals as better portraying the changing data, and the acquisition timeintervals are kept the same. Equation (1) formalizes these situations. \[ \begin{cases}\left|x_{i}-x_{i}^{\prime}\right|/\overline{D}_{i}^{m}>\varepsilon ^{+}&\text{ shorten collecting interval}\\ \left|x_{i}-x_{i}^{\prime}\right|/\overline{D}_{i}^{m}<\varepsilon^{-}&\text { increase collecting interval}\\ \text{otherwise}&\text{ mantain collecting interval}\end{cases}  \tag{1}\]  
In Equation (1), \(x_{i}\) takes values according to the domain knowledge; \(x_{i}\)' is the predicted value of \(x_{i}\), whose unit is the same as \(x_{i}\); \(m\) is the size of the collection window, i.e., the number of samples; \(\overline{D}_{i}^{m}\) is the variance of \(m\) samples; \(\varepsilon^{-}\) is the minimum threshold of data changing degree; \(\varepsilon^{+}\) is the maximum threshold of data changing degree. The size of the collection window, \(m\), is set according to the domain, and the values of \(m\) are different in different fields. If \(m\) takes the larger values, more historical data is used for prediction and the predicting precision is higher, but the time consumption is larger. If \(m\) takes the smaller  
**Definition 1** (acquisition time slice, \(\Delta\tau\)). : The acquisition time slice is the basic unit of acquisition time, and the acquisition time interval consists of one or more acquisition time slices. Suppose acquisition timeinterval to be T and T = K\(\Delta\tau\), where K takes the integers greater than or equal to 1.