## 3 Proposed Ranging-Compensated Temperature-Sensing Sensor Design Method
### Data Preprocessing Flow and Method  
The data preprocessing flow includes the data collection of temperature versus delay measurement, deviation delay data processing, compensation data storage, and compensation data calling. Each step involves a corresponding mathematical processing method, as described in details below. We assume that the number of sampling bits of the ADC is \(N\) and the ambient temperature range in space is \(\Delta T\). Then, the temperature resolution is \(\frac{\Delta T}{2^{N}}\). We also assume that the sampling rate of the ADC is \(S\) Hz and the sampling value is \(x_{n}\). Because the space-temperature change is a gradual process, to avoid acquisition of instantaneous noise by the ADC resulting in compensation data bias, we first integrate sampling data \(x_{n}\). The integration time is \(t\). The starting point for the integration is the transmission or reception moment of the ISL payload ranging signal, and \(t\) is much smaller than the time of ambient temperature change \(\frac{\Delta T}{2^{N}}\). Then, we calculate the arithmetic mean of the integral result and obtain sample value \(V\). Traversing the entire temperature range can provide sequence \(V_{i}\), which is expressed as follows:  
\[V_{i}=\frac{\sum\limits_{n=0}^{St}x_{n}}{St}\,\ n\in[0,\ 2^{N}-1]. \tag{2}\]  
Each \(V_{i}\) corresponds to transmission-delay value \(\tau_{i}^{T}\) and reception-delay value \(\tau_{i}^{R}\). Because the ground temperature-control equipment cannot achieve precise temperature control with resolution of \(\frac{\Delta T}{2^{N}}\), measured sequence \(V_{i}\) cannot traverse the data space \([0,2^{N}-1]\). Therefore, we need to use the MATLAB (R2014a, MathWorks, Natick, Massachusetts, USA) tool function \(polyfit(x,y,n)\) to perform data fitting for \(\tau_{i}^{T}\) and \(\tau_{i}^{R}\), which yields the following:  
\[\left\{ \begin{array}{c}\left[p^{T},S^{T}\right]=polyfit\left(V_{i},\tau_{i}^ {T},k\right),\\ \left[p^{R},S^{R}\right]=polyfit\left(V_{i},\tau_{i}^{R},k\right),\end{array} \right. \tag{3}\]  
where \(k\) is the order of the fitting polynomial, \(p^{T}\) and \(p^{R}\) are the coefficients of the fitting polynomial, and structures \(S^{T}\) and \(S^{R}\) are used to obtain error estimates with function \(polyval(p,x)\). Then, we use function \(polyval(p,x)\) to determine fitting sequences \(\widetilde{\tau_{i}^{T}}\) and \(\widetilde{\tau_{i}^{R}}\), which are expressed as  
\[\left\{ \begin{array}{c}\left[\frac{\tau_{i}^{T}}{\tau_{i}^{R}},delta\right] =polyval\left(p^{T},V_{N},S^{T}\right),\ \ V_{N}=\left(V_{0},V_{1},V_{2},\cdots,V_{2^{N}-1}\right),\\ \left[\frac{\tau_{i}^{R}}{\tau_{i}^{R}},delta\right]=polyval\left(p^{R},V_{N},S^{R}\right),\ \ V_{N}=\left(V_{0},V_{1},V_{2},\cdots,V_{2^{N}-1}\right),\end{array} \right. \tag{4}\]  
where \(delta\) is the estimate of the standard deviation of the fitting error and \(V_{N}\) is the sample sequence of the \(N\)-bit ADC. To ensure accuracy of the collected data, we keep the ISL payload connection state  
Figure 3: Architecture of the ranging compensation temperature-sensing sensor. unchanged, traverse again the temperature change interval, and fit the test data \(j\) times. Then, we obtain transmission-delay matrix \(\widetilde{\tau_{i,j}^{T}}\) and reception-delay matrix \(\widetilde{\tau_{i,j}^{R}}\) as follows:  
\[\left\{\begin{array}{l}\widetilde{\tau_{i,j}^{T}}=\left( \begin{array}{ccc} \widetilde{\tau_{i,1}^{T}}&\ldots&\widetilde{\tau_{i,j}^{T}}\\ \vdots&\ddots&\vdots\\ \widetilde{\tau_{i,N-1,1}^{T}}&\ldots&\widetilde{\tau_{i,N-1,j}^{T}}\\ \widetilde{\tau_{i,j}^{R}}=\left(\begin{array}{ccc}\widetilde{\tau_{i,1}^{R }}&\ldots&\widetilde{\tau_{i,j}^{R}}\\ \vdots&\ddots&\vdots\\ \widetilde{\tau_{i,N-1,1}^{R}}&\ldots&\widetilde{\tau_{i,N-1,j}^{R}}\\ \end{array}\right).\end{array} \right.