## Appendix A  
In this appendix, we will introduce the least squares method to calculate the equivalent velocity of the LEO satellite. The fitted polynomial of the range from the satellite to the target is supposed as \(y^{\prime}\). \(a_{0}\) and \(a_{1}\) are the fitting coefficients of the constant and first order term, respectively. \(a_{k}\) is the fitting coefficient of the \(k_{th}\) (\(k_{nd}\), \(k_{rd}\), \(k\in N\), \(N\) is the natural number) order term. Then, \(y^{\prime}\) is expressed as follows:  
\[y^{\prime}=a_{0}+a_{1}x+\ldots+a_{k}x^{k} \tag{1}\]  
Assume that the curve to be fitted is \(y\), then the sum of distances between \(y^{\prime}\) and \(y\) can be expressed as follows:  
\[R^{2}=\sum_{i=1}^{n}[y_{i}-(a_{0}+a_{1}x_{i}+\ldots+a_{k}(x_{i})^{k})]^{2} \tag{2}\]  
Find the minimum value of the above variance, and the partial derivatives of \(a_{0}\),..., \(a_{k}\) are sequentially calculated as 0:  
\[\begin{cases}\frac{\partial R^{2}}{\partial a_{0}}=-2\sum_{i=1}^{n}[y_{i}-(a_ {0}+a_{1}x_{i}+\ldots+a_{k}(x_{i})^{k})]=0\\ \frac{\partial R^{2}}{\partial a_{1}}=-2\sum_{i=1}^{n}[y_{i}-(a_{0}+a_{1}x_{ i}+\ldots+a_{k}(x_{i})^{k})]x=0\\ \ldots\\ \frac{\partial R^{2}}{\partial a_{k}}=-2\sum_{i=1}^{n}[y_{i}-(a_{0}+a_{1}x_{ i}+\ldots+a_{k}(x_{i})^{k})]x_{k}=0\end{cases} \tag{3}\]  
After derivations of the above formula, we obtain the following equations:  
\[\begin{split} a_{0}n+a_{1}\sum_{i=1}^{n}x_{i}+\ldots+a_{k}\sum_{ i=1}^{n}x_{i}^{k}=\sum_{i=1}^{n}y_{i}\\ a_{0}\sum_{i=1}^{n}x_{i}+a_{1}\sum_{i=1}^{n}x_{i}^{2}+\ldots+a_{k}\sum_{i=1} ^{n}x_{i}^{k+1}=\sum_{i=1}^{n}x_{i}y_{i}\\ \ldots\\ a_{0}\sum_{i=1}^{n}x_{i}^{k}+a_{1}\sum_{i=1}^{n}x_{i}^{k+1}+\ldots+a_{k} \sum_{i=1}^{n}x_{i}^{2k}=\sum_{i=1}^{n}x_{i}^{k}y_{i}\end{split} \tag{4}\]Express the above equations in the form of matrix:  
\[\left[\begin{array}{cccc}n&\sum_{i=1}^{n}x_{i}&\cdots&\sum_{i=1}^{n}x_{i}^{k}\\ \sum_{i=1}^{n}x_{i}&\sum_{i=1}^{n}x_{i}^{2}&\cdots&\sum_{i=1}^{n}x_{i}^{k+1}\\ \vdots&\vdots&\ddots&\vdots\\ \sum_{i=1}^{n}x_{i}^{k}&\sum_{i=1}^{n}x_{i}^{k+1}&\cdots&\sum_{i=1}^{n}x_{i}^{ 2k}\end{array}\right]\left[\begin{array}{c}a_{0}\\ a_{1}\\ \vdots\\ a_{k}\end{array}\right]=\left[\begin{array}{c}\sum_{i=1}^{n}y_{i}\\ \sum_{i=1}^{n}x_{i}y_{i}\\ \vdots\\ \sum_{i=1}^{n}x_{i}^{k}y_{i}\end{array}\right] \tag{10}\]  
We transform the first item of the matrix equation to the Vandermonde form:  
\[\left[\begin{array}{cccc}1&1&\cdots&1\\ x_{1}&x_{2}&\cdots&x_{n}\\ \vdots&\vdots&\ddots&\vdots\\ x_{1}^{k}&x_{2}^{k}&\cdots&x_{n}^{k}\end{array}\right]\left[\begin{array}[] {c}1&x_{1}&\cdots&x_{1}^{k}\\ 1&x_{2}&\cdots&x_{2}^{k}\\ \vdots&\vdots&\ddots&\vdots\\ 1&x_{n}&\cdots&x_{n}^{k}\end{array}\right]\left[\begin{array}{c}a_{0}\\ a_{1}\\ \vdots\\ a_{k}\end{array}\right]=\left[\begin{array}{c}1&1&\cdots&1\\ x_{1}&x_{2}&\cdots&x_{n}\\ \vdots&\vdots&\ddots&\vdots\\ x_{1}^{k}&x_{2}^{k}&\cdots&x_{n}^{k}\end{array}\right]\left[\begin{array}[] {c}y_{1}\\ y_{2}\\ \vdots\\ y_{n}\end{array}\right] \tag{11}\]  
\[\text{Assume }X=\left[\begin{array}{cccc}1&x_{1}&\cdots&x_{1}^{k}\\ 1&x_{2}&\cdots&x_{2}^{k}\\ \vdots&\vdots&\ddots&\vdots\\ 1&x_{n}&\cdots&x_{n}^{k}\end{array}\right],A=\left[\begin{array}{c}a_{0}\\ a_{1}\\ \vdots\\ a_{k}\end{array}\right],Y=\left[\begin{array}{c}y_{1}\\ y_{2}\\ \vdots\\ y_{n}\end{array}\right],\text{ then the above matrix equation can be simplified as }X^{\prime}XA=X^{\prime}Y\). The coefficient vector \(A\) is obtained by \(A=(X^{\prime}X)^{-1}X^{\prime}Y\), and the effective radar velocity is calculated according to the coefficients.