???? 本程序采用VB.net語言編寫。

???? 本程序采用插值算法，來完成對精密星歷鐘差文件（.clk)的加密工作。如可以將30S鐘差間隔的鐘差文件加密到15s、10s、2s、1s等。 程序中寫有四種經典的插值算法，分別是Lagrange插值算法、Newton插值算法、三次樣條插值算法、分段線性插值算法等，這幾種算法的正確性以得到過驗證。

??? 首先導入精密星歷鐘差文件，根據導入的鐘差文件進行判斷，將其信息進行整理并繪制可視化圖表以顯示24H內每顆衛星的鐘差變化趨勢。

??? 導入文件之后，可以根據用戶自身的插值需求將鐘差文件加密到更小的鐘差間隔，如導入的精密星歷衛星鐘差文件為5min鐘差間隔，用戶可以將其加密到30s、15s、10s以及更小的鐘差間隔，并根據結果生成相應的clk文件。

插值算法：

Lagrange插值：

Public Function Lagrange(X() As Double, Y() As Double, xx As Double)Dim yy As Double = 0 '最后返回的多項式值Dim ll(X.Length - 1) As Double '中間變量For i = 0 To X.Length - 1Dim l1 As Double = 1 '多項式系數分子Dim l2 As Double = 1 '多項式系數分母For j = 0 To X.Length - 1If i <> j Thenl1 = l1 * (xx - X(j))l2 = l2 * (X(i) - X(j))ElseContinue ForEnd IfNextll(i) = l1 / l2NextFor i = 0 To X.Length - 1yy = yy + ll(i) * Y(i)NextReturn yyEnd Function

Newton插值：

Public Function Newton(X() As Double, Y() As Double, xx As Double)Dim yy As Double = 0 '最后返回的多項式值Dim n As Integer = UBound(X) '節點數Dim A(n, n) As Double '差商表Dim dx(n) As Double '牛頓多項式中（x-x0）項'計算差商表For i = 0 To nA(i, 0) = Y(i)NextFor i = 1 To nFor j = 1 To iA(i, j) = (A(i, j - 1) - A(i - 1, j - 1)) / (X(i) - X(i - j))NextNext'計算II（x-xi)dx(0) = 1For i = 1 To ndx(i) = dx(i - 1) * (xx - X(i - 1))Next'計算牛頓多項式For i = 0 To nyy = yy + A(i, i) * dx(i)NextReturn yyEnd Function

三次樣條插值：

Public Function CubicSpline(X As Double(), Y As Double(), xx() As Double)Dim yy(xx.Length - 1) As Double '函數返回的對應xx 的插值Dim n As Integer = UBound(X)Dim S2(n, 0), m(n, 0), AA(n, n) As Double '用于矩陣運算,即AA*M=S2Dim h(n - 1) As Double '計算步長，即X(i+1)-X(i)Dim dy(n - 1) As Double 'y的微分For i = 0 To n - 1h(i) = X(i + 1) - X(i)dy(i) = (Y(i + 1) - Y(i)) / h(i)Next'自然邊界型三次樣條，二階導數兩個端點值為0S2(0, 0) = 0 : S2(n, 0) = 0For i = 1 To n - 1S2(i, 0) = 6.0 * (dy(i) - dy(i - 1))Next'確定系數陣AAAA(0, 0) = 1AA(n, n) = 1For i = 1 To n - 1AA(i, i - 1) = h(i - 1)AA(i, i) = 2 * (h(i - 1) + h(i))AA(i, i + 1) = h(i)Next'求二次微分陣mm = Multiply(Inv(AA), S2)'求多項式Dim a, b, c, d, dx As DoubleFor j = 0 To xx.Length - 1For i = 0 To nIf (xx(j) > X(i) Or xx(j) = X(i)) And (xx(j) < X(i + 1) Or xx(j) = X(i + 1)) Thena = Y(i)b = (Y(i + 1) - Y(i)) / h(i) - h(i) / 2.0 * m(i, 0) - h(i) * (m(i + 1, 0) - m(i, 0)) / 6c = m(i, 0) / 2d = (m(i + 1, 0) - m(i, 0)) / (6.0 * h(i))dx = xx(j) - X(i)yy(j) = a + b * dx + c * dx ^ 2 + d * dx ^ 3Exit ForElseContinue ForEnd IfNextNextReturn yyEnd Function

線性插值：

Public Function PiecewiseLinearity(X As Double(), Y As Double(), xx As Double)Dim yy As Double '函數返回的對應xx 的插值For i = 1 To X.Length - 1If xx >= X(i - 1) And xx <= X(i) Thenyy = (xx - X(i)) / (X(i - 1) - X(i)) * Y(i - 1) + (xx - X(i - 1)) / (X(i) - X(i - 1)) * Y(i)Exit ForElseContinue ForEnd IfNextReturn yyEnd Function

源程序與exe文件下載地址：精密星歷衛星鐘差插值程序

畢業答辯PPT：https://download.csdn.net/download/weixin_44705612/85820126

歡迎喜歡vb語言的朋友一起交流探討。 本人VB.NET語言水平尚可，有需要代寫程序可以私信我。

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