MATLAB编写高斯投影反算程序有错，求帮助解决

2025-04-05 22:29:50

推荐回答（2个）

回答1：

我有VB的，自己很多年前写的，一直用，但是正算－>反算－>正算后，Y坐标与原来的差了0.5－0.7mm，不知道怎么回事，这两年工作忙也没有时间再深究，但是这样的计算精度做控制足够了，如果楼主或是者是哪位同仁见此贴能顺便把这个问题解决了，咱们就一起进步了！代码如下：

'高斯坐标正算
Private Sub DadiZs()
Dim t As Double, Itp As Double, X0 As Double, N As Double, L0 As Double
Dim V As Double, ll As Double, W As Double, M As Double
Lat = Radian(Lat)
Lon = Radian(Lon)
L0 = Radian(Lo)
If Tq = 0 Then
a = 6378245 '54椭球参数
b = 6356863.01877305
ep = 0.006693421622966
ep1 = 0.006738525414683
f = (a - b) / a
c = a ^ 2 / b
d = b ^ 2 / a
X0 = 111134.8611 * (Lat * 180# / Pi) - (32005.7799 * Sin(Lat) + 133.9238 * (Sin(Lat)) ^ 3 + 0.6973 * (Sin(Lat)) ^ 5 + 0.0039 * (Sin(Lat)) ^ 7) * Cos(Lat)
'X0 = 111134.8611 * (Lat * 180# / Pi) - (32005.7798 * Sin(Lat) + 133.9238 * (Sin(Lat)) ^ 3 + 0.6972 * (Sin(Lat)) ^ 5 + 0.0039 * (Sin(Lat)) ^ 7) * Cos(Lat)

Else
a = 6378140 '75椭球参数
b = 6356755.28815753
ep = 0.006694384999588
ep1 = 0.006739501819473
f = (a - b) / a
c = a ^ 2 / b
d = b ^ 2 / a
X0 = 111133.0047 * (Lat * 180 / Pi) - (32009.8575 * Sin(Lat) + 133.9602 * (Sin(Lat)) ^ 3 + 0.6976 * (Sin(Lat)) ^ 5 + 0.0039 * (Sin(Lat)) ^ 7) * Cos(Lat)
End If
ll = Lon - L0
t = Tan(Lat)
Itp = ep1 * Cos(Lat) ^ 2
W = Sqr(1 - ep * Sin(Lat) ^ 2)
V = Sqr(1 + ep1 * Cos(Lat) ^ 2)
M = c / V ^ 3
N = a / W
'x = X0 + N * t * (Cos(Lat)) ^ 2 * ll ^ 2 / 2 + N * t * (5 - t * t + 9 * Itp + 4 * Itp * Itp) * (Cos(Lat)) ^ 4 * ll ^ 4 / 24 + N * t * (61 - 58 * t ^ 2 + t ^ 4 + 270 * Itp - 330 * t ^ 2 * Itp) * (Cos(Lat)) ^ 6 * ll ^ 6 / 720 + N * t * (1385 - 3111 * t ^ 2 + 543 * t ^ 4 - t ^ 6) * Cos(Lat) ^ 8 * ll ^ 8 / 40320
x = X0 + N * t * (Cos(Lat)) ^ 2 * ll ^ 2 / 2 + N * t * (5 - t * t + 9 * Itp ^ 2 + 4 * Itp ^ 4) * (Cos(Lat)) ^ 4 * ll ^ 4 / 24 + N * t * (61 - 58 * t ^ 2 + t ^ 4 + 270 * Itp ^ 2 - 330 * t ^ 2 * Itp ^ 2) * (Cos(Lat)) ^ 6 * ll ^ 6 / 720 + N * t * (1385 - 3111 * t ^ 2 + 543 * t ^ 4 - t ^ 6) * Cos(Lat) ^ 8 * ll ^ 8 / 40320

y = N * Cos(Lat) * ll + N * (1 - t * t + Itp) * (Cos(Lat)) ^ 3 * ll ^ 3 / 6 + N * (5 - 18 * t * t + t ^ 4 + 14 * Itp - 58 * Itp * t * t) * (Cos(Lat)) ^ 5 * ll ^ 5 / 120 + N * (61 - 479 * t ^ 2 + 179 * t ^ 4 - t ^ 6) * Cos(Lat) ^ 7 * ll ^ 7 / 5040
r = Sin(Lat) * ll + Sin(Lat) * (Cos(Lat)) ^ 2 * ll ^ 3 * (1 + 3 * Itp + 2 * Itp ^ 2) / 3 + Sin(Lat) * (Cos(Lat)) ^ 4 * ll ^ 5 * (2 - t * t) / 15
r = Degree(r)
y = y + 500000#
End Sub

'高斯反算
Private Sub DadiFs()
Dim t As Double, Itp As Double, X0 As Double, Bf As Double, N As Double
Dim v As Double, ll As Double, W As Double, M As Double, L0 As Double
L0 = Radian(Lo)
X0 = x * 0.000001
y = y - 500000#
If Tq = 0 Then
a = 6378245 '54椭球参数
b = 6356863.01877305
ep = 0.006693421622966
ep1 = 0.006738525414683
f = (a - b) / a
c = a ^ 2 / b
d = b ^ 2 / a
If X0 < 3 Then
Bf = 9.04353301294 * X0 - 0.00000049604 * X0 ^ 2 - 0.00075310733 * X0 ^ 3 - 0.00000084307 * X0 ^ 4 - 0.00000426055 * X0 ^ 5 - 0.00000010148 * X0 ^ 6
ElseIf X0 < 6 Then
Bf = 27.11115372595 + 9.02468257083 * (X0 - 3) - 0.00579740442 * (X0 - 3) ^ 2 - 0.00043532572 * (X0 - 3) ^ 3 + 0.00004857285 * (X0 - 3) ^ 4 + 0.00000215727 * (X0 - 3) ^ 5 - 0.00000019399 * (X0 - 3) ^ 6
End If
Else
a = 6378140 '75椭球参数
b = 6356755.28815753
ep = 0.006694384999588
ep1 = 0.006739501819473
f = (a - b) / a
c = a ^ 2 / b
d = b ^ 2 / a
If X0 < 3 Then
Bf = 9.04369066313 * X0 - 0.00000049618 * X0 ^ 2 - 0.00075325505 * X0 ^ 3 - 0.0000008433 * X0 ^ 4 - 0.00000426157 * X0 ^ 5 - 0.0000001015 * X0 ^ 6
ElseIf X0 < 6 Then
Bf = 27.11162289465 + 9.02483657729 * (X0 - 3) - 0.00579850656 * (X0 - 3) ^ 2 - 0.00043540029 * (X0 - 3) ^ 3 + 0.00004858357 * (X0 - 3) ^ 4 + 0.00000215769 * (X0 - 3) ^ 5 - 0.00000019404 * (X0 - 3) ^ 6
End If
End If
Bf = Bf * Pi / 180#
t = Tan(Bf)
Itp = ep1 * Cos(Bf) ^ 2
W = Sqr(1 - ep * Sin(Bf) ^ 2)
v = Sqr(1 + ep1 * Cos(Bf) ^ 2)
M = c / v ^ 3
N = a / W
Lat = Bf - 0.5 * v ^ 2 * t * ((y / N) ^ 2 - (5 + 3 * t * t + Itp - 9 * Itp * t * t) * (y / N) ^ 4 / 12 + (61 + 90 * t * t + 45 * t ^ 4) * (y / N) ^ 6 / 360)
ll = ((y / N) - (1 + 2 * t * t + Itp) * (y / N) ^ 3 / 6 + (5 + 28 * t * t + 24 * t ^ 4 + 6 * Itp + 8 * Itp * t * t) * (y / N) ^ 5 / 120) / Cos(Bf)
r = y * t / N - y ^ 3 * t * (1 + t * t - Itp) / (3 * N ^ 3) + y ^ 5 * t * (2 + 5 * t * t + 3 * t ^ 4) / (15 * N ^ 5)
Lat = Degree(Lat)
Lon = Degree(L0 + ll)
r = Degree(r)
End Sub
有了正反算，换带也就完成了！
用到的子程序：
Public Const Pi = 3.14159265358979, p = 206264.806
Public Cktq As String

'角度化弧度
Public Function Radian(a As Double) As Double
Dim Ro As Double
Dim c As Double
Dim Fs As Double
Dim Ib As Integer
Dim Ic As Integer
If a < 0 Then a = -a: t = 1
Ro = Pi / 180#
Ib = Int(a)
c = (a - Ib) * 100#
Ic = Int(c + 0.000000000001)
Fs = (c - Ic) * 100#
If t = 1 Then Radian = -(Ib + Ic / 60# + Fs / 3600#) * Ro Else Radian = (Ib + Ic / 60# + Fs / 3600#) * Ro
End Function
'弧度化角度
Public Function Degree(a As Double) As Double
Dim Bo As Double
Dim Fs As Double
Dim Im As Integer
Dim Id As Integer
If a < 0 Then a = -a: t = 1
Bo = a
Call DMS(Bo, Id, Im, Fs)
If t = 1 Then Degree = -(Id + Im / 100# + Fs / 10000#) Else Degree = Id + Im / 100# + Fs / 10000#
End Function
Public Sub DMS(a As Double, Id As Integer, Im As Integer, Fs As Double)
Dim Bo As Double
Dim c As Double
c = a
c = 180# / Pi * c
Id = Int(c)
Bo = (c - Id) * 60
Im = Int(Bo)
Fs = (Bo - Im) * 60
End Sub
'取位计算
Public Function Qw(a As Double, Ws As Integer) As Double
Qw = Int(a * 10 ^ Ws + 0.5) / 10 ^ Ws
End Function
另外,站长团上有产品团购,便宜有保证

回答2：

/*
方程组维数?:?3
控制精度?:?0.0000006
系数矩阵
2?1?-1
3?-1?1
1?3?-1
系数矩阵输入完毕!
常数项矩阵
-1?6?2
常数项矩阵输入完毕!
整理完毕，此时方程组为
1 -0.333333 0.333333 2
0 1 -0.4 0
0 0 1 5

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