测量专业基本计算与编程(4)

m m m m 参 考 值

注：例1取自朱华统：《椭球大地计算》P97算例；例2取自陈键、晁定波主编《椭球大地测量学》P90面的数据；例3、例4取自赵文光著《椭球大地测量学》。

大地主题正算

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计算方法： 高斯平均引数法 ( S< 200公里 ) 参考椭球：克拉索夫斯基椭球

N01 NO2 B1/B2 L1/L2 A12/A21 S12 1 2 30.29582043 120.05402184 247.2750428 28230.9350 30.24058365 119.49233864 67.19353743

3 4 40.02356784 130.10122676 328.12367500 48741.7580 40.24574365 129.52031587 148.00533348

5 6 40.02356784 130.10122676 1.49430000 80000.0000 40.45479037 130.12011050 181.50535462

7 8 40.02356784 115.10000000 36.12010300 414306.5380 *43.00558744 118.10030113 218.11268087 2)、反算范例 算例 例1( 30km ) 例2(50 km) 例3(80 km) 例4( 410 km) 参考椭球 克拉索夫斯基 贝塞尔椭球 克拉索夫斯基 克拉索夫斯基 已 知 数 据 m 参 考 值

注：例1取自朱华统：《椭球大地计算》P100算例；例2自陈键、晁定波主编《椭球大地测量学》P98面的数据；例3、例4取自赵文光著《椭球大地测量学》。

大地主题反算

================== 计算方法： 高斯平均引数法 ( S< 200公里 ) 参考椭球：克拉索夫斯基椭球

N01 NO2 B1/B2 L1/L2 A12/A21 S12 1 2 30.29582043 120.05402184 247.27504227 28230.9379 30.24058354 119.49233853 67.19353680 30.24058354 119.49233853 67.19354031

*3 4 53.50028809 10.12041772 25.16319782 47652.5967 54.13152891 10.30472430 205.31408796

5 6 40.02356784 130.10122627 1.49432983 80000.0044 40.45479027 130.12011040 181.50538462

*7 8 40.02356784 115.10000000 36.12012391 414306.5531 43.00558784 118.10030000 218.11265892

注：例2参考椭球为贝塞尔椭球；例4计算结果未能满足计算精度。 3)、高斯平均引数正反算计算程序

Sub DDZT_GS(B1 As Double, L1 As Double, A1 As Double, S12 As Double, B2 As Double, L2 As Double, A2 As Double, k As Integer) eps = e2 / (1# - e2) Select Case k Case 1

t1 = Sin(B1): t2 = Cos(B1)

NB = a / Sqr(1# - e2 * t1 * t1)

MB = a * (1 - e2) / Sqr((1# - e2 * t1 * t1) ^ 3) dB = S12 * Cos(A1) / MB

dL = S12 * Sin(A1) / NB / Cos(B1) dA = dL * Sin(B1) Do

dB0 = dB: dL0 = dL: dA0 = dA

Bm = B1 + dB0 / 2: LM = L1 + dL0 / 2: Am = A1 + dA0 / 2 t1 = Sin(Am)：t2 = Cos(Am)：t = Tan(Bm) q = eps * Cos(Bm) * Cos(Bm) n = a / Sqr(1# - e2 * Sin(Bm) * Sin(Bm)) MB = a * (1 - e2) / Sqr((1# - e2 * Sin(Bm) * Sin(Bm)) ^ 3) db1 = t1 * t1 * (2 + 3 * t * t + 2 * q) db2 = 3 * t2 * t2 * q * (t * t - 1 - (1 + 4 * t * t) * q)

dB = S12 * t2 * (1 + S12 * S12 * (db1 + db2) / n / n / 24) / MB xt = t * t xt1 = t1 * t1 xt2 = t2 * t2 dL1 = S12 * S12 * (xt * xt1 - xt2 * (1 + (1 - 9 * xt) * q)) / n / n / 24 dL = S12 * t1 * (1 + dL1) / n / Cos(Bm) da1 = xt2 * (2 + (7 + 9 * xt + 5 * q) * q) da2 = xt1 * (2 + xt + 2 * q)

dA = S12 * t * t1 * (1 + S12 * S12 * (da1 + da2) / NB / NB / 24) / NB XdB = Abs(dB - dB0) * P0 '常数P0=206265 XdL = Abs(dL - dL0) * P0 XdA = Abs(dA - dA0) * P0

Loop While XdB > 0.0001 And XdL > 0.0001 And XdA > 0.0001 B2 = B1 + dB: L2 = L1 + dL: A2 = A1 + dA If A1 > pi Then A2 = A2 - pi If A1 < pi Then A2 = A2 + pi Case 2

Bm = (B1 + B2) / 2: dB = B2 - B1: dL = L2 - L1 CosBm = Cos(Bm)

NB = a / Sqr(1# - e2 * Sin(Bm) * Sin(Bm)) t = Tan(Bm)

q = eps * CosBm * CosBm

v2 = 1 + q: v4 = v2 * v2: v6 = v4 * v2 r10 = NB * CosBm

r12 = NB * CosBm * (1 + q - 9 * q * t * t + q * q) / 24 / v4 r30 = -NB * CosBm ^ 3 * t ^ 2 / 24 s01 = NB / v2

s21 = -NB * CosBm ^ 2 * (2 + 3 * t * t + 2 * q) / 24 / v2 s03 = NB * q * (1 - t * t) / 8 / v6 't10 = CosBm * t

't12 = CosBm * t * (3 + 2 * q - 2 * q * q) / 24 't30 = CosBm ^ 3 * t * (1 + q) / 12 t10 = CosBm * t

t12 = CosBm * t * (2 + 7 * q + 9 * t * t * q) / 24 / v4 t30 = CosBm ^ 3 * t * (2 + t * t + 2 * q) / 24

SsinAm = r10 * dL + r12 * dL * dB ^ 2 + r30 * dL ^ 3 ScosAm = s01 * dB + s21 * dB * dL ^ 2 + s03 * dB ^ 3 dA = t10 * dL + t12 * dL * dB ^ 2 + t30 * dL ^ 3 '计算大地正反方位角

Am = Atn(SsinAm / ScosAm) If Am < 0 Then Am = Am + pi If SsinAm < 0 Then Am = Am + pi A1 = Am - dA / 2 A2 = Am + dA / 2

If A1 > pi Then A2 = A2 - pi If A1 < pi Then A2 = A2 + pi S12 = SsinAm / Sin(Am) End Select End Sub

4.2 白塞尔大地主题解算

高斯平均大地问题解算，是将大地经差、大地纬差和方位角展开为大地线的幂级数，在一定的精度条件下，距离愈长，公式的结构就愈复杂，收敛就愈慢。因此这种公式不适合于解长距离大地问题。

白塞尔大地问题解算公式是首先建立以椭球中心为中心，以任意长（一般为单位长）为半径的辅助球，按以下三个 …… 此处隐藏：1897字，全部文档内容请下载后查看。喜欢就下载吧 ……