DOP Dilution Of Precision；多点定位 Multilateration；测向交叉定位三角定位；DAE；无人机

DOP Dilution Of Precision

通常为了描述定位误差与伪距误差之间的关系，定义如下精度因子来衡量测量的结果：
几何精度因子(Geometric Dilution Of Precision GDOP)
位置精度因子(Position(3D) Dilution Of Precision PDOP)
水平精度因子(Horizontal Dilution Of Precision HDOP)
垂直精度因子(Vertical Dilution Of Precision VDOP)
钟差精度因子(Time Dilution Of Precision TDOP)

σP=σE2+σN2+σU2\sigma_P=\sqrt{\sigma_E^2+\sigma_N^2+\sigma_U^2}σP=σE2+σN2+σU2

σH=σE2+σN2\sigma_H=\sqrt{\sigma_E^2+\sigma_N^2}σH=σE2+σN2

σU=σU2\sigma_U=\sqrt{\sigma_U^2}σU=σU2

σT=σT2\sigma_T=\sqrt{\sigma_T^2}σT=σT2

PDOP=σE2+σN2+σU2σ=D11+D22+D33PDOP=\frac{\sqrt{\sigma_E^2+\sigma_N^2+\sigma_U^2}}\sigma=\sqrt{D_{11}+D_{22}+D_{33}}PDOP=σσE2+σN2+σU2=D11+D22+D33

HDOP=σE2+σN2σ=D11+D22HDOP=\frac{\sqrt{\sigma_E^2+\sigma_N^2}}\sigma=\sqrt{D_{11}+D_{22}}HDOP=σσE2+σN2=D11+D22

VDOP=σU2σ=D33VDOP=\frac{\sigma_U^2}\sigma=\sqrt{ D_{33}}VDOP=σσU2=D33

TDOP=σT2σ=D44TDOP=\frac{\sigma_T^2}\sigma=\sqrt{ D_{44}}TDOP=σσT2=D44

σG=σE2+σN2+σU2+σT2=D11+D22+D33+D44σ\sigma_G=\sqrt{\sigma_E^2+\sigma_N^2+\sigma_U^2+\sigma_T^2} =\sqrt{D_{11}+D_{22}+D_{33}+D_{44}}\sigmaσG=σE2+σN2+σU2+σT2=D11+D22+D33+D44σ

多点定位 Multilateration

TDOA (Time difference of arrival)
FDOA (Frequency difference of arrival)
TOA (Time of arrival, also time of flight) (ToF)
AOA (Angle of arrival)
DOA (Direction Of Arrival)

Trilateration 三边测量
Triangulation 三角测量
True-range multilateration

测向交叉定位三角定位

在这里假设有两个观测站在大地直角坐标系下对目标进行定位，两观测站的位置分别为
S0(x0,y0,z0),S1(x1,y1,z1)S_0(x_0,y_0,z_0),S_1(x_1,y_1,z_1)S0(x0,y0,z0),S1(x1,y1,z1)，目标的位置为S(x,y,z)S(x,y,z)S(x,y,z)，观测站与目标的位置关系如图所示。观测站S0S_0S0获得目标相对于它的方位角和俯仰角为(α0,β0)(\alpha_0,\beta_0)(α0,β0)，观测站S1获得目标相对于它的方位角和俯仰角为(α1,β1)(\alpha_1,\beta_1)(α1,β1)

xtan⁡α0−y=x0tan⁡α0−y0x\tan\alpha_0-y=x_0\tan\alpha_0-y_0xtanα0−y=x0tanα0−y0

xtan⁡α1−y=x1tan⁡α1−y1x\tan\alpha_1-y=x_1\tan\alpha_1-y_1xtanα1−y=x1tanα1−y1

ytan⁡β0−zsin⁡α0=y0tan⁡β0−z0sin⁡α0y\tan\beta_0-z\sin\alpha_0=y_0\tan\beta_0-z_0\sin\alpha_0ytanβ0−zsinα0=y0tanβ0−z0sinα0

[tan⁡α0−10tan⁡α1−100tan⁡β0−sin⁡α0][xyz]=[x0tan⁡α0−y0x1tan⁡α1−y1y0tan⁡β0−z0sin⁡α0]\left[\begin{matrix}\tan\alpha_0 &-1 &0\\\tan\alpha_1 &-1 &0\\0 &\tan\beta_0 &-\sin\alpha_0\end{matrix}\right]\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}x_0\tan\alpha_0-y_0\\x_1\tan\alpha_1-y_1\\y_0\tan\beta_0-z_0\sin\alpha_0\end{bmatrix}⎣⎡tanα0tanα10−1−1tanβ000−sinα0⎦⎤⎣⎡xyz⎦⎤=⎣⎡x0tanα0−y0x1tanα1−y1y0tanβ0−z0sinα0⎦⎤

DAE

测物距离D，方向角A和俯仰角E

Matlab Mapping Toolbox 3-D Coordinate Systems
Octave 中有开源实现代码

geodetic2ecef
ecef2geodeticgeodetic2enu
enu2geodeticecef2enu
enu2ecefecef2acr
aer2ecefaer2geodetic
geodetic2aer[lat,lon,h] = aer2geodetic(az,elev,slantRange,lat0,lon0,h0,spheroid)
[az,elev,slantRange] = geodetic2aer(lat,lon,h,lat0,lon0,h0,spheroid)

Geometric Geodesy
wgs84Elipsoid

Great-circle navigation
Geodesics on an ellipsoid

经度 lon L
纬度 lat B
great circle track
rhumb line track

无人机

偏航角=航线角-航向角
空速=地速-风速

参考文献

Matlab官方文档
双无人机协同测向时差定位误差分析研究