(window.webpackJsonp=window.webpackJsonp||[]).push([[48],{374:function(t,a,_){"use strict";_.r(a);var e=_(10),s=Object(e.a)({},(function(){var t=this,a=t._self._c;return a("ContentSlotsDistributor",{attrs:{"slot-key":t.$parent.slotKey}},[a("h1",{attrs:{id:"问题-ned-与-ecef"}},[a("a",{staticClass:"header-anchor",attrs:{href:"#问题-ned-与-ecef"}},[t._v("#")]),t._v(" 问题：NED 与 ECEF")]),t._v(" "),a("cite-panel",{attrs:{title:"问题：经纬高、当地导航坐标系（NED）与地心地固坐标系（ECEF）的关系是什么？"}},[a("p",[a("strong",[t._v("答：")])]),t._v(" "),a("h3",{attrs:{id:"ned-坐标系"}},[a("a",{staticClass:"header-anchor",attrs:{href:"#ned-坐标系"}},[t._v("#")]),t._v(" NED 坐标系")]),t._v(" "),a("p",[t._v("NED（North–East–Down）为当地导航坐标系，常用符号 (n)，各轴定义为：")]),t._v(" "),a("ul",[a("li",[a("strong",[t._v("N")]),t._v("：指向地理北；")]),t._v(" "),a("li",[a("strong",[t._v("E")]),t._v("：指向地理东；")]),t._v(" "),a("li",[a("strong",[t._v("D")]),t._v("：垂直地表指向下。")])]),t._v(" "),a("fdi-img",{attrs:{width:"100%",alt:"NED 坐标系示意",src:"/knowledge-base/04/040103.png",caption:""}}),t._v(" "),a("p",[a("strong",[t._v("基准点（NED 原点）")]),t._v("：取第一个“定位有效”的点。定位有效指 GNSS 水平、垂直精度均小于设定阈值；满足后，模块自动保存当时经纬高作为基准点。设基准点为 ((L_0,\\lambda_0))，当前点为 ((L,\\lambda,h))，则 NED 位置可写为：")]),t._v(" "),a("fdi-math",{attrs:{content:"\\begin{aligned}\n&\\begin{cases}N=(L-L_0)^*(R_N(L_0)+h)\\\\E=(\\lambda-\\lambda_0)^*(R_E(L_0)+h)^*\\cos L_0\\\\D=-h\\end{cases} \\\\\n&R_{_N}(L_{0})=a^{*}(1-e^{2})/(1-e^{2}\\sin^{2}L_{0})^{^{3/2}}; \\\\\n&R_{E}(L_{0})=a/(1-e^{2}\\sin^{2}L_{0})^{1/2};\n\\end{aligned}"}}),t._v(" "),a("p",[t._v("其中 (h) 为大地高，(R_N)、(R_E) 分别为子午圈与卯酉圈曲率半径，(L)、(\\lambda) 为大地纬度与经度，(a)、(e) 为地球椭球长半轴与第一偏心率：")]),t._v(" "),a("fdi-math",{attrs:{content:"a=6378137.07m;~e^2=0.00669434915"}}),t._v(" "),a("h3",{attrs:{id:"ecef-坐标系"}},[a("a",{staticClass:"header-anchor",attrs:{href:"#ecef-坐标系"}},[t._v("#")]),t._v(" ECEF 坐标系")]),t._v(" "),a("p",[t._v("ECEF 以 WGS84 椭球中心为原点，常用符号 (e)：")]),t._v(" "),a("ul",[a("li",[a("strong",[t._v("z")]),t._v("：沿自转轴指向北极；")]),t._v(" "),a("li",[a("strong",[t._v("x")]),t._v("：指向赤道与 IERS 参考子午线交点；")]),t._v(" "),a("li",[a("strong",[t._v("y")]),t._v("：指向赤道与 90°E 子午线交点。")])]),t._v(" "),a("fdi-img",{attrs:{width:"48%",alt:"ECEF 坐标系示意",src:"/FQA/FQA_DETA100/图片9.png",caption:""}}),t._v(" "),a("p",[t._v("经纬高到 ECEF 直角坐标的转换：")]),t._v(" "),a("fdi-math",{attrs:{content:"\\begin{cases}x^e=(R_E\\left(L\\right)+h)\\cos L\\cos\\lambda\\\\y^e=(R_E\\left(L\\right)+h)\\cos L\\sin\\lambda\\\\z^e=[(1-e^2)R_E\\left(L\\right)+h)]\\sin L\\end{cases}\n"}})],1)],1)}),[],!1,null,null,null);a.default=s.exports}}]);