从位置和速度计算验证轨道到地心坐标系的旋转矩阵

pkg/calculator/orbit.go

@@ -0,0 +1,65 @@
+package calculator
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/mat"
+	"gonum.org/v1/gonum/spatial/r3"
+)
+
+// OrbitToECMatrix 轨道坐标系到ECI、ECEF坐标系的变换矩阵
+func OrbitToECMatrix(pos, vec []float64) *mat.Dense {
+	r := r3.Vec{X: pos[0], Y: pos[1], Z: pos[2]}
+	rmag := r3.Norm(r) // Magnitude
+	v := r3.Vec{X: vec[0], Y: vec[1], Z: vec[2]}
+	vmag := r3.Norm(v) // Magnitude of velocity vector
+	w := r3.Cross(v, r)
+	wmag := r3.Norm(w)
+
+	z0 := r3.Scale(-1/rmag, r) // z方向指向地心
+	y0 := r3.Scale(1/wmag, w)
+	x0 := r3.Scale(1/vmag, v)
+
+	m := mat.NewDense(3, 3, []float64{
+		x0.X, y0.X, z0.X,
+		x0.Y, y0.Y, z0.Y,
+		x0.Z, y0.Z, z0.Z,
+	})
+
+	return m
+}
+
+// IntersectionECEF 计算卫星与相机的交点，返回经纬度和高度
+// FIXME: 该计算方法有误，待修正
+func IntersectionECEF(Qsat2orbit Quaternion, satPos84, vec84 []float64, ucam int) (IntersectionPoint, error) {
+	alpha := FOV * math.Pi / 180.0
+	alpha = -alpha/2.0 + float64(ucam)*(alpha/float64(PANPixels))
+	direction := []float64{0, math.Tan(alpha), -1.3} // 卫星（相机）坐标系下CCD成像方向向量
+
+	// -------- 相机坐标系下CCD成像方向向量转到卫星坐标系 --------
+	Rcam := CameraRotMatrix(AngleCamSatX*math.Pi/180.0, AngleCamSatY*math.Pi/180.0, 0)
+	var dCam mat.VecDense
+	dCam.MulVec(Rcam, mat.NewVecDense(3, direction))
+
+	// -------- 转到轨道坐标系 --------
+	Rsat2orbit := Qsat2orbit.ToRotationMatrix()
+	var r0 mat.VecDense
+	r0.MulVec(Rsat2orbit, &dCam)
+	dOrbit := r0.RawVector().Data
+
+	// -------- 转到ECEF坐标系 --------
+	Rorbit2ecef := OrbitToECMatrix(satPos84, vec84)
+	var r1 mat.VecDense
+	r1.MulVec(Rorbit2ecef, mat.NewVecDense(3, dOrbit))
+	dECEF := r1.RawVector().Data
+
+	// -------- 计算交点 --------}
+	intersection, err := intersectWithEllipsoid(satPos84, dECEF)
+	if err != nil {
+		return IntersectionPoint{}, err
+	}
+
+	lat, lon, h := ECEFToGeodetic(intersection[0], intersection[1], intersection[2])
+
+	return IntersectionPoint{Lat: lat, Lon: lon, H: h}, err
+}