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insmech.py
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insmech.py
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import numpy as np
import types_my as ty
import kf_gins_types as kf
from earth import Earth
from scipy.spatial.transform import Rotation
from rotation import Rotation_my as ro
class INSMech:
def insMech(pvapre:kf.PVA,imupre:ty.IMU,imucur:ty.IMU):
pvacur = kf.PVA()
## 依次进行速度更新、位置更新、姿态更新, 不可调换顺序
pvacur = INSMech.velUpdate(pvapre, pvacur, imupre, imucur)
pvacur = INSMech.posUpdate(pvapre, pvacur, imupre, imucur)
pvacur = INSMech.attUpdate(pvapre, pvacur, imupre, imucur)
return pvacur
def velUpdate(pvapre:kf.PVA,pvacur:kf.PVA,imupre:ty.IMU,imucur:ty.IMU):
d_vfb, d_vfn, d_vgn, gl, midvel, midpos = np.zeros(3),np.zeros(3),np.zeros(3),np.zeros(3),np.zeros(3),np.zeros(3)
temp1, temp2, temp3 = np.zeros(3),np.zeros(3),np.zeros(3)
cnn = np.zeros((3, 3))
I33 = np.eye(3)
qne, qee, qnn = np.zeros(4),np.zeros(4),np.zeros(4)
## 计算地理参数，子午圈半径和卯酉圈半径，地球自转角速度投影到n系, n系相对于e系转动角速度投影到n系，重力值
rmrn = Earth.meridianPrimeVerticalRadius(pvapre.pos[0])
wie_n = np.array([Earth.WGS84_WIE * np.cos(pvapre.pos[0]), 0, -Earth.WGS84_WIE * np.sin(pvapre.pos[0])])
wen_n = np.array([pvapre.vel[1] / (rmrn[1] + pvapre.pos[2]), -pvapre.vel[0] / (rmrn[0] + pvapre.pos[2]),
-pvapre.vel[1] * np.tan(pvapre.pos[0]) / (rmrn[1] + pvapre.pos[2])])
gravity = Earth.gravity(pvapre.pos)
## 旋转效应和双子样划桨效应
temp1 = np.cross(imucur.dtheta, imucur.dvel) / 2
temp2 = np.cross(imupre.dtheta, imucur.dvel) / 12
temp3 = np.cross(imupre.dvel, imucur.dtheta) / 12
## b系比力积分项
d_vfb = imucur.dvel + temp1 + temp2 + temp3
## 比力积分项投影到n系
temp1 = (wie_n + wen_n) * imucur.dt / 2
cnn = I33 - ro.skewSymmetric(temp1)
d_vfn = cnn @ pvapre.att.cbn @ d_vfb
## 计算重力/哥式积分项
gl = np.array([0.0,0.0,gravity])
d_vgn = (gl - np.cross((2 * wie_n + wen_n), pvapre.vel)) * imucur.dt
## 得到中间时刻速度
midvel = pvapre.vel + (d_vfn + d_vgn) / 2
## 外推得到中间时刻位置
qnn = ro.rotvec2quaternion(temp1)
temp2 = np.array([0.0,0.0,-Earth.WGS84_WIE * imucur.dt / 2])
qee = ro.rotvec2quaternion(temp2)
qne = Earth.qne(pvapre.pos)
qne = Rotation.from_quat(qee) * Rotation.from_quat(qne) * Rotation.from_quat(qnn)
qne = qne.as_quat()
midpos[2] = pvapre.pos[2] - midvel[2] * imucur.dt / 2
midpos = Earth.blh(qne, midpos[2])
## 重新计算中间时刻的rmrn, wie_e, wen_n
rmrn = Earth.meridianPrimeVerticalRadius(midpos[0])
wie_n =np.array([Earth.WGS84_WIE * np.cos(midpos[0]), 0, -Earth.WGS84_WIE * np.sin(midpos[0])])
wen_n = np.array([midvel[1] / (rmrn[1] + midpos[2]), -midvel[0] / (rmrn[0] + midpos[2]), -midvel[1] * np.tan(midpos[0]) / (rmrn[1] + midpos[2])])
## 重新计算n系下平均比力积分项
temp3 = (wie_n + wen_n) * imucur.dt / 2
cnn = I33 - ro.skewSymmetric(temp3)
d_vfn = cnn @ pvapre.att.cbn @ d_vfb
## 重新计算重力、哥式积分项
a = Earth.gravity(midpos)
gl = np.array([0.0,0.0,a])
d_vgn = (gl - np.cross((2 * wie_n + wen_n), midvel)) * imucur.dt
## 速度更新完成
pvacur.vel = pvapre.vel + d_vfn + d_vgn
return pvacur
def posUpdate(pvapre:kf.PVA,pvacur:kf.PVA,imupre:ty.IMU,imucur:ty.IMU):
temp1, temp2, midvel, midpos = np.zeros(3),np.zeros(3),np.zeros(3),np.zeros(3)
qne, qee, qnn = np.zeros(4) ,np.zeros(4) ,np.zeros(4)
## 重新计算中间时刻的速度和位置
midvel = (pvacur.vel + pvapre.vel) / 2
midpos = pvapre.pos + Earth.DRi(pvapre.pos) @ midvel * imucur.dt / 2
## 重新计算中间时刻地理参数
rmrn = Earth.meridianPrimeVerticalRadius(midpos[0])
wie_n = np.array([Earth.WGS84_WIE * np.cos(midpos[0]), 0, -Earth.WGS84_WIE * np.sin(midpos[0])])
wen_n = np.array([midvel[1] / (rmrn[1] + midpos[2]), -midvel[0] / (rmrn[0] + midpos[2]),-midvel[1] * np.tan(midpos[0]) / (rmrn[1] + midpos[2])])
## 重新计算 k时刻到k-1时刻 n系旋转矢量
temp1 = (wie_n + wen_n) * imucur.dt
qnn = ro.rotvec2quaternion(temp1)
temp2 = np.array([ 0.0, 0.0, -Earth.WGS84_WIE * imucur.dt])
qee = ro.rotvec2quaternion(temp2)
## 位置更新完成
qne = Earth.qne(pvapre.pos)
qne = Rotation.from_quat(qee) * Rotation.from_quat(qne) * Rotation.from_quat(qnn)
qne = qne.as_quat()
pvacur.pos[2] = pvapre.pos[2] - midvel[2] * imucur.dt
pvacur.pos = Earth.blh(qne, pvacur.pos[2])
return pvacur
def attUpdate(pvapre:kf.PVA,pvacur:kf.PVA,imupre:ty.IMU,imucur:ty.IMU):
qne_pre, qne_cur, qne_mid, qnn, qbb = np.zeros(4),np.zeros(4),np.zeros(4),np.zeros(4),np.zeros(4)
temp1, midpos, midvel = np.zeros(3),np.zeros(3),np.zeros(3)
## 重新计算中间时刻的速度和位置
midvel = (pvapre.vel + pvacur.vel) / 2
qne_pre = Earth.qne(pvapre.pos)
qne_cur = Earth.qne(pvacur.pos)
q = Rotation.from_quat(qne_cur).inv()* Rotation.from_quat(qne_pre)
q = q.as_quat()
temp1 = ro.quaternion2vector(q)
qne_mid = Rotation.from_quat(qne_pre) * Rotation.from_quat(ro.rotvec2quaternion(temp1 / 2)).inv()
midpos[2] = (pvacur.pos[2] + pvapre.pos[2]) / 2
midpos = Earth.blh(qne_mid.as_quat(), midpos[2])
## 重新计算中间时刻地理参数
rmrn = Earth.meridianPrimeVerticalRadius(midpos[0])
wie_n = np.array([Earth.WGS84_WIE * np.cos(midpos[0]), 0, -Earth.WGS84_WIE * np.sin(midpos[0])])
wen_n = np.array([midvel[1] / (rmrn[1] + midpos[2]), -midvel[0] / (rmrn[0] + midpos[2]),
-midvel[1] * np.tan(midpos[0]) / (rmrn[1] + midpos[2])])
## 计算n系的旋转四元数 k-1时刻到k时刻变换
temp1 = -(wie_n + wen_n) * imucur.dt
qnn = ro.rotvec2quaternion(temp1)
## 计算b系旋转四元数 补偿二阶圆锥误差
temp1 = imucur.dtheta + np.cross(imupre.dtheta,imucur.dtheta) / 12
qbb = ro.rotvec2quaternion(temp1)
## 姿态更新完成
if np.all(pvapre.att.qbn == 0):
pvacur.att.qbn = Rotation.from_quat(qnn) * Rotation.from_quat(qbb)
else:
pvacur.att.qbn = Rotation.from_quat(qnn) * Rotation.from_quat(pvapre.att.qbn) * Rotation.from_quat(qbb)
pvacur.att.qbn = pvacur.att.qbn.as_quat()
pvacur.att.cbn = ro.quaternion2matrix(pvacur.att.qbn)
pvacur.att.euler = ro.matrix2euler(pvacur.att.cbn)
return pvacur