acc gyro mag
时间: 2023-09-25 22:07:53 浏览: 33
ACC, gyro, and mag are sensors commonly found in electronic devices, such as smartphones and drones.
ACC stands for accelerometer, which measures the acceleration and tilt of the device. It is used to detect changes in motion, such as when the device is shaken or moved.
Gyro, short for gyroscope, measures the angular velocity or rotational motion of the device. It is used to detect changes in orientation, such as when the device is rotated.
Mag, short for magnetometer, measures the magnetic field around the device. It is used to detect the device's direction and orientation relative to the Earth's magnetic field, and is often used in navigation applications.
相关问题
现有‘time’、'ACC_X', 'ACC_Y', 'ACC_Z', 'GYRO_X', 'GYRO_Y', 'GYRO_Z', 'MAG_X', 'MAG_Y', 'MAG_Z'的txt文件,帮我解算位姿,计算角度和位置上的累计变化,使用python
为了解算位姿,我们需要使用姿态解算算法,例如Mahony滤波器或Kalman滤波器。而为了计算角度和位置上的累计变化,我们需要对加速度计和陀螺仪数据进行积分。下面是一个可能的Python实现:
```python
import numpy as np
# 读取数据
data = np.loadtxt('data.txt', delimiter=',')
# 初始姿态
q = np.array([1, 0, 0, 0])
# 初始位置
pos = np.array([0, 0, 0])
# 初始速度
vel = np.array([0, 0, 0])
# 加速度计偏移
acc_offset = np.array([0, 0, 0])
# 陀螺仪偏移
gyro_offset = np.array([0, 0, 0])
# 采样时间
dt = 0.01
# 重力加速度
g = np.array([0, 0, -9.8])
# 循环处理每个时间步
for i in range(len(data)):
# 读取传感器数据
t, ax, ay, az, gx, gy, gz, mx, my, mz = data[i]
acc = np.array([ax, ay, az]) - acc_offset
gyro = np.array([gx, gy, gz]) - gyro_offset
# 计算姿态
q_dot = np.array([0.5 * (q[0] * gyro[0] - q[1] * gyro[1] - q[2] * gyro[2] - q[3] * gyro[3]),
0.5 * (q[1] * gyro[0] + q[0] * gyro[1] + q[3] * gyro[2] - q[2] * gyro[3]),
0.5 * (q[2] * gyro[0] - q[3] * gyro[1] + q[0] * gyro[2] + q[1] * gyro[3]),
0.5 * (q[3] * gyro[0] + q[2] * gyro[1] - q[1] * gyro[2] + q[0] * gyro[3])])
q += q_dot * dt
q /= np.linalg.norm(q)
# 计算重力矢量
g_rotated = np.quaternion(q[0], q[1], q[2], q[3]) * np.quaternion(0, *g) * np.conj(np.quaternion(q[0], q[1], q[2], q[3]))
g_norm = np.array([g_rotated.x, g_rotated.y, g_rotated.z])
# 计算加速度和角速度在世界坐标系下的值
acc_world = np.quaternion(q[0], q[1], q[2], q[3]) * np.quaternion(0, *acc) * np.conj(np.quaternion(q[0], q[1], q[2], q[3]))
acc_world -= np.quaternion(0, *g_norm)
acc_world = np.array([acc_world.x, acc_world.y, acc_world.z])
gyro_world = np.quaternion(q[0], q[1], q[2], q[3]) * np.quaternion(0, *gyro) * np.conj(np.quaternion(q[0], q[1], q[2], q[3]))
gyro_world = np.array([gyro_world.x, gyro_world.y, gyro_world.z])
# 计算速度和位置
vel += acc_world * dt
pos += vel * dt + 0.5 * acc_world * dt ** 2
# 输出结果
print(f"Time: {t:.2f} sec, Position: ({pos[0]:.2f}, {pos[1]:.2f}, {pos[2]:.2f}) m, "
f"Orientation: ({q[0]:.2f}, {q[1]:.2f}, {q[2]:.2f}, {q[3]:.2f}), "
f"Angular Velocity: ({gyro_world[0]:.2f}, {gyro_world[1]:.2f}, {gyro_world[2]:.2f}) rad/sec")
```
该代码假设传感器数据文件的格式如下:
```
time,ACC_X,ACC_Y,ACC_Z,GYRO_X,GYRO_Y,GYRO_Z,MAG_X,MAG_Y,MAG_Z
0.00,-0.01,0.01,9.79,-1.89,-0.33,-0.05,-59.00,-152.00,-397.00
0.01,-0.02,0.01,9.78,-1.80,-0.40,-0.05,-59.00,-152.00,-397.00
0.02,-0.02,0.02,9.79,-1.68,-0.39,-0.05,-59.00,-152.00,-397.00
...
```
其中,加速度计和陀螺仪数据已经减去了偏移量。代码中的输出包括当前时间、位置、姿态和角速度。你可以根据需要进行修改,例如添加数据记录或者保存结果到文件。
现有‘time’、'ACC_X', 'ACC_Y', 'ACC_Z', 'GYRO_X', 'GYRO_Y', 'GYRO_Z', 'MAG_X', 'MAG_Y', 'MAG_Z',帮我解算位姿,计算角度和位置上的累计变化,使用python
要计算位姿的话,需要使用传感器数据进行融合,一般使用卡尔曼滤波或者扩展卡尔曼滤波。在这里,我们使用扩展卡尔曼滤波进行数据融合。
首先,我们需要定义一个状态变量$x$,它包含了位置、速度、姿态角和角速度等信息。状态变量的维度由应用场景而定,这里我们暂时定义为$x=[p_x,\ p_y,\ p_z,\ v_x,\ v_y,\ v_z,\ \phi,\ \theta,\ \psi,\ p,\ q,\ r]^T$,其中$p_x,\ p_y,\ p_z$是位置坐标,$v_x,\ v_y,\ v_z$是速度,$\phi,\ \theta,\ \psi$是欧拉角,$p,\ q,\ r$是角速度。
在扩展卡尔曼滤波中,我们需要定义状态转移方程和观测方程。状态转移方程描述了状态变量在时间上的演化,观测方程描述了传感器数据与状态变量之间的关系。
状态转移方程可以写成如下形式:
$$
x_k = f(x_{k-1}, u_k, w_k)
$$
其中,$u_k$是控制输入,$w_k$是过程噪声。
观测方程可以写成如下形式:
$$
z_k = h(x_k, v_k)
$$
其中,$z_k$是传感器测量值,$v_k$是观测噪声。
接下来,我们需要对状态转移方程和观测方程进行数学建模。
状态转移方程:
$$
\begin{aligned}
p_x(k) &= p_x(k-1) + v_x(k-1)\Delta t + \frac{1}{2}a_x(k-1)\Delta t^2 \\
p_y(k) &= p_y(k-1) + v_y(k-1)\Delta t + \frac{1}{2}a_y(k-1)\Delta t^2 \\
p_z(k) &= p_z(k-1) + v_z(k-1)\Delta t + \frac{1}{2}a_z(k-1)\Delta t^2 \\
v_x(k) &= v_x(k-1) + a_x(k-1)\Delta t \\
v_y(k) &= v_y(k-1) + a_y(k-1)\Delta t \\
v_z(k) &= v_z(k-1) + a_z(k-1)\Delta t \\
\phi(k) &= \phi(k-1) + p(k-1)\Delta t + \frac{1}{2}q(k-1)\Delta t^2 \\
\theta(k) &= \theta(k-1) + q(k-1)\Delta t + \frac{1}{2}r(k-1)\Delta t^2 \\
\psi(k) &= \psi(k-1) + r(k-1)\Delta t \\
p(k) &= p(k-1) + q(k-1)\Delta t \\
q(k) &= q(k-1) + r(k-1)\Delta t \\
r(k) &= r(k-1)
\end{aligned}
$$
观测方程:
$$
\begin{aligned}
ACC_X &= a_x + g\sin\theta \\
ACC_Y &= a_y - g\sin\phi\cos\theta \\
ACC_Z &= a_z - g\cos\phi\cos\theta \\
GYRO_X &= p + q\sin\phi\tan\theta + r\cos\phi\tan\theta \\
GYRO_Y &= q\cos\phi - r\sin\phi \\
GYRO_Z &= q\sin\phi\sec\theta + r\cos\phi\sec\theta \\
MAG_X &= m_x\cos\theta\cos\psi + m_y\sin\phi\sin\theta\cos\psi + m_z\cos\phi\sin\theta\cos\psi \\
MAG_Y &= m_y\cos\phi - m_z\sin\phi \\
MAG_Z &= -m_x\sin\theta\cos\psi + m_y\sin\phi\cos\theta\cos\psi + m_z\cos\phi\cos\theta\cos\psi
\end{aligned}
$$
其中,$g$是重力加速度,$m_x,\ m_y,\ m_z$是地磁传感器测量值。
现在我们就可以使用扩展卡尔曼滤波进行数据融合了。具体步骤如下:
1. 初始化状态变量$x_0$和误差协方差矩阵$P_0$。
2. 对于每个时刻$k$,根据状态转移方程预测状态变量$x_k$和误差协方差矩阵$P_k$。
3. 根据观测方程计算卡尔曼增益$K_k$。
4. 根据传感器测量值$z_k$和观测方程更新状态变量$x_k$和误差协方差矩阵$P_k$。
5. 重复步骤2-4,直到结束。
下面是使用Python实现的代码示例:
```python
import numpy as np
# 定义状态变量的维度
n = 12
# 定义状态转移矩阵
F = np.eye(n)
F[0:3, 3:6] = np.eye(3) * dt
F[3:6, 6:9] = np.eye(3) * dt
F[0:3, 6:9] = np.eye(3) * (dt**2) / 2
F[6:9, 9:12] = np.eye(3) * dt
# 定义观测矩阵
H = np.zeros((9, n))
H[0:3, 3:6] = np.eye(3)
H[3:6, 6:9] = np.eye(3)
H[6:9, 9:12] = np.eye(3)
# 定义过程噪声协方差矩阵Q和观测噪声协方差矩阵R
Q = np.eye(n) * 0.1
R = np.eye(9) * 10
# 初始化状态变量和误差协方差矩阵
x = np.zeros(n)
P = np.eye(n)
# 扩展卡尔曼滤波
for i in range(len(data)):
# 预测状态变量和误差协方差矩阵
x = np.dot(F, x)
P = np.dot(np.dot(F, P), F.T) + Q
# 计算卡尔曼增益
K = np.dot(np.dot(P, H.T), np.linalg.inv(np.dot(np.dot(H, P), H.T) + R))
# 更新状态变量和误差协方差矩阵
z = np.array([data[i]['ACC_X'], data[i]['ACC_Y'], data[i]['ACC_Z'], data[i]['GYRO_X'], data[i]['GYRO_Y'], data[i]['GYRO_Z'], data[i]['MAG_X'], data[i]['MAG_Y'], data[i]['MAG_Z']])
y = z - np.dot(H, x)
x = x + np.dot(K, y)
P = np.dot((np.eye(n) - np.dot(K, H)), P)
# 计算姿态角和角速度
phi = x[6]
theta = x[7]
psi = x[8]
p = x[9]
q = x[10]
r = x[11]
# 计算位移和速度
vx = x[3]
vy = x[4]
vz = x[5]
px = x[0] + vx * dt
py = x[1] + vy * dt
pz = x[2] + vz * dt
# 更新状态变量
x[0] = px
x[1] = py
x[2] = pz
x[3] = vx
x[4] = vy
x[5] = vz
x[6] = phi + p * dt + (q**2 + r**2) * dt**2 / 2
x[7] = theta + q * dt + p * r * dt**2 / 2
x[8] = psi + r * dt + q * p * dt**2 / 2
x[9] = p + q * np.sin(phi) * np.tan(theta) + r * np.cos(phi) * np.tan(theta)
x[10] = q * np.cos(phi) - r * np.sin(phi)
x[11] = q * np.sin(phi) / np.cos(theta) + r * np.cos(phi) / np.cos(theta)
# 保存结果
result.append({'time': data[i]['time'], 'px': px, 'py': py, 'pz': pz, 'phi': phi, 'theta': theta, 'psi': psi})
```
注:上述代码中使用了一些变量和计算方法,需要自行定义和实现具体的函数和方法。
现在我们就可以使用上述代码来解算位姿,并计算角度和位置上的累计变化了。