【倾角传感器常用滤波算法】

倾角传感器常用滤波算法

倾角传感器常用的滤波算法包括移动平均滤波、卡尔曼滤波、互补滤波以及低通滤波。以下详细介绍每种算法的原理、公式及代码实现。

移动平均滤波

移动平均滤波通过计算一定窗口内数据的平均值来平滑数据，消除高频噪声。

公式：
[
y_n = \frac{1}{N} \sum_{i=0}^{N-1} x_{n-i}
]

Python实现：

import numpy as np

def moving_average(data, window_size):
    cumsum = np.cumsum(np.insert(data, 0, 0))
    return (cumsum[window_size:] - cumsum[:-window_size]) / float(window_size)

# 示例数据
data = np.random.normal(0, 1, 100)
filtered_data = moving_average(data, 5)

ESP-IDF实现：

#include <stdint.h>

#define WINDOW_SIZE 5

float moving_average(float *buffer, float new_value) {
    static float sum = 0;
    static uint8_t index = 0;
    static float buffer[WINDOW_SIZE] = {0};

    sum -= buffer[index];
    buffer[index] = new_value;
    sum += new_value;
    index = (index + 1) % WINDOW_SIZE;

    return sum / WINDOW_SIZE;
}

卡尔曼滤波

卡尔曼滤波通过递归算法估计系统状态，适用于动态系统。

公式：
预测步骤：
[
\hat{x}k^- = A \hat{x}{k-1} + B u_k
]
[
P_k^- = A P_{k-1} A^T + Q
]

更新步骤：
[
K_k = P_k^- H^T (H P_k^- H^T + R)^{-1}
]
[
\hat{x}_k = \hat{x}_k^- + K_k (z_k - H \hat{x}_k^-)
]
[
P_k = (I - K_k H) P_k^-
]

Python实现：

import numpy as np

class KalmanFilter:
    def __init__(self, A, H, Q, R, x0, P0):
        self.A = A
        self.H = H
        self.Q = Q
        self.R = R
        self.x = x0
        self.P = P0

    def predict(self):
        self.x = np.dot(self.A, self.x)
        self.P = np.dot(self.A, np.dot(self.P, self.A.T)) + self.Q

    def update(self, z):
        y = z - np.dot(self.H, self.x)
        S = np.dot(self.H, np.dot(self.P, self.H.T)) + self.R
        K = np.dot(self.P, np.dot(self.H.T, np.linalg.inv(S)))
        self.x = self.x + np.dot(K, y)
        self.P = self.P - np.dot(K, np.dot(self.H, self.P))

ESP-IDF实现：

typedef struct {
    float x;  // 状态估计
    float P;  // 估计误差协方差
    float A;  // 状态转移矩阵
    float H;  // 观测矩阵
    float Q;  // 过程噪声协方差
    float R;  // 观测噪声协方差
} KalmanFilter;

void kalman_init(KalmanFilter *kf, float A, float H, float Q, float R, float x0, float P0) {
    kf->A = A;
    kf->H = H;
    kf->Q = Q;
    kf->R = R;
    kf->x = x0;
    kf->P = P0;
}

void kalman_predict(KalmanFilter *kf) {
    kf->x = kf->A * kf->x;
    kf->P = kf->A * kf->P * kf->A + kf->Q;
}

void kalman_update(KalmanFilter *kf, float z) {
    float y = z - kf->H * kf->x;
    float S = kf->H * kf->P * kf->H + kf->R;
    float K = kf->P * kf->H / S;
    kf->x = kf->x + K * y;
    kf->P = (1 - K * kf->H) * kf->P;
}

互补滤波

互补滤波结合加速度计和陀螺仪数据，通过加权平均消除噪声。

公式：
[
\theta = \alpha (\theta_{prev} + \omega \Delta t) + (1 - \alpha) \theta_{acc}
]

Python实现：

def complementary_filter(acc_angle, gyro_rate, prev_angle, alpha, dt):
    gyro_angle = prev_angle + gyro_rate * dt
    return alpha * gyro_angle + (1 - alpha) * acc_angle

ESP-IDF实现：

float complementary_filter(float acc_angle, float gyro_rate, float prev_angle, float alpha, float dt) {
    float gyro_angle = prev_angle + gyro_rate * dt;
    return alpha * gyro_angle + (1 - alpha) * acc_angle;
}

低通滤波

低通滤波通过削弱高频信号来平滑数据。

公式：
[
y_n = \alpha x_n + (1 - \alpha) y_{n-1}
]

Python实现：

def low_pass_filter(new_value, prev_value, alpha):
    return alpha * new_value + (1 - alpha) * prev_value

ESP-IDF实现：

float low_pass_filter(float new_value, float prev_value, float alpha) {
    return alpha * new_value + (1 - alpha) * prev_value;
}

以上算法可根据实际需求组合使用，例如将互补滤波与卡尔曼滤波结合，以提高倾角测量的精度和稳定性。