Arduino MPU6050加速度传感器 卡尔曼滤波求解姿态角

1、mpu6050与单片机的连接

①使用uno和nano：VCC-5V  GND-GND  SDA-A4  SCL-A5

②使用esp8266：VCC-3V  GND-GND   SDA-D2  SCL-D1

2、代码

#include 
#include 
#include 

// 卡尔曼滤波器参数
float dt = 0.01; // 时间步长
float Q_angle = 0.001; // 过程噪声方差
float Q_gyro = 0.003; // 过程噪声方差
float R_angle = 0.5; // 测量噪声方差

// 状态变量
float pitch = 0;
float roll = 0;
float gyro_x_bias = 0;
float gyro_y_bias = 0;

// 卡尔曼滤波器矩阵
float Xk[4][1] = {{0},
                  {0},
                  {0},
                  {0}};
float Pk[4][4] = {{1, 1, 0, 0},
                  {1, 1, 0, 0},
                  {0, 0, 1, 1},
                  {0, 0, 1, 1}};
const float Ak[4][4] = {{1, -dt, 0, 0},
                        {0, 1, 0, 0},
                        {0, 0, 1, -dt},
                        {0, 0, 0, 1}};
const float Hk[2][4] = {{1, 0, 0, 0},
                        {0, 0, 1, 0}};
const float Qk[4][4] = {{Q_angle, 0, 0, 0},
                        {0, Q_gyro, 0, 0},
                        {0, 0, Q_angle, 0},
                        {0, 0, 0, Q_gyro}};
const float Rk[2][2] = {{R_angle, 0},
                        {0, R_angle}};

Adafruit_MPU6050 mpu;

void setup() {
  Serial.begin(115200);
  // Try to initialize!
  if (!mpu.begin()) {
    Serial.println("Failed to find MPU6050 chip");
    while (1) {
      delay(10);
    }
  }
  Serial.println("MPU6050 Found!");
  // 设置加速计范围为 +-8G
  mpu.setAccelerometerRange(MPU6050_RANGE_8_G);
  // 设置陀螺仪范围为 +- 500 deg/s
  mpu.setGyroRange(MPU6050_RANGE_500_DEG);
  // 设置滤波器带宽为21 Hz
  mpu.setFilterBandwidth(MPU6050_BAND_21_HZ);
  delay(100);
}

/* 计算姿态角度 */
void calculateAttitude(sensors_event_t a, sensors_event_t g) {
  /* 获取传感器读数 */
  float gyro_x = g.gyro.x / 57.296 - gyro_x_bias; // 将陀螺仪读数转换为弧度并减去静态偏差
  float gyro_y = g.gyro.y / 57.296 - gyro_y_bias;
  
  /* 计算加速度计测得的姿态角度 */
  float accel_pitch = atan2(a.acceleration.x, sqrt(pow(a.acceleration.y, 2) + pow(a.acceleration.z, 2)));
  float accel_roll = atan2(a.acceleration.y, sqrt(pow(a.acceleration.x, 2) + pow(a.acceleration.z, 2)));
  
  /* 融合加速度计和陀螺仪数据 */
  float alpha = 0.96; // 加速度计和陀螺仪融合的权重因子
  pitch = alpha * (pitch + dt * gyro_x) + (1 - alpha) * accel_pitch;
  roll = alpha * (roll + dt * gyro_y) + (1 - alpha) * accel_roll;
}

/* 使用卡尔曼滤波器进行姿态角度滤波 */
void kalmanFilter() {
  float Yk[2][1] = {{pitch},
                    {roll}};
  // 卡尔曼滤波器预测
  float Xk_1[4][1] = {{0},
                      {0},
                      {0},
                      {0}};
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < 4; j++) {
      Xk_1[i][0] += Ak[i][j] * Xk[j][0];
    }
  }
  float Pk_1[4][4] = {{0, 0, 0, 0},
                      {0, 0, 0, 0},
                      {0, 0, 0, 0},
                      {0, 0, 0, 0}};
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < 4; j++) {
      for (int k = 0; k < 4; k++) {
        Pk_1[i][j] += Ak[i][k] * Pk[k][j];
      }
    }
  }
  for (int i = 0; i < 4; i++) {
    Pk_1[i][i] += Qk[i][i];
  }
  // 卡尔曼滤波器更新
  float temp1[2][4];
  float temp2[4][4];
  float S[2][2];
  for (int i = 0; i < 2; i++) {
    for (int j = 0; j < 4; j++) {
      temp1[i][j] = 0;
      for (int k = 0; k < 4; k++) {
        temp1[i][j] += Hk[i][k] * Pk_1[k][j];
      }
    }
  }
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < 4; j++) {
      temp2[i][j] = 0;
      for (int k = 0; k < 4; k++) {
        temp2[i][j] += Pk_1[i][k] * Hk[k][j];
      }
    }
  }
  for (int i = 0; i < 2; i++) {
    for (int j = 0; j < 2; j++) {
      float temp3 = 0;
      for (int k = 0; k < 4; k++) {
        temp3 += Hk[i][k] * temp1[k][j];
      }
      S[i][j] = Rk[i][j] + temp3;
    }
  }
  float K[4][2];
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < 2; j++) {
      float temp3 = 0;
      for (int k = 0; k < 4; k++) {
        temp3 += temp2[i][k] * Hk[j][k];
      }
      K[i][j] = temp1[j][i] / S[j][j];
    }
  }
  for (int i = 0; i < 4; i++) {
    Xk[i][0] = Xk_1[i][0] + K[i][0] * (Yk[0][0] - Hk[0][i] * Xk_1[i][0] + Yk[1][0] - Hk[1][i] * Xk_1[i][0]);
    for (int j = 0; j < 4; j++) {
      Pk[i][j] = (1 - K[i][0] * Hk[0][j] - K[i][1] * Hk[1][j]) * Pk_1[i][j];
    }
  }
}

void loop() {
  /* 获取新的传感器读数 */
  sensors_event_t a, g, temp;
  mpu.getEvent(&a, &g, &temp);

  /* 计算姿态角度 */
  calculateAttitude(a, g);

  /* 使用卡尔曼滤波器进行姿态角度滤波 */
  kalmanFilter();

  /* 打印输出姿态角度 */
  Serial.print("Pitch: ");
  Serial.print(pitch*180/PI, 2);
  Serial.print("  Roll: ");
  Serial.println(roll*180/PI, 2);
  delay(10);

}