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TuxMonkey
2025-11-15 22:18:00 +08:00
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User_Code/module/algorithm/QuaternionEKF/QuaternionEKF.c Normal file
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/**
******************************************************************************
* @file QuaternionEKF.c
* @author Wang Hongxi
* @version V1.2.0
* @date 2022/3/8
* @brief attitude update with gyro bias estimate and chi-square test
******************************************************************************
* @attention
* 1st order LPF transfer function:
* 1
* ———————
* as + 1
*
******************************************************************************
*/
#include "QuaternionEKF.h"
QEKF_INS_t QEKF_INS;
const float IMU_QuaternionEKF_F[36] = {1, 0, 0, 0, 0, 0,
0, 1, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0,
0, 0, 0, 1, 0, 0,
0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 0, 1};
float IMU_QuaternionEKF_P[36] = {100000, 0.1, 0.1, 0.1, 0.1, 0.1,
0.1, 100000, 0.1, 0.1, 0.1, 0.1,
0.1, 0.1, 100000, 0.1, 0.1, 0.1,
0.1, 0.1, 0.1, 100000, 0.1, 0.1,
0.1, 0.1, 0.1, 0.1, 100, 0.1,
0.1, 0.1, 0.1, 0.1, 0.1, 100};
float IMU_QuaternionEKF_K[18];
float IMU_QuaternionEKF_H[18];
static float invSqrt(float x);
static void IMU_QuaternionEKF_Observe(KalmanFilter_t *kf);
static void IMU_QuaternionEKF_F_Linearization_P_Fading(KalmanFilter_t *kf);
static void IMU_QuaternionEKF_SetH(KalmanFilter_t *kf);
static void IMU_QuaternionEKF_xhatUpdate(KalmanFilter_t *kf);
/**
* @brief Quaternion EKF initialization and some reference value
* @param[in] process_noise1 quaternion process noise 10
* @param[in] process_noise2 gyro bias process noise 0.001
* @param[in] measure_noise accel measure noise 1000000
* @param[in] lambda fading coefficient 0.9996
* @param[in] lpf lowpass filter coefficient 0
*/
void IMU_QuaternionEKF_Init(float *init_quaternion, float process_noise1, float process_noise2, float measure_noise,
float lambda, float lpf)
{
QEKF_INS.Initialized = 1;
QEKF_INS.Q1 = process_noise1;
QEKF_INS.Q2 = process_noise2;
QEKF_INS.R = measure_noise;
QEKF_INS.ChiSquareTestThreshold = 1e-8;
QEKF_INS.ConvergeFlag = 0;
QEKF_INS.ErrorCount = 0;
QEKF_INS.UpdateCount = 0;
if (lambda > 1)
{
lambda = 1;
}
QEKF_INS.lambda = lambda;
QEKF_INS.accLPFcoef = lpf;
// 初始化矩阵维度信息
Kalman_Filter_Init(&QEKF_INS.IMU_QuaternionEKF, 6, 0, 3);
Matrix_Init(&QEKF_INS.ChiSquare, 1, 1, (float *) QEKF_INS.ChiSquare_Data);
// 姿态初始化
for (int i = 0; i < 4; i++)
{
QEKF_INS.IMU_QuaternionEKF.xhat_data[i] = init_quaternion[i];
}
// 自定义函数初始化,用于扩展或增加kf的基础功能
QEKF_INS.IMU_QuaternionEKF.User_Func0_f = IMU_QuaternionEKF_Observe;
QEKF_INS.IMU_QuaternionEKF.User_Func1_f = IMU_QuaternionEKF_F_Linearization_P_Fading;
QEKF_INS.IMU_QuaternionEKF.User_Func2_f = IMU_QuaternionEKF_SetH;
QEKF_INS.IMU_QuaternionEKF.User_Func3_f = IMU_QuaternionEKF_xhatUpdate;
// 设定标志位,用自定函数替换kf标准步骤中的SetK(计算增益)以及xhatupdate(后验估计/融合)
QEKF_INS.IMU_QuaternionEKF.SkipEq3 = TRUE;
QEKF_INS.IMU_QuaternionEKF.SkipEq4 = TRUE;
memcpy(QEKF_INS.IMU_QuaternionEKF.F_data, IMU_QuaternionEKF_F, sizeof(IMU_QuaternionEKF_F));
memcpy(QEKF_INS.IMU_QuaternionEKF.P_data, IMU_QuaternionEKF_P, sizeof(IMU_QuaternionEKF_P));
}
/**
* @brief Quaternion EKF update
* @param[in] gyro x y z in rad/s
* @param[in] accel x y z in m/s²
* @param[in] update period in s
*/
void IMU_QuaternionEKF_Update(float gx, float gy, float gz, float ax, float ay, float az, float dt)
{
// 0.5(Ohm-Ohm^bias)*deltaT,用于更新工作点处的状态转移F矩阵
static float halfgxdt, halfgydt, halfgzdt;
static float accelInvNorm;
/* F, number with * represent vals to be set
0 1* 2* 3* 4 5
6* 7 8* 9* 10 11
12* 13* 14 15* 16 17
18* 19* 20* 21 22 23
24 25 26 27 28 29
30 31 32 33 34 35
*/
QEKF_INS.dt = dt;
QEKF_INS.Gyro[0] = gx - QEKF_INS.GyroBias[0];
QEKF_INS.Gyro[1] = gy - QEKF_INS.GyroBias[1];
QEKF_INS.Gyro[2] = gz - QEKF_INS.GyroBias[2];
// set F
halfgxdt = 0.5f * QEKF_INS.Gyro[0] * dt;
halfgydt = 0.5f * QEKF_INS.Gyro[1] * dt;
halfgzdt = 0.5f * QEKF_INS.Gyro[2] * dt;
// 此部分设定状态转移矩阵F的左上角部分 4x4子矩阵,即0.5(Ohm-Ohm^bias)*deltaT,右下角有一个2x2单位阵已经初始化好了
// 注意在predict步F的右上角是4x2的零矩阵,因此每次predict的时候都会调用memcpy用单位阵覆盖前一轮线性化后的矩阵
memcpy(QEKF_INS.IMU_QuaternionEKF.F_data, IMU_QuaternionEKF_F, sizeof(IMU_QuaternionEKF_F));
QEKF_INS.IMU_QuaternionEKF.F_data[1] = -halfgxdt;
QEKF_INS.IMU_QuaternionEKF.F_data[2] = -halfgydt;
QEKF_INS.IMU_QuaternionEKF.F_data[3] = -halfgzdt;
QEKF_INS.IMU_QuaternionEKF.F_data[6] = halfgxdt;
QEKF_INS.IMU_QuaternionEKF.F_data[8] = halfgzdt;
QEKF_INS.IMU_QuaternionEKF.F_data[9] = -halfgydt;
QEKF_INS.IMU_QuaternionEKF.F_data[12] = halfgydt;
QEKF_INS.IMU_QuaternionEKF.F_data[13] = -halfgzdt;
QEKF_INS.IMU_QuaternionEKF.F_data[15] = halfgxdt;
QEKF_INS.IMU_QuaternionEKF.F_data[18] = halfgzdt;
QEKF_INS.IMU_QuaternionEKF.F_data[19] = halfgydt;
QEKF_INS.IMU_QuaternionEKF.F_data[20] = -halfgxdt;
// accel low pass filter,加速度过一下低通滤波平滑数据,降低撞击和异常的影响
if (QEKF_INS.UpdateCount == 0) // 如果是第一次进入,需要初始化低通滤波
{
QEKF_INS.Accel[0] = ax;
QEKF_INS.Accel[1] = ay;
QEKF_INS.Accel[2] = az;
}
QEKF_INS.Accel[0] = QEKF_INS.Accel[0] * QEKF_INS.accLPFcoef / (QEKF_INS.dt + QEKF_INS.accLPFcoef) + ax * QEKF_INS.dt
/ (QEKF_INS.dt + QEKF_INS.accLPFcoef);
QEKF_INS.Accel[1] = QEKF_INS.Accel[1] * QEKF_INS.accLPFcoef / (QEKF_INS.dt + QEKF_INS.accLPFcoef) + ay * QEKF_INS.dt
/ (QEKF_INS.dt + QEKF_INS.accLPFcoef);
QEKF_INS.Accel[2] = QEKF_INS.Accel[2] * QEKF_INS.accLPFcoef / (QEKF_INS.dt + QEKF_INS.accLPFcoef) + az * QEKF_INS.dt
/ (QEKF_INS.dt + QEKF_INS.accLPFcoef);
// set z,单位化重力加速度向量
accelInvNorm = invSqrt(
QEKF_INS.Accel[0] * QEKF_INS.Accel[0] + QEKF_INS.Accel[1] * QEKF_INS.Accel[1] + QEKF_INS.Accel[2] * QEKF_INS
.Accel[2]);
// accelInvNorm = invSqrt(1);
for (uint8_t i = 0; i < 3; ++i)
{
QEKF_INS.IMU_QuaternionEKF.MeasuredVector[i] = QEKF_INS.Accel[i] * accelInvNorm; // 用加速度向量更新量测值
}
// get body state
QEKF_INS.gyro_norm = 1.0f / invSqrt(QEKF_INS.Gyro[0] * QEKF_INS.Gyro[0] +
QEKF_INS.Gyro[1] * QEKF_INS.Gyro[1] +
QEKF_INS.Gyro[2] * QEKF_INS.Gyro[2]);
QEKF_INS.accl_norm = 1.0f / accelInvNorm;
// 如果角速度小于阈值且加速度处于设定范围内,认为运动稳定,加速度可以用于修正角速度
// 稍后在最后的姿态更新部分会利用StableFlag来确定
if (QEKF_INS.gyro_norm < 0.3f && QEKF_INS.accl_norm > 9.8f - 0.5f && QEKF_INS.accl_norm < 9.8f + 0.5f)
{
QEKF_INS.StableFlag = 1;
}
else
{
QEKF_INS.StableFlag = 0;
}
// set Q R,过程噪声和观测噪声矩阵
QEKF_INS.IMU_QuaternionEKF.Q_data[0] = QEKF_INS.Q1 * QEKF_INS.dt;
QEKF_INS.IMU_QuaternionEKF.Q_data[7] = QEKF_INS.Q1 * QEKF_INS.dt;
QEKF_INS.IMU_QuaternionEKF.Q_data[14] = QEKF_INS.Q1 * QEKF_INS.dt;
QEKF_INS.IMU_QuaternionEKF.Q_data[21] = QEKF_INS.Q1 * QEKF_INS.dt;
QEKF_INS.IMU_QuaternionEKF.Q_data[28] = QEKF_INS.Q2 * QEKF_INS.dt;
QEKF_INS.IMU_QuaternionEKF.Q_data[35] = QEKF_INS.Q2 * QEKF_INS.dt;
QEKF_INS.IMU_QuaternionEKF.R_data[0] = QEKF_INS.R;
QEKF_INS.IMU_QuaternionEKF.R_data[4] = QEKF_INS.R;
QEKF_INS.IMU_QuaternionEKF.R_data[8] = QEKF_INS.R;
// 调用kalman_filter.c封装好的函数,注意几个User_Funcx_f的调用
Kalman_Filter_Update(&QEKF_INS.IMU_QuaternionEKF);
// 获取融合后的数据,包括四元数和xy零飘值
QEKF_INS.q[0] = QEKF_INS.IMU_QuaternionEKF.FilteredValue[0];
QEKF_INS.q[1] = QEKF_INS.IMU_QuaternionEKF.FilteredValue[1];
QEKF_INS.q[2] = QEKF_INS.IMU_QuaternionEKF.FilteredValue[2];
QEKF_INS.q[3] = QEKF_INS.IMU_QuaternionEKF.FilteredValue[3];
QEKF_INS.GyroBias[0] = QEKF_INS.IMU_QuaternionEKF.FilteredValue[4];
QEKF_INS.GyroBias[1] = QEKF_INS.IMU_QuaternionEKF.FilteredValue[5];
QEKF_INS.GyroBias[2] = 0; // 大部分时候z轴通天,无法观测yaw的漂移
// 利用四元数反解欧拉角
QEKF_INS.Yaw = atan2f(2.0f * (QEKF_INS.q[0] * QEKF_INS.q[3] + QEKF_INS.q[1] * QEKF_INS.q[2]),
2.0f * (QEKF_INS.q[0] * QEKF_INS.q[0] + QEKF_INS.q[1] * QEKF_INS.q[1]) - 1.0f) *
57.295779513f;
QEKF_INS.Pitch = asinf(-2.0f * (QEKF_INS.q[1] * QEKF_INS.q[3] - QEKF_INS.q[0] * QEKF_INS.q[2])) * 57.295779513f;
QEKF_INS.Roll = atan2f(2.0f * (QEKF_INS.q[0] * QEKF_INS.q[1] + QEKF_INS.q[2] * QEKF_INS.q[3]),
2.0f * (QEKF_INS.q[0] * QEKF_INS.q[0] + QEKF_INS.q[3] * QEKF_INS.q[3]) - 1.0f) *
57.295779513f;
// 翻了的话改变一下2.0前面的符号，长短边朝前也记得调整一下=号右边的内容就ok
// get Yaw total, yaw数据可能会超过360,处理一下方便其他功能使用(如小陀螺)
if (QEKF_INS.Yaw - QEKF_INS.YawAngleLast > 180.0f)
{
QEKF_INS.YawRoundCount--;
}
else if (QEKF_INS.Yaw - QEKF_INS.YawAngleLast < -180.0f)
{
QEKF_INS.YawRoundCount++;
}
QEKF_INS.YawTotalAngle = 360.0f * QEKF_INS.YawRoundCount + QEKF_INS.Yaw;
QEKF_INS.YawAngleLast = QEKF_INS.Yaw;
QEKF_INS.UpdateCount++; // 初始化低通滤波用,计数测试用
}
/**
* @brief 用于更新线性化后的状态转移矩阵F右上角的一个4x2分块矩阵,稍后用于协方差矩阵P的更新;
* 并对零漂的方差进行限制,防止过度收敛并限幅防止发散
*
* @param kf
*/
static void IMU_QuaternionEKF_F_Linearization_P_Fading(KalmanFilter_t *kf)
{
static float q0, q1, q2, q3;
static float qInvNorm;
q0 = kf->xhatminus_data[0];
q1 = kf->xhatminus_data[1];
q2 = kf->xhatminus_data[2];
q3 = kf->xhatminus_data[3];
// quaternion normalize
qInvNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
for (uint8_t i = 0; i < 4; ++i)
{
kf->xhatminus_data[i] *= qInvNorm;
}
/* F, number with * represent vals to be set
0 1 2 3 4* 5*
6 7 8 9 10* 11*
12 13 14 15 16* 17*
18 19 20 21 22* 23*
24 25 26 27 28 29
30 31 32 33 34 35
*/
// set F
kf->F_data[4] = q1 * QEKF_INS.dt / 2;
kf->F_data[5] = q2 * QEKF_INS.dt / 2;
kf->F_data[10] = -q0 * QEKF_INS.dt / 2;
kf->F_data[11] = q3 * QEKF_INS.dt / 2;
kf->F_data[16] = -q3 * QEKF_INS.dt / 2;
kf->F_data[17] = -q0 * QEKF_INS.dt / 2;
kf->F_data[22] = q2 * QEKF_INS.dt / 2;
kf->F_data[23] = -q1 * QEKF_INS.dt / 2;
// fading filter,防止零飘参数过度收敛
kf->P_data[28] /= QEKF_INS.lambda;
kf->P_data[35] /= QEKF_INS.lambda;
// 限幅,防止发散
if (kf->P_data[28] > 10000)
{
kf->P_data[28] = 10000;
}
if (kf->P_data[35] > 10000)
{
kf->P_data[35] = 10000;
}
}
/**
* @brief 在工作点处计算观测函数h(x)的Jacobi矩阵H
*
* @param kf
*/
static void IMU_QuaternionEKF_SetH(KalmanFilter_t *kf)
{
static float doubleq0, doubleq1, doubleq2, doubleq3;
/* H
0 1 2 3 4 5
6 7 8 9 10 11
12 13 14 15 16 17
last two cols are zero
*/
// set H
doubleq0 = 2 * kf->xhatminus_data[0];
doubleq1 = 2 * kf->xhatminus_data[1];
doubleq2 = 2 * kf->xhatminus_data[2];
doubleq3 = 2 * kf->xhatminus_data[3];
memset(kf->H_data, 0, sizeof_float * kf->zSize * kf->xhatSize);
kf->H_data[0] = -doubleq2;
kf->H_data[1] = doubleq3;
kf->H_data[2] = -doubleq0;
kf->H_data[3] = doubleq1;
kf->H_data[6] = doubleq1;
kf->H_data[7] = doubleq0;
kf->H_data[8] = doubleq3;
kf->H_data[9] = doubleq2;
kf->H_data[12] = doubleq0;
kf->H_data[13] = -doubleq1;
kf->H_data[14] = -doubleq2;
kf->H_data[15] = doubleq3;
}
/**
* @brief 利用观测值和先验估计得到最优的后验估计
* 加入了卡方检验以判断融合加速度的条件是否满足
* 同时引入发散保护保证恶劣工况下的必要量测更新
*
* @param kf
*/
static void IMU_QuaternionEKF_xhatUpdate(KalmanFilter_t *kf)
{
static float q0, q1, q2, q3;
kf->MatStatus = Matrix_Transpose(&kf->H, &kf->HT); // z|x => x|z
kf->temp_matrix.numRows = kf->H.numRows;
kf->temp_matrix.numCols = kf->Pminus.numCols;
kf->MatStatus = Matrix_Multiply(&kf->H, &kf->Pminus, &kf->temp_matrix); // temp_matrix = H·P'(k)
kf->temp_matrix1.numRows = kf->temp_matrix.numRows;
kf->temp_matrix1.numCols = kf->HT.numCols;
kf->MatStatus = Matrix_Multiply(&kf->temp_matrix, &kf->HT, &kf->temp_matrix1); // temp_matrix1 = H·P'(k)·HT
kf->S.numRows = kf->R.numRows;
kf->S.numCols = kf->R.numCols;
kf->MatStatus = Matrix_Add(&kf->temp_matrix1, &kf->R, &kf->S); // S = H P'(k) HT + R
kf->MatStatus = Matrix_Inverse(&kf->S, &kf->temp_matrix1); // temp_matrix1 = inv(H·P'(k)·HT + R)
q0 = kf->xhatminus_data[0];
q1 = kf->xhatminus_data[1];
q2 = kf->xhatminus_data[2];
q3 = kf->xhatminus_data[3];
kf->temp_vector.numRows = kf->H.numRows;
kf->temp_vector.numCols = 1;
// 计算预测得到的重力加速度方向(通过姿态获取的)
kf->temp_vector_data[0] = 2 * (q1 * q3 - q0 * q2);
kf->temp_vector_data[1] = 2 * (q0 * q1 + q2 * q3);
kf->temp_vector_data[2] = q0 * q0 - q1 * q1 - q2 * q2 + q3 * q3; // temp_vector = h(xhat'(k))
// 计算预测值和各个轴的方向余弦
for (uint8_t i = 0; i < 3; ++i)
{
QEKF_INS.OrientationCosine[i] = acosf(fabsf(kf->temp_vector_data[i]));
}
// 利用加速度计数据修正
kf->temp_vector1.numRows = kf->z.numRows;
kf->temp_vector1.numCols = 1;
kf->MatStatus = Matrix_Subtract(&kf->z, &kf->temp_vector, &kf->temp_vector1); // temp_vector1 = z(k) - h(xhat'(k))
// chi-square test,卡方检验
kf->temp_matrix.numRows = kf->temp_vector1.numRows;
kf->temp_matrix.numCols = 1;
kf->MatStatus = Matrix_Multiply(&kf->temp_matrix1, &kf->temp_vector1, &kf->temp_matrix);
// temp_matrix = inv(H·P'(k)·HT + R)·(z(k) - h(xhat'(k)))
kf->temp_vector.numRows = 1;
kf->temp_vector.numCols = kf->temp_vector1.numRows;
kf->MatStatus = Matrix_Transpose(&kf->temp_vector1, &kf->temp_vector); // temp_vector = z(k) - h(xhat'(k))'
kf->MatStatus = Matrix_Multiply(&kf->temp_vector, &kf->temp_matrix, &QEKF_INS.ChiSquare);
// rk is small,filter converged/converging
if (QEKF_INS.ChiSquare_Data[0] < 0.5f * QEKF_INS.ChiSquareTestThreshold)
{
QEKF_INS.ConvergeFlag = 1;
}
// rk is bigger than thre but once converged
if (QEKF_INS.ChiSquare_Data[0] > QEKF_INS.ChiSquareTestThreshold && QEKF_INS.ConvergeFlag)
{
if (QEKF_INS.StableFlag)
{
QEKF_INS.ErrorCount++; // 载体静止时仍无法通过卡方检验
}
else
{
QEKF_INS.ErrorCount = 0;
}
if (QEKF_INS.ErrorCount > 50)
{
// 滤波器发散
QEKF_INS.ConvergeFlag = 0;
kf->SkipEq5 = FALSE; // step-5 is cov mat P updating
}
else
{
// 残差未通过卡方检验 仅预测
// xhat(k) = xhat'(k)
// P(k) = P'(k)
memcpy(kf->xhat_data, kf->xhatminus_data, sizeof_float * kf->xhatSize);
memcpy(kf->P_data, kf->Pminus_data, sizeof_float * kf->xhatSize * kf->xhatSize);
kf->SkipEq5 = TRUE; // part5 is P updating
return;
}
}
else // if divergent or rk is not that big/acceptable,use adaptive gain
{
// scale adaptive,rk越小则增益越大,否则更相信预测值
if (QEKF_INS.ChiSquare_Data[0] > 0.1f * QEKF_INS.ChiSquareTestThreshold && QEKF_INS.ConvergeFlag)
{
QEKF_INS.AdaptiveGainScale = (QEKF_INS.ChiSquareTestThreshold - QEKF_INS.ChiSquare_Data[0]) / (
0.9f * QEKF_INS.ChiSquareTestThreshold);
}
else
{
QEKF_INS.AdaptiveGainScale = 1;
}
QEKF_INS.ErrorCount = 0;
kf->SkipEq5 = FALSE;
}
// cal kf-gain K
kf->temp_matrix.numRows = kf->Pminus.numRows;
kf->temp_matrix.numCols = kf->HT.numCols;
kf->MatStatus = Matrix_Multiply(&kf->Pminus, &kf->HT, &kf->temp_matrix); // temp_matrix = P'(k)·HT
kf->MatStatus = Matrix_Multiply(&kf->temp_matrix, &kf->temp_matrix1, &kf->K);
// implement adaptive
for (uint8_t i = 0; i < kf->K.numRows * kf->K.numCols; ++i)
{
kf->K_data[i] *= QEKF_INS.AdaptiveGainScale;
}
for (uint8_t i = 4; i < 6; ++i)
{
for (uint8_t j = 0; j < 3; ++j)
{
kf->K_data[i * 3 + j] *= QEKF_INS.OrientationCosine[i - 4] / 1.5707963f; // 1 rad
}
}
kf->temp_vector.numRows = kf->K.numRows;
kf->temp_vector.numCols = 1;
kf->MatStatus = Matrix_Multiply(&kf->K, &kf->temp_vector1, &kf->temp_vector);
// temp_vector = K(k)·(z(k) - H·xhat'(k))
// 零漂修正限幅,一般不会有过大的漂移
if (QEKF_INS.ConvergeFlag)
{
for (uint8_t i = 4; i < 6; ++i)
{
if (kf->temp_vector.pData[i] > 1e-2f * QEKF_INS.dt)
{
kf->temp_vector.pData[i] = 1e-2f * QEKF_INS.dt;
}
if (kf->temp_vector.pData[i] < -1e-2f * QEKF_INS.dt)
{
kf->temp_vector.pData[i] = -1e-2f * QEKF_INS.dt;
}
}
}
// 不修正yaw轴数据
kf->temp_vector.pData[3] = 0;
kf->MatStatus = Matrix_Add(&kf->xhatminus, &kf->temp_vector, &kf->xhat);
}
/**
* @brief EKF观测环节,其实就是把数据复制一下
*
* @param kf kf类型定义
*/
static void IMU_QuaternionEKF_Observe(KalmanFilter_t *kf)
{
memcpy(IMU_QuaternionEKF_P, kf->P_data, sizeof(IMU_QuaternionEKF_P));
memcpy(IMU_QuaternionEKF_K, kf->K_data, sizeof(IMU_QuaternionEKF_K));
memcpy(IMU_QuaternionEKF_H, kf->H_data, sizeof(IMU_QuaternionEKF_H));
}
/**
* @brief 自定义1/sqrt(x),速度更快
*
* @param x x
* @return float
*/
static float invSqrt(float x)
{
float halfx = 0.5f * x;
float y = x;
long i = *(long *) &y;
i = 0x5f375a86 - (i >> 1);
y = *(float *) &i;
y = y * (1.5f - (halfx * y * y));
return y;
}

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/**
******************************************************************************
* @file QuaternionEKF.h
* @author Wang Hongxi
* @version V1.2.0
* @date 2022/3/8
* @brief attitude update with gyro bias estimate and chi-square test
******************************************************************************
* @attention
*
******************************************************************************
*/
#ifndef _QUAT_EKF_H
#define _QUAT_EKF_H
#include "kalman_filter.h"
/* boolean type definitions */
#ifndef TRUE
#define TRUE 1 /**< boolean true */
#endif
#ifndef FALSE
#define FALSE 0 /**< boolean fails */
#endif
typedef struct
{
uint8_t Initialized;
KalmanFilter_t IMU_QuaternionEKF;
uint8_t ConvergeFlag;
uint8_t StableFlag;
uint64_t ErrorCount;
uint64_t UpdateCount;
float q[4]; // 四元数估计值
float GyroBias[3]; // 陀螺仪零偏估计值
float Gyro[3];
float Accel[3];
float OrientationCosine[3];
float accLPFcoef;
float gyro_norm;
float accl_norm;
float AdaptiveGainScale;
float Roll;
float Pitch;
float Yaw;
float YawTotalAngle;
float Q1; // 四元数更新过程噪声
float Q2; // 陀螺仪零偏过程噪声
float R; // 加速度计量测噪声
float dt; // 姿态更新周期
mat ChiSquare;
float ChiSquare_Data[1]; // 卡方检验检测函数
float ChiSquareTestThreshold; // 卡方检验阈值
float lambda; // 渐消因子
int16_t YawRoundCount;
float YawAngleLast;
} QEKF_INS_t;
extern QEKF_INS_t QEKF_INS;
extern float chiSquare;
extern float ChiSquareTestThreshold;
void IMU_QuaternionEKF_Init(float *init_quaternion, float process_noise1, float process_noise2, float measure_noise,
float lambda, float lpf);
void IMU_QuaternionEKF_Update(float gx, float gy, float gz, float ax, float ay, float az, float dt);
#endif

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//
// Created by ASUS on 2025/11/15.
//
#include "controller.h"

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//
// Created by ASUS on 2025/11/15.
//
#ifndef TRONONEH7_SCAFFOLD_CONTROLLER_H
#define TRONONEH7_SCAFFOLD_CONTROLLER_H
#endif //TRONONEH7_SCAFFOLD_CONTROLLER_H

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//
// Created by ASUS on 2025/11/15.
//
#include "crc16.h"

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//
// Created by ASUS on 2025/11/15.
//
#ifndef TRONONEH7_SCAFFOLD_CRC16_H
#define TRONONEH7_SCAFFOLD_CRC16_H
#endif //TRONONEH7_SCAFFOLD_CRC16_H

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//
// Created by ASUS on 2025/11/15.
//
#include "crc8.h"

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//
// Created by ASUS on 2025/11/15.
//
#ifndef TRONONEH7_SCAFFOLD_CRC8_H
#define TRONONEH7_SCAFFOLD_CRC8_H
#endif //TRONONEH7_SCAFFOLD_CRC8_H

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//
// Created by ASUS on 2025/11/15.
//
#include "kalman_filter.h"

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//
// Created by ASUS on 2025/11/15.
//
#ifndef TRONONEH7_SCAFFOLD_KALMAN_FILTER_H
#define TRONONEH7_SCAFFOLD_KALMAN_FILTER_H
#endif //TRONONEH7_SCAFFOLD_KALMAN_FILTER_H

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/**
******************************************************************************
* @file user_lib.c
* @author Wang Hongxi
* @author modified by neozng
* @version 0.2 beta
* @date 2021/2/18
* @brief
******************************************************************************
* @attention
*
******************************************************************************
*/
#include "stdlib.h"
#include "memory.h"
#include "user_lib.h"
#include "math.h"
#include "main.h"
#ifdef _CMSIS_OS_H
#define user_malloc pvPortMalloc
#else
#define user_malloc malloc
#endif
void *zmalloc(size_t size)
{
void *ptr = malloc(size);
memset(ptr, 0, size);
return ptr;
}
// 快速开方
float Sqrt(float x)
{
float y;
float delta;
float maxError;
if (x <= 0)
{
return 0;
}
// initial guess
y = x / 2;
// refine
maxError = x * 0.001f;
do
{
delta = (y * y) - x;
y -= delta / (2 * y);
}
while (delta > maxError || delta < -maxError);
return y;
}
// 绝对值限制
float abs_limit(float num, float Limit)
{
if (num > Limit)
{
num = Limit;
}
else if (num < -Limit)
{
num = -Limit;
}
return num;
}
// 判断符号位
float sign(float value)
{
if (value >= 0.0f)
{
return 1.0f;
}
else
{
return -1.0f;
}
}
// 浮点死区
float float_deadband(float Value, float minValue, float maxValue)
{
if (Value < maxValue && Value > minValue)
{
Value = 0.0f;
}
return Value;
}
// 限幅函数
float float_constrain(float Value, float minValue, float maxValue)
{
if (Value < minValue)
return minValue;
else if (Value > maxValue)
return maxValue;
else
return Value;
}
// 限幅函数
int16_t int16_constrain(int16_t Value, int16_t minValue, int16_t maxValue)
{
if (Value < minValue)
return minValue;
else if (Value > maxValue)
return maxValue;
else
return Value;
}
// 循环限幅函数
float loop_float_constrain(float Input, float minValue, float maxValue)
{
if (maxValue < minValue)
{
return Input;
}
if (Input > maxValue)
{
float len = maxValue - minValue;
while (Input > maxValue)
{
Input -= len;
}
}
else if (Input < minValue)
{
float len = maxValue - minValue;
while (Input < minValue)
{
Input += len;
}
}
return Input;
}
// 弧度格式化为-PI~PI
// 角度格式化为-180~180
float theta_format(float Ang)
{
return loop_float_constrain(Ang, -180.0f, 180.0f);
}
int float_rounding(float raw)
{
static int integer;
static float decimal;
integer = (int) raw;
decimal = raw - integer;
if (decimal > 0.5f)
integer++;
return integer;
}
// 三维向量归一化
float *Norm3d(float *v)
{
float len = Sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
v[0] /= len;
v[1] /= len;
v[2] /= len;
return v;
}
// 计算模长
float NormOf3d(float *v)
{
return Sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
}
// 三维向量叉乘v1 x v2
void Cross3d(float *v1, float *v2, float *res)
{
res[0] = v1[1] * v2[2] - v1[2] * v2[1];
res[1] = v1[2] * v2[0] - v1[0] * v2[2];
res[2] = v1[0] * v2[1] - v1[1] * v2[0];
}
// 三维向量点乘
float Dot3d(float *v1, float *v2)
{
return v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2];
}
// 均值滤波,删除buffer中的最后一个元素,填入新的元素并求平均值
float AverageFilter(float new_data, float *buf, uint8_t len)
{
float sum = 0;
for (uint8_t i = 0; i < len - 1; i++)
{
buf[i] = buf[i + 1];
sum += buf[i];
}
buf[len - 1] = new_data;
sum += new_data;
return sum / len;
}
void MatInit(mat *m, uint8_t row, uint8_t col)
{
m->numCols = col;
m->numRows = row;
m->pData = (float *) zmalloc(row * col * sizeof(float));
}

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/**
******************************************************************************
* @file user_lib.h
* @author Wang Hongxi
* @version V1.0.0
* @date 2021/2/18
* @brief
******************************************************************************
* @attention
*
******************************************************************************
*/
#ifndef _USER_LIB_H
#define _USER_LIB_H
#include "stdint.h"
#include "main.h"
#include "cmsis_os.h"
enum
{
CHASSIS_DEBUG = 1,
GIMBAL_DEBUG,
INS_DEBUG,
RC_DEBUG,
IMU_HEAT_DEBUG,
SHOOT_DEBUG,
AIMASSIST_DEBUG,
};
extern uint8_t GlobalDebugMode;
#ifndef user_malloc
#ifdef _CMSIS_OS_H
#define user_malloc pvPortMalloc
#else
#define user_malloc malloc
#endif
#endif
/* boolean type definitions */
#ifndef TRUE
#define TRUE 1 /**< boolean true */
#endif
#ifndef FALSE
#define FALSE 0 /**< boolean fails */
#endif
/* math relevant */
/* radian coefficient */
#ifndef RADIAN_COEF
#define RADIAN_COEF 57.295779513f
#endif
/* circumference ratio */
#ifndef PI
#define PI 3.14159265354f
#endif
#define VAL_LIMIT(val, min, max) \
do \
{ \
if ((val) <= (min)) \
{ \
(val) = (min); \
} \
else if ((val) >= (max)) \
{ \
(val) = (max); \
} \
} while (0)
#define ANGLE_LIMIT_360(val, angle) \
do \
{ \
(val) = (angle) - (int)(angle); \
(val) += (int)(angle) % 360; \
} while (0)
#define ANGLE_LIMIT_360_TO_180(val) \
do \
{ \
if ((val) > 180) \
(val) -= 360; \
} while (0)
#define VAL_MIN(a, b) ((a) < (b) ? (a) : (b))
#define VAL_MAX(a, b) ((a) > (b) ? (a) : (b))
typedef struct
{
float input; //输入数据
float out; //输出数据
float min_value; //限幅最小值
float max_value; //限幅最大值
float frame_period; //时间间隔
} ramp_function_source_t;
typedef __packed struct
{
uint16_t Order;
uint32_t Count;
float *x;
float *y;
float k;
float b;
float StandardDeviation;
float t[4];
} Ordinary_Least_Squares_t;
//快速开方
float Sqrt(float x);
//斜波函数初始化
void ramp_init(ramp_function_source_t *ramp_source_type, float frame_period, float max, float min);
//斜波函数计算
float ramp_calc(ramp_function_source_t *ramp_source_type, float input);
//绝对限制
float abs_limit(float num, float Limit);
//判断符号位
float sign(float value);
//浮点死区
float float_deadband(float Value, float minValue, float maxValue);
// int26死区
int16_t int16_deadline(int16_t Value, int16_t minValue, int16_t maxValue);
//限幅函数
float float_constrain(float Value, float minValue, float maxValue);
//限幅函数
int16_t int16_constrain(int16_t Value, int16_t minValue, int16_t maxValue);
//循环限幅函数
float loop_float_constrain(float Input, float minValue, float maxValue);
//角度 °限幅 180 ~ -180
float theta_format(float Ang);
int float_rounding(float raw);
//弧度格式化为-PI~PI
#define rad_format(Ang) loop_float_constrain((Ang), -PI, PI)
void OLS_Init(Ordinary_Least_Squares_t *OLS, uint16_t order);
void OLS_Update(Ordinary_Least_Squares_t *OLS, float deltax, float y);
float OLS_Derivative(Ordinary_Least_Squares_t *OLS, float deltax, float y);
float OLS_Smooth(Ordinary_Least_Squares_t *OLS, float deltax, float y);
float Get_OLS_Derivative(Ordinary_Least_Squares_t *OLS);
float Get_OLS_Smooth(Ordinary_Least_Squares_t *OLS);
#endif