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ASER-NAV/App/est/corridor_ekf.c

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导航部分效果最好的版本，主分支
2026-04-13 23:30:22 +08:00
/**
* @file corridor_ekf.c
* @brief 鲁棒 EKF 走廊相对定位滤波器实现
*
* 完整算法流程：
*
* 【预测步】Predict(vx, wz, dt)
* x_pred = f(x, u) -- 非线性状态转移
* P_pred = F * P * F^T + Q -- 协方差预测
*
* 【更新步】Update(obs)
* z = h(x_pred) -- 观测预测
* y = z_meas - z -- 新息 (Innovation)
* S = H * P_pred * H^T + R -- 新息协方差
* d² = y^T * S^(-1) * y -- 马氏距离平方
* if d² > χ²_threshold: 拒绝观测 (鲁棒)
* K = P_pred * H^T * S^(-1) -- 卡尔曼增益
* x = x_pred + K * y -- 状态更新
* P = (I - K * H) * P_pred -- 协方差更新
*/
#include "corridor_ekf.h"
#include <math.h>
#include <string.h>
/* =========================================================
* 内部静态状态
* ========================================================= */
static CorridorEKFConfig_t s_cfg;
static CorridorEKFState_t s_state;
static bool s_initialized = false;
static uint32_t s_last_update_ms = 0U;
/* 协方差上界保护阈值 */
#define P_MAX_DIAG 100.0f
/* =========================================================
* 内部辅助函数
* ========================================================= */
/** 限幅 */
static inline float clampf(float val, float lo, float hi)
{
if (val < lo) return lo;
if (val > hi) return hi;
return val;
}
/** 对称矩阵拷贝 + 双向取平均 (减少舍入误差传播) */
static void symmetrize(float M[3][3])
{
float avg;
avg = (M[0][1] + M[1][0]) * 0.5f;
M[0][1] = M[1][0] = avg;
avg = (M[0][2] + M[2][0]) * 0.5f;
M[0][2] = M[2][0] = avg;
avg = (M[1][2] + M[2][1]) * 0.5f;
M[1][2] = M[2][1] = avg;
}
/** 角度归一化到 [-π, π]
* 防止 IMU yaw 累积角度跨越 ±π 时导致新息突变
*/
static float wrap_angle(float angle)
{
const float PI = 3.14159265358979323846f;
while (angle > PI) angle -= 2.0f * PI;
while (angle < -PI) angle += 2.0f * PI;
return angle;
}
/** P 上界保护 */
static void protect_P(float P[3][3])
{
for (int i = 0; i < 3; i++) {
if (P[i][i] > P_MAX_DIAG) P[i][i] = P_MAX_DIAG;
if (P[i][i] < 0.0f) P[i][i] = 0.0f;
}
}
/** Joseph 形式协方差更新 (1DOF 标量观测)
* P_new = (I - K*H) * P * (I - K*H)^T + K * R * K^T
*
* 参数:
* P[3][3] - 先验协方差 (输入/输出)
* K[3] - 卡尔曼增益向量
* H[3] - 观测矩阵 (1x3 行向量)
* R - 观测噪声方差 (标量)
*
* 优点: 保证数值稳定性，即使有舍入误差也能保持 P 正定
*/
static void joseph_update_P(float P[3][3], const float K[3], const float H[3], float R)
{
/* 计算 A = (I - K*H) */
float A[3][3];
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
A[i][j] = (i == j ? 1.0f : 0.0f) - K[i] * H[j];
}
}
/* 计算 A * P */
float AP[3][3];
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
AP[i][j] = 0.0f;
for (int k = 0; k < 3; k++) {
AP[i][j] += A[i][k] * P[k][j];
}
}
}
/* 计算 A * P * A^T */
float APAT[3][3];
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
APAT[i][j] = 0.0f;
for (int k = 0; k < 3; k++) {
APAT[i][j] += AP[i][k] * A[j][k]; // A^T[k][j] = A[j][k]
}
}
}
/* 计算 K * R * K^T 并加到 APAT */
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
P[i][j] = APAT[i][j] + K[i] * R * K[j];
}
}
}
/** 计算 2x2 对称矩阵的逆 (原地) */
static bool invert_2x2_sym(float S[2][2])
{
float det = S[0][0] * S[1][1] - S[0][1] * S[1][0];
if (fabsf(det) < 1e-8f) {
return false; // 奇异矩阵
}
float inv_det = 1.0f / det;
float S00 = S[0][0];
S[0][0] = inv_det * S[1][1];
S[1][1] = inv_det * S00;
S[0][1] = -inv_det * S[0][1];
S[1][0] = S[0][1];
return true;
}
/** 2x2 对称矩阵求逆 (原地) */
static bool invert_3x3_cholesky(float S[3][3])
{
// 使用 Cholesky 分解求逆
float L[3][3] = {0};
for (int i = 0; i < 3; i++) {
for (int j = 0; j <= i; j++) {
float sum = S[i][j];
for (int k = 0; k < j; k++) {
sum -= L[i][k] * L[j][k];
}
if (i == j) {
if (sum <= 0.0f) return false;
L[i][j] = sqrtf(sum);
} else {
L[i][j] = sum / L[j][j];
}
}
}
// 求逆: S_inv = L^(-T) * L^(-1)
float Linv[3][3] = {0};
for (int i = 0; i < 3; i++) {
Linv[i][i] = 1.0f / L[i][i];
for (int j = i - 1; j >= 0; j--) {
float sum = 0.0f;
for (int k = j + 1; k <= i; k++) {
sum += L[k][j] * Linv[k][i];
}
Linv[j][i] = -sum / L[j][j];
}
}
// S_inv = Linv^T * Linv
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
float sum = 0.0f;
for (int k = 0; k < 3; k++) {
sum += Linv[k][i] * Linv[k][j];
}
S[i][j] = sum;
}
}
return true;
}
/** 计算马氏距离平方 (新息向量 y, 新息协方差 S_inv) */
static float mahalanobis_d2_3dof(const float y[3], const float S_inv[3][3])
{
// d² = y^T * S_inv * y
float tmp[3] = {0};
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
tmp[i] += S_inv[i][j] * y[j];
}
}
float d2 = 0.0f;
for (int i = 0; i < 3; i++) {
d2 += y[i] * tmp[i];
}
return d2;
}
/** 计算马氏距离平方 (1DOF: 只用 e_y) */
static float mahalanobis_d2_1dof(float y_ey, float S_inv_00)
{
return y_ey * y_ey * S_inv_00;
}
/** 计算马氏距离平方 (2DOF: e_ey + e_th_avg) */
static float mahalanobis_d2_2dof(const float y[2], const float S_inv[2][2])
{
float tmp[2] = {0};
for (int i = 0; i < 2; i++) {
for (int j = 0; j < 2; j++) {
tmp[i] += S_inv[i][j] * y[j];
}
}
float d2 = 0.0f;
for (int i = 0; i < 2; i++) {
d2 += y[i] * tmp[i];
}
return d2;
}
/** 零矩阵 */
static void zero_3x3(float M[3][3])
{
memset(M, 0, sizeof(float) * 9);
}
/** 单位矩阵 */
static void eye_3x3(float M[3][3])
{
zero_3x3(M);
M[0][0] = M[1][1] = M[2][2] = 1.0f;
}
/* =========================================================
* API 实现
* ========================================================= */
void CorridorEKF_Init(const CorridorEKFConfig_t *config)
{
s_cfg = *config;
memset(&s_state, 0, sizeof(s_state));
/* 初始化状态 */
s_state.x[0] = 0.0f; // e_y
s_state.x[1] = 0.0f; // e_th
s_state.x[2] = 0.0f; // s
/* 初始化协方差 */
eye_3x3(s_state.P);
s_state.P[0][0] = config->P0_diag[0];
s_state.P[1][1] = config->P0_diag[1];
s_state.P[2][2] = config->P0_diag[2];
s_initialized = true;
}
void CorridorEKF_Reset(void)
{
if (!s_initialized) return;
s_state.x[0] = 0.0f;
s_state.x[1] = 0.0f;
s_state.x[2] = 0.0f;
eye_3x3(s_state.P);
s_state.P[0][0] = s_cfg.P0_diag[0];
s_state.P[1][1] = s_cfg.P0_diag[1];
s_state.P[2][2] = s_cfg.P0_diag[2];
s_last_update_ms = 0U;
}
void CorridorEKF_ResetHeading(void)
{
if (!s_initialized) return;
s_state.x[1] = 0.0f;
/* 清理航向与其它状态的耦合，避免旧航向误差继续通过协方差传播。 */
s_state.P[0][1] = 0.0f;
s_state.P[1][0] = 0.0f;
s_state.P[1][2] = 0.0f;
s_state.P[2][1] = 0.0f;
s_state.P[1][1] = s_cfg.P0_diag[1];
}
void CorridorEKF_RebaseAfterTurnaround(void)
{
if (!s_initialized) return;
/* 同一条走廊掉头后，新的前进方向相反，横向误差符号需要镜像。 */
s_state.x[0] = -s_state.x[0];
s_state.x[1] = 0.0f;
/* e_y 与 e_th 的相关项在掉头后不再可直接沿用，清零重新收敛。 */
s_state.P[0][1] = 0.0f;
s_state.P[1][0] = 0.0f;
s_state.P[1][2] = 0.0f;
s_state.P[2][1] = 0.0f;
s_state.P[1][1] = s_cfg.P0_diag[1];
}
void CorridorEKF_SetProcessNoise(float q_ey, float q_eth, float q_s)
{
s_cfg.q_ey = q_ey;
s_cfg.q_eth = q_eth;
s_cfg.q_s = q_s;
}
void CorridorEKF_SetMeasurementNoise(float r_ey, float r_eth)
{
s_cfg.r_ey = r_ey;
s_cfg.r_eth = r_eth;
}
/* =========================================================
* 预测步 (Predict)
* ========================================================= */
void CorridorEKF_Predict(float odom_vx, float imu_wz, float dt)
{
if (!s_initialized || dt <= 0.0f) return;
float e_y = s_state.x[0];
float e_th = s_state.x[1];
float s = s_state.x[2];
float vx = odom_vx;
float wz = imu_wz;
/* 状态预测: x_pred = f(x, u) */
float cos_th = cosf(e_th);
float sin_th = sinf(e_th);
/* 安全检查: cos_th 不能太小 (防止数值爆炸) */
if (fabsf(cos_th) < 0.01f) cos_th = (cos_th >= 0.0f) ? 0.01f : -0.01f;
float e_y_pred = e_y + vx * sin_th * dt;
float e_th_pred = e_th + wz * dt;
float s_pred = s + vx * cos_th * dt;
s_state.x[0] = e_y_pred;
s_state.x[1] = e_th_pred;
s_state.x[2] = s_pred;
/* 雅可比矩阵 F (状态转移的 Jacobian) */
float F[3][3] = {0};
F[0][0] = 1.0f;
F[0][1] = vx * cos_th * dt; // de_y/de_th
F[0][2] = 0.0f;
F[1][0] = 0.0f;
F[1][1] = 1.0f;
F[1][2] = 0.0f;
F[2][0] = 0.0f;
F[2][1] = -vx * sin_th * dt; // ds/de_th
F[2][2] = 1.0f;
/* 过程噪声协方差 Q (含耦合项)
* [改进] 添加 e_y 和 e_th 的耦合噪声，反映横向-航向动力学耦合 */
float Q[3][3] = {0};
Q[0][0] = s_cfg.q_ey * dt * dt;
Q[1][1] = s_cfg.q_eth * dt * dt;
Q[2][2] = s_cfg.q_s * dt * dt;
Q[0][1] = Q[1][0] = s_cfg.q_ey_eth * dt * dt; // 横向-航向耦合
/* 协方差预测: P_pred = F * P * F^T + Q */
float F_P[3][3] = {0};
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
for (int k = 0; k < 3; k++) {
F_P[i][j] += F[i][k] * s_state.P[k][j];
}
}
}
float P_pred[3][3] = {0};
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
for (int k = 0; k < 3; k++) {
P_pred[i][j] += F_P[i][k] * F[j][k]; // F^T: F[j][k] = F[k][j]
}
P_pred[i][j] += Q[i][j]; // 加过程噪声 (含非对角项)
}
}
symmetrize(P_pred);
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
s_state.P[i][j] = P_pred[i][j];
}
}
protect_P(s_state.P);
}
/* =========================================================
* 观测步 (Update) - 鲁棒 EKF
*
* 设计决策 (方向 B — IMU 主导航向)：
* 侧墙激光仅用于更新横向位置 e_y，不再构建航向观测 z_eth_L/z_eth_R。
* 航向 e_th 完全由 IMU 主导：
* - 预测步: imu_wz 驱动 e_th 积分
* - 观测步: CorridorEKF_UpdateIMUYaw() 提供 yaw_continuous 标量约束
* 侧墙前后差分 (d_lr-d_lf) 的噪声在 ±2cm 误差下过大，不适合做航向主观测。
* ========================================================= */
int CorridorEKF_Update(const CorridorObs_t *obs, CorridorState_t *out_state)
{
if (!s_initialized) return 0;
/* 维护最近一次 EKF 输出对应的观测时间戳，供 GetState() 返回一致结果。 */
s_last_update_ms = obs->t_ms;
int updated_obs_count = 0;
/* 清除新息和拒绝掩码 */
memset(s_state.K, 0, sizeof(s_state.K));
uint8_t reject_mask = 0U;
float max_maha_d2 = 0.0f;
/* ----------------------------------------------------
* 提取有效观测
* ---------------------------------------------------- */
bool left_ok = ((obs->valid_mask & (1U << 0)) != 0U) &&
((obs->valid_mask & (1U << 1)) != 0U);
bool right_ok = ((obs->valid_mask & (1U << 2)) != 0U) &&
((obs->valid_mask & (1U << 3)) != 0U);
/* 左右侧横向平均距离 */
float d_lf = obs->d_lf, d_lr = obs->d_lr;
float d_rf = obs->d_rf, d_rr = obs->d_rr;
float W = s_cfg.corridor_width;
float yoff = s_cfg.y_offset;
float Rw = s_cfg.robot_width;
/* [改进A] 分侧传感器内缩补偿 — 消除左右安装不对称引起的系统性偏置
* 左右各自使用独立的 inset 值计算期望居中读数 d_center */
float d_center_left = (W - Rw) / 2.0f + s_cfg.left_sensor_inset;
float d_center_right = (W - Rw) / 2.0f + s_cfg.right_sensor_inset;
/* 观测值 (测量) — 仅横向位置，不含航向 */
float z_ey = 0.0f;
int valid_sides = 0;
if (left_ok) {
z_ey += d_center_left - ((d_lf + d_lr) / 2.0f) - yoff;
valid_sides++;
}
if (right_ok) {
z_ey += ((d_rf + d_rr) / 2.0f) - d_center_right - yoff;
valid_sides++;
}
if (valid_sides == 0) {
out_state->t_ms = obs->t_ms;
out_state->e_y = s_state.x[0];
out_state->e_th = s_state.x[1];
out_state->s = s_state.x[2];
out_state->conf = clampf(1.0f - (s_state.P[0][0] + s_state.P[1][1]) * 0.1f, 0.0f, 1.0f);
out_state->obs_reject_mask = 0xFF;
out_state->mahalanobis_d2 = 0.0f;
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
out_state->P[i][j] = s_state.P[i][j];
}
}
/* 协方差膨胀 (无观测时的信任衰减) — 仅膨胀 e_y */
s_state.P[0][0] += s_cfg.q_ey * 5.0f;
protect_P(s_state.P);
return 0;
}
if (valid_sides == 2) {
z_ey /= 2.0f;
}
/* ----------------------------------------------------
* 1DOF 标量 EKF 更新 — 仅 e_y
* ---------------------------------------------------- */
float e_y = s_state.x[0];
float y_ey = z_ey - e_y;
/* [改进F] 自适应观测噪声 R:
* 双侧观测: R × 0.5 (噪声互相平均)
* 单侧观测: R × 3.0 (缺少交叉验证, VL53 可信度低时尤需降低信任)
*/
float R_ey = s_cfg.r_ey;
if (valid_sides == 2) {
R_ey *= 0.5f;
} else if (valid_sides == 1) {
R_ey *= 3.0f;
}
float S_ey = s_state.P[0][0] + R_ey;
if (fabsf(S_ey) < 1e-8f) {
goto output_result;
}
float d2_ey = y_ey * y_ey / S_ey;
max_maha_d2 = d2_ey;
if (d2_ey > s_cfg.chi2_1dof) {
reject_mask |= (1U << 0);
goto output_result;
}
float S_inv_ey = 1.0f / S_ey;
float K_ey[3];
K_ey[0] = s_state.P[0][0] * S_inv_ey;
K_ey[1] = s_state.P[1][0] * S_inv_ey;
K_ey[2] = s_state.P[2][0] * S_inv_ey;
s_state.x[0] += K_ey[0] * y_ey;
s_state.x[1] += K_ey[1] * y_ey;
s_state.x[2] += K_ey[2] * y_ey;
/* Joseph 形式协方差更新: P = (I-KH)*P*(I-KH)^T + K*R*K^T
* H = [1, 0, 0] (仅观测 e_y) */
float H_ey[3] = {1.0f, 0.0f, 0.0f};
joseph_update_P(s_state.P, K_ey, H_ey, R_ey);
symmetrize(s_state.P);
protect_P(s_state.P);
updated_obs_count = 1;
output_result:
out_state->t_ms = obs->t_ms;
out_state->e_y = s_state.x[0];
out_state->e_th = s_state.x[1];
out_state->s = s_state.x[2];
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
out_state->P[i][j] = s_state.P[i][j];
}
}
out_state->mahalanobis_d2 = max_maha_d2;
out_state->obs_reject_mask = reject_mask;
float P_trace = s_state.P[0][0] + s_state.P[1][1] + s_state.P[2][2];
float conf_from_P = clampf(1.0f - P_trace * 0.5f, 0.0f, 1.0f);
float side_factor = (valid_sides == 2) ? 1.0f : 0.7f;
float reject_penalty = (reject_mask & (1U << 0)) ? 0.5f : 1.0f;
out_state->conf = clampf(conf_from_P * side_factor * reject_penalty, 0.0f, 1.0f);
return updated_obs_count;
}
/* =========================================================
* 辅助 API
* ========================================================= */
/* =========================================================
* IMU 航向观测更新 (独立 1DOF 标量 EKF 更新)
*
* 观测方程: z_eth_imu = imu_yaw_rad - imu_yaw_ref_rad
* 对应状态: e_th (x[1])
* H = [0, 1, 0] (只观测 e_th)
*
* 设计意图：
* - IMU 内部维护的 yaw 经过模块校准，比外部积分 wz 更稳定
* - 在侧墙观测丢失 (转弯/单侧退化) 时提供航向约束
* - 使用较大 R 值，让侧墙观测在有效时主导
* ========================================================= */
void CorridorEKF_UpdateIMUYaw(float imu_yaw_rad, float imu_yaw_ref_rad, bool valid)
{
if (!s_initialized || !valid) return;
/* 观测值: IMU 相对于走廊参考方向的航向偏差
* [改进] 角度归一化防止 ±π 跨越时新息突变 */
float z_eth_imu = wrap_angle(imu_yaw_rad - imu_yaw_ref_rad);
/* 新息: y = z - h(x), h(x) = e_th = x[1]
* [改进] 再次归一化，防止 e_th 和 z_eth_imu 符号不同时差值超出 [-π, π] */
float y_imu = wrap_angle(z_eth_imu - s_state.x[1]);
/* H = [0, 1, 0] → S = P[1][1] + R_imu */
float R_imu = s_cfg.r_eth_imu;
float S_imu = s_state.P[1][1] + R_imu;
if (fabsf(S_imu) < 1e-8f) return;
/* χ² 1DOF 检验: d² = y² / S */
float d2_imu = y_imu * y_imu / S_imu;
if (d2_imu > s_cfg.chi2_1dof) return; /* 拒绝异常观测 */
/* 卡尔曼增益: K = P * H^T / S = P[:][1] / S */
float K[3];
float S_inv = 1.0f / S_imu;
K[0] = s_state.P[0][1] * S_inv;
K[1] = s_state.P[1][1] * S_inv;
K[2] = s_state.P[2][1] * S_inv;
/* 状态更新: x += K * y */
s_state.x[0] += K[0] * y_imu;
s_state.x[1] += K[1] * y_imu;
s_state.x[2] += K[2] * y_imu;
/* Joseph 形式协方差更新: P = (I-KH)*P*(I-KH)^T + K*R*K^T
* H = [0, 1, 0] (仅观测 e_th) */
float H_imu[3] = {0.0f, 1.0f, 0.0f};
joseph_update_P(s_state.P, K, H_imu, R_imu);
symmetrize(s_state.P);
protect_P(s_state.P);
}
void CorridorEKF_GetState(CorridorState_t *out)
{
if (!s_initialized || out == NULL) return;
out->t_ms = s_last_update_ms;
out->e_y = s_state.x[0];
out->e_th = s_state.x[1];
out->s = s_state.x[2];
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
out->P[i][j] = s_state.P[i][j];
}
}
out->mahalanobis_d2 = 0.0f;
out->obs_reject_mask = 0U;
float P_trace = s_state.P[0][0] + s_state.P[1][1] + s_state.P[2][2];
out->conf = clampf(1.0f - P_trace * 0.5f, 0.0f, 1.0f);
}
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