650 lines
19 KiB
C
650 lines
19 KiB
C
/**
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* @file corridor_ekf.c
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* @brief 鲁棒 EKF 走廊相对定位滤波器实现
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*
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* 完整算法流程：
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*
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* 【预测步】Predict(vx, wz, dt)
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* x_pred = f(x, u) -- 非线性状态转移
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* P_pred = F * P * F^T + Q -- 协方差预测
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*
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* 【更新步】Update(obs)
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* z = h(x_pred) -- 观测预测
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* y = z_meas - z -- 新息 (Innovation)
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* S = H * P_pred * H^T + R -- 新息协方差
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* d² = y^T * S^(-1) * y -- 马氏距离平方
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* if d² > χ²_threshold: 拒绝观测 (鲁棒)
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* K = P_pred * H^T * S^(-1) -- 卡尔曼增益
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* x = x_pred + K * y -- 状态更新
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* P = (I - K * H) * P_pred -- 协方差更新
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*/
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#include "corridor_ekf.h"
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#include <math.h>
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#include <string.h>
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/* =========================================================
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* 内部静态状态
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* ========================================================= */
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static CorridorEKFConfig_t s_cfg;
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static CorridorEKFState_t s_state;
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static bool s_initialized = false;
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static uint32_t s_last_update_ms = 0U;
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/* 协方差上界保护阈值 */
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#define P_MAX_DIAG 100.0f
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/* =========================================================
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* 内部辅助函数
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* ========================================================= */
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/** 限幅 */
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static inline float clampf(float val, float lo, float hi)
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{
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if (val < lo) return lo;
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if (val > hi) return hi;
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return val;
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}
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/** 对称矩阵拷贝 + 双向取平均 (减少舍入误差传播) */
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static void symmetrize(float M[3][3])
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{
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float avg;
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avg = (M[0][1] + M[1][0]) * 0.5f;
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M[0][1] = M[1][0] = avg;
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avg = (M[0][2] + M[2][0]) * 0.5f;
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M[0][2] = M[2][0] = avg;
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avg = (M[1][2] + M[2][1]) * 0.5f;
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M[1][2] = M[2][1] = avg;
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}
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/** 角度归一化到 [-π, π]
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* 防止 IMU yaw 累积角度跨越 ±π 时导致新息突变
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*/
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static float wrap_angle(float angle)
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{
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const float PI = 3.14159265358979323846f;
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while (angle > PI) angle -= 2.0f * PI;
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while (angle < -PI) angle += 2.0f * PI;
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return angle;
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}
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/** P 上界保护 */
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static void protect_P(float P[3][3])
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{
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for (int i = 0; i < 3; i++) {
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if (P[i][i] > P_MAX_DIAG) P[i][i] = P_MAX_DIAG;
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if (P[i][i] < 0.0f) P[i][i] = 0.0f;
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}
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}
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/** Joseph 形式协方差更新 (1DOF 标量观测)
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* P_new = (I - K*H) * P * (I - K*H)^T + K * R * K^T
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*
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* 参数:
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* P[3][3] - 先验协方差 (输入/输出)
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* K[3] - 卡尔曼增益向量
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* H[3] - 观测矩阵 (1x3 行向量)
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* R - 观测噪声方差 (标量)
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*
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* 优点: 保证数值稳定性，即使有舍入误差也能保持 P 正定
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*/
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static void joseph_update_P(float P[3][3], const float K[3], const float H[3], float R)
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{
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/* 计算 A = (I - K*H) */
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float A[3][3];
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for (int i = 0; i < 3; i++) {
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for (int j = 0; j < 3; j++) {
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A[i][j] = (i == j ? 1.0f : 0.0f) - K[i] * H[j];
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}
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}
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/* 计算 A * P */
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float AP[3][3];
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for (int i = 0; i < 3; i++) {
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for (int j = 0; j < 3; j++) {
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AP[i][j] = 0.0f;
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for (int k = 0; k < 3; k++) {
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AP[i][j] += A[i][k] * P[k][j];
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}
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}
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}
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/* 计算 A * P * A^T */
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float APAT[3][3];
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for (int i = 0; i < 3; i++) {
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for (int j = 0; j < 3; j++) {
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APAT[i][j] = 0.0f;
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for (int k = 0; k < 3; k++) {
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APAT[i][j] += AP[i][k] * A[j][k]; // A^T[k][j] = A[j][k]
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}
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}
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}
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/* 计算 K * R * K^T 并加到 APAT */
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for (int i = 0; i < 3; i++) {
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for (int j = 0; j < 3; j++) {
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P[i][j] = APAT[i][j] + K[i] * R * K[j];
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}
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}
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}
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/** 计算 2x2 对称矩阵的逆 (原地) */
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static bool invert_2x2_sym(float S[2][2])
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{
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float det = S[0][0] * S[1][1] - S[0][1] * S[1][0];
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if (fabsf(det) < 1e-8f) {
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return false; // 奇异矩阵
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}
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float inv_det = 1.0f / det;
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float S00 = S[0][0];
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S[0][0] = inv_det * S[1][1];
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S[1][1] = inv_det * S00;
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S[0][1] = -inv_det * S[0][1];
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S[1][0] = S[0][1];
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return true;
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}
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/** 2x2 对称矩阵求逆 (原地) */
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static bool invert_3x3_cholesky(float S[3][3])
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{
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// 使用 Cholesky 分解求逆
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float L[3][3] = {0};
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for (int i = 0; i < 3; i++) {
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for (int j = 0; j <= i; j++) {
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float sum = S[i][j];
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for (int k = 0; k < j; k++) {
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sum -= L[i][k] * L[j][k];
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}
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if (i == j) {
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if (sum <= 0.0f) return false;
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L[i][j] = sqrtf(sum);
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} else {
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L[i][j] = sum / L[j][j];
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}
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}
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}
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// 求逆: S_inv = L^(-T) * L^(-1)
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float Linv[3][3] = {0};
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for (int i = 0; i < 3; i++) {
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Linv[i][i] = 1.0f / L[i][i];
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for (int j = i - 1; j >= 0; j--) {
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float sum = 0.0f;
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for (int k = j + 1; k <= i; k++) {
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sum += L[k][j] * Linv[k][i];
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}
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Linv[j][i] = -sum / L[j][j];
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}
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}
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// S_inv = Linv^T * Linv
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for (int i = 0; i < 3; i++) {
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for (int j = 0; j < 3; j++) {
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float sum = 0.0f;
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for (int k = 0; k < 3; k++) {
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sum += Linv[k][i] * Linv[k][j];
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}
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S[i][j] = sum;
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}
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}
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return true;
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}
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/** 计算马氏距离平方 (新息向量 y, 新息协方差 S_inv) */
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static float mahalanobis_d2_3dof(const float y[3], const float S_inv[3][3])
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{
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// d² = y^T * S_inv * y
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float tmp[3] = {0};
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for (int i = 0; i < 3; i++) {
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for (int j = 0; j < 3; j++) {
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tmp[i] += S_inv[i][j] * y[j];
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}
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}
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float d2 = 0.0f;
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for (int i = 0; i < 3; i++) {
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d2 += y[i] * tmp[i];
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}
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return d2;
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}
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/** 计算马氏距离平方 (1DOF: 只用 e_y) */
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static float mahalanobis_d2_1dof(float y_ey, float S_inv_00)
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{
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return y_ey * y_ey * S_inv_00;
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}
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/** 计算马氏距离平方 (2DOF: e_ey + e_th_avg) */
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static float mahalanobis_d2_2dof(const float y[2], const float S_inv[2][2])
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{
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float tmp[2] = {0};
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for (int i = 0; i < 2; i++) {
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for (int j = 0; j < 2; j++) {
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tmp[i] += S_inv[i][j] * y[j];
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}
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}
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float d2 = 0.0f;
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for (int i = 0; i < 2; i++) {
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d2 += y[i] * tmp[i];
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}
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return d2;
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}
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/** 零矩阵 */
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static void zero_3x3(float M[3][3])
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{
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memset(M, 0, sizeof(float) * 9);
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}
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/** 单位矩阵 */
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static void eye_3x3(float M[3][3])
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{
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zero_3x3(M);
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M[0][0] = M[1][1] = M[2][2] = 1.0f;
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}
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/* =========================================================
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* API 实现
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* ========================================================= */
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void CorridorEKF_Init(const CorridorEKFConfig_t *config)
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{
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s_cfg = *config;
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memset(&s_state, 0, sizeof(s_state));
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/* 初始化状态 */
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s_state.x[0] = 0.0f; // e_y
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s_state.x[1] = 0.0f; // e_th
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s_state.x[2] = 0.0f; // s
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/* 初始化协方差 */
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eye_3x3(s_state.P);
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s_state.P[0][0] = config->P0_diag[0];
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s_state.P[1][1] = config->P0_diag[1];
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s_state.P[2][2] = config->P0_diag[2];
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s_initialized = true;
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}
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void CorridorEKF_Reset(void)
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{
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if (!s_initialized) return;
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s_state.x[0] = 0.0f;
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s_state.x[1] = 0.0f;
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s_state.x[2] = 0.0f;
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eye_3x3(s_state.P);
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s_state.P[0][0] = s_cfg.P0_diag[0];
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s_state.P[1][1] = s_cfg.P0_diag[1];
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s_state.P[2][2] = s_cfg.P0_diag[2];
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s_last_update_ms = 0U;
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}
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void CorridorEKF_ResetHeading(void)
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{
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if (!s_initialized) return;
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s_state.x[1] = 0.0f;
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/* 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。 */
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s_state.P[0][1] = 0.0f;
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s_state.P[1][0] = 0.0f;
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s_state.P[1][2] = 0.0f;
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s_state.P[2][1] = 0.0f;
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s_state.P[1][1] = s_cfg.P0_diag[1];
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}
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void CorridorEKF_RebaseAfterTurnaround(void)
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{
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if (!s_initialized) return;
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/* 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。 */
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s_state.x[0] = -s_state.x[0];
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s_state.x[1] = 0.0f;
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/* 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。 */
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s_state.P[0][1] = 0.0f;
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s_state.P[1][0] = 0.0f;
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s_state.P[1][2] = 0.0f;
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s_state.P[2][1] = 0.0f;
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s_state.P[1][1] = s_cfg.P0_diag[1];
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}
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void CorridorEKF_SetProcessNoise(float q_ey, float q_eth, float q_s)
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{
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s_cfg.q_ey = q_ey;
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s_cfg.q_eth = q_eth;
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s_cfg.q_s = q_s;
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}
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void CorridorEKF_SetMeasurementNoise(float r_ey, float r_eth)
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{
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s_cfg.r_ey = r_ey;
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s_cfg.r_eth = r_eth;
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}
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/* =========================================================
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* 预测步 (Predict)
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* ========================================================= */
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void CorridorEKF_Predict(float odom_vx, float imu_wz, float dt)
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{
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if (!s_initialized || dt <= 0.0f) return;
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float e_y = s_state.x[0];
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float e_th = s_state.x[1];
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float s = s_state.x[2];
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float vx = odom_vx;
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float wz = imu_wz;
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/* 状态预测: x_pred = f(x, u) */
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float cos_th = cosf(e_th);
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float sin_th = sinf(e_th);
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/* 安全检查: cos_th 不能太小 (防止数值爆炸) */
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if (fabsf(cos_th) < 0.01f) cos_th = (cos_th >= 0.0f) ? 0.01f : -0.01f;
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float e_y_pred = e_y + vx * sin_th * dt;
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float e_th_pred = e_th + wz * dt;
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float s_pred = s + vx * cos_th * dt;
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s_state.x[0] = e_y_pred;
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s_state.x[1] = e_th_pred;
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s_state.x[2] = s_pred;
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/* 雅可比矩阵 F (状态转移的 Jacobian) */
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float F[3][3] = {0};
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F[0][0] = 1.0f;
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F[0][1] = vx * cos_th * dt; // de_y/de_th
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F[0][2] = 0.0f;
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F[1][0] = 0.0f;
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F[1][1] = 1.0f;
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F[1][2] = 0.0f;
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F[2][0] = 0.0f;
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F[2][1] = -vx * sin_th * dt; // ds/de_th
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F[2][2] = 1.0f;
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/* 过程噪声协方差 Q (含耦合项)
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* [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 */
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float Q[3][3] = {0};
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Q[0][0] = s_cfg.q_ey * dt * dt;
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Q[1][1] = s_cfg.q_eth * dt * dt;
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Q[2][2] = s_cfg.q_s * dt * dt;
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Q[0][1] = Q[1][0] = s_cfg.q_ey_eth * dt * dt; // 横向-航向耦合
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/* 协方差预测: P_pred = F * P * F^T + Q */
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float F_P[3][3] = {0};
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for (int i = 0; i < 3; i++) {
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for (int j = 0; j < 3; j++) {
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for (int k = 0; k < 3; k++) {
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F_P[i][j] += F[i][k] * s_state.P[k][j];
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}
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}
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}
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float P_pred[3][3] = {0};
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for (int i = 0; i < 3; i++) {
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for (int j = 0; j < 3; j++) {
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for (int k = 0; k < 3; k++) {
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P_pred[i][j] += F_P[i][k] * F[j][k]; // F^T: F[j][k] = F[k][j]
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}
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P_pred[i][j] += Q[i][j]; // 加过程噪声 (含非对角项)
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}
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}
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symmetrize(P_pred);
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for (int i = 0; i < 3; i++) {
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for (int j = 0; j < 3; j++) {
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s_state.P[i][j] = P_pred[i][j];
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}
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}
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protect_P(s_state.P);
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}
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/* =========================================================
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* 观测步 (Update) - 鲁棒 EKF
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*
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* 设计决策 (方向 B — IMU 主导航向)：
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* 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。
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* 航向 e_th 完全由 IMU 主导：
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* - 预测步: imu_wz 驱动 e_th 积分
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* - 观测步: CorridorEKF_UpdateIMUYaw() 提供 yaw_continuous 标量约束
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* 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。
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* ========================================================= */
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int CorridorEKF_Update(const CorridorObs_t *obs, CorridorState_t *out_state)
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{
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if (!s_initialized) return 0;
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/* 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。 */
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s_last_update_ms = obs->t_ms;
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int updated_obs_count = 0;
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/* 清除新息和拒绝掩码 */
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||
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);
|
||
}
|