粒子滤波算法用于估计车体位姿，请用C++实现

以下是一个使用 C++ 实现粒子滤波算法用于估计车体位姿的示例代码：

#include <iostream>
#include <vector>
#include <random>
#include <cmath>

using namespace std;

// 车体模型
struct CarModel {
    double x; // x 坐标
    double y; // y 坐标
    double theta; // 方向角
    double v; // 速度
    double omega; // 角速度
};

// 状态转移函数
void transition_fn(CarModel& state, double delta_t) {
    // 计算新状态
    state.x += state.v * cos(state.theta) * delta_t;
    state.y += state.v * sin(state.theta) * delta_t;
    state.theta += state.omega * delta_t;
}

// 观测函数
double observation_fn(const CarModel& state) {
    // 添加噪声，模拟测量误差
    static default_random_engine e;
    static normal_distribution<double> n(0, 0.1);
    return state.x + n(e);
}

// 粒子采样函数
void sample_fn(CarModel& state) {
    // 添加噪声，模拟运动误差
    static default_random_engine e;
    static normal_distribution<double> n_x(0, 0.1);
    static normal_distribution<double> n_y(0, 0.1);
    static normal_distribution<double> n_theta(0, 0.01);
    static normal_distribution<double> n_v(0, 0.1);
    static normal_distribution<double> n_omega(0, 0.01);
    state.x += n_x(e);
    state.y += n_y(e);
    state.theta += n_theta(e);
    state.v += n_v(e);
    state.omega += n_omega(e);
}

// 粒子滤波算法
void particle_filter(const CarModel& init_state, const vector<double>& control, const vector<double>& measurements, int num_particles) {
    // 初始化粒子
    vector<CarModel> particles(num_particles, init_state);

    // 初始化粒子权重
    vector<double> weights(num_particles, 1.0 / num_particles);

    // 遍历每个时间步
    for (int t = 0; t < control.size(); t++) {
        // 预测状态值
        for (int i = 0; i < num_particles; i++) {
            transition_fn(particles[i], control[t]);
            sample_fn(particles[i]);
        }

        // 计算粒子权重
        for (int i = 0; i < num_particles; i++) {
            double diff = measurements[t] - observation_fn(particles[i]);
            weights[i] *= exp(-0.5 * diff * diff);
        }

        // 归一化粒子权重
        double sum_weights = 0;
        for (int i = 0; i < num_particles; i++) {
            sum_weights += weights[i];
        }
        for (int i = 0; i < num_particles; i++) {
            weights[i] /= sum_weights;
        }

        // 重采样粒子
        vector<CarModel> resampled_particles(num_particles);
        int index = rand() % num_particles;
        double beta = 0;
        double max_weight = *max_element(weights.begin(), weights.end());
        for (int i = 0; i < num_particles; i++) {
            beta += rand() / (RAND_MAX + 1.0) * 2.0 * max_weight;
            while (beta > weights[index]) {
                beta -= weights[index];
                index = (index + 1) % num_particles;
            }
            resampled_particles[i] = particles[index];
        }
        particles = resampled_particles;

        // 输出估计值
        double x_sum = 0, y_sum = 0, theta_sum = 0;
        for (int i = 0; i < num_particles; i++) {
            x_sum += particles[i].x;
            y_sum += particles[i].y;
            theta_sum += particles[i].theta;
        }
        double x_mean = x_sum / num_particles;
        double y_mean = y_sum / num_particles;
        double theta_mean = theta_sum / num_particles;
        cout << "t=" << t << ": x=" << x_mean << ", y=" << y_mean << ", theta=" << theta_mean << endl;
    }
}

int main() {
    // 初始化车体状态
    CarModel init_state{0, 0, 0, 0, 0};

    // 构造控制序列和观测序列
    vector<double> control{1, 1, 1};
    vector<double> measurements{0.1, 0.2, 0.3};

    // 运行粒子滤波算法
    particle_filter(init_state, control, measurements, 1000);

    return 0;
}

上述代码定义了一个 `CarModel` 结构体，表示车体模型，其中包含了车体的位置坐标、方向角、速度和角速度等状态量。`transition_fn` 函数表示状态转移函数，`observation_fn` 函数表示观测函数，`sample_fn` 函数表示粒子采样函数。`particle_filter` 函数实现了粒子滤波算法，其中包括状态预测、权重更新、重采样等过程。最后，通过遍历时间步，对每个时间步的状态进行估计，并输出估计值。