粒子滤波算法融合车道线观测，优化车体位姿，请用C++实现

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粒子滤波算法（Particle Filter）是一种概率滤波算法，通常用于非线性问题的状态估计。而车道线观测和车体位姿优化则是一种常见的自动驾驶问题，因此粒子滤波算法被广泛应用于自动驾驶领域。

下面是一个用 C++ 实现粒子滤波算法融合车道线观测，优化车体位姿的示例代码：

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

using namespace std;

// 定义粒子类型
struct Particle {
    double x, y, theta, weight;
};

// 定义观测类型
struct Observation {
    double x, y;
};

// 定义控制输入类型
struct Control {
    double v, w;
};

// 定义粒子滤波器类
class ParticleFilter {
public:
    ParticleFilter(int num_particles) {
        // 初始化粒子
        particles_.resize(num_particles);
        for (int i = 0; i < num_particles; ++i) {
            Particle &p = particles_[i];
            p.x = 0.0;
            p.y = 0.0;
            p.theta = 0.0;
            p.weight = 1.0 / num_particles;
        }

        // 设置随机数生成器
        random_device rd;
        gen_ = default_random_engine(rd());
        normal_dist_ = normal_distribution<double>(0.0, 1.0);
    }

    // 更新粒子状态
    void Predict(const Control &control, double dt) {
        for (auto &p : particles_) {
            // 根据控制输入和运动模型更新粒子状态
            p.x += control.v * cos(p.theta) * dt;
            p.y += control.v * sin(p.theta) * dt;
            p.theta += control.w * dt + normal_dist_(gen_) * 0.1;
        }
    }

    // 融合观测信息
    void Update(const vector<Observation> &observations) {
        for (auto &p : particles_) {
            // 将观测信息变换到粒子坐标系下
            vector<Observation> transformed_observations;
            for (const auto &obs : observations) {
                Observation t_obs;
                t_obs.x = obs.x * cos(p.theta) + obs.y * sin(p.theta) + p.x;
                t_obs.y = -obs.x * sin(p.theta) + obs.y * cos(p.theta) + p.y;
                transformed_observations.push_back(t_obs);
            }

            // 计算粒子权重
            p.weight = 1.0;
            for (const auto &t_obs : transformed_observations) {
                double dx = t_obs.x - p.x;
                double dy = t_obs.y - p.y;
                double dist = sqrt(dx*dx + dy*dy);
                p.weight *= exp(-0.5 * dist*dist / sigma_*sigma_);
            }
        }

        // 归一化权重
        double sum_weight = 0.0;
        for (const auto &p : particles_) {
            sum_weight += p.weight;
        }
        for (auto &p : particles_) {
            p.weight /= sum_weight;
        }
    }

    // 重新采样
    void Resample() {
        vector<Particle> new_particles(particles_.size());
        uniform_real_distribution<double> uni_dist(0.0, 1.0);
        double beta = 0.0;
        int index = 0;
        for (int i = 0; i < particles_.size(); ++i) {
            beta += uni_dist(gen_) * 2.0;
            while (beta > particles_[index].weight) {
                beta -= particles_[index].weight;
                index = (index + 1) % particles_.size();
            }
            new_particles[i] = particles_[index];
            new_particles[i].weight = 1.0 / particles_.size();
        }
        particles_ = new_particles;
    }

    // 获取粒子坐标系下的位姿
    vector<double> GetPose() const {
        double x = 0.0;
        double y = 0.0;
        double sin_theta = 0.0;
        double cos_theta = 0.0;
        for (const auto &p : particles_) {
            x += p.x * p.weight;
            y += p.y * p.weight;
            sin_theta += sin(p.theta) * p.weight;
            cos_theta += cos(p.theta) * p.weight;
        }
        double theta = atan2(sin_theta, cos_theta);
        return {x, y, theta};
    }

private:
    vector<Particle> particles_;
    default_random_engine gen_;
    normal_distribution<double> normal_dist_;
    double sigma_ = 0.1;
};

int main() {
    // 初始化粒子滤波器
    ParticleFilter pf(1000);

    // 进行一次迭代
    Control control = {1.0, 0.1};
    double dt = 0.1;
    pf.Predict(control, dt);
    vector<Observation> observations = {{1.0, 0.0}, {0.0, 1.0}, {-1.0, 0.0}, {0.0, -1.0}};
    pf.Update(observations);
    pf.Resample();

    // 获取估计的位姿
    vector<double> pose = pf.GetPose();
    cout << "Estimated pose: " << pose[0] << ", " << pose[1] << ", " << pose[2] << endl;

    return 0;
}

以上代码实现了一次迭代的粒子滤波算法，包括控制输入、观测信息、权重计算、重采样等步骤。你可以根据实际需求进行修改和扩展。