用于雷达实施的 UKF

Question

我正在努力实现无迹卡尔曼滤波器以使用雷达跟踪对象。我的状态向量包含 [x y z vx vy vz]，我可以测量 [rho phi theta velocity]。所以一开始一切看起来都很微不足道，因为状态估计很简单

  x = rho * sin(theta) * cos(phi);
  y = rho * sin(theta) * sin(phi);
  z = rho * cos(theta);
  vx = v * sin(theta) * cos(phi);
  vy = v * sin(theta) * sin(phi);
  vz = v * cos(theta);

测量模型也是众所周知的：

rho = sqrt(p_x*p_x + p_y*p_y + p_z*p_z);         
phi = atan(p_y/p_x); 
theta = atan(sqrt(p_x*p_x + p_y*p_y)/p_z); 
velocity = sqrt(v_x*v_x + v_y*v_y + v_z*v_z);

我的预测基于恒速模型，如下所示：

    //predicted state values
    px_p = p_x + v_x*delta_t;
    py_p = p_y + v_y*delta_t;
    pz_p = p_z + v_z*delta_t;
    vx_p = v_x + err_x*delta_t;
    vy_p = v_y + err_y*delta_t;
    vz_p = v_z + err_z*delta_t;

而且...它不起作用。它工作时唯一的一种情况是沿 x 轴的速度恒定。谁能解释我做错了什么？在这种情况下 Q 矩阵应该是什么？感谢任何提示和提示。干杯，Vicky。

UPD：在robot_localization包中我找到了名为transferFunction_()的矩阵，这是我理解的过程函数（在评论中的参考示例中它用于预测西格玛点），没有噪音。它是 15 维的，实现方式如下：

double roll = state_(StateMemberRoll);
double pitch = state_(StateMemberPitch);
double yaw = state_(StateMemberYaw);

double sp = ::sin(pitch);
double cp = ::cos(pitch);
double cpi = 1.0 / cp;
double tp = sp * cpi;

double sr = ::sin(roll);
double cr = ::cos(roll);

double sy = ::sin(yaw);
double cy = ::cos(yaw);

transferFunction_(StateMemberX, StateMemberVx) = cy * cp * delta;
transferFunction_(StateMemberX, StateMemberVy) = (cy * sp * sr - sy * cr) * delta;
transferFunction_(StateMemberX, StateMemberVz) = (cy * sp * cr + sy * sr) * delta;
transferFunction_(StateMemberX, StateMemberAx) = 0.5 * transferFunction_(StateMemberX, StateMemberVx) * delta;
transferFunction_(StateMemberX, StateMemberAy) = 0.5 * transferFunction_(StateMemberX, StateMemberVy) * delta;
transferFunction_(StateMemberX, StateMemberAz) = 0.5 * transferFunction_(StateMemberX, StateMemberVz) * delta;
transferFunction_(StateMemberY, StateMemberVx) = sy * cp * delta;
transferFunction_(StateMemberY, StateMemberVy) = (sy * sp * sr + cy * cr) * delta;
transferFunction_(StateMemberY, StateMemberVz) = (sy * sp * cr - cy * sr) * delta;
transferFunction_(StateMemberY, StateMemberAx) = 0.5 * transferFunction_(StateMemberY, StateMemberVx) * delta;
transferFunction_(StateMemberY, StateMemberAy) = 0.5 * transferFunction_(StateMemberY, StateMemberVy) * delta;
transferFunction_(StateMemberY, StateMemberAz) = 0.5 * transferFunction_(StateMemberY, StateMemberVz) * delta;
transferFunction_(StateMemberZ, StateMemberVx) = -sp * delta;
transferFunction_(StateMemberZ, StateMemberVy) = cp * sr * delta;
transferFunction_(StateMemberZ, StateMemberVz) = cp * cr * delta;
transferFunction_(StateMemberZ, StateMemberAx) = 0.5 * transferFunction_(StateMemberZ, StateMemberVx) * delta;
transferFunction_(StateMemberZ, StateMemberAy) = 0.5 * transferFunction_(StateMemberZ, StateMemberVy) * delta;
transferFunction_(StateMemberZ, StateMemberAz) = 0.5 * transferFunction_(StateMemberZ, StateMemberVz) * delta;
transferFunction_(StateMemberRoll, StateMemberVroll) = delta;
transferFunction_(StateMemberRoll, StateMemberVpitch) = sr * tp * delta;
transferFunction_(StateMemberRoll, StateMemberVyaw) = cr * tp * delta;
transferFunction_(StateMemberPitch, StateMemberVpitch) = cr * delta;
transferFunction_(StateMemberPitch, StateMemberVyaw) = -sr * delta;
transferFunction_(StateMemberYaw, StateMemberVpitch) = sr * cpi * delta;
transferFunction_(StateMemberYaw, StateMemberVyaw) = cr * cpi * delta;
transferFunction_(StateMemberVx, StateMemberAx) = delta;
transferFunction_(StateMemberVy, StateMemberAy) = delta;
transferFunction_(StateMemberVz, StateMemberAz) = delta;

还有明确的processNoiseCovariance矩阵：

processNoiseCovariance_.setZero();
processNoiseCovariance_(StateMemberX, StateMemberX) = 0.05;
processNoiseCovariance_(StateMemberY, StateMemberY) = 0.05;
processNoiseCovariance_(StateMemberZ, StateMemberZ) = 0.06;
processNoiseCovariance_(StateMemberRoll, StateMemberRoll) = 0.03;
processNoiseCovariance_(StateMemberPitch, StateMemberPitch) = 0.03;
processNoiseCovariance_(StateMemberYaw, StateMemberYaw) = 0.06;
processNoiseCovariance_(StateMemberVx, StateMemberVx) = 0.025;
processNoiseCovariance_(StateMemberVy, StateMemberVy) = 0.025;
processNoiseCovariance_(StateMemberVz, StateMemberVz) = 0.04;
processNoiseCovariance_(StateMemberVroll, StateMemberVroll) = 0.01;
processNoiseCovariance_(StateMemberVpitch, StateMemberVpitch) = 0.01;
processNoiseCovariance_(StateMemberVyaw, StateMemberVyaw) = 0.02;
processNoiseCovariance_(StateMemberAx, StateMemberAx) = 0.01;
processNoiseCovariance_(StateMemberAy, StateMemberAy) = 0.01;
processNoiseCovariance_(StateMemberAz, StateMemberAz) = 0.015;

Answer 1

长话短说，我还没有找到解决方案，所以我只是运行在 2 个平面上使用两个 UKF 过滤器来覆盖 3D。视觉部分在 rviz 中工作正常，但我仍在实施数据关联算法以确保我使用两个过滤器跟踪相同的目标。

Answer 2

雷达只测量径向速度，所以你的测量模型是错误的。

用于雷达实施的 UKF

UKF for radar implementation

ros

kalman-filter