This paper addresses the problem of tracking a moving source, e.g., a robot, equipped with both receivers and a source, that is tracking its own location and simultaneously estimating the locations of multiple plane reflectors. We assume a noisy knowledge of the robot’s movement. We formulate this problem, which is also known as simultaneous localization and mapping (SLAM), as a hybrid estimation problem. We derive the extended Kalman filter (EKF) for both tracking the robot’s own location and estimating the room geometry. Since the EKF employs linearization at every step, we incorporate a regulated kinematic model, which facilitates a successful tracking. In addition, we consider the echo-labeling problem as solved and beyond the scope of this paper. We then develop the hybrid Cramér-Rao lower bound on the estimation accuracy of both the localization and mapping parameters. The algorithm is evaluated with respect to the bound via simulations, which shows that the EKF approaches the hybrid Cramér-Rao bound (CRB) (HCRB) as the number of observation increases. This result implies that for the examples tested in simulation, the HCRB is an asymptotically tight bound and that the EKF is an optimal estimator. Whether this property is true in general remains an open question.

本文解决了跟踪移动源（例如配备了接收器和源的机器人）的问题，该源正在跟踪其自身的位置并同时估计多个平面反射器的位置。我们假设对机器人的运动有一定的了解。我们将此问题（也称为同时定位和映射（SLAM））表述为混合估计问题。我们导出了扩展的卡尔曼滤波器（EKF），用于跟踪机器人自身的位置并估计房间的几何形状。由于EKF在每个步骤都采用线性化，因此我们合并了受规制的运动学模型，这有助于成功进行跟踪。另外，我们认为回声标记问题已经解决，超出了本文的范围。然后，我们针对定位参数和制图参数的估计精度开发混合Cramér-Rao下限。通过模拟对算法进行了边界评估，结果表明，随着观察次数的增加，EKF接近混合Cramér-Rao边界（CRB）（HCRB）。该结果表明，对于在模拟中测试的示例，HCRB是一个渐近紧边界，而EKF是最佳估计量。这个属性在一般情况下是否正确仍然是一个悬而未决的问题。HCRB是一个渐近紧定界，而EKF是最佳估计。这个属性在一般情况下是否正确仍然是一个悬而未决的问题。HCRB是一个渐近紧定界，而EKF是最佳估计。这个属性在一般情况下是否正确仍然是一个悬而未决的问题。