室内可见光成像传感器定位系统的理论极限

Theoretical limit of the indoor visible light-image sensor positioning system

针对室内可见光定位系统的参数优化问题,计算了基于成像传感器接收的接收机位置的估计理论极限,求出了估计量的克拉美罗下界.对于室内典型的应用场景,当接收机的成像点测量值受高斯白噪声影响时,计算出接收机位置的最大似然估计量,并推出克拉美罗下界.采用LED发射机和成像传感器接收机的真实参数进行数值仿真,结果表明:可实现精确的定位估计,定位精度一般处于毫米量级.定位误差取决于接收机距房顶的垂直距离、透镜焦距、成像传感器的像素大小以及帧速率等参数.

To guide the optimization problem of the parameters in the image sensor-based visible light positioning system, theoretical limits on the location estimation of the receiver are calculated by deriving the Cramer-Rao Lower Bound （CRLB）. For typical indoor scenes, the observations of the image points at the receiver are affected by the Gaussian white noise, the maximum likelihood estimation（MLE） for the location of the receiver is calculated, and the CRLB for the MLE is derived. By using the real parameters of the location are achievable, with positioning error usually in the order of millimeters. The positioning error depends on the number of transmitters, the focal length of the lens, the vertical distance from roof to receiver, the pixel size and the frame rate of the image sensor.