Non-Line-of-Sight Ultraviolet Positioning Using Linearly-Arrayed Photon-Counting Receivers

Traditional optical positioning techniques employing visible light signals or infrared light signals require line-of-sight links between transmitters and receivers. The wireless positioning techniques using ultraviolet (UV) signals can enjoy both non-line-of-sight (NLOS) positioning ability and immunity to electromagnetic jamming. In this work, we focus on NLOS UV positioning techniques using linearly-arrayed photon-counting receivers. We first derive the geometrical and physical constrains for the NLOS UV positioning using linearly-arrayed receivers. We then derive the analytical relation between location parameters and pointing parameters of unknown transmitter and propose a NLOS UV positioning method with acceptable computational complexity. We further derive the Cramér-Rao bounds for the positioning method when the separate distance between adjacent receivers equals zero. Numerical results demonstrate that the proposed NLOS UV positioning methods using photon-counting receivers can achieve a distance error less than 2 m when the transmitting elevation angle is greater than 30 degrees and the separate distance is greater than 2 m. Besides, we demonstrate that at least three receivers are required to avoid multiple solution problem; and three receivers are enough for achieving an acceptable positioning error for NLOS UV positioning using photon-counting receivers.