Hybrid Position and Orientation Estimation for Visible Light Systems in the Presence of Prior Information on the Orientation

Abstract

Visible light communication (VLC) is seen as a potential access option for fifth-generation (5G) wireless communication (Wang <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , 2014) and (Ayyash <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , 2016) and beyond 5G (Strinati <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , 2019). A reliable VLC system benefits from an accurate estimate of the receiver’s position and orientation. In many cases, the orientation of the receiver is estimated with an external orientation estimation device. However, these devices generally suffer from drift and misalignment, causing an uncertainty in the orientation presented to the receiver. Hence, the external device can only provide a probability distribution of the orientation to the position estimator, which can be used as prior information for the position estimation. Since the orientation of a receiver greatly affects the performance of a visible light system, the orientation uncertainty will degrade the performance of standard positioning algorithms, implying it should be taken into account when designing a robust positioning algorithm. In this paper, we design an received signal strength (RSS)-based hybrid position and orientation estimation algorithm using the hybrid maximum likelihood (ML)/maximum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> (MAP) (HyMM) principle for a multiple LEDs - multiple photodiodes (PDs) (MLMP) system to take into account the presence of prior information on the orientation. The proposed HyMM estimator is compared with three existing estimators, i.e., the simultaneous position and orientation (SPO) estimator, the misspecified maximum likelihood (MML) estimator and the first-order-approximation-based positioning algorithm, subject to the orientation uncertainty. Further, in order to analytically assess the performance of the proposed estimator, the theoretical lower bound on the mean squared error (MSE), i.e. the hybrid Cramér-Rao bound (HCRB) for HyMM is derived. Computer simulations show an asymptotic tightness between the performance of the estimator and its associated theoretical lower bound.