Radio-based positioning systems are typically utilized to provide high-precision position information for automatic-guided vehicles (AGVs). However, the presence of obstacles in harsh environments, as well as carried cargoes on the AGV, will degrade the localization performance, since they block the propagation of radio signals. In this paper, a distributed multi-antenna positioning system is proposed, where multiple synchronous antennas are equipped on corners of an AGV to improve the availability and accuracy of positioning. An estimator based on the Levenberg–Marquardt algorithm is introduced to solve the nonlinear pseudo-range equations. To obtain the global optimal solutions, we propose a coarse estimator that utilizes the displacement knowledge of the antennas to provide a rough initial guess. Simulation results show a better availability of our system compared with the single antenna positioning system. Decimeter accuracy can be obtained under a Gaussian measurement noise with a standard deviation of 0.2 m. The results also demonstrate that the proposed algorithm can achieve positioning accuracy close to the theoretical Cramer–Rao lower bound. Furthermore, given prior information of the yaw angle, the same level of accuracy can be obtained by the proposed algorithm without the coarse estimation step.

For radio-based time-of-arrival (TOA) positioning systems applied in harsh environments, obstacles in the surroundings and on the vehicle itself will block the signals from the anchors, reduce the number of available TOA measurements and thus degrade the localization performance. Conventional multi-antenna positioning technique requires a good initialization to avoid local minima, and suffers from location ambiguity due to insufficient number of TOA measurements and/or poor geometry of anchors at a single epoch. In this paper, taking advantage of the multi-epoch and multi-antenna (MEMA) TOA measurements bridged by inter-epoch constraints to utilize more information and improve the geometry of visible anchors, we propose a new positioning method, namely MEMA-TOA method. A new initialization method based on semidefinite programming (SDP), namely MEMA-SDP, is first designed to address the initialization problem of the MEMA-TOA method. Then, an iterative refinement step is developed to obtain the optimal positioning result based on the MEMA-SDP initialization. We derive the Cramér-Rao lower bound (CRLB) to analyze the accuracy of the new MEMA-TOA method theoretically, and show its superior positioning performance over the conventional single-epoch and multi-antenna (SEMA) localization method. Simulation results in harsh environments demonstrate that i) the new MEMA-SDP provides an initial estimation that is close to the real location, and empirically guarantees the global optimality of the final refined positioning solution, and ii) compared with the conventional SEMA method, the new MEMA-TOA method has higher positioning accuracy without location ambiguity, consistent with the theoretical analysis.

In real-world applications for automatic guided vehicle (AGV) navigation, the positioning system based on the time-of-flight (TOF) measurements between anchors and tags is confronted with the problem of insufficient measurements caused by blockages to radio signals or lasers, etc. Mounting multiple tags at different positions of the AGV to collect more TOFs is a feasible solution to tackle this difficulty. Vehicle localization by exploiting the measurements between multiple tags and anchors is a rigid body localization (RBL) problem, which estimates both the position and attitude of the vehicle. However, to the best of the authors' knowledge, the state-of-the-art solutions to the RBL problem do not deal with missing measurements, and thus will result in degraded localization availability and accuracy in harsh environments. In this paper, different from these existing solutions for RBL, we model this problem as a sensor network localization problem with missing TOFs. To solve this problem, we propose a new efficient RBL solution based on Euclidean distance matrix (EDM) completion, abbreviated as ERBL-EDMC. Firstly, we develop a method to determine the upper and lower bounds of the missing measurements to complete the EDM reliably, using the known relative positions between tags and the statistics of the TOF measurements. Then, based on the completed EDM, the global tag positions are obtained from a coarse estimation followed by a refinement step assisted with inter-tag distances. Finally, the optimal vehicle position and attitude are obtained iteratively based on the estimated tag positions from the previous step. Theoretical analysis and simulation results show that the proposed ERBL-EDMC method effectively solves the RBL problem with incomplete measurements. It obtains the optimal positioning results while maintaining low computational complexity compared with the existing RBL methods based on semi-definite relaxation (SDR).

In real-world applications for automatic guided vehicle (AGV) navigation, the positioning system based on the time-of-flight (TOF) measurements between anchors and tags is confronted with the problem of insufficient measurements caused by blockages to radio signals or lasers, etc. Mounting multiple tags at different positions of the AGV to collect more TOFs is a feasible solution to tackle this difficulty. Vehicle localization by exploiting the measurements between multiple tags and anchors is a rigid body localization (RBL) problem, which estimates both the position and attitude of the vehicle. However, the state-of-the-art solutions to the RBL problem do not deal with missing measurements, and thus will result in degraded localization availability and accuracy in harsh environments. In this paper, different from these existing solutions for RBL, we model this problem as a sensor network localization problem with missing TOFs. To solve this problem, we propose a new efficient RBL solution based on Euclidean distance matrix (EDM) completion, abbreviated as ERBL-EDMC. Firstly, we develop a method to determine the upper and lower bounds of the missing measurements to complete the EDM reliably, using the known relative positions between tags and the statistics of the TOF measurements. Then, based on the completed EDM, the global tag positions are obtained from a coarse estimation followed by a refinement step assisted with inter-tag distances. Finally, the optimal vehicle position and attitude are obtained iteratively based on the estimated tag positions from the previous step. Theoretical analysis and simulation results show that the proposed ERBL-EDMC method effectively solves the RBL problem with incomplete measurements. It obtains the optimal positioning results while maintaining low computational complexity compared with the existing RBL methods based on semi-definite relaxation.