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تسجيل مستخدم جديدOptimal Two-way TOA Localization and Synchronization for Moving User Devices with Clock Drift
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In two-way time-of-arrival (TOA) systems, a user device (UD) obtains its position and timing information by round-trip communications to a number of anchor nodes (ANs) at known locations. Compared with the one-way TOA technique, the two-way TOA scheme is easy to implement and has higher localization and synchronization accuracy. Existing two-way TOA methods assume a stationary UD. This will cause uncompensated position and timing errors. In this article, we propose an optimal maximum likelihood (ML) based two-way TOA localization and synchronization method, namely TWLAS. Different from the existing methods, it takes the UD mobility into account to compensate the error caused by the UD motion. We analyze its estimation error and derive the Cramer-Rao lower bound (CRLB). We show that the conventional two-way TOA method is a special case of the TWLAS when the UD is stationary, and the TWLAS has high estimation accuracy than the conventional one-way TOA method. We also derive the estimation error in the case of deviated UD velocity information. Numerical result demonstrates that the estimation accuracy of the new TWLAS for a moving UD reaches CRLB, better than that of the conventional one-way TOA method, and the estimation error caused by the deviated UD velocity information is consistent with the theoretical analysis.
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In two-way time-of-arrival (TOA) systems, a user device (UD) obtains its position by round-trip communications to a number of anchor nodes (ANs) at known locations. The objective function of the maximum likelihood (ML) method for two-way TOA localiza
tion is nonconvex. Thus, the widely-adopted Gauss-Newton iterative method to solve the ML estimator usually suffers from the local minima problem. In this paper, we convert the original estimator into a convex problem by relaxation, and develop a new semidefinite programming (SDP) based localization method for moving UDs, namely SDP-M. Numerical result demonstrates that compared with the iterative method, which often fall into local minima, the SDP-M always converge to the global optimal solution and significantly reduces the localization error by more than 40%. It also has stable localization accuracy regardless of the UD movement, and outperforms the conventional method for stationary UDs, which has larger error with growing UD velocity.
In this article, we design a new time-of-arrival (TOA) system for simultaneous user device (UD) localization and synchronization with a periodic asymmetric ranging network, namely PARN. The PARN includes one primary anchor node (PAN) transmitting and
receiving signals, and many secondary ANs (SAN) only receiving signals. All the UDs can transmit and receive signals. The PAN periodically transmits sync signal and the UD transmits response signal after reception of the sync signal. Using TOA measurements from the periodic sync signal at SANs, we develop a Kalman filtering method to virtually synchronize ANs with high accuracy estimation of clock parameters. Employing the virtual synchronization, and TOA measurements from the response signal and sync signal, we then develop a maximum likelihood (ML) approach, namely ML-LAS, to simultaneously localize and synchronize a moving UD. We analyze the UD localization and synchronization error, and derive the Cramer-Rao lower bound (CRLB). Different from existing asymmetric ranging network-based TOA systems, the new PARN i) uses the periodic sync signals at the SAN to exploit the temporal correlated clock information for high accuracy virtual synchronization, and ii) compensates the UD movement and clock drift using various TOA measurements to achieve consistent and simultaneous localization and synchronization performance. Numerical results verify the theoretical analysis that the new system has high accuracy in AN clock offset estimation and simultaneous localization and synchronization for a moving UD. We implement a prototype hardware system and demonstrate the feasibility and superiority of the PARN in real-world applications by experiments.
Positioning with one single communication between base stations and user devices can effectively save air time and thus expand the user volume to infinite. However, this usually demands accurate synchronization between base stations. Wireless synchro
nization between base stations can simplify the deployment of the positioning system but requires accurate clock offset estimation between base stations. A time division multiple access (TDMA) localization system in which user devices only receive signals from base stations to generate time of arrival (TOA) measurements to position themselves and no cables are needed to interconnect base stations for clock synchronization is proposed, implemented and tested. In this system, the user devices can easily join in or exit without influence to other users and the update rate of each user can be easily adjusted independently according to its specific requirement.
In a joint localization and synchronization (JLAS) system comprised of anchor nodes (ANs) and user nodes (UNs), a relative spatiotemporal coordinate is established by the ANs with known positions. It is an essential technique for the moving UNs with
clock offset and skew to resolve the JLAS problem. Existing methods using sequential one-way time-of-arrival (TOA) measurements from the ANs broadcast signals require a good initial guess and have high computational complexity. In this paper, we propose a new closed-form JLAS approach, namely CFJLAS, which achieves optimal solution without initialization, and has low computational complexity. We first linearize the relation between the estimated parameter and the sequential TOA measurement by squaring and differencing the TOA measurement equations. By devising two intermediate variables, we then simplify the problem to finding the solution of a quadratic equation set. Finally, we apply a weighted least squares (WLS) step using the residuals of all the measurements to optimize the estimation. We derive the Cramer-Rao lower bound (CRLB), analyze the estimation error, and show that the estimation accuracy of the CFJLAS reaches CRLB under the small noise condition. The complexity of the CFJLAS is studied and compared with the conventional iterative method. Simulations in the 2D scene verify that the estimation accuracy of the new CFJLAS method in position, velocity, clock offset, and clock skew all reaches CRLB. Compared with the conventional iterative method, which requires a good initial guess to converge to the correct estimation and has growing complexity with more iterations, the proposed new CFJLAS method does not require initialization, always obtains the optimal solution and has constant low computational complexity.
In a time division broadcast positioning system (TDBPS), a user device (UD) determines its position by obtaining sequential time-of-arrival (TOA) or pseudorange measurements from signals broadcast by multiple synchronized base stations (BSs). The exi
sting localization method using sequential pseudorange measurements and a linear clock drift model for the TDPBS, namely LSPM-D, does not compensate the position displacement caused by the UD movement and will result in position error. In this paper, depending on the knowledge of the UD velocity, we develop a set of optimal localization methods for different cases. First, for known UD velocity, we develop the optimal localization method, namely LSPM-KVD, to compensate the movement-caused position error. We show that the LSPM-D is a special case of the LSPM-KVD when the UD is stationary with zero velocity. Second, for the case with unknown UD velocity, we develop a maximum likelihood (ML) method to jointly estimate the UD position and velocity, namely LSPM-UVD. Third, in the case that we have prior distribution information of the UD velocity, we present a maximum a posteriori (MAP) estimator for localization, namely LSPM-PVD. We derive the Cramer-Rao lower bound (CRLB) for all three estimators and analyze their localization error performance. We show that the position error of the LSPM-KVD increases as the assumed known velocity deviates from the true value. As expected, the LSPM-KVD has the smallest position error while the LSPM-PVD and the LSPM-UVD are more robust when the prior knowledge of the UD velocity is limited. Numerical results verify the theoretical analysis on the optimality and the positioning accuracy of the proposed methods.
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