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Register a new userSemidefinite Programming Two-way TOA Localization for User Devices with Motion and Clock Drift
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Added by
Sihao Zhao
Publication date
2021
fields
Electronic Engineering
and research's language is
English
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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 localization 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.
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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.
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 synchronization 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 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.
Some important indoor localization applications, such as localizing a lost kid in a shopping mall, call for a new peer-to-peer localization technique that can localize an individuals smartphone or wearables by directly using anothers on-body devices in unknown indoor environments. However, current localization solutions either require pre-deployed infrastructures or multiple antennas in both transceivers, impending their wide-scale application. In this paper, we present P2PLocate, a peer-to-peer localization system that enables a single-antenna device co-located with a batteryless backscatter tag to localize another single-antenna device with decimeter-level accuracy. P2PLocate leverages the multipath variations intentionally created by an on-body backscatter tag, coupled with spatial information offered by user movements, to accomplish this objective without relying on any pre-deployed infrastructures or pre-training. P2PLocate incorporates novel algorithms to address two major challenges: (i) interference with strong direct-path signal while extracting multipath variations, and (ii) lack of direction information while using single-antenna transceivers. We implement P2PLocate on commercial off-the-shelf Google Nexus 6p, Intel 5300 WiFi card, and Raspberry Pi B4. Real-world experiments reveal that P2PLocate can localize both static and mobile targets with a median accuracy of 0.88 m.
Semidefinite Programming (SDP) is a class of convex optimization programs with vast applications in control theory, quantum information, combinatorial optimization and operational research. Noisy intermediate-scale quantum (NISQ) algorithms aim to make an efficient use of the current generation of quantum hardware. However, optimizing variational quantum algorithms is a challenge as it is an NP-hard problem that in general requires an exponential time to solve and can contain many far from optimal local minima. Here, we present a current term NISQ algorithm for SDP. The classical optimization program of our NISQ solver is another SDP over a smaller dimensional ansatz space. We harness the SDP based formulation of the Hamiltonian ground state problem to design a NISQ eigensolver. Unlike variational quantum eigensolvers, the classical optimization program of our eigensolver is convex, can be solved in polynomial time with the number of ansatz parameters and every local minimum is a global minimum. Further, we demonstrate the potential of our NISQ SDP solver by finding the largest eigenvalue of up to $2^{1000}$ dimensional matrices and solving graph problems related to quantum contextuality. We also discuss NISQ algorithms for rank-constrained SDPs. Our work extends the application of NISQ computers onto one of the most successful algorithmic frameworks of the past few decades.
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