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In developing a high accuracy terrestrial radio navigation system, as a complement to a global navigation satellite system (GNSS), it is recognized that the performance of time delay estimation is proportional to, and thereby limited by, the signal bandwidth. Given a possibly narrow signal bandwidth, the central carrier phase can, alternatively, provide a better distance accuracy, though the central carrier phase cycle ambiguity should be resolved. In practice, the carrier phase may be perturbed by multipath. In this paper, considering an orthogonal frequency division multiplexing (OFDM) signal, we propose a twostep carrier phase estimation method to reduce the error introduced by multipath. First, the propagation delay of the LoS path is coarsely determined, then the carrier phase is estimated using the earlier determined coarse time delays. Furthermore, a positioning model only based on carrier phase estimates is presented in this paper. The proposed technique is evaluated by statistical analyses and a simulated OFDM-based terrestrial positioning system in different roadway multipath environments. The results show that the impact of multipath on carrier phase estimation can be largely mitigated, so that the carrier phase can be used for precise positioning. In addition, fixing the integer carrier phase cycle ambiguities can significantly reduce the time for the position solution to converge to high precision. INDEX TERMS Multipath channels, OFDM, phase estimation, radio navigation, multipath mitigation, phase ambiguity. HAN DUN received the B.Sc. degree in communication engineering and the M.Sc. degree in communication and information engineering from Shanghai University, China, in 2013 and 2016, respectively. He is currently pursuing the Ph.D. degree with the

Time-based ranging accuracy is inversely proportional to the signal bandwidth. A larger the signal bandwidth leads to a higher accuracy of time delay estimation, but more complex hardware is needed. Alternatively, we explore the idea of using multiple narrow signal bands (e.g., 10 MHz of each) to create a large virtual signal bandwidth, which maintains the spectral efficiency but largely improves the ranging accuracy. Considering the impact of multipath, the propagation delay of the LoS path is computed from the estimated channel impulse response (CIR). In this paper, we propose an approach to sparsely select signal bands for ranging and positioning based on convex optimization. The Cramér-Rao lower bound (CRLB) for the propagation delay and gain estimators, as a performance criterion, is employed in the constraint of the optimization. The CRLB is derived in a two-path channel, so that the accuracy and the correlation between the LoS path and the reflection are taken into account. Experiments are conducted in a laboratory environment to illustrate the proposed signal design methodology dedicated for ranging with a sub-decimeter accuracy.

Abstract. In this paper, we introduce the notion of excellent extension of rings. Let Γ be an excellent extension of an artin algebra Λ, we prove that Λ satisfies the Gorenstein symmetry conjecture (resp. finitistic dimension conjecture, AuslanderGorenstein conjecture, Nakayama conjecture) if and only if so does Γ. As a special case of excellent extensions, if G is a finite group whose order is invertible in Λ acting on Λ and Λ is G-stable, we prove that if the skew group algebras ΛG satisfies strong Nakayama conjecture (resp. generalized Nakayama conjecture), then so does Λ.

This contribution implements the Kriging interpolation in predicting the tropospheric wet delays using global navigation satellite system networks. The predicted tropospheric delays can be used in strengthening the precise point positioning models and numerical weather prediction models. In order to evaluate the performances of the Kriging interpolation, a sparse network with 8 stations and a dense network with 19 stations from continuously operating reference stations (CORS) of the Netherlands are selected as the reference. In addition, other 15 CORS stations are selected as users, which are divided into three blocks: 5 stations located approximately in the center of the networks, 5 stations on the edge of the networks and 5 stations outside the networks. The zenith tropospheric wet delays are estimated at the network and user stations through the ionosphere-free positioning model; meanwhile, the predicted wet delays at the user stations are generated by the Kriging interpolation in the use of the tropospheric estimations at the network. The root mean square errors (RMSE) are calculated by comparing the predicted wet delays and estimated wet delays at the same user station. The results show that RMSEs of the stations inside the network are at a sub-centimeter level with an average value of 0.74 cm in the sparse network and 0.69 cm in the dense network. The stations on edge and outside the network can also achieve 1-cm level accuracy, which overcomes the limitation that accurate interpolations can only be attained inside the network. This contribution also presents an insignificant improvement of the prediction accuracy from the sparse network to the dense network over 1-year’s data processing and a seasonal effect on the tropospheric wet delay predictions.