A Novel Ambiguity Parameter Estimation and Elimination Strategy for GNSS/INS Tightly Coupled Integration

The estimation of ambiguity in the global navigation satellite system/inertial navigation system (GNSS/INS) tightly coupled system is a key issue for GNSS/INS precise navigation positioning. Only when the ambiguity is solved correctly can the integrated navigation system obtain high-precision positioning results. Aiming at the problem of ambiguity parameter estimation in GNSS/INS tightly coupled system, a new strategy for ambiguity parameter estimation and elimination is proposed in this paper. Here, the ambiguity parameter is first added to the state equations of GNSS/INS in the estimation process. Then, the strategy of eliminating the parameter is used to improve efficiency. A residual test is carried out based on introducing the ambiguity parameter, thereby reducing or avoiding its influence on the filtering estimation process. Two groups of experiments were carried out and compared with GNSS positioning results. The results showed that, in the open sky observation environment, the positioning accuracy of the GNSS/INS tightly coupled method proposed in this paper was within 5 cm, and the ambiguity fixed rate was more than 97%, which is basically consistent. In a GNSS-denied environment, the positioning accuracy of the GNSS/INS tightly coupled method proposed in this paper was obviously better than that of GNSS, and the positioning accuracy in X, Y, and Z directions was improved by 82.46%, 78.87%, and 79.67%, respectively. The fixed rate of ambiguity increased from 73% to 78.57%. Therefore, in a GNSS-challenged environment, the novel strategy of the GNSS/INS tightly coupled system has higher ambiguity fixed rate and significantly improves positioning accuracy and continuity.

LEO Onboard Real-Time Orbit Determination Using GPS/BDS Data with an Optimal Stochastic Model

The advancements of Earth observations, remote sensing, communications and navigation augmentation based on low Earth orbit (LEO) platforms present strong requirements for accurate, real-time and autonomous navigation of LEO satellites. Precise onboard real-time orbit determination (RTOD) using the space-borne data of multiple global navigation satellite systems (multi-GNSS) becomes practicable along with the availability of multi-GNSS. We study the onboard RTOD algorithm and experiments by using America’s Global Positioning System (GPS) and China’s regional BeiDou Navigation Satellite System (BDS-2) space-borne data of the FengYun-3C satellite. A new pseudo-ambiguity parameter, which combines the constant phase ambiguity, the orbit and clock offset error of the GPS/BDS broadcast ephemeris in the line-of-sight (LOS), is defined and estimated in order to reduce the negative effect of the LOS error on onboard RTOD. The analyses on the variation of the LOS error in the GPS/BDS broadcast ephemeris indicate that the pseudo-ambiguity parameter could be modeled as a random walk, and the setting of the power spectral density in the random walk model decides whether the pseudo-ambiguity can be estimated reasonably and the LOS error could be reduced or not. For different types of GPS/BDS satellites, the LOS errors show different variation characteristics, so the power spectral density should be set separately and differently. A numerical search approach is presented in this paper to find the optimal setting of the power spectral density for each type of GPS/BDS satellite by a series of tests. Based on the optimal stochastic model, a 3-dimensional (3D) real-time orbit accuracy of 0.7–2.0 m for position and 0.7–1.7 mm/s for velocity could be achieved only with dual-frequency BDS measurements and the broadcast ephemeris, while a notably superior orbit accuracy of 0.3–0.5 m for position and 0.3–0.5 mm/s for velocity is achievable using dual-frequency GPS/BDS measurements, due to the absorption effect of the estimated pseudo-ambiguity on the LOS error of the GPS/BDS broadcast ephemeris. Compared to using GPS-alone data, the GPS/BDS fusion only marginally improves the onboard RTOD orbit accuracy by about 1–3 cm, but the inclusion of BDS satellites increases the number of the tracked GNSS satellites and thus speeds up the convergence of the filter. Furthermore, the GPS/BDS fusion could help suppress the local orbit errors, ensure the orbit accuracy and improve the reliability and availability of the onboard RTOD when fewer GPS satellites are tracked in some anomalous arcs.

Unparticle in (1+1) dimension with one-loop correction

The possible emergence of unparticle has been mooted recently including a mass-like term for gauge field with the Schwinger model at the classical level. A one-loop correction due to bosonization is taken into account and investigation is carried out to study its effect on the unparticle scenario. It is observed that the physical mass, viz., unparticle scale acquires a new definition, i.e. the effect of this correction enters into the unparticle scale in a significant manner. The fermionic propagator is calculated which also agrees with the new scale. It has also been noticed that a novel restoration of the lost gauge invariance reappears when the ambiguity parameter related to the current anomaly acquires a specific expression. We have also observed that a quantum effect can nullify the effect of violation of gauge symmetry caused by some classical terms.

RENORMALIZED NEW SOLUTIONS FOR THE MASSLESS THIRRING MODEL

We present a nonperturbative study of the (1+1)-dimensional massless Thirring model by using path integral methods. The regularization ambiguities — coming from the computation of the fermionic determinant — allow to find new solution types for the model. At quantum level the Ward identity for the 1PI 2-point function for the fermionic current separates such solutions in two phases or sectors, the first one has a local gauge symmetry that is implemented at quantum level and the other one without this symmetry. The symmetric phase is a new solution which is unrelated to the previous studies of the model and, in the nonsymmetric phase there are solutions that for some values of the ambiguity parameter are related to well-known solutions of the model. We construct the Schwinger–Dyson equations and the Ward identities. We make a detailed analysis of their UV divergence structure and, after, we perform a nonperturbative regularization and renormalization of the model.