Search Results (8)

Many natural signals exhibit quasi-periodic behaviors and are conveniently modeled as combinations of several harmonic sinusoids whose relative frequencies, magnitudes, and phases vary with time. The waveform shapes of those signals reflect important physical phenomena underlying their generation, requiring those parameters to be accurately estimated and modeled. In the literature, accurate phase estimation and modeling have received significantly less attention than frequency or magnitude estimation. This paper first addresses accurate DFT-based phase estimation of individual sinusoids across six scenarios involving two DFT-based filter banks and three different windows. It has been shown that bias in phase estimation is less than 0.001 radians when the SNR is equal to or larger than 2.5 dB. Using the Cramér–Rao lower bound as a reference, it has been demonstrated that one particular window offers performance of practical interest by better approximating the CRLB under favorable signal conditions and minimizing performance deviation under adverse conditions. This paper describes the development of a shift-invariant phase-related feature that characterizes the harmonic phase structure. This feature motivates a new signal processing paradigm that greatly simplifies the parametric modeling, transformation, and synthesis of harmonic signals. It also aids in understanding and reverse engineering the phasegram. The theory and results are discussed from a reproducible perspective, with dedicated experiments supported by code, allowing for the replication of figures and results presented in this paper and facilitating further research. Full article

The legacy Global Navigation Satellite System (GNSS) satellite clock offsets obtained by the dual-frequency undifferenced (UD) ionospheric-free (IF) model absorb the code and phase time-variant hardware delays, which leads to the inconsistency of the precise satellite clock estimated by different frequencies. The dissimilarity of the satellite clock offsets generated by different frequencies is called the inter-frequency clock bias (IFCB). Estimates of the IFCB typically employ epoch-differenced (ED) geometry-free ionosphere-free (GFIF) observations from global networks. However, this method has certain theoretical flaws by ignoring the receiver time-variant biases. We proposed a new undifferenced model coupled with satellite clock offsets, and further converted the IFCB into the code and phase time-variant mixed observable-specific signal bias (OSB) to overcome the defects of the traditional model and simplify the bias correction process of multi-frequency precise point positioning (PPP). The new model not only improves the mixed OSB performance, but also avoids the negative impact of the receiver time-variant biases on the satellite mixed OSB estimation. The STD and RMS of the original OSB can be improved by 7.5–60.9% and 9.4–66.1%, and that of ED OSB (it can reflect noise levels) can be improved by 50.0–87.5% and 60.0–88.9%, respectively. Similarly, the corresponding PPP performance for using new mixed OSB is better than that of using the traditional IFCB products. Thus, the proposed pseudorange and phase time-variant mixed OSB concept and the new undifferenced model coupled with satellite clock offsets are reliable, applicable, and effective in multi-frequency PPP. Full article

The multi-global navigation satellite system (GNSS) undifferenced and uncombined precise point positioning (UU-PPP), as a high-precision ionospheric observables extraction technology superior to the traditional carrier-to-code leveling (CCL) method, has received increasing attention. In previous research, only dual-frequency (DF) or multi-frequency (MF) observations are used to extract slant ionospheric delay with the UU-PPP. To reduce the cost of ionospheric modeling, the feasibility of extracting ionospheric observables from the multi-GNSS single-frequency (SF) UU-PPP was investigated in this study. Meanwhile, the between-satellite single-differenced (SD) method was applied to remove the effects of the receiver differential code bias (DCB) with short-term time-varying characteristics in regional ionospheric modeling. In the assessment of the regional real-time (RT) between-satellite SD ionospheric model, the internal accord accuracy of the SD ionospheric delay can be better than 0.5 TECU, and its external accord accuracy within 1.0 TECU is significantly superior to three global RT ionospheric models. With the introduction of the proposed SD ionospheric model into the multi-GNSS kinematic RT SF-PPP, the initialization speed of vertical positioning errors can be improved by 21.3% in comparison with the GRAPHIC (GRoup And PHase Ionospheric Correction) SF-PPP model. After reinitialization, both horizontal and vertical positioning errors of the SD ionospheric constrained (IC) SF-PPP can be maintained within 0.2 m. This proves that the proposed SDIC SF-PPP model can enhance the continuity and stability of kinematic positioning in the case of some GNSS signals missing or blocked. Compared with the GRAPHIC SF-PPP, the horizontal positioning accuracy of the SDIC SF-PPP in kinematic mode can be improved by 37.9%, but its vertical positioning accuracy may be decreased. Overall, the 3D positioning accuracy of the SD ionospheric-constrained RT SF-PPP can be better than 0.3 m. Full article

Global navigation satellite system (GNSS)-based attitude determination has been widely applied in a variety of fields due to its high precision, no error accumulation, low power consumption, and low cost. Recently, the emergence of common-clock receivers and construction of GNSS systems have brought new opportunities for high-precision GNSS-based attitude determination. In this contribution, we focus on evaluating the performance of the BeiDou regional navigation satellite system (BDS-2)/BeiDou global navigation satellite system (BDS-3)/Global Positioning System (GPS)/Galileo navigation satellite system (Galileo) attitude determination based on the single-differenced (SD) model with a common-clock receiver. We first investigate the time-varying characteristics of BDS-2/BDS-3/GPS/Galileo line bias (LB) with two different types of common-clock receivers. The results have confirmed that both the phase and code LBs are relatively stable in the time domain once the receivers have started. However, the phase LB is expected to change to an arbitrary value after each restart of the common-clock receivers. For the first time, it is also found that the phase LBs of overlapping frequencies shared by different GNSS systems are identical. Then, we primarily evaluated the performance of BDS-2/BDS-3/GPS/Galileo precise relative positioning and attitude determination based on the SD model with a common-clock receiver, using a static dataset collected at Wuhan. Experimental results demonstrated that, compared with the double-differenced (DD) model, the SD model can deliver a comparable root–mean–square (RMS) error of yaw but a significantly smaller RMS error of pitch, whether for BDS-2, BDS-3, GPS, or Galileo alone or a combination of them. The improvements of pitch accuracy are approximately 20.8–47.5% and 40.7–57.5% with single- and dual-frequency observations, respectively. Additionally, BDS-3 can deliver relatively superior positioning and attitude accuracy with respect to GPS and Galileo, due to its better geometry. The three-dimensional positioning and attitude (including yaw and pitch) accuracy for both the DD and SD models can be remarkably improved by the BDS-2, BDS-3, GPS, and Galileo combination with respect to a single system alone. Full article

Continuous and stable precision satellite clock offsets are an important guarantee for real-time precise point positioning (PPP). However, in real-time PPP, the estimation of a satellite clock is often interrupted for various reasons such as network fluctuations, which leads to a long time for clocks to converge again. Typically, code biases are assumed to stay constant over time in clock estimation according to the current literature. In this contribution, it is shown that this assumption reduces the convergence speed of estimation, and the satellite clocks are still unstable for several hours after convergence. For this reason, we study the influence of different code bias extraction schemes, that is, taking code biases as constants, extracting satellite code biases (SCBs), extracting receiver code biases (RCBs) and simultaneously extracting SCBs and RCBs, on satellite clock estimation. Results show that, the time-varying SCBs are the main factors leading to the instability of satellite clocks, and considering SCBs in the estimation can significantly accelerate the filter convergence and improve the stability of clocks. Then, the products generated by introducing SCBs in the clock estimation based on undifferenced observations are applied to PPP experiments. Compared with the original undifferenced model, clocks estimated using the new method can significantly accelerate the convergence speed of PPP and improve the positioning accuracy, which illustrates that our estimated clocks are effective and superior. Full article

With the combination of multi-GNSS data, the precise-point positioning (PPP) technique can improve its accuracy, availability and reliability: Inter-system bias (ISB) is the non-negligible parameter in multi-GNSS PPP. To further enhance the performance of multi-GNSS PPP, it is crucial to analyze the characterization of inter system biases (ISBs) and model them properly. In this contribution, we comprehensively investigate the characterization of ISBs between global positioning system (GPS) and BeiDou navigation satellite system (BDS) in different situations. (1) We estimate ISB by using different precise products from the Center for Orbit Determination (CODE), Deutsches GeoForschungsZentrum (GFZ) and Wuhan University (WHU). The results indicate that the one-day estimates of ISB are stable when using CODE and WHU products, whereas the estimates based on GFZ products vary remarkably. As for the three-day time series of ISB, a sudden jump exists between two adjacent days, which is due to the change of satellite clock datum; (2) We investigate the ISB characterization affected by the ambient environments of the receivers. The result shows that the ISBs estimated from receivers (and antennas) with same type are still inconsistent, which indicates that the ambient environment, probably the temperature, influences the ISB characterization as well, since the receivers are in different areas; (3) We analyze the ISB characterization affected by receiver and antenna type with the same ambient environment. To ensure the same ambient environment, the ultra-short baselines were applied to investigate the ISB characterization affected by the receiver and antenna type. With the insights into ISB characterizations, we carry out combined GPS and BDS PPP with modeling the ISB as time constant, random walk process and white noise. The results suggest that the random walk process outperforms in most cases, since it strengthens the model to some extend and, at the same time, considers the variation of ISBs. Full article

The long convergence time required to achieve high-precision position solutions with integer ambiguity resolution-enabled precise point positioning (PPP-RTK) is driven by the presence of ionospheric delays. When precise real-time ionospheric information is available and properly applied, it can strengthen the underlying model and substantially reduce the time required to achieve centimeter-level accuracy. In this study, we present and analyze the real-time PPP-RTK user performance using ionospheric corrections from multi-scale regional networks during a day with medium ionospheric disturbance. It is the goal of this contribution to measure the impact the network dimension has on the ambiguity-resolved user position through the predicted ionospheric corrections. The user-specific undifferenced ionospheric corrections are computed at the network side, along with the satellite phase biases needed for single-receiver ambiguity resolution, using the best linear unbiased predictor. Such corrections necessitate the parameterization of an estimable user receiver code bias, on which emphasis is given in this study. To this end, we process GPS dual-frequency data from four four-station evenly distributed CORS networks in the United States with varying station spacings in order to evaluate if and to what extent the ionospheric corrections from multi-scale networks can improve the user convergence times. Based on a large number of samples, our experimental results showed that sub-10 cm horizontal accuracy can be achieved almost instantaneously in the ionosphere-weighted partially-ambiguity-fixed kinematic PPP-RTK solutions based on corrections from a network with 68 km spacing. Most of the solutions (90%) were shown to require less than 6.0 min, compared to the ionosphere-float PPP solutions that needed 68.5 min. In case of sparser networks with 115, 174 and 237 km spacing, 50% of the horizontal positioning errors are shown to become less than one decimeter after 1.5, 4.0 and 7.0 min, respectively, while 90% of them require 10.5, 16.5 and 20.0 min. We also numerically demonstrated that the user’s convergence times bear a linear relationship with the network density and get shorter as the density increases, for both full and partial ambiguity resolution. Full article

Ambiguity resolution (AR) is critical for achieving a fast, high-precision solution in precise point positioning (PPP). In the standard uncombined PPP (S-UPPP) method, ionosphere-free code biases are superimposed by ambiguity and receiver clock offsets to be estimated. However, besides the time-constant part of the receiver code bias, the complex and time-varying term in receivers destroy the stability of ambiguities and degrade the performance of the UPPP AR. The variation of receiver code bias can be confirmed by the analysis in terms of ionospheric observables, code multipath (MP) of the Melbourne–Wübbena (MW) combination and the ionosphere-free combination. Therefore, the effect of receiver code biases should be rigorously mitigated. We introduce a modified UPPP (M-UPPP) method to reduce the effects of receiver code biases in ambiguities and to decouple the correlation between receiver clock parameters, code biases, and ambiguities parameters. An extra receiver code bias is set to isolate the code biases from ambiguities. The more stable ambiguities without code biases are expected to achieve a higher success rate of ambiguity resolution and a shortened convergence time. The variations of the receiver code biases, which are the unmodeled errors in measurement residuals of the S-UPPP method, can be estimated in the M-UPPP method. The maximum variation of the code biases is up to 16 ns within two-hour data. In the M-UPPP method, the averaged epoch residuals for code and phase measurements recover their zero-mean features. For the ambiguity-fixed solutions in the M-UPPP method, the convergence times are 14 and 43 min with 17.7% and 69.2% improvements compared to that in the S-UPPP method which are 17 and 90 min under the 68% and 95% confidence levels. Full article