Comprehensive outage compensation of real-time orbit and clock corrections with broadcast ephemeris for ambiguity-fixed precise point positioning

The main challenge in real-time precise point positioning (PPP) is that the data outages or large time lags in receiving precise orbit and clock corrections greatly degrade the continuity and real-time performance of PPP positioning. To solve this problem, instead of directly predicting orbit and clock corrections in previous researches, this paper presents an alternative approach of generating combined corrections including orbit error, satellite clock and receiver-related error with broadcast ephemeris. Using ambiguities and satellite fractional-cycle biases (FCBs) of previous epoch and the short-term predicted tropospheric delay through linear extrapolation model (LEM), combined corrections at current epoch are retrieved and weighted with multiple reference stations, and further broadcast to user for continuous enhanced positioning during outages of orbit and clock corrections. To validate the proposed method, two reference station network with different inter-station distance from National Geodetic Survey (NGS) network are used for experiments with six different time lags (i.e., 5 s, 10 s, 15 s, 30 s, 45 s and 60 s), and one set of data collected by unmanned aerial vehicle (UAV) is also used. The performance of LEM is investigated, and the troposphere prediction accuracy of low elevation (e.g., 10–20degrees) satellites has been improved by 44.1% to 79.0%. The average accuracy of combined corrections before and after LEM is used is improved by 12.5% to 77.3%. Without LEM, an accuracy of 2–3 cm can be maintained only in case of small time lags, while the accuracies with LEM are all better than 2 cm in case of different time lags. The performance of simulated kinematic PPP at user end is assessed in terms of positioning accuracy and epoch fix rate. In case of different time lags, after LEM is used, the average accuracy in horizontal direction is better than 3 cm, and the accuracy in up direction is better than 5 cm. At the same time, the epoch fix rate has also increased to varying degrees. The results of the UAV data show that in real kinematic environment, the proposed method can still maintain a positioning accuracy of several centimeters in case of 20 s time lag.     

Performance improvement of real-time PPP ambiguity resolution using a regional integer clock

Obtaining reliable GNSS uncalibrated phase delay (UPD) or integer clock products is the key to achieving ambiguity-fixed solutions for real-time (RT) precise point positioning (PPP) users. However, due to the influence of RT orbit errors, the quality of UPD/integer clock products estimated with a globally distributed GNSS network is difficult to ensure, thereby affecting the ambiguity resolution (AR) performance of RT-PPP. In this contribution, by fully utilising the consistency of orbital errors in regional GNSS network coverage areas, a method is proposed for estimating regional integer clock products to compensate for RT orbit errors. Based on Centre National d’Études Spatiales (CNES) RT precise products, the regional GPS/BDS integer clock was estimated with a CORS network in the west of China. Results showed that the difference between the estimated regional and CNES global integer clock/bias products was generally less than 5 cm for GPS, whereas clock differences of greater than 10 cm were observed for BDS due to the large RT orbit error. Compared with PPP using global integer clock/bias products, the AR performance of PPP using the regional integer clock was obviously improved for four rover stations. For single GPS, the horizontal and vertical accuracies of ambiguity-fixed PPP solutions were improved by 56.2% and 45.3% on average, respectively, whereas improvements of 67.5% and 50.5% in the horizontal and vertical directions, respectively, were observed for the combined GPS/BDS situation. Based on a regional integer clock, the RMS error of a kinematic ambiguity-fixed PPP solution in the horizontal direction could reach 0.5 cm. In terms of initialisation time, the average time to first fix (TTFF) in combined GPS/BDS PPP was shortened from 18.2 min to 12.7 min. In view of the high AR performance realised with the use of regional integer clocks, this method can be applied to scenarios that require high positioning accuracy, such as deformation monitoring.     

Predicting atmospheric delays for rapid ambiguity resolution in precise point positioning

Integer ambiguity resolution in precise point positioning (PPP) can shorten the initialization and re-initialization time, and ambiguity-fixed PPP solutions are also more reliable and accurate than ambiguity-float PPP solutions. However, signal interruptions are unavoidable in practical applications, particularly while operating in urban areas. Such signal interruptions can cause discontinuity of carrier phase arc, which introduces new integer ambiguities. Usually it will take approximately 15 min of continuous tracking to a reasonable number of satellites to fix new integer ambiguities. In many applications, it is impractical for a PPP user to wait for such a long time for the re-initialization. In this paper, a method for rapid ambiguity fixing in PPP is developed to avoid such a long re-initialization time. Firstly, the atmospheric delays were estimated epoch by epoch from ambiguity-fixed PPP solutions before the data gap or cycle slip occurs. A random walk procedure is then applied to predict the atmospheric delays accurately over a short time span. The predicted atmospheric delays then can be used to correct the observations which suffer from signal interruptions. Finally, the new ambiguities can be fixed with a distinct WL-LX-L3 (here LX denotes either of L1, L2) cascade ambiguity resolution strategy. Comprehensive experiments have demonstrated that the proposed method and strategy can fix zero-difference integer ambiguities successfully with only a single-epoch observation immediately after a short data gap. This technique works even when all satellites are interrupted at the same time. The duration of data gap bridged by this technique could be possibly extended if a more precise atmospheric delay prediction is found or on-the-fly (OTF) technology is applied. Based on the proposed method, real-time PPP with integer ambiguity fixing becomes more feasible in practice.     

GNSS carrier phase ambiguity resolution based on integrity restriction in ambiguity domain

Carrier phase ambiguity resolution of Global Navigation Satellite System (GNSS) is a key technology for high-precision navigation and positioning, and it is a challenge for applications which require both high accuracy and high integrity. This paper proposes efficient ambiguity resolution methods based on integrity restriction using Fixed Failure rate Ratio Test (FF-RT) and Doubly Non-central F-distribution Ratio Test (DNF-RT), and derives the related processing models and numerical algorithms compared with the traditional Ratio Test (RT) method. Firstly, the integer ambiguity resolution and validation procedures, especially the Least squares AMBiguity Decorrelation Adjustment (LAMBDA) estimation and RT validation are analyzed. Then the quality evaluation using success rate, the FF-RT method using Integer Aperture (IA) estimation and the NDF-RT method are proposed. Lastly, the simulation and analysis for LAMBDA using RT, FF-RT and DNF-RT methods are performed. Simulation results show that in case of unbiased scenario FF-RT and DNF-RT have similar performances, which are significantly better than RT. In case of biased scenario it is difficult for FF-RT to predict the biased success rate thus it should not be used for bias detection, while DNF-RT can detect biases in most cases except for the biases are approximate or equal to integer, which has the important benefit for early detection of potential threat to the position solution.     

最小相位误差单星无源定位法

基于卫星在不同位置测得的信号相位差,提出了一种用最小二乘使误差最小化的单星无源定位方法。给出了定位和去模糊的原理与计算方法,以及数学模型,建立了定位误差的解析表达式,用仿真验证了误差表达式。结果表明该法有一定的去模糊定位和单基线测量相位差定位能力。     

雷达方程在星载合成孔径雷达中的应用研究

首先推导出多工作模式合成孔径雷达的通用雷达方程，并对方程中各参数的物理意义和应用方法作了详细说明，然后论述了在星载条件下考虑距离模糊和方位模糊影响时，如何选择脉冲重复频率并进行工程优化设计，最后给出了上述模型的计算机仿真结果。     

Conceptual design of near-space synthetic aperture radar for high-resolution and wide-swath imaging

Airborne synthetic aperture radar (SAR) has the capability of high-resolution, and spaceborne SAR has the capability of wide-swath. Inspired by recent advances in near-space defined as the region between 20 km and 100 km, this paper conceptually designed near-space vehicle-borne SAR. The near-space vehicle-borne SAR has the synthetical advantages of the satellite and airplane platforms. By placing SAR transmitter or receiver in near-space vehicles, many functions that are currently performed with satellites or airplanes could be performed in low cost way. These advantages make simultaneous high-resolution and wide-swath SAR imaging possible. As such, this paper focuses on the role of near-space vehicle for high-resolution and wide-swath SAR imaging, and deals with conceptual performance, as opposed to technological implementation. The concepts, models and processing algorithms are provided. To further suppress the azimuth ambiguities and extend swath width, multiple beams in azimuth is applied. Furthermore, an example near-space vehicle-borne SAR is designed. It is shown that the use of cost effective near-space vehicles can provide the solutions that were previously thought to be out of reach for remote sensing scientists and customers.     

Enhanced baseline determination for formation flying LEOs by relative corrections of phase center and code residual variations

Formation flying Low Earth Orbiters(LEOs) are important for implementing new and advanced concepts in Earth observation missions. Precise Baseline Determination(PBD) is a prerequisite for LEOs to complete specified mission targets. PBD is usually performed based on space-borne GNSS data, the relative corrections of phase center and code residual variations play crucial roles in achieving the best relative orbit accuracy. Herein, the influences of antenna Relative Phase Centre Variations(RPCVs) a...     

Evaluation of rapid phase clock/bias products for PPP ambiguity resolution and its application to the M7.1 2019 Ridgecrest,California earthquake

Precise point positioning with ambiguity resolution (PPP-AR) is a useful tool for high-precision geodetic and geophysical applications, while phase bias products are the prerequisite to implement PPP-AR. Wuhan University has been providing the final (the best operationally post-processing solution based) phase clock/bias products with a latency of two weeks since March of 2019, while a dedicated open-source software package PRIDE PPP-AR is released to leverage these products for high-precision positioning. In order to satisfy some both time and precision critical applications, such as rapid earthquake response, Wuhan University also released rapid (with comparable quality but with much shorter delivery latency) phase clock/bias products with a latency of less than 24 h and updated PRIDE PPP-AR in July 2019. We first introduce the phase clock/bias generation and validation schemes and the maintenance of routine products provision. Then, with 14 days (July 2 to July 15 in 2019) of GPS data collected from 146 globally distributed IGS (International GNSS Service) stations, we evaluated the positioning performance of the rapid products with respect to their final counterparts. It is found that positioning precision of PPP-AR using rapid products is comparable to that using final products, especially in kinematic positioning mode. When rapid products are used, the RMS of PPP-AR in static mode with respect to IGS weekly solutions can reach 1.7 mm, 1.8 mm and 5.5 mm in the east, north and up components, respectively. Furthermore, the RMS of epoch-wise positions with respect to daily solutions for the east, north and up components are 0.51 cm, 0.57 cm and 1.51 cm for PPP-AR with rapid products in kinematic mode. It demonstrates that the rapid phase clock/bias products can sufficiently meet the precision requirement of most geodetic and geophysical applications yet with much shorter time delay. Finally, we study the July 6th M7.1 2019 Ridgecrest, California earthquake using the rapid phase clock/bias products and demonstrate their comparable performance against the final products.     

Inter-agency comparison of TanDEM-X baseline solutions

TanDEM-X (TerraSAR-X add-on for Digital Elevation Measurement) is the first Synthetic Aperture Radar (SAR) mission using close formation flying for bistatic SAR interferometry. The primary goal of the mission is to generate a global digital elevation model (DEM) with 2 m height precision and 10 m ground resolution from the configurable SAR interferometer with space baselines of a few hundred meters. As a key mission requirement for the interferometric SAR processing, the relative position, or baseline vector, of the two satellites must be determined with an accuracy of 1 mm (1D RMS) from GPS measurements collected by the onboard receivers. The operational baseline products for the TanDEM-X mission are routinely generated by the German Research Center for Geosciences (GFZ) and the German Space Operations Center (DLR/GSOC) using different software packages (EPOS/BSW, GHOST) and analysis strategies. For a further independent performance assessment, TanDEM-X baseline solutions are generated at the Astronomical Institute of the University of Bern (AIUB) on a best effort basis using the Bernese Software (BSW).