# GPS Solutions

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### Accounting for perturbing forces acting on Galileo using a box-wing model

Thu, 05/16/2019 - 00:00
Abstract

In November 2017, the European Global Navigation Satellite System Agency (GSA) released geometrical and optical information for the Galileo satellites which allowed for the composition of a box-wing model whose main goal is absorption of the direct solar radiation pressure, earth’s albedo, and infrared radiation. In order to evaluate the efficiency of the box-wing model, we test solutions based solely on the empirical models, the pure analytical box-wing model, and a series of hybrid models including the box-wing with different sets of additionally estimated empirical parameters. The hybrid solution, which is based on the box-wing model and on a reduced number of estimated empirical parameters, substantially reduces variabilities of the satellite laser ranging (SLR) residuals, especially for the low elevation angles of the sun above the orbital plane (β), i.e., for eclipsing Galileo satellites. The standard deviation of SLR residuals for |β| < 12.3° decreases from 37 to 25 mm between the solution based on the ECOM2 and the hybrid solution, respectively. We found significant mitigation of the spurious geocenter signal in the Z component and its formal errors, when reducing the number of estimated empirical parameters, and a substantial reduction of the dependency between geocenter coordinates, the geometry of Galileo orbital planes, and the position of the sun. The hybrid box-wing solution with a reduced set of empirical parameters provides thus the best solution for precise orbit determination, orbit predictions, and estimation of geodetic parameters.

### Observation of BDS-2 IGSO/MEOs yaw-attitude behavior during eclipse seasons

Tue, 05/14/2019 - 00:00
Abstract

The yaw mode history of BDS-2 IGSO/MEOs since 2016 is inferred from reverse kinematic precise point positioning. Experimental results show that C06 (IGSO-1) and C14 (MEO-6) satellites have abandoned the orbit-normal (ON) attitude mode in favor of continuous yaw-steering (CYS) mode since March and September 2017, respectively. BDS C13 (IGSO-6), launched in March 2016, and C16 (IGSO-7) always adopt the CYS mode during eclipse seasons. The majority of BDS-2 IGSO/MEOs still experience attitude switches between nominal and ON mode. Most of the attitude switches from nominal to ON mode take place when the sun elevation angle above the orbital plane (β angle) decreases below 4° $$(\left| \beta \right| < 4^\circ )$$ . A few switches also occur for $$\left| \beta \right|$$ slightly above 4°. However, most of the attitude switches from ON to nominal mode are undertaken when $$\left| \beta \right|$$ increases to above 4°, but a few switches with $$\left| \beta \right|$$ just below 4° happen. The exact switch condition between the two attitude modes is presented in this study. For BDS-2 IGSO/MEOs using the CYS mode, the yaw-attitude model previously established by the Wuhan University (indicated by WHU model) can basically reproduce their yaw maneuvers. However, reverse midnight-turn maneuvers occasionally occur for C13 and C14 for β angles falling into the range $$(0^\circ ,0.14^\circ )$$ . This discrepancy in the form of a reversal in the yaw direction during the noon-turn maneuvers is first observed for C13 and C14 when the β angle is in the range of $$( - \,0.14^\circ ,0^\circ )$$ . The mismodeling of the satellites attitudes during reverse yaw maneuvers significantly degrades the performance of BDS precise orbit determination (POD). The phase observation residuals extracted from BDS POD reach 40 cm, which thereby leads to the misidentification of a substantial number of observations around orbital midnight and noon points as outliers when the WHU model is applied in our experiments. The WHU model is modified to reproduce the reverse yaw maneuvers of satellites in the post-processing BDS POD. The derived phase residuals decrease to normal levels, and the clock solutions become smoother relative to solutions employing the WHU model.

### On the detectability of mis-modeled biases in the network-derived positioning corrections and their user impact

Tue, 05/14/2019 - 00:00
Abstract

High-precision single-receiver positioning requires the provision of reliable network-derived corrections. Care must therefore be exercised to continuously check the quality of the corrections and to detect the possible presence of mis-modeled biases in the network data. In network-RTK or its state-space implementation, PPP-RTK, quality control of the solutions is executed in two separate phases: the network component and the user component. Once confidence in the network-derived solutions is declared, a subset of the solutions is sent as corrections to a single-receiver user, thereby allowing the user to separately check the integrity of his network-aided model. In such a two-step integrity monitoring procedure, an intermediate step is missing, the integrity monitoring of the corrections themselves. It is the goal of this contribution to provide a quality control procedure for GNSS parameter solutions at the correction level, and to measure the impact a missed detection bias has on the (ambiguity-resolved) user position. New detection test statistics are derived with which the single-receiver user can check the overall validity of the corrections even before applying them to his data. A small-scale network of receivers is utilized to provide numerical insights into the detectability of mis-modeled biases using the proposed detectors and to analyze the impact of such biases on the user positioning performance.

### A SIMD intrinsic correlator library for GNSS software receivers

Tue, 05/14/2019 - 00:00
Abstract

An open-source implementation of a code division multiple access software correlator library that leverages single instruction multiple data (SIMD) is presented. We initially discuss the key aspects involved in the correlation operation for software radio applications. Afterward, we present the state-of-the-art application programming interface that provides SIMD capable methods for each of the components in a correlation operation, including the first of its kind parallelized code and carrier generation using lookup tables and SIMD instructions. The library was developed using SIMD intrinsic instructions, which are a C-type nomenclature offering access to the assembly instructions originally designed for the SIMD extensions in the processor. This design paradigm presents an advantage in terms of readability and simplified code development to accommodate future modifications. Recorded data were used with a standalone global navigation satellite system software receiver where the methods hereby presented were tested and profiled to validate theoretical assumptions.

### Parallel computation of regional CORS network corrections based on ionospheric-free PPP

Mon, 05/13/2019 - 00:00
Abstract

Global navigation satellite system real-time processing requires low latency, high timeliness, and high computational efficiency. A typical application is providing corrections using data from a regional Continuously Operating Reference Station (CORS) network. Usually the wide-lane and narrow-lane fractional cycle biases (FCBs) are determined at the server and broadcast to users to fix undifferenced ambiguity. Also, a tropospheric model is established at the server and broadcast to users to obtain accurate and reliable a priori zenith total delays for precise point positioning (PPP) using the ionospheric-free (IF) observation combination. Currently, serial methods are typically applied, i.e., all reference stations are involved in estimating the wide-lane and narrow-lane FCBs and establishing a regional tropospheric delay model. To improve the efficiency and shorten the latency, we develop a parallel computation method for regional CORS network corrections based on IF PPP by adopting a multicore parallel computing technology task parallel library, wherein parallel computations involving the FCBs, tropospheric delays, and tropospheric model are successively performed based on data parallelism, in which the same operation is performed concurrently on elements in an array, and task parallelism, which refers to one or more independent tasks running concurrently. Data covering four seasons from the Hong Kong and southwestern America CORS networks are utilized in the experiment. The single differenced FCBs between satellites are determined within each full pass, and a tropospheric model with an internal accuracy better than 1.4 cm and an external accuracy better than 1.6 cm is derived at the server. With the parallel implementation, the speedup ratios of FCB estimation and tropospheric modeling are 1.79, 3.15, 5.59, and 9.69 times higher for dual-core, quad-core, octa-core, and hexadeca-core platforms, respectively, than for a single-core platform.

### Theoretical evaluation of group delay on pseudorange bias

Sat, 05/11/2019 - 00:00
Abstract

The phenomenon of pseudorange bias, which is also called S-Curve bias, becomes more obvious with the combined use of multiple satellite systems or navigation satellites with different phases. The different characteristics of the transmitting channel of a navigation satellite result in different distortions of the pseudorange bias in navigation signals; in particular, this issue worsens when the RF channel is not optimized to decrease the pseudorange bias. Therefore, it is interesting to reveal the essential relationship between pseudorange bias and the non-ideal channel and to present an analytic model of the effect of a non-ideal channel on pseudorange bias. Instead of using the numerical method of finding the bias of the zero-crossing point of the discriminator, we provide a theoretical evaluation of the S-Curve bias for the given parameters of channel and signals. Based on the model and presented analyses, we find that second-order group delay plays an important role in the distortion of S-Curve bias and should be avoided in the design of the RF channel for navigation satellites and receivers.

### An efficiency optimal dual-frequency constant-envelope multiplexing technique for GNSS signals

Thu, 05/09/2019 - 00:00
Abstract

With the development of global navigation satellite systems (GNSSs), an increasing number of navigation signals are broadcast to provide diversified services for users. In order to save payload resources, multiple signals are required to be multiplexed into a composite signal. Furthermore, the composite signal should have a constant-envelope characteristic to mitigate signal distortion caused by nonlinear amplification. Existing constant-envelope multiplexing (CEM) application cases could be roughly divided into two categories, single-frequency CEM and dual-frequency CEM. The research on single-frequency CEM is relatively mature. However, existing dual-frequency CEM techniques still need improving. Although a series of dual-frequency CEM methods have been proposed in the past few years, the theoretical research on this issue still needs to be strengthened. Besides, multiplexing efficiency and flexibility of dual-frequency CEM techniques should also be improved. Therefore, we mainly focus on dual-frequency CEM. We first derive an upper bound of multiplexing efficiency in CEM problem via Chebyshev norm minimization. Subsequently, we prove the upper bound is just the supremum in dual-frequency CEM and propose a new dual-frequency CEM technique, which can achieve optimal multiplexing efficiency. The proposed method also takes the suppression of direct current (DC) component into consideration to avoid the potential hazard caused by the DC component. Utilizing the proposed technique, storage complexity of dual-frequency CEM is also decreased. Simulations and performance analysis are also given, which shows that the proposed technique outperforms existing CEM methods in terms of multiplexing efficiency, flexibility and storage complexity.

### A new datum jump detection and mitigation method of Real-Time Service (RTS) clock products

Thu, 05/09/2019 - 00:00
Abstract

Real-time orbit and clock products are crucial for real-time precise point positioning (PPP) applications. The International Global Navigation Satellite System (GNSS) Service (IGS) launched the Real-Time Service (RTS) in 2013 to provide real-time satellite orbit and clock products which have since found wide applications. Currently, the IGS RTS provides two different types of satellite orbit and clock products: the products generated from individual Analysis Centers such as CLK01, CLK22 and CLK90 and the combination products such as IGS01 and IGS03. These IGS RTS products are different in terms of precision and reliability. First, we verify that the phenomenon of clock datum jumps is obvious in IGS01, which has not been considered by the GNSS community when applying the IGS01 product to the real-time PPP. Afterward, the causes of the clock datum jump are investigated. The results indicate that a switchover of the reference product or a datum jump in the reference product will cause a clock datum jump. In order to solve the clock datum jumps issue, a new clock datum jump detection and mitigation algorithm is proposed. Real-time kinematic PPP experiments are then carried out to validate the proposed satellite clock detection and mitigation algorithm. The positioning results with 27 globally distributed IGS stations show that the root mean square improvements in the north, east and up components are 61.5%, 36.5% and 55.1% after detecting and mitigating the datum jumps.

### Investigation of the performance of real-time BDS-only precise point positioning using the IGS real-time service

Thu, 05/02/2019 - 00:00
Abstract

With the development of China’s BeiDou Navigation Satellite System (BDS) and the operation of the real-time service (RTS) of the International GNSS service, BDS real-time precise point positioning (RTPPP) has become possible. In this contribution, the RTS product CLK93 is employed for BDS RTPPP, and its quality for BDS orbit and clock corrections is first assessed by availability and accuracy over a period of 24 days. Following this, the convergence time and positioning accuracy of BDS-only RTPPP are evaluated by performing a 24-day processing with ten stations from the multi-GNSS experiment (MGEX) network. Finally, a real-time kinematic test is conducted in an urban environment to further investigate the performance of BDS-only RTPPP. Experimental results show that the average availabilities of the CLK93 corrections are approximately 95% for the inclined geosynchronous satellite orbit (IGSO) satellites, 90% for the medium earth orbit (MEO) satellites and 65% for the geostationary earth orbit satellites. The mean accuracy of the real-time corrections, which is represented by the signal-in-space ranging error (SISRE) value, is 10 cm for the IGSO and MEO satellites. Furthermore, the average positioning accuracies in the north, east and up components of the ten MGEX stations are approximately 1.7, 2.2 and 2.6 cm, respectively, for the static mode and 10.3, 15.6 and 29.2 cm, respectively, for the kinematic mode. In addition, the average time required to converge to a 20-cm accuracy in the three-dimensional component is approximately 100 and 136 min for BDS-only RTPPP in the static and kinematic modes, respectively. In addition, the positioning accuracy of BDS-only RTPPP in the real-time kinematic test is 0.86, 0.92 and 1.68 m in the east, north and up components, respectively, for the whole solutions during the test, which is obviously worse than that obtained by GPS-only RTPPP.

### Discovery of new code interference phenomenon in GPS observables

Mon, 04/29/2019 - 00:00
Abstract

The Global Positioning System (GPS) provides satellite-based navigation signals, which are employed in many fields, including agriculture, transportation, aviation, and military/personal navigation. In an effort to minimize interference among GPS satellites and to enable GPS receivers to discern satellite identity, each satellite is assigned a specific pseudorandom noise (PRN) sequence that is used to modulate the phase of the corresponding signal. The codes that modulate the current GPS landscape are constructed in such a way that cross-correlation among codes is kept to a bounded minimum, which should significantly limit harmful signal interference. In this study, the efficacy of the current PRN-based modulation system is called into question as GPS signal amplitude and carrier phase data over the past decade show frequent interference between satellite signals.

### A new troposphere tomography algorithm with a truncation factor model (TFM) for GNSS networks

Wed, 04/17/2019 - 00:00
Abstract

For previous studies of global navigation satellite system (GNSS) troposphere tomography, only the GNSS observations derived from ground-based stations located inside the tomographic area were considered; however, stations distributed outside the area of interest in a dense regional network were neglected. This wastes valuable GNSS data and decreases the number of voxels traveled by satellite rays. This becomes the focus of this work, which tries to use GNSS receivers located outside the tomographic region to participate in the establishment of a tomographic observation equation. A new troposphere tomography algorithm is proposed with a truncation factor model (TFM), while the ability of the TFM to calculate the sectional slant water vapor inside the tomographic area, derived from the receivers outside this area, has been verified. The proposed algorithm is validated using the observed data collected over 31 days from the continuously operating reference system network of Zhejiang Province, China. At elevation angle masks of 10°, the number of satellite rays used has increased by 21.27% while the number of voxels transited by satellite rays has increased by 13.97% from 65.44 to 79.23% when adopting the TFM. The compared result of integrated water vapor with those from radiosonde data reveals that the RMS error and bias of the proposed algorithm are 4.1 mm and 0.06 mm, respectively, while those of the conventional method are 4.8 mm and − 0.34 mm, respectively. Water vapor profile comparison also shows that the RMS error and bias of the proposed algorithm are superior with average values of 1.17 g m−3 and 0.02 g m−3 to that of the conventional algorithm with values of 1.44 g m−3 and 0.03 g m−3, respectively. The PWV differences between tomography and GAMIT further indicate a good performance of the proposed algorithm with the values of RMS error and bias of 8.7 mm and 0.5 mm, respectively, while those of the traditional method are 12.6 mm and 0.9 mm, respectively.

### Precise point positioning ambiguity resolution by integrating BDS-3e into BDS-2 and GPS

Fri, 04/12/2019 - 00:00
Abstract

With the development of BDS-3, more BDS satellites are in orbits which can contribute to the reduction in the initial time of ambiguity fixing as well as the increase in the ambiguity fixing rate. We focus on the improvement in the BDS-based PPP AR as well as the GPS- and BDS-integrated PPP AR, using newly available BDS-3e satellites. To achieve this goal, the wide-lane (WL) and narrow-lane (NL) fractional cycle biases (FCBs) of B1I and B3I observations of BDS-2 IGSO and MEO satellites as well as of observations of BDS-3e satellites are generated using a network of globally distributed reference stations, while the BDS-2 GEO satellites are excluded from the FCBs estimation for their poor orbit accuracy due to the poor geometry. Both static and kinematic PPP AR solutions have been compared and analyzed in five combination strategies, including BDS-2 AR, BDS-2/3e AR, GPS AR, GPS/BDS-2 AR and GPS/BDS-2/3e AR. The experimental results illustrate that the inclusion of BDS-3e satellites is able to significantly improve the performance of the BDS-based PPP AR but only marginally improves the performance of the GPS- and BDS-integrated PPP AR. An average TTFF of 57.2 min (static) and 60.3 min (kinematic) and a fixing rate of 88.7% (static) and 87.3% (kinematic) have been achieved in the static and kinematic PPP AR for BDS-2/3e. The average time of TTFF is shortened to 15.3 min (static) and 16.4 min (kinematic) with a fixing rate of 96.9% (static) and 96.2% (kinematic) for GPS/BDS-2. The PPP AR of GPS/BDS-2/3e is found to perform the best among the five combination strategies of solutions, and an average TTFF of 13.1 min (static) and 14.3 min (kinematic) and a fixing rate of 97.0% (static) and 96.7% (kinematic) have been obtained.

### Fuzzy-adaptive constrained data fusion algorithm for indirect centralized integrated SINS/GNSS navigation system

Thu, 04/11/2019 - 00:00
Abstract

The main challenge of low-cost strap-down inertial navigation systems (SINSs) is time-growing positioning error due to erroneous measurements of micro-electro mechanical system (MEMS)-based inertial sensors. The global navigation satellite system (GNSS) provides drift-free positioning data that can be appropriately utilized to prevent the cumulative error of stand-alone SINS. The primary aim of this research is to enhance the positioning accuracy, performance, and reliability of low-cost SINS/GNSS-integrated navigation system. To attain this, we propose an applied data fusion algorithm for indirect centralized (IC) integrated SINS/GNSS. The proposed data fusion algorithm is based on fuzzy-adaptive constrained estimation filter. Velocity and altitude constraints are embedded in the integration scheme of the proposed SINS/GNSS system to preserve system reliability during abrupt GNSS outage. In an innovative way, the state constraints of altitude are defined based on the measurements of air-data sensors. The state estimation is effectively optimized since the respective states are projected on a constraint surface. Furthermore, a fuzzy type-2 inference system is developed for adaptively changing the covariance matrix of the estimation algorithm. Inertial measurements are used as the input of the fuzzy inference system. Accordingly, the state estimation algorithm is adaptively modified based on the vehicle’s maneuvering during the navigation trajectory. The proposed SINS/GNSS system is experimentally assessed through several vehicular tests. The results indicate that not only does the proposed algorithm improve the navigation accuracy, it will also enhance the reliability of the integrated navigation system during GNSS outage.

### Design and implementation of an open-source BDS-3 B1C/B2a SDR receiver

Wed, 04/10/2019 - 00:00
Abstract

GNSS software-defined radio (SDR) receiver has been and will continue to be a tremendous research enabler given its flexibility and GNSS modernization as well as improvements to complimentary technologies. An open-source suite of GNSS SDRs capable of post-processing all open-service GNSS signals has been developed by the GNSS Lab at the University of Colorado, Boulder. As the latest expansion, processing capabilities for the B1C/B2a signals of the third-generation BeiDou navigation satellite system (BDS-3) are incorporated into this SDR package. To provide a basic implementation framework for GNSS community, separate or joint processing of the data and pilot channels are realized in the B1C/B2a SDR; and both narrowband and wideband tracking modes are implemented specifically for B1C pilot channel. Soon after the launch of the first two BDS-3 satellites, the B1C/B2a signals have been captured and the initial tracking results have been obtained. We describe the design strategy and implementation of the BDS-3 B1C/B2a SDR and report the processing results. The emphasis is placed on the B1C processing due to the novelty and complexity of the quadrature multiplexed binary offset carrier modulation employed by B1C.

### Real-time sea-level monitoring using Kalman filtering of GNSS-R data

Wed, 04/10/2019 - 00:00
Abstract

Current GNSS-R (GNSS reflectometry) techniques for sea surface measurements require data collection over longer periods, limiting their usability for real-time applications. In this work, we present a new, alternative GNSS-R approach based on the unscented Kalman filter and the so-called inverse modeling approach. The new method makes use of a mathematical description that relates SNR (signal-to-noise ratio) variations to multipath effects and uses a B-spline formalism to obtain time series of reflector height. The presented algorithm can provide results in real time with a precision that is significantly better than spectral inversion methods and almost comparable to results from inverse modeling in post-processing mode. To verify the performance, the method has been tested at station GTGU at the Onsala Space Observatory, Sweden, and at the station SPBY in Spring Bay, Australia. The RMS (root mean square) error with respect to nearby tide gauge data was found to be 2.0 cm at GTGU and 4.8 cm at SPBY when evaluating the output corresponding to real-time analysis. The method can also be applied in post-processing, resulting in RMS errors of 1.5 cm and 3.3 cm for GTGU and SPBY, respectively. Finally, based on SNR data from GTGU, it is also shown that the Kalman filter approach is able to detect the presence of sea ice with a higher temporal resolution than the previous methods and traditional remote sensing techniques which monitor ice in coastal regions.

### Influence of stochastic modeling for inter-system biases on multi-GNSS undifferenced and uncombined precise point positioning

Tue, 04/09/2019 - 00:00
Abstract

The focus of this study is on proper modeling of the dynamics for inter-system biases (ISBs) in multi-constellation Global Navigation Satellite System (GNSS) precise point positioning (PPP) processing. First, the theoretical derivation demonstrates that the ISBs originate from not only the receiver-dependent hardware delay differences among different GNSSs but also the receiver-independent time differences caused by the different clock datum constraints among different GNSS satellite clock products. Afterward, a comprehensive evaluation of the influence of ISB stochastic modeling on undifferenced and uncombined PPP performance is conducted, i.e., random constant, random walk process, and white noise process are considered. We use data based on a 1-month period (September 2017) Multi-GNSS Experiment (MGEX) precise orbit and clock products from four analysis centers (CODE, GFZ, CNES, and WHU) and 160 MGEX tracking stations. The results demonstrate that generally, the positioning performance of PPP in terms of convergence time and positioning accuracy with the final products from CODE, CNES, and WHU is comparable among the three ISB handling schemes. However, estimating ISBs as random walk process or white noise process outperforms that as the random constant when using the GFZ products. These results indicate that the traditional estimation of ISBs as the random constant may not always be reasonable in multi-GNSS PPP processing. To achieve more reliable positioning results, it is highly recommended to consider the ISBs as random walk process or white noise process in multi-GNSS PPP processing.

### A new unambiguous tracking algorithm for sine-BOC( m, n ) signals

Mon, 04/08/2019 - 00:00
Abstract

Binary offset carrier (BOC) modulation technology is widely used in newly developed and modernized global navigation satellite systems. BOC signal offers superior performance over conventional binary phase-shift keying signal due to its sharp auto-correlation function. However, the main drawback of BOC signal tracking is the ambiguity problem caused by the presence of multiple side-peaks in the auto-correlation function. We derive a new analytical model to solve the ambiguity issue. Based on the derived analytical model, a code tracking algorithm that completely removes all ambiguities is introduced. Theoretical analysis and simulation show that the proposed technique significantly improves the multipath mitigation performance and code tracking accuracy in thermal noise over those of existing side-peaks-cancellation techniques.

### FY-3D and FY-3C onboard observations for differential code biases estimation

Wed, 04/03/2019 - 00:00
Abstract

With the development of Low Earth Orbit satellites, differential code biases (DCBs) estimation based on onboard observations has been widely studied. In this study, onboard observations of BDS and GPS satellites by the Chinese Fengyun-3D (FY-3D) and Fengyun-3C (FY-3C) satellites are applied to estimate BDS and GPS DCBs. Since only the code observations of C1C and C2W for GPS, and C2I and C7I for BDS are tracked by FY-3D and FY-3C, the DCB types of GPS C1C-C2W and BDS C2I-C7I are estimated with code multipath considered. First, the DCB estimates based on FY-3D onboard observations are analyzed. When jointly processing BDS + GPS onboard observations, the stability of satellite and receiver DCBs for both BDS and GPS has better consistency with the DCB products of the German Aerospace Center (DLR) and the Chinese Academy of Science than that for the single-system solutions (BDS-only solution and GPS-only solution). This is reasonable because more onboard observations are used in BDS + GPS solution, which can improve the strength of the DCB estimation. The variations of receiver DCB are analyzed as a function of geomagnetism and solar activity, but little relationship between them has been found. Compared with the FY-3C solution, the FY-3D solution can achieve a more stable satellite DCB with a stability improvement of 33%, 48%, 62% and 56% for GPS, BDS GEO, IGSO, and MEO satellites, respectively. Meanwhile, the receiver DCB of FY-3D is more stable than that of FY-3C as well. These improvements of satellite and receiver DCBs can be due to the enhancement of FY-3D GNSS Occultation Sounder (GNOS) instrument, which provides more observations with higher quality. Furthermore, both FY-3D and FY-3C onboard observations are processed together to estimate BDS and GPS DCBs. Compared with the FY-3D solution, the stability of satellite DCB can be improved by 16%, 9% and 7% for GPS, BDS GEO and IGSO satellites DCB, respectively, when both FY-3D and FY-3C onboard observations are jointly processed. The impact of DCB estimation on estimating the vertical total electron content (VTEC) is also investigated. Compared with FY-3D GPS-only and BDS + GPS solutions, the VTEC estimates along the FY-3D orbit can achieve more realistic results for FY-3D + FY-3C solution.

### Performance of BDS-3: satellite visibility and dilution of precision

Mon, 03/25/2019 - 00:00
Abstract

We describe a method to assess the performance of the third-generation BeiDou navigation satellite system (BDS-3), in terms of satellite visibility and dilution of precision (DOP), on global and regional scales. Different from traditional methods, this method estimates the satellite visibility and DOP without requiring real or simulated ephemerides. Validated by the reference values derived from real ephemerides of GPS and GLONASS, the estimated number of visible satellites achieves an accuracy better than 0.15, and the estimated DOP values are lower than their reference values by less than 10% on average. Applying this method to BDS-3, with a 5° cutoff elevation angle, results show that the geostationary earth orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites of BDS-3 together contribute 3–6 visible satellites in the area of 60°S–60°N and 50°E–170°E. In this area, the number of visible BDS-3 satellites is 11–14, which is more than GPS and Galileo by 1–3, and GLONASS by 3–7. With better satellite visibility, the average BDS-3 horizontal, vertical, and time DOPs over this area are 0.74, 1.08, and 0.67, which are, respectively, 5%, 9%, and 3% lower than those of GPS and Galileo, 14%, 16%, and 21% lower than those of GLONASS, and 16%, 19% and 14% lower than those of the 24-MEO-only BDS-3.

### A state-constrained tracking approach for Kalman filter-based ultra-tightly coupled GPS/INS integration

Thu, 03/21/2019 - 00:00
Abstract

The traditional design of tracking loop in global positioning system (GPS), known as the combination of phase-locked loop and delay-locked loop, is fragile under complex environments. With the increasing requirements for tracking performance under more harsh applications, several implementations have emerged in recent years, among which Kalman filter (KF)-based tracking loop is widely used due to its adaptive nature and robust feature, and it could achieve a higher dynamics performance with the aid of inertial navigation system (INS). However, even more critical conditions, such as severe fading, abrupt phase changes, and signal interference coexisting with high user dynamics, are now challenging the traditional carrier tracking architectures, thus calling for the enhancement of robust carrier tracking techniques. A state-constrained Kalman filter-based (SC-KF) approach is proposed to restrict the errors of the tracking loop and to enhance the robustness of the tracking process in high dynamics and signal attenuation environments. In the SC-KF, the system model of INS-aided KF-based tracking loop is built from a perspective of control theory. Based on the ultra-tight GPS/INS integrated scheme, a Doppler-constrained method and moving horizon estimation architecture are introduced to correct the Doppler state and the code, carrier phase states in KF-based tracking loop, respectively. Software and hardware simulations indicate that the proposed architecture has a better performance in tracking and navigation domains comparing with the conventional INS-aided KF-based tracking loop under severe environments.

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