Multiplexing modulation design optimization and quality evaluation of BDS-3 PPP service signal

The Precise Point Positioning (PPP) service of BeiDou-3 Navigation Satellite System (BDS-3) is implemented on its Geostationary Earth Orbit (GEO) satellites. However, its signal design is limited by the actual power of satellite and other conditions. Furthermore, the design needs to fully consider the compatibility of different service phases. Starting from the actual state of the BDS-3 GEO satellite, this paper studies the multiplexing modulation of the BDS PPP service signal that is based on the Asymmetric Constant Envelope Binary Offset Carrier (ACE-BOC) technique and proposes several feasible schemes for this signal. Comparison and optimization of these techniques are made from the aspects of transmission efficiency, multiplexing efficiency, and service forward compatibility. Based on the Type-III ACE-BOC multiplexing modulation technique, phase rotation and intermodulation reconstruction techniques are proposed to suppress the intermodulation interference issue. Finally, a signal based on improved ACE-BOC multiplexing is designed. The quality of the proposed signal was continuously monitored and tested using large-diameter antennas. The evaluation results show that the power spectrum deviation of the signal is 0.228 dB, the correlation loss is 0.110 dB, the S-curve slope deviation is 1.558% on average, the average length difference between the positive/negative chip and the ideal chip is only 0.0006 ns, and the coherence between the carrier and the pseudo code is 0.082°. All quality indicators are satisfactory, indicating that the proposed signal multiplexing modulation technique is an ideal solution that meets all the requirements of the design constraints, and can achieve efficient information broadcasting and forward compatibility of the BDS PPP service.

Equivariant filtering framework for inertial-integrated navigation

This paper proposes an Equivariant Filtering (EqF) framework for the inertial-integrated state estimation. As the kinematic system of the inertial-integrated navigation can be naturally modeled on the matrix Lie group SE2(3), the symmetry of the Lie group can be exploited to design an equivariant filter which extends the invariant extended Kalman filtering on the group-affine system and overcomes the inconsitency issue of the traditional extend Kalman filter. We firstly formulate the inertial-integrated dynamics as the group-affine systems. Then, we prove the left equivariant properties of the inertial-integrated dynamics. Finally, we design an equivariant filtering framework on the earth-centered earth-fixed frame and the local geodetic navigation frame. The experiments show the superiority of the proposed filters when confronting large misalignment angles in Global Navigation Satellite Navigation (GNSS)/Inertial Navigation System (INS) loosely integrated navigation experiments.

A universal Wi-Fi fingerprint localization method based on machine learning and sample differences

Wi-Fi technology has become an important candidate for localization due to its low cost and no need of additional installation. The Wi-Fi fingerprint-based positioning is widely used because of its ready hardware and acceptable accuracy, especially with the current fingerprint localization algorithms based on Machine Learning (ML) and Deep Learning (DL). However, there exists two challenges. Firstly, the traditional ML methods train a specific classification model for each scene; therefore, it is hard to deploy and manage it on the cloud. Secondly, it is difficult to train an effective multi-classification model by using a small number of fingerprint samples. To solve these two problems, a novel binary classification model based on the samples’ differences is proposed in this paper. We divide the raw fingerprint pairs into positive and negative samples based on each pair’s distance. New relative features (e.g., sort features) are introduced to replace the traditional pair features which use the Media Access Control (MAC) address and Received Signal Strength (RSS). Finally, the boosting algorithm is used to train the classification model. The UJIndoorLoc dataset including the data from three different buildings is used to evaluate our proposed method. The preliminary results show that the floor success detection rate of the proposed method can reach 99.54% (eXtreme Gradient Boosting, XGBoost) and 99.22% (Gradient Boosting Decision Tree, GBDT), and the positioning error can reach 3.460 m (XGBoost) and 4.022 m (GBDT). Another important advantage of the proposed algorithm is that the model trained by one building’s data can be well applied to another building, which shows strong generalizable ability.

A variant of raw observation approach for BDS/GNSS precise point positioning with fast integer ambiguity resolution

The Precise Point Positioning (PPP) technique uses a single Global Navigation Satellite System (GNSS) receiver to collect carrier-phase and code observations and perform centimeter-accuracy positioning together with the precise satellite orbit and clock corrections provided. According to the observations used, there are basically two approaches, namely, the ionosphere-free combination approach and the raw observation approach. The former eliminates the ionosphere effects in the observation domain, while the latter estimates the ionosphere effects using uncombined and undifferenced observations, i.e., so-called raw observations. These traditional techniques do not fix carrier-phase ambiguities to integers, if the additional corrections of satellite hardware biases are not provided to the users. To derive the corrections of hardware biases in network side, the ionosphere-free combination operation is often used to obtain the ionosphere-free ambiguities from the L1 and L2 ones produced even with the raw observation approach in earlier studies. This contribution introduces a variant of the raw observation approach that does not use any ionosphere-free (or narrow-lane) combination operator to derive satellite hardware bias and compute PPP ambiguity float and fixed solution. The reparameterization and the manipulation of design matrix coefficients are described. A computational procedure is developed to derive the satellite hardware biases on WL and L1 directly. The PPP ambiguity-fixed solutions are obtained also directly with WL/L1 integer ambiguity resolutions. The proposed method is applied to process the data of a GNSS network covering a large part of China. We produce the satellite biases of BeiDou, GPS and Galileo. The results demonstrate that both accuracy and convergence are significantly improved with integer ambiguity resolution. The BeiDou contributions on accuracy and convergence are also assessed. It is disclosed for the first time that BeiDou only ambiguity-fixed solutions achieve the similar accuracy with that of GPS/Galileo combined, at least in mainland China. The numerical analysis demonstrates that the best solutions are achieved by GPS/Galileo/BeiDou solutions. The accuracy in horizontal components is better than 6 mm, and in the height component better than 20 mm (one sigma). The mean convergence time for reliable ambiguity-fixing is about 1.37 min with 0.12 min standard deviation among stations without using ionosphere corrections and the third frequency measurements. The contribution of BDS is numerically highlighted.

A square root information filter for multi-GNSS real-time precise clock estimation

Real-time satellite orbit and clock estimations are the prerequisite for Global Navigation Satellite System (GNSS) real-time precise positioning services. To meet the high-rate update requirement of satellite clock corrections, the computational efficiency is a key factor and a challenge due to the rapid development of multi-GNSS constellations. The Square Root Information Filter (SRIF) is widely used in real-time GNSS data processing thanks to its high numerical stability and computational efficiency. In real-time clock estimation, the outlier detection and elimination are critical to guarantee the precision and stability of the product but could be time-consuming. In this study, we developed a new quality control procedure including the three standard steps: i.e., detection, identification, and adaption, for real-time data processing of huge GNSS networks. Effort is made to improve the computational efficiency by optimizing the algorithm to provide only the essential information required in the processing, so that it can be applied in real-time and high-rate estimation of satellite clocks. The processing procedure is implemented in the PANDA (Positioning and Navigation Data Analyst) software package and evaluated in the operational generation of real-time GNSS orbit and clock products. We demonstrated that the new algorithm can efficiently eliminate outliers, and a clock precision of 0.06 ns, 0.24 ns, 0.06 ns, and 0.11 ns can be achieved for the GPS, GLONASS, Galileo, and BDS-2 IGSO/MEO satellites, respectively. The computation time per epoch is about 2 to 3 s depending on the number of existing outliers. Overall, the algorithm can satisfy the IGS real-time clock estimation in terms of both the computational efficiency and product quality.

GIL: a tightly coupled GNSS PPP/INS/LiDAR method for precise vehicle navigation

Accurate positioning and navigation play a vital role in vehicle-related applications, such as autonomous driving and precision agriculture. With the rapid development of Global Navigation Satellite Systems (GNSS), Precise Point Positioning (PPP) technique, as a global positioning solution, has been widely applied due to its convenient operation. Nevertheless, the performance of PPP is severely affected by signal interference, especially in GNSS-challenged environments. Inertial Navigation System (INS) aided GNSS can significantly improve the continuity and accuracy of navigation in harsh environments, but suffers from degradation during GNSS outages. LiDAR (Laser Imaging, Detection, and Ranging)-Inertial Odometry (LIO), which has performed well in local navigation, can restrain the divergence of Inertial Measurement Units (IMU). However, in long-range navigation, error accumulation is inevitable if no external aids are applied. To improve vehicle navigation performance, we proposed a tightly coupled GNSS PPP/INS/LiDAR (GIL) integration method, which tightly integrates the raw measurements from multi-GNSS PPP, Micro-Electro-Mechanical System (MEMS)-IMU, and LiDAR to achieve high-accuracy and reliable navigation in urban environments. Several experiments were conducted to evaluate this method. The results indicate that in comparison with the multi-GNSS PPP/INS tightly coupled solution the positioning Root-Mean-Square Errors (RMSEs) of the proposed GIL method have the improvements of 63.0%, 51.3%, and 62.2% in east, north, and vertical components, respectively. The GIL method can achieve decimeter-level positioning accuracy in GNSS partly-blocked environment (i.e., the environment with GNSS signals partly-blocked) and meter-level positioning accuracy in GNSS difficult environment (i.e., the environment with GNSS hardly used). Besides, the accuracy of velocity and attitude estimation can also be enhanced with the GIL method.

Semi-analytical assessment of the relative accuracy of the GNSS/INS in railway track irregularity measurements

An aided Inertial Navigation System (INS) is increasingly exploited in precise engineering surveying, such as railway track irregularity measurement, where a high relative measurement accuracy rather than absolute accuracy is emphasized. However, how to evaluate the relative measurement accuracy of the aided INS has rarely been studied. We address this problem with a semi-analytical method to analyze the relative measurement error propagation of the Global Navigation Satellite System (GNSS) and INS integrated system, specifically for the railway track irregularity measurement application. The GNSS/INS integration in this application is simplified as a linear time-invariant stochastic system driven only by white Gaussian noise, and an analytical solution for the navigation errors in the Laplace domain is obtained by analyzing the resulting steady-state Kalman filter. Then, a time series of the error is obtained through a subsequent Monte Carlo simulation based on the derived error propagation model. The proposed analysis method is then validated through data simulation and field tests. The results indicate that a 1 mm accuracy in measuring the track irregularity is achievable for the GNSS/INS integrated system. Meanwhile, the influences of the dominant inertial sensor errors on the final measurement accuracy are analyzed quantitatively and discussed comprehensively.

GNSS smartphones positioning: advances, challenges, opportunities, and future perspectives

Starting from 2016, the raw Global Navigation Satellite System (GNSS) measurements can be extracted from the Android Nougat (or later) operating systems. Since then, GNSS smartphone positioning has been given much attention. A high number of related publications indicates the importance of the research in this field, as it has been doing in recent years. Due to the cost-effectiveness of the GNSS smartphones, they can be employed in a wide variety of applications such as cadastral surveys, mapping surveying applications, vehicle and pedestrian navigation and etc. However, there are still some challenges regarding the noisy smartphone GNSS observations, the environment effect and smartphone holding modes and the algorithm development part which restrict the users to achieve high-precision smartphone positioning. In this review paper, we overview the research works carried out in this field with a focus on the following aspects: first, to provide a review of fundamental work on raw smartphone observations and quality assessment of GNSS observations from major smart devices including Google Pixel 4, Google Pixel 5, Xiaomi Mi 8 and Samsung Ultra S20 in terms of their signal strengths and carrier-phase continuities, second, to describe the current state of smartphone positioning research field until most recently in 2021 and, last, to summarize major challenges and opportunities in this filed. Finally, the paper is concluded with some remarks as well as future research perspectives.

The nighttime ionospheric response and occurrence of equatorial plasma irregularities during geomagnetic storms: a case study

Recent studies revealed that the long-lasting daytime ionospheric enhancements of Total Electron Content (TEC) were sometimes observed in the Asian sector during the recovery phase of geomagnetic storms (e.g., Lei (J Geophys Res Space Phys 123: 3217–3232, 2018), Li (J Geophys Res Space Phys 125: e2020JA028238, 2020). However, they focused only on the dayside ionosphere, and no dedicated studies have been performed to investigate the nighttime ionospheric behavior during such kinds of storm recovery phases. In this study, we focused on two geomagnetic storms that happened on 7–8 September 2017 and 25–26 August 2018, which showed the prominent daytime TEC enhancements in the Asian sector during their recovery phases, to explore the nighttime large-scale ionospheric responses as well as the small-scale Equatorial Plasma Irregularities (EPIs). It is found that during the September 2017 storm recovery phase, the nighttime ionosphere in the American sector is largely depressed, which is similar to the daytime ionospheric response in the same longitude sector; while in the Asian sector, only a small TEC increase is observed at nighttime, which is much weaker than the prominent daytime TEC enhancement in this longitude sector. During the recovery phase of the August 2018 storm, a slight TEC increase is observed on the night side at all longitudes, which is also weaker than the prominent daytime TEC enhancement. For the small-scale EPIs, they are enhanced and extended to higher latitudes during the main phase of both storms. However, during the recovery phases of the first storm, the EPIs are largely enhanced and suppressed in the Asian and American sectors, respectively, while no prominent nighttime EPIs are observed during the second storm recovery phase. The clear north–south asymmetry of equatorial ionization anomaly crests during the second storm should be responsible for the suppression of EPIs during this storm. In addition, our results also suggest that the dusk side ionospheric response could be affected by the daytime ionospheric plasma density/TEC variations during the recovery phase of geomagnetic storms, which further modulates the vertical plasma drift and plasma gradient. As a result, the growth rate of post-sunset EPIs will be enhanced or inhibited.

Distributed Kalman filter for UWB/INS integrated pedestrian localization under colored measurement noise

Colored Measurement Noise (CMN) has a great impact on the accuracy of human localization in indoor environments with Inertial Navigation System (INS) integrated with Ultra Wide Band (UWB). To mitigate its influence, a distributed Kalman Filter (dKF) is developed for Gauss–Markov CMN with switching Colouredness Factor Matrix (CFM). In the proposed scheme, a data fusion filter employs the difference between the INS- and UWB-based distance measurements. The main filter produces a final optimal estimate of the human position by fusing the estimates from local filters. The effect of CMN is overcome by using measurement differencing of noisy observations. The tests show that the proposed dKF developed for CMN with CFM can reduce the localization error compared to the original dKF, and thus effectively improve the localization accuracy.