**1. Introduction**

With the continuous development and improvement of the Global Navigation Satellite System (GNSS), the number of visible satellites has been greatly increased, which effectively improves the positioning accuracy, reliability, and availability. However, in complex environments such as under trees, urban canyons, tunnels, deep mine pits, and indoors, etc., GNSS signal attenuation is severe, observation quality is poor, or the visible satellites are insufficient and there is the serious multipath effect. These drawbacks will lead to decreased positioning accuracy or even unable to locate, which greatly limit the availability and application of GNSS [1,2]. Combining GNSS with other multi-source sensor technologies to realize the complementary advantages of each system and improve the location-based

**Citation:** Wang, S.; Dong, X.; Liu, G.; Gao, M.; Zhao, W.; Lv, D.; Cao, S. Low-Cost Single-Frequency DGNSS/DBA Combined Positioning Research and Performance Evaluation. *Remote Sens.* **2022**, *14*, 586. https://doi.org/10.3390/rs14030586

Academic Editors: Changhui Jiang, Yuwei Chen, Qian Meng, Panlong Wu, Bing Xu, Lianwu Guan, Wang Gao and Zeyu Li

Received: 18 December 2021 Accepted: 24 January 2022 Published: 26 January 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

services (LBS) accuracy of user terminals in harsh scenarios has become a major research hotspot in the field of navigation.

Single-frequency low-cost GNSS receivers, such as u-blox series, SkyTraq S2525F8, etc., are widely used in various industries, providing solutions for surveying and mapping applications [3], landslide deformation monitoring [4,5], pedestrian navigation, vehicle tracking [6], and small unmanned aerial vehicles (UAV) navigation [7]. Low-cost GNSS receivers are smaller in size and mass, but their hardware performance is inferior to that of geodetic GNSS receivers. For example, lower signal-to-noise ratio (SNR), poor observed values, and more frequent satellite out-of-lock and observation data are missing. The main reason is that the observation quality of the low-cost patch antenna is poor. Low-cost GNSS receivers for standard point positioning (SPP) can only obtain meter-level positioning accuracy, which means positioning accuracy and reliability will significantly reduce with positioning errors up to tens of meters in complex urban environments [8]. The singlefrequency low-cost u-blox receiver for GNSS RTK positioning has a low fixed rate of carrier phase ambiguity in practical applications due to the poor observed data quality [9].

Compared with GNSS RTK positioning to achieve centimeter-level positioning accuracy, the DGNSS positioning with code pseudorange can only achieve 1–2 m positioning accuracy [10]. However, DGNSS is simpler to implement and can avoid positioning failure caused by RTK ambiguity fixed incorrectly. DGNSS can be widely used in many fields, for example, in the location of mobile devices [11,12], marine navigation, and in coastal navigation and in dynamic vessel positioning [10,13], in hydrography for positioning of acoustic systems [14], in autonomous vehicle positioning [15,16], and civil aviation during precision approach procedures [17]. DGNSS is currently the most widely used augmentation system around the world.

The idea behind DGNSS operation lies in determination of the error related to pseudorange observations and calculated comparing the actual value received by the GNSS receiver and the true value calculated using the satellite and the reference station antenna coordinates. This difference, referred to as a pseudorange correction, is transmitted to users who use a GNSS receiver and take it into account in the positioning process [18]. They can be divided into so-called local-area DGNSS (LADGNSS) services for small areas, such as a relatively small area of several dozen to several hundred square kilometers, and wide-area DGNSS (WADGNSS) services for larger areas such as an entire continent or even worldwide. The positioning accuracy achieved by LADGNSS method is 1–3 m and it decreases with increasing distance between a user and the single reference station [19]. WADGNSS can extend the service area using a few geosynchronous equatorial orbit (GEO) satellites and overcome the error due to the spatial decorrelation, as in, for example, the Wide-Area Augmentation System (WAAS, USA), European Geostationary Navigation Overlay Service (EGNOS, Europe), and MTSAT Satellite Augmentation System (MSAS, Japan). This system is used to obtain a meter-level accuracy over a large region while using a fraction of the number of reference stations [10].

Most studies and analyses of DGNSS positioning with low-cost GNSS receivers have used geodetic antennas. For example, an Flächen Korrektur parameter (FKP)-DGPS algorithm [19] is studied as a new augmentation method for the low-cost GPS receivers by integrating the conventional DGPS correction with the modified FKP correction to mitigate the positioning error due to the spatial decorrelation. Single-frequency DGPS aided lowcost inertial navigation system (INS) positioning [20] was studied to achieve the real-time high-frequency state output with decimeter position accuracy and centimeter velocity accuracy. However, there is still little research on DGNSS for low-cost GNSS receivers with low-cost patch antenna and fusion positioning with other low-cost sensors.

Height constraint is an effective method to improve the GNSS positioning accuracy, for example, due to the insufficient number of available satellites, the BDS-1 has used electronic maps as height constraints to improve the users' positioning accuracy [21]. This method is more complicated to implement and it is difficult to promote its application. The barometric altimetry is low-cost, independent of environmental restrictions, and can be

used both indoors and outdoors. Low-cost barometer altimetry-assisted GNSS positioning navigation is also widely used in the field of aviation flights and smartphone navigation, etc. [22–25]. The basic principle of barometric altimetry is to use the physical phenomenon that the atmospheric pressure on the Earth's surface gradually decreases with increasing height, but, due to the irregular changes of atmospheric pressure, the altitude error directly calculated by a single barometer is as high as tens or even hundreds of meters, which cannot be used as a constraint to improve GNSS positioning accuracy. Similar to DGNSS, the accurate height can be obtained by barometric correction compensation or differential barometric altitude (DBA). That is, using the property that local atmospheric pressure changes are similar, a barometer is placed at the reference station and another barometer is used as a mobile station to determine its high-precision relative altitude by the differential equation. The altitude accuracy and reliability obtained by DBA mode are high, which can effectively constrain other technology to improve positioning and navigation accuracy.

The user altitude obtained by the DBA system was applied as a virtual satellite in the China Area Positioning System (CAPS), and the construction of independent earth ellipsoidal constraint equations by users' altitude can effectively solve the insufficient number of CAPS satellites and improve its 3D positioning accuracy and availability [26–28]. The DBA system also be applied to mobile cellular network positioning for accurately determining the user's height, and reduced 3D positioning to planar positioning which can obtain more desirable positioning accuracy [29]. Mobile cellular base stations can be used as DBA reference stations and transmitted the relevant atmosphere pressure data to the user side through mobile communication networks, achieving GNSS SPP/DBA combined 3D positioning with the altitude accuracy better than 1 m [30]. Inertial/barometric altitude can be fused to measure vertical velocity and height with velocity root mean squared error (RMSE) between 0.04 to 0.24 m/s and RMSE in height between 5 to 68 cm [31]. In addition, a barometer installed on a wearable device can measure vital signs such as blood pressure by detecting the position and orientation of the human body, thus providing a better telemedicine solution for precision medicine [32,33].

At present, to our knowledge, little research has been reported on the DGNSS/DBA combined positioning with low-cost GNSS receivers and a patch antenna, and there is also a lack of research and analysis on the theoretical methods and application effects of DBA, which is worth further study. In this study, we firstly propose a DGNSS/DBA combined positioning algorithm. Second, the DBA altitude accuracy at different baseline lengths is evaluated in detail. Then, the DGNSS performance of single-frequency low-cost NEO-M8T receiver and the accuracy and reliability of DGNSS/DBA combined positioning with low-cost BMP280 barometer are fully evaluated through actual measurement data.

This manuscript is organized as follows: Section 1 is the introduction. Section 2 is the mathematical model of DGNSS/DBA combined positioning, which contains Section 2.1 about DGNSS positioning observation equations; Section 2.2 about the principle of the DBA system; and Section 2.3 on the DGNSS/DBA combined positioning algorithm. Section 3 reports the experiment results, containing Section 3.1 that introduces experimental data; Section 3.2 about DBA altitude accuracy evaluation at different baseline lengths; Sections 3.3 and 3.4 on the DGNSS/DBA combined static and kinematic vehicle positioning performance evaluation for the single-frequency low-cost NEO-M8T receiver and BMP280 barometer, respectively. Section 4 presents the discussions. Section 5 is the conclusion.
