A New Ground-Based Pseudolite System Deployment Algorithm Based on MOPSO

Pseudolite deployment is the premise of ground-based pseudolite system networking, which affects the coverage and positioning accuracy of ground-based pseudolite systems. Optimal deployment algorithms can help to achieve a higher signal coverage and lower mean horizontal precision factor (HDOP) with a limited number of pseudolites. In this paper, we proposed a multi-objective particle swarm optimization (MOPSO) algorithm for the deployment of a ground-based pseudolite system. The new algorithm combines Digital Elevation Model (DEM) data and uses the mean HDOP of the DEM grid to measure the geometry of the pseudolite system. The signal coverage of the pseudolite system was calculated based on the visual area analysis with respect to reference planes, which effectively avoids the repeated calculation of the intersection and improves the calculation efficiency. A selected area covering 10 km×10 km in the Jiuzhaigou area of China was used to verify the new algorithm. The results showed that both the coverage and HDOP achieved were optimal using the new algorithm, where the coverage area can be up to approximately 50% and 30% more than using the existing particle swarm optimization (PSO) and convex polyhedron volume optimization (CPVO) algorithms, respectively.

Doppler Differential Positioning Technology Using the BDS/GPS Indoor Array Pseudolite System

A Global Satellite Navigation System (GNSS) cannot provide normal location services in an indoor environment because the signals are blocked by buildings. The Beidou satellite navigation system (BDS)/GPS indoor array pseudolite system is proposed to overcome the problems of indoor positioning with conventional pseudolite, such as time synchronization, ambiguity resolution and base stations. At the same time, an algorithm for Doppler differential positioning is proposed to improve the indoor positioning accuracy and the positioning coverage of the system, which uses the Doppler difference equation and Known Point Initialization (KPI) to determinate the velocity and position of the receiver. Experiments were conducted to verify the proposed system under different conditions; the average positioning error of the Doppler differential positioning algorithm was 7.86 mm in the kinematic test and 2.9 mm in the static test. The results show that BDS/GPS indoor array pseudolite system has the potential to make indoor positioning achieve sub-centimeter precision. Finally, the positioning error of the proposed algorithm is also analyzed, and the data tests show that the dilution of precision (DOP) and cycle- slips have a significant impact on the indoor positioning accuracy; a cycle-slip of a half-wavelength can cause positioning errors of tens of millimeters. Therefore, the Doppler-aided cycle-slip detection method (DACS) is proposed to detect cycle-slips of one cycle or greater than one, and the carrier phase double difference cycle-slip detection method (CPDD) is used to detect cycle slips of a half-wavelength.

Correction Method for the Observed Global Navigation Satellite System Ultra-Rapid Orbit Based on Dilution of Precision Values

For ultra-rapid orbits provided by the Global Navigation Satellite System (GNSS), the key parameters, accuracy and timeliness, must be taken into consideration in real-time and near real-time applications. However, insufficient observations in later epochs appear to generate low accuracy in observed orbits, for which a correlation between the Dilution of Precision (DOP) of the orbit parameters and their accuracy is found. To correct the observed GNSS ultra-rapid orbit, a correction method based on the DOP values is proposed by building the function models between DOP values and the orbit accuracy. With 10-day orbit determination experiments, the results show that the observed ultra-rapid-orbit errors, generated by insufficient observations, can be corrected by 12–22% for the last three hours of the observed orbits. Moreover, considering the timeliness constraints in ultra-rapid-orbit determination, a DOP amplification factor is defined to weight the contribution of each tracking station and optimize the station distribution in the orbit determination procedure. Finally, six schemes are designed to verify the method and strategy in determining the ultra-rapid orbit based on one-month observations. The orbit accuracy is found to decrease by 1.27–6.34 cm with increasing amplification factor from 5–20%. Thus, the observed ultra-orbit correction method proposed is ideal when considering accuracy and timeliness in ultra-rapid orbit determination.

Enhanced Positioning Algorithm of ARPS for Improving Accuracy and Expanding Service Coverage

The airborne relay-based positioning system (ARPS), which employs the relaying of navigation signals, was proposed as an alternative positioning system. However, the ARPS has limitations, such as relatively large vertical error and service restrictions, because firstly, the user position is estimated based on airborne relays that are located in one direction, and secondly, the positioning is processed using only relayed navigation signals. In this paper, we propose an enhanced positioning algorithm to improve the performance of the ARPS. The main idea of the enhanced algorithm is the adaptable use of either virtual or direct measurements of reference stations in the calculation process based on the structural features of the ARPS. Unlike the existing two-step algorithm for airborne relay and user positioning, the enhanced algorithm is divided into two cases based on whether the required number of navigation signals for user positioning is met. In the first case, where the number of signals is greater than four, the user first estimates the positions of the airborne relays and its own initial position. Then, the user position is re-estimated by integrating a virtual measurement of a reference station that is calculated using the initial estimated user position and known reference positions. To prevent performance degradation, the re-estimation is performed after determining its requirement through comparing the expected position errors. If the navigation signals are insufficient, such as when the user is outside of airborne relay coverage, the user position is estimated by additionally using direct signal measurements of the reference stations in place of absent relayed signals. The simulation results demonstrate that a higher accuracy level can be achieved because the user position is estimated based on the measurements of airborne relays and a ground station. Furthermore, the service coverage is expanded by using direct measurements of reference stations for user positioning.