Geometry Dilution Of Precision Research Articles

Satellite Availability and Service Performance Evaluation for Next-Generation GNSS, RNSS and LEO Augmentation Constellation

Positioning accuracy is affected by the combined effect of user range errors and the geometric distribution of satellites. Dilution of precision (DOP) is defined as the geometric strength of visible satellites. DOP is calculated based on the satellite broadcast or precise ephemerides. However, because the modernization program of next-generation navigation satellite systems is still under construction, there is a lack of real ephemerides to assess the performance of next-generation constellations. Without requiring real ephemerides, we describe a method to estimate satellite visibility and DOP. The improvement of four next-generation Global Navigation Satellite Systems (four-GNSS-NG), compared to the navigation constellations that are currently in operation (four-GNSS), is statistically analyzed. The augmentation of the full constellation the Quasi-Zenith Satellite System (7-QZSS) and the Navigation with Indian Constellation (11-NavIC) for regional users and the low Earth orbit (LEO) constellation enhancing four-GNSS performance are also analyzed based on this method. The results indicate that the average number visible satellites of the four-GNSS-NG will reach 44.86, and the average geometry DOP (GDOP) will be 1.19, which is an improvement of 17.3% and 7.8%, respectively. With the augmentation of the 120-satellite mixed-orbit LEO constellation, the multi-GNSS visible satellites will increase by 5 to 8 at all latitudes, while the GDOP will be reduced by 6.2% on average. Adding 7-QZSS and 11-NavIC to the four-GNSS-NG, 37.51 to 71.58 satellites are available on global scales. The average position DOP (PDOP), horizontal DOP (HDOP), vertical DOP (VDOP), and time DOP (TDOP) are reduced to 0.82, 0.46, 0.67 and 0.44, respectively.

Spatial Geometry Design of a Low Earth Orbit Constellation for Iranian Regional Navigation Satellite System

The regional navigation satellite system (RNSS) is recently used in some countries to cover or enhance their local navigation. The most important satellite navigation systems to date are in the Earth medium orbit (MEO) and Earth synchronous Earth orbit (GEO), which are characterized by big satellites, and high launch, construction, and operation costs. In contrast, low Earth orbit (LEO) small-satellite constellations have recently become attractive because of their advantages, such as a significant reduction in system cost, an increase in communication volume, and a reduction in latency. Therefore, in this study, the spatial geometry of a LEO constellation is designed for Iran to increase the required regional navigation performance. For this purpose, the optimal constellation configuration is obtained through a multi-objective genetic algorithm (MOGA) utilizing a cost function with a combination of the geometry dilution of precision (GDOP), the number of satellites, and orbital height in the form of a design procedure. Moreover, reducing the feasible region of longitude of the ascending nodes of orbit planes is applied in the design process to reduce the search space. The simulation results indicate the constellation designed performance.

LEO enhanced Global Navigation Satellite System (LeGNSS) for real-time precise positioning services

Global Navigation Satellite System (GNSS) has been widely used in many geosciences areas with its Positioning, Navigation and Timing (PNT) service. However, GNSS still has its own bottleneck, such as the long initialization period of Precise Point Positioning (PPP) without dense reference network. Recently, the concept of PNTRC (Positioning, Navigation, Timing, Remote sensing and Communication) has been put forward, where Low Earth Orbit (LEO) satellite constellations are recruited to fulfill diverse missions. In navigation aspect, a number of selected LEO satellites can be equipped with a transmitter to transmit similar navigation signals to ground users, so that they can serve as GNSS satellites but with much faster geometric change to enhance GNSS capability, which is named as LEO constellation enhanced GNSS (LeGNSS). As a result, the initialization time of PPP is expected to be shortened to the level of a few minutes or even seconds depending on the number of the LEO satellites involved. In this article, we simulate all the relevant data from June 8th to 14th, 2014 and investigate the feasibility of LeGNSS with the concentration on the key issues in the whole data processing for providing real-time PPP service based on a system configuration with fourteen satellites of BeiDou Navigation Satellite System (BDS), twenty-four satellites of the Global Positioning System (GPS), and sixty-six satellites of the Iridium satellite constellations. At the server-end, Precise Orbit Determination (POD) and Precise Clock Estimation (PCE) with various operational modes are investigated using simulated observations. It is found out that GNSS POD with partial LEO satellites is the most practical mode of LeGNSS operation. At the user-end, the Geometry Dilution Of Precision (GDOP) and Signal-In-Space Ranging Error (SISRE) are calculated and assessed for different positioning schemes in order to demonstrate the performance of LeGNSS. Centimeter level SISRE can be achieved for LeGNSS.

Initial Assessment of Precise Point Positioning with LEO Enhanced Global Navigation Satellite Systems (LeGNSS)

The main challenge of precise point positioning (PPP) applications is the long convergence time of typically a half hour, or even more, to achieve centimeter accuracy. Even when the multi-constellation is involved and ambiguity resolution is implemented, it still requires about ten minutes. It is becoming a hot spot to incorporate the low Earth orbit (LEO) satellite constellation for enhancing the Global Navigation Satellite System (GNSS), named here as LEO-enhanced GNSS (LeGNSS). In this system, the LEO satellites cannot only receive GNSS signals, but also serve as GNSS satellites by transmitting similar navigation signals to the ground users, but with higher signal strength and much faster geometric change due to their low altitude. As a result, the convergence time of PPP is expected to be shortened to a few minutes, or even seconds. Simulation software is developed to simulate GNSS and LEO observations for ground stations taking into account tropospheric delay, satellite clock errors, observation noises, as well as other error sources. Then the number of visible satellites, the geometry dilution of precision (GDOP), and the convergence time of the kinematic mode of PPP are evaluated on a global scale compared to those of GNSS systems. The simulation results show that LeGNSS can decrease the PPP convergence to 5 min. If there are more LEO satellites included in the LeGNSS, it is expected that the initialization of PPP can be further shortened.

TDOA Measurement Based GDOP Analysis for Radio Source Localization

The revolution brought by GPS has lead to the development of various positioning applications. These applications use measurements (travel time of signal or time of flight) in determining the position. The time of flight requirement in GPS has restricted its use in positioning of unknown objects. Whereas, localization of an unknown enemy Radio Source (URS) such as enemy radar system, tracking of Unmanned Aerial Vehicle (UAV) etc., have high demand in the field of defence in a country like India, they require a new type of measurement technique called Time difference of Arrival (TDOA). There are various factors that affect the position accuracy including amount of measurement noise, algorithm employed for positioning and sensor URS geometry. The sensor-URS geometry is one of the most predominant factors in determining the accuracy estimate and is referred to as Geometry Dilution of Precision (GDOP). This is a well defined problem in positioning systems that use GPS/Time of arrival (TOA) measurements. However, it needs to be refined for URS localization systems/TDOA measurements. This paper mainly focuses on explaining and deriving the concepts of GDOP in relation to TDOA measurement based URS localization systems. For a comprehensive understanding, an illustrative example of localizing an URS with TDOA measurements is explained and discusses the effect of sensor geometry with the help of GDOP profiles. In addition, this paper explains the process of identifying an optimal sensor configuration for URS localization systems. For the purpose of simulation, five sensors arranged in two different configurations are considered. A target surveillance area of 3600 Sq-Kms with 169 target zones is used in generation of GDOP profiles over the Indian subcontinent.

The Training Method of General Regression Neural Network for GDOP Approximation

Aimed at the problem of real-time and accurate Geometry Dilution of Precision (GDOP) approximation, a new method using general regression neural network (GRNN) was proposed firstly, and the training samples selection and normalization method was studied by using spectrum analysis. The computation results show that the symmetrical constellation needs 24 hours continuous samples while the hybrid one needs 72 hours to train the neural network sufficiently. Finally, the performance analysis shows that this new method has excellent performance on temporal and spatial generalization approximation accuracy, when trained GRNN are used, the GDOP computational error is less than 0.25 within 30 days, and the error is less than 0.3 within 10 degrees latitude/longitude area.

Neural network-based GPS GDOP approximation and classification

In this paper, the neural network (NN)-based navigation satellite subset selection is presented. The approach is based on approximation or classification of the satellite geometry dilution of precision (GDOP) factors utilizing the NN approach. Without matrix inversion required, the NN-based approach is capable of evaluating all subsets of satellites and hence reduces the computational burden. This would enable the use of a high-integrity navigation solution without the delay required for many matrix inversions. For overcoming the problem of slow learning in the BPNN, three other NNs that feature very fast learning speed, including the optimal interpolative (OI) Net, probabilistic neural network (PNN) and general regression neural network (GRNN), are employed. The network performance and computational expense on NN-based GDOP approximation and classification are explored. All the networks are able to provide sufficiently good accuracy, given enough time (for BPNN) or enough training data (for the other three networks).

Neural Network-Based Geometry Classification for Navigation Satellite Selection

The neural networks (NN)-based geometry classification for good or acceptable navigation satellite subset selection is presented. The approach is based on classifying the values of satellite Geometry Dilution of Precision (GDOP) utilizing the classification-type NNs. Unlike some of the NNs that approximate the function, such as the back-propagation neural network (BPNN), the NNs here are employed as classifiers. Although BPNN can also be employed as a classifier, it takes a long training time. Two other methods that feature a fast learning speed will be implemented, including Optimal Interpolative (OI) Net and Probabilistic Neural Network (PNN). Simulation results from these three neural networks are presented. The classification performance and computational expense of neural network-based GDOP classification are explored.