The Minimum of GDOP for Satellite Navigation System

Code phase GNSS receivers convert the measured satellite pseudoranges into estimates of the position and clock offset of the receiver, typically via an iterative, linearized least squares method. Since the pseudoranges themselves are noisy, the resulting estimates of position and time are random variables. To describe the accuracy of this solution, it is common to describe it statistically via the error covariance matrix. Rather than considering the individual elements of this covariance matrix, users frequently reduce it to a scalar performance indicator; the most common of these is the Geometric Dilution of Precision (GDOP). It is well known that the GDOP is a function of the satellite geometry; with only a few visible satellites in poor locations, the GDOP can become quite large. However, for a future with multiple, fully occupied GNSS constellations it is expected that receivers would select those satellites to track so as to achieve the best possible performance. Hence, an understanding of both how small the GDOP can be as a function of the number of satellites visible and the characteristics of the constellations that meet that bound are of value. Further, once identified, a receiver could exploit those constellation characteristics in selecting a subset of satellites. Investigating the best possible GNSS satellite constellation with respect to the GDOP is not a new problem. Recently, these authors developed achievable lower bounds to the GDOP as a function of the number of satellites; the bounds were also extended to non-zero mask angle and to multiple GNSS constellations. Further, using actual GPS satellite ephemeris data, it was shown by example that good GDOP performance resulted from constellations similar to the “best” constellations resulting from the bounds. This paper examines augmentation of the GNSS pseudoragnes with data from non-GNSS sensors; specifically, ranges. While integration of GNSS and non-GNSS sensors is not novel, the perspective in the paper is how such external sensors impact potential receiver performance (i.e. minimum GDOP) and what role they play in satellite selection. Specifically, tight lower bounds to GDOP when the GNSS is augmented by this additional measurement (barometric altimeter or a DME slant range) are presented; achievability of the bounds is also examined.

Global Positioning System (GPS) satellites signal processing to obtain all in view satellite measurements and to use them to find a solution and to do integrity monitoring forms a major component of the load on the receiver's processing element. If processing capability is limited there is restriction on the number of measurements which can be obtained and processed. Alternatively, the number of measurements can be restricted and the resulting saving in load on the processor can be used to offer more spare processing time which can be used for other user specific requirements. Thus if m visible satellites can provide measurements only n measurements can be used (n < m). The arrangement and the number of GPS satellites influence measurement accuracy. Dilution of Precision (DOP) is an index evaluating the arrangement of satellites. Geometric DOP (GDOP) is, in effect, the amplification factor of pseudo-range measurement errors into user errors due to the effect of satellite geometry. The GDOP approximation is an essential feature in determining the performance of a positioning system. In this paper, knowledge-based methods such as neural networks and evolutionary adaptive filters are presented for optimum approximation of GDOP. Without matrix inversion required, the knowledge-based approaches are capable of evaluating all subsets of satellites and hence reduce the computational burden. This would enable the use of a high-integrity navigation solution without the delay required for many matrix inversions. Models validity is verified with test data. The results are highly effective techniques for GDOP approximation.

The number of visible satellites has significantly increased, which provides a possibility for high-precision positioning of global navigation satellite systems (GNSSs). However, GNSS receivers with higher computing power will be required owing to the usage of a large number of visible satellites, and selection of partial satellites with better spatial geometry is required for obtaining high positioning precision schemes for a variety of applications. The geometric dilution of precision (GDOP) is related to the geometrical arrangement of the user and the satellites and computationally intensive, involving matrix multiplication and inversion operations. Various intelligent algorithms for satellite selection have been suggested recently, such as genetic algorithms (GAs). the computation number of GDOP was reduced, owing to the adoption and optimization of these algorithms. However, the algorithms suffer from two issues: 1) the computation process is complex, and significant parametric tuning is required. 2) the algorithms may fall into local optima, instead of the global optimum, owing to the stochasticity of the optimization process. In the paper, we have proposed a novel algorithm for satellite selection, based on chaotic particle swarm optimization (CPSO), which has the advantages of faster convergence, a smaller number of adjustable parameters, and stronger adaptability, compared with the existing algorithms. Firstly, the visible satellites received by the GNSS receiver are continuously encoded and randomly grouped, form the initial population. Afterward, the positions of the particles are updated by the PSO’s velocitydisplacement model. Finally, the CPSO-based algorithm for selection of satellites is designed to replace poor-performing particles with particles in the initial population, which helps to effectively avoid sub-optimal solutions. The proposed algorithm was compared with the traversal method. The simulation results demonstrated that if more than five satellites are selected, the satellite selection time amounts to 37.5% of the time required by the traversal method, and the GDOP error is in the 0.7 range. The proposed algorithm was further validated on the BDS/GPS integrated navigation satellite selection, suggesting the effectiveness of the application in the multiple GNSSs integrated navigation.

A binary discrete particle swarm optimization satellite selection algorithm with a queen informant for Multi-GNSS continuous positioning

PDOP parameters improvement using multi-GNSS and signal re-transmission at lunar distances

Global and regional satellite navigation systems are constellations orbiting the Earth and transmitting radio signals for determining position and velocity of users around the globe. The state-of-the-art navigation satellite systems are located in medium Earth orbits and geosynchronous Earth orbits and are characterized by high launching, building and maintenance costs. For applications that require only regional coverage, the continuous and global coverage that existing systems provide may be unnecessary. Thus, a nano-satellites-based regional navigation satellite system in Low Earth Orbit (LEO), with significantly reduced launching, building and maintenance costs, can be considered. Thus, this paper is aimed at developing a LEO constellation optimization and design method, using genetic algorithms and gradient-based optimization. The preliminary results of this study include 268 LEO constellations, aimed at regional navigation in an approximately 1000 km $$\times $$ 1000 km area centered at the geographic coordinates [30, 30] degrees. The constellations performance is examined using simulations, and the figures of merit include total coverage time, revisit time, and geometric dilution of precision (GDOP) percentiles. The GDOP is a quantity that determines the positioning solution accuracy and solely depends on the spatial geometry of the satellites. Whereas the optimization method takes into account only the Earth’s second zonal harmonic coefficient, the simulations include the Earth’s gravitational field with zonal and tesseral harmonics up to degree 10 and order 10, Solar radiation pressure, drag, and the lunisolar gravitational perturbation.

The navigation performance of Iridium satellite is simulated and analyzed based on STK from two aspects—the number of visible satellites and geometric dilution of precision (GDOP). Meanwhile we compare it with GPS and GALILEO system to demonstrate its performance. Experiment shows that the Iridium satellite system has a good coverage merit at two poles, which is even better than that of GPS and GALILEO. However, its global coverage is unstable and GDOP changes sharply from high latitude area to low latitude area which means Iridium satellite cannot orientate or navigate around the equator well. Then we explore the application fields of the Iridium satellite system.

Multi-constellation integrated navigation receiver will increase the number of visible satellites and improve positioning accuracy of the receiver. If all-in-view satellites are used for receiver positioning, the computational burden of the receiver will be increased. The traditional satellite selection algorithm is traversal algorithm; however, as the number of visible satellites increases, the traversal algorithm exists huge computation. In order to the problem, the improved particle swarm optimization (PSO) is given for satellite selection, in the proposed algorithm, each satellite subset is considered a particle without mass in search space, and the selected objective function is the geometric dilution of precision (GDOP). Particles update their position based on the proposed algorithm model. Moreover, the optimal satellite subset and the corresponding GDOP value are obtained. The performance of the algorithms is compared based on real navigation data. The simulation results show that proposed algorithm can improve satellite selection speed, and the satellite selection accuracy is better than that of the basic PSO satellite selection algorithm.

Satellite Radio Navigation System (SRNS) is a satellite navigation system which provides autonomous geo-spatial positioning with global coverage. Among the several SRNS available across the world, one among them is Navigation with Indian Constellation (NavIC) developed and operated by ISRO. The performance evaluation of this new Indian system is very much needed. Hence, this work discusses about the performance accuracy. In this paper, NavIC receiver position parameters evaluated i.e 2DRMS, 3DRMS CEP, SEP, and Geometric Dilution of Precision (GDOP) for NavIC System. The quiet day (18-06-2019) and disturbed day (14-06-2019) are considered for the analysis over the Hyderabad station, India(17.40°N, 78.51° E). The real time NavIC data is acquired for ISRO IGS receiver. The NavIC receiver is operated in Hybrid mode(L5 and S1).The results obtained from this study indicate that for Hybrid mode of operation) position values are better for quiet day than that of the disturbed day.

In order to improve the accuracy and engineering feasibility of four-Satellite localization system, the frequency difference measurement is introduced to the four-Satellite TDOA (Time Difference of Arrival) localization algorithm. The TDOA/FDOA (Frequency Difference of Arrival) localization algorithm is used to optimize the GDOP (geometric dilution of precision) of four-Satellite localization. The simulation results show that the absolute position measurement accuracy has little influence on TDOA/FDOA localization accuracy as compared with TDOA localization. Under the same conditions, TDOA/FDOA localization has better accuracy and its GDOP shows more uniform distribution in diamond configuration case. The localization accuracy of four-Satellite TDOA/FDOA is better than the localization accuracy of four-Satellite TDOA.

The paper discusses the functionality of the Satellite Navigation Equipment (SNE) for the advanced Crew Transportation Spacecraft (CTS) Federatsiya, algorithms for determining its attitude exclusively from measurements of a global satellite navigation system without using any additional navigational or gyroscopic devices. It proposes methods for determining the attitude with successive increases in accuracy, providing attitude determination in minimal time: — the method based on the filling of fields of view of the antennae with signals from navigation satellites, which provides a rough determination of the attitude to within 20–30° over a period of 2 to 3 seconds; — the method based on phase increments, which provides attitude determination to within 2–3° over a period of 50 to 100 seconds; — the method based on phase measurements, which provides continuous attitude determination to within −0,5° in 10 seconds after the mode is started. The paper defines the solvability criterion for the attitude problem, introduces the notion of Attitude Dilution of Precision (ADOP) and provides its rigorous definition by analogy with the standard notion of Geometric Dilution of Precision (GDOP) in the navigation problem. The paper compares the performance of an SNE, which fulfils the functions of a Strapdown Inertial Navigation System (SINS) with the performance of a conventional SINS built around various gyroscopic devices.

The position and attitude information obtained by the position and orientation system (POS) are defined by using the navigation coordinate system, but the actual production application is generally carried out under the map projection frame. Therefore, it is necessary to transform POS data into the map projection frame before it is applied in practice. Considering the complexity of the existing algorithms, and the geocentric coordinate systems that are currently widely used, such as WGS84 and CGCS2000, this letter proposes a simplified transformation method (ST-method) for the POS attitude transformation. It is obviously different from the classical Legat's method which is widely used at present. The algorithm in this letter can be called one-step transformation method, in which the geocentric coordinate system and the local tangent plane coordinate system are not involved. The conversion process has been deeply analyzed and the conversion formula is deduced, directly from navigation coordinate system to projection coordinate system. Compared with the classical methods, the most important contribution of this letter is to simplify the conversion process, and the experimental results show that the proposed method can achieve the same effect as the existing methods with no loss of accuracy.

Geometric Dilution Of Precision (GDOP) is a factor that describes the effect of geometry on the relationship between measurement error and position determination error. It is used to provide an indication of the quality of the solution. Conventional closed-form GDOP calculation formula applied to all possible combinations of visible satellites is rather time consuming, especially as the number of satellites grows. Approximations, such as the maximum volume method, are faster but optimum selection is not guaranteed. In this paper, a more concise but efficient solution for the calculation of GDOP value in the case of four Global Positioning System (GPS) satellites is firstly reviewed and then extended to cover the other forms of dilution of precision (DOP) values, including vertical DOP (VDOP) and horizontal DOP (HDOP). Secondly, a review and extension of the conventional solution is performed in the case of three GPS satellites aided by an altimeter. Based on the ideas gained from these two approaches, a simpler closed-form DOP formula for three GPS satellites aided by an altimeter is derived. The advantage of the proposed formulation is that it is simpler and thus reduces the computational load in comparison to the conventional one.

This paper presents a model to predict the GDOP value (Geometric Dilution of Precision) and the probability of its occurrence at a point in space and time using airborne LiDAR (Light Detection and Ranging) data and the ultra-rapid product (URP) available from the International GPS Service. LiDAR data help to classify the terrain around a GPS (Global Positioning System) receiver into categories such as ground, opaque objects, translucent objects and transparent regions as per their response to the transmission of GPS signal. Through field experiments it is established that URP can be used satisfactorily to determine GDOP. Further experiments have shown that the translucent objects (mainly trees here) lower the GDOP quality as they obstruct the GPS signal. LiDAR data density on trees is used as a measure of the translucency of trees to the GPS signal. Through GPS observations taken in field a relationship has been established between LiDAR data density on trees and the probability that a satellite which is behind the tree is visible at the GPS receiver. A model is presented which, for all possible combinations of visible satellites, computes the GDOP value along with the probability of occurrence of this GDOP. A few results are presented to show the performance of the model developed and its possible application in location based queries.

An estimation fusion algorithm based on a group of hybrid coordinate (HC) filters is presented to the position and velocity estimation using angle-only measurements extracted from multiple maneuverable aircrafts with onboard passive sensor. The algorithm is a hierarchical architecture which consists of several local processors and a global processor. In each local processor, an extended Kalman (EK) filter utilizes the reference Cartesian coordinate (RCC) system for state and state covariance extrapolation and utilizes the modified spherical coordinate (MSC) system for state and state covariance updating. In the global processor, a recursive least squares (RLS) estimator sequentially computes a global estimate in the local inertial Cartesian coordinate (LICC) system. The estimator is developed by utilizing RCC updated state covariance to compute each filter weight for combining the outputs of local processors. The typical case of target motion analysis is investigated through computer simulation. In simulation study the proposed algorithm is compared to each HC EK filter. The EK filter encounters slow convergence problem under both circular arc and waving flight scenarios. By using a RLS estimator, the convergence is greatly accelerated. The algorithm markedly improves the tracking accuracy as well.