scholarly journals A Geometric Layout Method for Synchronous Pseudolite Positioning Systems Based on a New Weighted HDOP

2021 ◽  
Vol 10 (9) ◽  
pp. 601
Author(s):  
Xinyang Zhao ◽  
Qiangqiang Shuai ◽  
Guangchen Li ◽  
Fangzhou Lu ◽  
Bocheng Zhu
Keyword(s):  
Indoor Environment ◽  
Simulated Annealing Algorithm ◽  
Time Synchronization ◽  
Simple Calculation ◽  
Positioning Systems ◽  
Dilution Of Precision ◽  
The Monte Carlo Method ◽  
Connection System ◽  
Geometric Dilution Of Precision ◽  
Geometric Layout

The positioning accuracy of a ground-based system in an indoor environment is closely related to the geometric configuration of pseudolites. This paper presents a simple closed-form equation for computing the weighted horizontal dilution of precision (WHDOP) with four eigenvalues, which can reduce the amount of calculation. By comparing the result of WHDOP with traditional matrix inversion operation, the effectiveness of WHDOP of the proposed simple calculation method is analyzed. The proposed WHDOP has a linear relationship with the actual static positioning result error in an indoor environment proved by the Pearson analysis method. Twenty positioning points are randomly selected, and the positioning variance and WHDOP of each positioning point have been calculated. The correlation coefficient of WHDOP and the positioning variance is calculated to be 0.82. A pseudolite system layout method based on a simulated annealing algorithm is proposed by using WHDOP, instead of Geometric dilution of precision (GDOP). In this paper, the constraints of time synchronization are discussed. In wireless connection system, the distance between master station and slave station should be kept within a certain range. Specifically, for a given indoor scene, many positioning target points are randomly generated in this area by using the Monte Carlo method. The mean WHDOP value of all positioning points corresponding to the synchronous pseudolite layout is used as the objective function. The results of brute force search are compared with the method, which proves the accuracy of the new algorithm.

scholarly journals Calculation of Weighted Geometric Dilution of Precision

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Chien-Sheng Chen ◽  
Yi-Jen Chiu ◽  
Chin-Tan Lee ◽  
Jium-Ming Lin
Keyword(s):  
Communication Systems ◽  
Approximation Error ◽  
Matrix Inversion ◽  
Location Estimation ◽  
Inversion Method ◽  
Error Statistics ◽  
Positioning Systems ◽  
Dilution Of Precision ◽  
Measurement Units ◽  
Geometric Dilution Of Precision

To achieve high accuracy in wireless positioning systems, both accurate measurements and good geometric relationship between the mobile device and the measurement units are required. Geometric dilution of precision (GDOP) is widely used as a criterion for selecting measurement units, since it represents the geometric effect on the relationship between measurement error and positioning determination error. In the calculation of GDOP value, the maximum volume method does not necessarily guarantee the selection of the optimal four measurement units with minimum GDOP. The conventional matrix inversion method for GDOP calculation demands a large amount of operation and causes high power consumption. To select the subset of the most appropriate location measurement units which give the minimum positioning error, we need to consider not only the GDOP effect but also the error statistics property. In this paper, we employ the weighted GDOP (WGDOP), instead of GDOP, to select measurement units so as to improve the accuracy of location. The handheld global positioning system (GPS) devices and mobile phones with GPS chips can merely provide limited calculation ability and power capacity. Therefore, it is very imperative to obtain WGDOP accurately and efficiently. This paper proposed two formations of WGDOP with less computation when four measurements are available for location purposes. The proposed formulae can reduce the computational complexity required for computing the matrix inversion. The simpler WGDOP formulae for both the 2D and the 3D location estimation, without inverting a matrix, can be applied not only to GPS but also to wireless sensor networks (WSN) and cellular communication systems. Furthermore, the proposed formulae are able to provide precise solution of WGDOP calculation without incurring any approximation error.

scholarly journals GEOMETRIC DILUTION OF PRECISION OF THE GNSS FOR MARS (GNSS FATIMA)

Aviation ◽  
2016 ◽  
Vol 20 (4) ◽  
pp. 183-190
Author(s):  
Jozef KOZAR ◽  
Stanislav DURCO ◽  
Frantisek ADAMCIK
Keyword(s):  
Satellite System ◽  
Navigation Satellite ◽  
Positioning Systems ◽  
Dilution Of Precision ◽  
Positioning Errors ◽  
Factors Influencing ◽  
Main Factors ◽  
Geometric Dilution Of Precision ◽  
Global Navigation Satellite ◽  
Critical Aspects

Positioning on Mars is one of the critical aspects of every planetary mission. Current complex planetary exploration systems (orbital and surface) rely on complex navigation and positioning systems, which make these systems complicated, expensive and their missions dangerous. The project of the global navigation satellite system for Mars (proposed system name – FATIMA) can make this and even future manned missions more safe, less expensive and the whole positioning in real time more reliable. The GNSS can be used by more systems or users simultaneously. In this research paper we focus on possible positioning errors when such a system is used. This research is focused on the GDOP – Geometric Dilution of Precision as one of the main factors influencing the GNSS.

scholarly journals Uncertainty Analysis of Mixing Efficiency Variation in Passive Micromixers due to Geometric Tolerances

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Irina Stanciu
Keyword(s):  
Simulation Model ◽  
Numerical Study ◽  
Geometric Parameters ◽  
Mixing Efficiency ◽  
Mixing Performance ◽  
Probabilistic Simulation ◽  
Geometric Tolerances ◽  
The Monte Carlo Method ◽  
Key Factor ◽  
Geometric Layout

The geometric layout is the key factor for enhancing the efficiency of the fluid mixing in passive micromixers. Therefore, by adjusting the geometric design and by controlling the geometric parameters, one can enhance the mixing process. However, through any fabrication process, the geometric parameters present slight, inherent variation from the designed values than might affect the performance of the micromixer. This paper proposes a numerical study on the influence of the unavoidable geometric tolerances on the mixing efficiency in passive micromixers. A probabilistic simulation model, based on the Monte Carlo method, is developed and implemented for this purpose. An uncertainty simulation model shows that significant deviations from the deterministic design can appear due to small variations in the geometric parameters values and demonstrates how a more realistic mixing performance can be estimated.

Unbiased Nonlinear Least Squares Estimations of Short-distance Equations

2017 ◽  
Vol 70 (4) ◽  
pp. 810-828 ◽  
Author(s):  
Shuqiang Xue ◽  
Yuanxi Yang
Keyword(s):  
Least Squares ◽  
Short Distance ◽  
Iterative Procedure ◽  
Nonlinear Least Squares ◽  
Long Distance ◽  
Geometrical Condition ◽  
Least Squares Solution ◽  
The Monte Carlo Method ◽  
Linearization Error ◽  
Geometric Dilution Of Precision

Nonlinear least squares estimations have been widely applied in positioning. However, nonlinear least squares estimations are generally biased. As the Gauss-Newton method has been widely applied to obtain a nonlinear least squares solution, we propose an iterative procedure for obtaining unbiased estimations with this method. The characteristics of the linearization error are discussed and a systematic error source of the linearization error needs to be removed to guarantee the unbiasedness. Both the geometrical condition and the statistical condition for unbiased nonlinear least squares estimations are revealed. It is shown that for long-distance observations of high precision, or for a positioning configuration with the lowest Geometric Dilution Of Precision (GDOP), the nonlinear least squares estimations tend to be unbiased; but for short-distance cases, the bias in the nonlinear least squares solution should be estimated to obtain unbiased values by removing the bias from the nonlinear least squares solution. The proposed results are verified by the Monte Carlo method and this shows that the bias in nonlinear least squares solution of short-distance distances cannot be ignored.

Research on Maneuvering Trajectories Optimization in Bearings-Only Localization for Single Observer

2012 ◽  
Vol 433-440 ◽  
pp. 5946-5950 ◽  
Author(s):  
Zhang Song Shi ◽  
Rui Li ◽  
Hang Yu Wang
Keyword(s):  
Genetic Algorithm ◽  
Lower Bound ◽  
Performance Index ◽  
Constant Velocity ◽  
Dilution Of Precision ◽  
Localization Precision ◽  
Course Sequence ◽  
Geometric Dilution Of Precision

Based on Crammer-Rao Lower Bound (CRLB), this paper adopts Geometric Dilution of Precision (GDOP) as the optimizing performance index to analyze the localization precision in Bearing-only localization for single observer. And the genetic algorithm is employed to calculate the optimal course sequence. The movement straight with constant velocity and movement with constant prefix angles are analyzed. Simulations show that maneuvering trajectory is propitious to improve localization precision.

scholarly journals Neural Network for WGDOP Approximation and Mobile Location

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Chien-Sheng Chen ◽  
Jium-Ming Lin ◽  
Chin-Tan Lee
Keyword(s):  
Neural Network ◽  
Communication Systems ◽  
Learning Algorithm ◽  
Location Estimation ◽  
Estimation Accuracy ◽  
Neural Network Learning ◽  
Mobile Location ◽  
Positioning Systems ◽  
Geometric Dilution Of Precision ◽  
Location Methods

This paper considers location methods that are applicable in global positioning systems (GPS), wireless sensor networks (WSN), and cellular communication systems. The approach is to employ the resilient backpropagation (Rprop), an artificial neural network learning algorithm, to compute weighted geometric dilution of precision (WGDOP), which represents the geometric effect on the relationship between measurement error and positioning error. The original four kinds of input-output mapping based on BPNN for GDOP calculation are extended to WGDOP based on Rprop. In addition, we propose two novel Rprop–based architectures to approximate WGDOP. To further reduce the complexity of our approach, the first is to select the serving BS and then combines it with three other measurements to estimate MS location. As such, the number of subsets is reduced greatly without compromising the location estimation accuracy. We further employed another Rprop that takes the higher precision MS locations of the first several minimum WGDOPs as the inputs into consideration to determine the final MS location estimation. This method can not only eliminate the poor geometry effects but also significantly improve the location accuracy.

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