Geometric Dilution Of Precision Calculation Research Articles

Weighted geometric dilution of precision calculations with matrix multiplication.

To enhance the performance of location estimation in wireless positioning systems, the geometric dilution of precision (GDOP) is widely used as a criterion for selecting measurement units. Since GDOP represents the geometric effect on the relationship between measurement error and positioning determination error, the smallest GDOP of the measurement unit subset is usually chosen for positioning. The conventional GDOP calculation using matrix inversion method requires many operations. Because more and more measurement units can be chosen nowadays, an efficient calculation should be designed to decrease the complexity. Since the performance of each measurement unit is different, the weighted GDOP (WGDOP), instead of GDOP, is used to select the measurement units to improve the accuracy of location. To calculate WGDOP effectively and efficiently, the closed-form solution for WGDOP calculation is proposed when more than four measurements are available. In this paper, an efficient WGDOP calculation method applying matrix multiplication that is easy for hardware implementation is proposed. In addition, the proposed method can be used when more than exactly four measurements are available. Even when using all-in-view method for positioning, the proposed method still can reduce the computational overhead. The proposed WGDOP methods with less computation are compatible with global positioning system (GPS), wireless sensor networks (WSN) and cellular communication systems.

Rapid and Precise GLONASS GDOP Approximation using Neural Networks

Russian global navigation satellite system (GLONASS) provides civilian and military users three-dimensional position determination and navigation services as same as US global positioning system. Geometric dilution of precision (GDOP) provides a simple interpretation of positioning precision. Usual method for GLONASS GDOP calculation is matrix inversion. However this process imposes a huge calculation load on receiver, especially when large number of visible satellites exists. To overcome this problem, artificial neural network is used. Different configurations and training methods are simulated on a data base obtained by a GLONASS receiver. Then navigation precision and execution times are explored and compared. Results show that recurrent neural network has 0.00024 RMS error, which is the best against other focused tools including feed forward back propagation and radial basis function neural network with usual training and with genetic algorithm adopted weights and biases.

Calculation of Weighted 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.

Dilution of Position Calculation for MS Location Improvement in Wireless Communication Systems

Geometric dilution of precision (GDOP) represents the geometric effect of base stations (BSs) and mobile station (MS) on the relationship between measurement error and positioning determination error. When the measurement variances are equal to each other, GDOP could be the most appropriate selection criterion of location measurement units. GDOP expression has simpler form if all the measurements are with the same variance. For time of arrival (TOA) schemes, the maximum volume method of GDOP calculation doesn’t guarantee the optimal selection of the four measurement units. The conventional method for calculating GDOP is to use matrix inversion to all subsets. GDOP was originally used as a criterion for selecting the right 3D geometric configuration of satellites in global positioning systems (GPS). In this paper, we employ GDOP using the matrix inversion method to select appropriate BSs in cellular communication systems. The proposed BS selection criterion performs better than using the random subsets of four or five BSs chosen from all seven BSs. After BS selection, the proposed distance-weighted method and threshold method for TOA schemes can yield superior MS location estimation accuracy. For time difference of arrival (TDOA) schemes, the proposed BS selection criterion provides better MS location estimation. From simulation results, the performances of MS location strongly depend on the relative position of the MS and BSs. Therefore, it is very important to select a subset with the most appropriate BSs rapidly and reasonably for positioning.

A Study on GPS GDOP Approximation Using Support-Vector Machines

Global Positioning System (GPS) has extensively been used in various fields. Geometric Dilution of Precision (GDOP) is an indicator showing how well the constellation of GPS satellites is geometrically organized. GPS positioning with a low GDOP value usually gains better accuracy. However, the calculation of GDOP is a time- and power-consuming task that involves complicated transformation and inversion of measurement matrices. When selecting from many GPS constellations the one with the lowest GDOP for positioning, methods that can fast and accurately obtain GPS GDOP are imperative. Previous studies have shown that numerical regression on GPS GDOP can get satisfactory results and save many calculation steps. This paper deals with the approximation of GPS GDOP using statistics and machine learning methods. The technique of support vector machines (SVMs) is mainly focused. This study compares the performance of several methods, such as linear regression, pace regression, isotonic regression, SVM, artificial neural networks, and genetic programming (GP). The experimental results show that SVM and GP have better performance than others.