Fault-tolerant training for optimal interpolative nets

IntroductionThe geometric dilution of precision (GDOP) is a geometrically determined factor that describes the effect of geometry on the relationship between measurement error and position error. It is used to provide an indication of the quality of the solution. Some of the GPS receivers may not be able to process all visible satellites due to limited number of channels. Consequently, it is sometimes necessary to select the satellite subset that offers the optimal or acceptable solutions. The optimal satellite subset is sometimes obtained by minimizing the GDOP factor.The most straightforward approach for obtaining GDOP is to use matrix inversion to all combinations and select the minimum one. However, the matrix inversion by computer presents a computational burden to the navigation computer. For the case of processing four satellite signals, it has been shown that GDOP is approximately inversely proportional to the volume of the tetrahedron formed by four satellites (Kihara and Okada 1984;Stein 1985). Therefore, it is optimum to select satellite such that the volume is as large as possible, which is sometimes called the maximum volume method. However, it is not universal acceptable since it does not guarantee optimum selection of satellites.The neural network (NN) approach provides a promising and very realistic computational alternative. The application of NN approach for navigation solution processing has not been widely explored yet in the GPS community. Simon and El-Sherief (1995a) initially proposed the NN approach to approximate and classify the GDOP factors for the benefit of computational efficiency, where it could be seen that a total of 160 floating Abstract 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).

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“…Further discussion on OI Net can be seen in Defigueiredo (1990), Sin and Defigueiredo (1992), and Simon and El-Sherief (1995b).…”

Section: Neural Network For Approximation and Classificationmentioning

confidence: 99%

Neural network-based GPS GDOP approximation and classification

Jwo

Lai

2006

GPS Solut

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“…The efficient recursive learning formulation presented in [20] makes the 01 Net an attractive architecture. In addition, fault tolerance can be implemented in 01 Net training in a straightforward manner [17,18].…”

Section: Neural-network Based Classificationmentioning

confidence: 99%

Navigation satellite selection using neural networks

Simon¹,

El-Sherief²

1995

Neurocomputing

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The application of neural networks to optimal satellite subset selection for navigation use is discussed. The methods presented in this paper are general enough to be applicable regardless of how many satellite signals are being processed by the receiver. The optimal satellite subset is chosen by minimizing a quantity known as Geometric Dilution of Precision (GOOP), which is given by the trace of the inverse of the measurement matrix. Ari artificial neural network learns the functional relationships between the entries of a measurement matrix and the eigenvalues of its inverse, and thus generates GDOP without inverting a matrix.. Simulation results are given, and the computationaJ benefit of neural network-based satellite selection is discussed.

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“…Researchers have employed the conventional BPNN to estimate GDOP; see, for example, [19,20,22]. This can reduce the computational complexity required to compute the matrix inversion in calculating GDOP.…”

Section: Proposed Network Architectures For Wgdop Approximationmentioning

confidence: 99%

“…Simon and El-Sherief [19,20] employed backpropagation neural network (BPNN), a supervised learning neural network [21], to obtain an approximation to the GDOP function. The BPNN was employed to "learn" the relationship between the entries of a measurement matrix and the eigenvalues of its inverse.…”

Section: Introductionmentioning

confidence: 99%

Neural Network for WGDOP Approximation and Mobile Location

Chen

Lin

Lee

2013

Mathematical Problems in Engineering

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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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Fault-tolerant training for optimal interpolative nets

Cited by 29 publications

References 7 publications

Neural network-based GPS GDOP approximation and classification

Neural network-based GPS GDOP approximation and classification

Navigation satellite selection using neural networks

Neural Network for WGDOP Approximation and Mobile Location

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