Performance Enhancement of GPS based Line Fault Location Using Radial Basis Function Neural NetworkThere are generally two kinds of approaches for nonlinear time series analysis and prediction. Statisticians usually invoke stochastic approaches while physicists often concentrate on deterministic approaches. Real world time series may be comprised of a low dimensional attractor (deterministic part of the time series) and high dimensional noise (stochastic part of the time series). By building an appropriate model, it is possible to predict the short time future of the deterministic part of chaotic and other nonlinear time series. The ability of such a prediction depends on the noise level, complexity of the deterministic dynamics, the amount of data available, and the flexibility of the model selected. Radial Basis Function (RBF) approximation is a global interpolation technique with good localization properties. It provides a smooth interpolation of scattered data in arbitrary dimension [9]. In this paper, a RBF NN for GPS receivers timing errors modeling and prediction is presented. A three layers RBF NN and its training algorithm in order to this purpose is proposed. The model validity is verified with experimental data from an actual data collection using a low cost GPS engine. The experimental results by using the practical implementations are provided to illustrate the effectiveness of the model. This paper is organized in the following sections. Section II presents principle of GPS traveling wave fault locators. Section III describes GPS timing errors modeling using proposed RBF NN. The experimental results are reported in section IV. Conclusions are provided in section V. II. Traveling Ware Fault Locator Principle Fig.1 illustrates the basic principle of operation of the Fault Locator System (FLS).  Fig.1 : Basic fault locator principle In Fig.1, length line is L . A FL remote is coupled to each end of this line via the high frequency tap from a Capacitive Potential Transformer (CPT). A FL remote is actually a fancy electronic stopwatch synchronized to the common timing standard of UTC from GPS. When a fault occurs at distance X from an end of the line, the resulting produces traveling waves. These transients, whit 2 to 5 microsecond leading edge rise-times, emanate towards the ends of the line at the speed of light (C) . The FL remotes time tag the transient arrival times to an accuracy of one microsecond. A microsecond time tagging accuracy will allow a FL accuracy to as good as 300 meters, the typical distance between transmission line towers. By knowing the line length L and the time-of-arrival difference (tb - ta ) , one can calculate the distance X , from substation A by using the well known FL equation:  ...........................................(1)
III. GPS Timing Error Modeling using RBF Fig.2 shows the topology scheme of RBF NN. This NN consists of three layers: one input layer, one hidden layer, and one output layer. RBF NNs have only one hidden layer with radial basis functions. The linear activation functions are at the output layer [11]. The hidden layer is a nonlinear processing layer, generally consisting of selected hidden centers determined by input training set. In general, the connection weights from the first layer to the second layer are 1s.  Fig.2: The topology scheme of RBF NN with (N,M, L) structure. In mathematic terminology, the i - th output of RBF NN can be written as:  IV. Experimental Results The method described above was installed into the firmware of a commercially available low cost GPS receiver module, the MicroTracker Low Power (MLP) manufactured by Rockwell Company. The actual data were collected on the building of Computer Control and Fuzzy Logic Research Lab in the Iran University of Science and Technology. Fig.3 shows scheme of designed and implemented hardware in this research.  Fig.3: Scheme of setup test |