Authors

1 Faculty of Electrical and Computer Engineering, Tarbiat Dabir Shahid Rajaee University,Tehran Iran

2 Faculty of Electrical and Computer Engineering, Shahid Beheshti University, Tehran, Iran

Abstract

For precise locating, Differentials Global Positioning System requires prediction of differential corrections for the future times. The system is comprised of both fixed and mobile stations. If the satellites of the two stations are exactly the same, the sources of errors will be close to each other at the two stations; in this case, reference position components factors can be used as corrective factors  for offsetting user station positioning error. In this paper, Genetic and Artificial Neural Network hybrid algorithms (Evolutionary Neural Network), Support Vector Machines, Autoregressive Moving Average and Recurrent Neural Network have been used for corrections. In order to test the algorithms, static sampling of the position data of an inexpensive receiver was used and the predicted reference position components error corrections were applied elsewhere. The tests performed as post-process showed that the positioning RMS error decreases up to 0.5 m. The evolutionary neural network prediction model is more accurate than other models and its RMS error is 0.12 m.

Keywords

  1. Morgan-Owen, G. J. and Johnston, G. T., “Differential GPS Positioning,” IEEE Transactions on Electronics & Communication Engineering, Vol. 7, Issue 1, 1995, pp.11-21.
  2. Mosavi, M. R. and Nabavi, H., “Improving DGPS Accuracy using Neural Network Modeling,” Australian Journal of Basic and Applied Sciences, Vol. 5, No. 5, 2011, pp. 848-856.
  3. Mosavi, M. R., Mohammadi, K., and Refan, M. H., “A New Approach for Improving of GPS Positioning Accuracy by Using an Adaptive Neuro fuzzy System, Before and After S/A Is Turned Off,” International Journal of Engineering Science, Iran University of Science and Technology, Vol. 15, No. 1, 2004, pp. 95-108.
  4. Mosavi S.M.R., Rahemi, N. and Mirza-Kuchaki, S., “Precise Positioning in GPS Receivers for Very High Elocities Using Combination of Recursive Least Squares and Fuzzy Logic,” Vol. 7, No. 3, 2015, pp.63-72.
  5. Kobayashi, K., Ka, C. C., Watanabe, K., and Munekata, F., “Accurate Differential Global Positioning System via Fuzzy Logic Kalman Filter Sensor Fusion Technique,” IEEE Transactions on Industrial Electronics, Vol. 45, No. 3, 1998, pp.510-518.
  6. RTCM Special Committee No. 104. “RTCM Recommended Standards for Differential NAVSTAR GPS Service.” Radio Technical Committee for Maritime Services. Paper 134-89/SC104- 68. Washington DC (USA), 1990.
  7. Keith, A., Using Wide Area Differential GPS to Improve Total System Error for Precision Flight Operations, (PhD Thesis) Stanford University (USA), 2000.
  8. Availabel, [on line]: http://www.u-blox.com/en/ download /documents-a-resources/gps-solutions.html.
  9. Refan, M. H., Mohammadi, K. and Mosavi, M. R., “Improvement on a Low Costpositioning Sensor Accuracy,” IEEE Conference on Sensors, Malaysia, 14–18 July, 2003, pp. 9–14.
  10. Donald, K. D. Mc., “The Modernization of GPS: Plans, New Capabilities, and the Future Relationship to Galileo,” Journal of Global Positioning System, Vol. 1, No.1, 2002, pp.1-17.
  11. Jwo, D. J. and Lai, C. C., “Neural Network-based GPS GDOP Approximation and Classification,” Journal of GPS Solutions, Vol. 11, No. 1, 2007, pp.51-60.
  12. Mosavi, M. R. and Azami, H., “Applying Neural Network for Clustering of GPS Satellites,” Journal of Geoinformatics, 7, No. 3, 2011, pp. 7-14.
  13. Güngör, Z. and Ünler, A., “K-harmonic Means Data Clustering with Simulated Annealing Heuristic,” Journal of Applied Mathematics and Computation, Vol. 184, Issue 2, 2007, pp.199- 209.
  14. Saraf, M., Mohammadi, K. and Mosavi, M. R., “Bayesian Framework on GPS GDOP Classification,” Journal of Computers & Electrical Engineering, Vol. 37, 2011, pp.1009-1018.
  15. Indriyatmoko, A. T., Kang, Y. J., Lee, G. I., Jee, Y. B., and Kim, J., “Artificial Neural Network for Predicting DGPS Carrier Phase and Pseudo-Range Correction,” Journal of GPS Solutions, Vol. 12, No. 4, 2008, pp. 237-247.
  16. Katio, D. and Stankovio, S., “Fast Learning Algorithms for Training of Feedforward Multilayer Perceptrons Based on Extended Kalman Filter,” IEEE Conference on Neural Networks, Vol. 1, 1996, pp. 196-201.
  17. Rocha, M., Cortez, P. and Neves, J., “Ensemble of Artificial Networks with Heterogeneous Topologies,” Proceeding of the Fourth Symposium on Engineering of Intelligence Systems, 2004.
  18. Yao, X., “Evolving Artificial Neural Networks,” Proceedings of IEEE, Vol. 87, No. 9, 1999, pp. 1423 – 1447.
  19. Phansalkar, V. V. and Sastry, P. S., “Analysis of the Back-Propagation Algorithm with Momentum,” IEEE Transactions on Neural Networks, 5, No. 3, 1994, pp. 505-506.
  20. Yao, X., “A Review of Evolutionary Artificial Neural Networks,” Internatoinal Journal Intelligent System, Vol. 8, No. 4, 1993, pp. 539–567.
  21. Huang, C. Y., Chen, L., Chen, Y. and chang, M., “Evaluation the Process of a Genetic Algorithm to Improve the Back-Propagation Network: A Mont Carlo Study,” Expert Systems with Applications, Vol. 36, Issue 2, Part1, 2009, pp. 1459-1465.
  22. Frank, H. F., Leung, Lam, H. K., Ling, S. H. and Tam, P. K. S., “Tuning of the Structure and Parameters of a Neural Network Using an Improved Genetic Algorithm,” IEEE Transactions on neural networks, 14, No. 1, 2003, pp. 79-88.
  23. Pal, M. and Deswal, S. “Modeling Pile Capacity using Support Vector Machines and Generalized Regression Neural Network,” Journal of Computing in Civil Engineering, ASCE, 134, No. 7, 2008, pp. 1021-1024.
  24. Dibike, Y.B., Velikov, S., Solomatine, D. and Abbot, M.B., “Model Induction with Support Vector Machines-Introduction and Applications,” Journal of Computing in Civil Engineering, ASCE, Vol. 15, No. 3, 2001, pp. 208-216.
  25. Corinna, C. and Vapnik, V., Support-Vector Networks, Machine Learning, Vol. 20, Kluwer Academic Publishers, Boston,
  26. Burgers, C.J.C., “A Tutorial on Support Vector Machines for Pattern Recognition,” Data Mining and Knowledge Discovery, Vol. 2, 1998, pp. 121–167.
  27. Cao, L.J. and Tay, F.E.H., “Support Vector Machine with Adaptive Parameters in Financial Time Series Forecasting,” IEEE Transactions on Neural Network, Vol. 14, No. 6, 2003, pp. 1506–1518.
  28. Ganapathiraju, A., Support Vector Machines for Speech Recognition, [PhD Thesis], Mississippi State University, USA. 2001.
  29. Drucker, H.C., Burges Kaufman, L., Smola, A. and Vapnik, V., “Support Vector Regression Machines,” MIT Press, Cambridge, Vol. 9, 1997, pp. 155-161.
  30. Smola, A.J. and Scolkopf, B., Tuotorial on Support Vector Regression, Neuro COLT2 Technical Report Series, NC2-TR-1998-03, 1998.
  31. Farag, A. and Refaat, M.M., Regression Using Support Vector Machines: Basic Foundations, Technical Report, December 2004.
  32. Minqiang, P., Dehuai, Z. and Gang, X. u., “Temperature Prediction of Hydrogen Producing Reactor Using SVM Regression with PSO-SVM”, Journal of Computers, Vol. 5, No. 3, 2010, pp. 388-393.
  33. Cai, X., Zhang, N., Vena, G.K. and Unsch, D.C.W., “Time Series Prediction with Recurrent Neural Networks Trained by a Hybrid PSO-EA Algorithm,” Journal of Neuro Computing, Vol. 70, Issue 13-15, pp. 2342-2353, 2007.
  34. Graves, A. and Schmidhuber, J., “Offline Handwriting Recognition with Multi-dimensional Recurrent Neural Networks,” Advances in Neural Information Processing Systems,
  35. Bengio, Y., Simard, P. and Frasconi, P., “Learning Long-Term Dependencies with Gradient Descent is Difficult,” IEEE Transactions on Neural Networks, Vol. 5, Issue 2, 1994, pp. 157–166.
  36. Hochreiter, S., Bengio, Y., Frasconi, P. and Schmidhuber, J., “A Field Guide to Dynamical Recurrent Neural Networks, Chapter Gradient flow in Recurrent Nets: the Difficulty of Learning Long-Term Dependencies,” IEEE press, 2001.
  37. Bod´en, M. and Wiles, J., “Context-Free and Context-Sensitive Dynamics in Recurrent Neural Networks,” Connection Science, Vol. 12, No. 3, 2000.
  38. Mosavi, M.R., “A Comparative Study between Performance of Recurrent Neural Network and Kalman Filter for DGPS Corrections Prediction,” IEEE Conference on Signal Processing, Beijing, China, 2004.
  39. Werbos, P.J., Beyond Regression: “New Tools for Prediction and Analysis in the Behavioral Sciences. Cambridge,” [Ph.D. Thesis], MA: Harvard University, 1974.
  40. Zhang, G.P., “Time Series Forecasting using a Hybrid ARIMA and Neural Network Model,” Neuro Computing, Vol. 50, 2003, pp. 159-175.
  41. Zhang, S. and Liu, R., “A Rapid Algorithm for Online and Real-time ARMA Modeling,” Signal Processing Proceedings, 2000. WCCC-ICSP 2000, 5th International Conference, 2003, pp. 230–233,
  42. Scha, C. and Schroder, D., “An Application of General Regression Neural Network to Nonlinear Adaptive Control,” Processing of 5th European Conference on Power Electronics and Applications, 1993, pp. 219–224.
  43. Wang, C.C., “A Comparison Study between Fuzzy Time Series Model and ARIMA Model for Forecasting Taiwan Export,” Expert Systems with Applications, 38, Issue 8, 2011, pp. 9296–9304.
  44. Jwo, D.J., Lee, T.Sh. and Tseng, Y.W., “ARMA Neural Networks for Predicting DGPS Pseudorang Correction”, the Journal of Navigation, Vol. 57, Issue 02, 2004, pp. 275–286.
  45. Alsmadi, Kh.M.S., Omar, Kh.B. and Noah, Sh.A., “Back Propagation Algorithm: The BestAlgorithm among the Multi-layer Perceptron Algorithm”, Journal of Computer Science and Network Security, Vol. 9, No. 4, 2009, pp. 378-383.
  46. Dameshghi, A., Design and Implementation of RTDGPS by Predictor’s Algorithms on Low Cost GPS Receivers, (M.Sc Thesis), Part 6, Jul 2013 (In Persian).