Fast GNSS ambiguity resolution by ant colony optimisation

References

• Amiri-Simkooei AR., 2007. Least-Squares Variance Component Estimation: Theory And Gps Applications. PhD. Thesis, Delft University of Technology, Publication on Geodesy, 64, Netherlands Geodetic Commission, Delft.
   Google Scholar
• Blum C., 2005. Ant Colony Optimization: Introduction and Recent Trends. Physics of Life Reviews, 2(4): 353–373.
   Web of Science ®Google Scholar
• Box GEP, Muller ME., 1958. A Note on the Generation of Random Normal Deviates. Annals of Mathematical Statistics, 29(2): 610–611.
   Google Scholar
• Chang XW, Yang X, Zhou T., 2005. MLAMBDA: a Modified LAMBDA Method for Integer Least-Squares Estimation. Journal of Geodesy, 79: 552–565.
   Web of Science ®Google Scholar
• Chen D, Lachapelle G., 1995. A Comparison of the FASF and Least-Squares Search Algorithms for on-the-fly Ambiguity Resolution, Navigation. Journal of The Institute of Navigation, 42(2): 371–390.
   Google Scholar
• Cohen CE., 1996. Attitude Determination. In Global Positioning System: Theory and Applications II. AIAA, Washington: 519–538.
   Google Scholar
• Dorigo M., 1992. Optimization, Learning and Natural Algorithms (in Italian). PhD Thesis, Dipartimento di Elettronica, Politecnico di Milano, Italy.
   Google Scholar
• Dorigo M, Di CaroG., Gambardella LM., 1999. Ant Algorithms for Discrete Optimization. Artificial Life, 5(2): 137–172.
   PubMed Web of Science ®Google Scholar
• Dorigo M, Stützle T., 2004. Ant Colony Optimization. MIT Press, Cambridge, MA, USA.
   Google Scholar
• Duran MA, Grossmann IE., 1986. An Outer-Approximation Algorithm for a Class of Mixed-Integer Nonlinear Programs. Mathematical Programming, 36(3): 307–339.
   Web of Science ®Google Scholar
• Exler O, Schittkowksi K., 2007. A Trust Region SQP Algorithm for Mixed-Integer Nonlinear Programming. Optimization Letters, 3(1): 269–280.
   Google Scholar
• Fletcher R, Leyffer S., 1994. Solving mixed-integer nonlinear programs by outer approximation. Mathematical Programming, 66(3): 327–349.
   Web of Science ®Google Scholar
• Frei E, Beutler G., 1990. Rapid Static Positioning Based on the Fast Ambiguity Resolution Approach ‘FARA’: Theory And First Results. Manuscripta Geodaetica, 15: 325–356.
   Google Scholar
• Geoffrion AM., 1972. Generalized Benders Decomposition. Journal of Optimization Theory and Applications, 10(4): 237–260.
   Google Scholar
• Glover F, Laguna M., 1997. Tabu Search. Boston, Kluwer Academic Publishers.
   Google Scholar
• Gupta OK, Ravindran A., 1985. Branch and Bound Experiments in Convex Nonlinear Integer Programming. Management Science, 31(12): 1533–1546.
   Web of Science ®Google Scholar
• Goss S, Aron S, Deneubourg JL, Pasteels JM., 1989. Self-Organized Shortcuts in the Argentine Ant. Naturwissenschaften, 76: 579–581.
   Web of Science ®Google Scholar
• Grafarend EW., 2000. Mixed Integer-Real Valued Adjustment (IRA) Problems: GPS Initial Cycle Ambiguity Resolution by Means of the LLL Algorithm. GPS Solutions, 4: 31–44.
   Google Scholar
• Grossmann IE., 2002. Review of Nonlinear Mixed-Integer and Disjunctive Programming Techniques. Optimization and Engineering, 3(3): 227–52.
   Web of Science ®Google Scholar
• Hassibi A, Boyd S., 1998. Integer Parameter Estimation in Linear Models with Applications to GPS. IEEE Transactions on Signal Processing, 46: 2938–2952.
   Web of Science ®Google Scholar
• Hoos HH, Stützle T., 2004. Stochastic Local Search: Foundations and Applications. Elsevier, The Netherlands.
   Google Scholar
• Jazaeri S, Amiri-Simkooei AR, Sharifi MA., 2012. Fast Integer Least-Squares Estimation for Gnss High-Dimensional Ambiguity Resolution Using Lattice Theory. Journal of Geodesy, 86(2): 123–136.
   Web of Science ®Google Scholar
• Jazaeri S, Amiri-Simkooei AR, Sharifi MA., 2012. Erratum to: Fast Integer Least-Squares Estimation for GNSS High-Dimensional Ambiguity Resolution Using Lattice Theory. Journal of Geodesy, DOI 10·1007/s00190-011-0518-3.
   Google Scholar
• Kim D, Langley RB., 2000. A Search Space Optimization Technique for Improving Ambiguity Resolution and Computational Efficiency. Earth Planets Space, 52(10): 807–812.
   Web of Science ®Google Scholar
• Langley RB, Beutler G, Delikaraoglou D, Nickerson B, Santerre R, Vanicek P, Well DE., 1984. Studies in the Application of the GPS to Differential Positioning. Technical Report No. 108, University of New Brunswick, Canada.
   Google Scholar
• Leyffer S., 2001. Integrating SQP and Branch-and-Bound for Mixed Integer Nonlinear Programming. Computational Optimization and Applications, 18(3): 295–309.
   Web of Science ®Google Scholar
• Liu LT, Hsu HT, Zhu YZ, Ou JK., 1999. A New Approach to GPS Ambiguity Decorrelation. Journal of Geodesy, 73: 478–490.
   Web of Science ®Google Scholar
• Schluter M, Egea JA, Banga JR., 2009. Extended Ant Colony Optimization for Non-Convex Mixed Integer Nonlinear Programming. Computers and Operations Research, 36(7): 2217–2229.
   Web of Science ®Google Scholar
• Shyu SJ, Tsai CY., 2009. Finding the longest commom subsequence for multiple biological sequencesly ant colony optimization. Computers and Operations Research, 36: 73–91.
   Web of Science ®Google Scholar
• Socha K., 2004. ACO for Continuous and Mixed-Variable Optimization. Ant Colony Optimization and Swarm Intelligence. Proceedings, 3172: 25–36.
   Web of Science ®Google Scholar
• Socha K 2008. Ant colony Optimization for Continuous and Mixed-Variable Domains. PhD Thesis, Université Libre de Bruxelles, Brussels, Belgium.
   Google Scholar
• Socha K, Dorigo M., 2008. Ant Colony Optimization For Continuous Domains. European Journal of Operational Research, 185: 1155–1173.
   Web of Science ®Google Scholar
• Teunissen PJG., 1993. Least-Squares Estimation of The Integer GPS Ambiguities. LGR-Series No. 6, Delft Geodetic Computing Centre, Delft University of Technology, 59–74.
   Google Scholar
• Teunissen PJG., 1995. The Least-Squares Ambiguity Decorrelation Adjustment: a Method for Fast GPS Integer Ambiguity Estimation. Journal of Geodesy, 70: 65–82.
   Web of Science ®Google Scholar
• Teunissen PJG., 1997. A Canonical Theory for Short GPS Baselines, parts I-IV. Journal of Geodesy, 71: 320–336389–401486–501513–525.
   Web of Science ®Google Scholar
• Teunissen PJG., 1998. Success Probability of Integer GPS Ambiguity Rounding and Bootstrapping. Journal of Geodesy, 72: 606–612.
   Web of Science ®Google Scholar
• Teunissen PJG, Amiri-Simkooei AR., 2008. Least-Squares Variance Component Estimation. Journal of Geodesy, 82(2): 65–82, DOI 10·1007/s00190-007-0157-x.
   Web of Science ®Google Scholar
• Turing AM., 1936. On Computable Numbers, with an Application to the Entscheidungsproblem. Proceedings of the London Mathematical Society, 42: 230–265.
   Web of Science ®Google Scholar
• Wei Z., 1986. Positioning with NAVSTAR, the Global Positioning System. Report No. 370, Department of Geodetic Science and Surveying, The Ohio State University, Columbus, OH, USA.
   Google Scholar
• Westerlund T, Pettersson F., 1995. An Extended Cutting Plane Method for Solving Convex MINLP Problems. Computers and Chemical Engineering, 19: S131–S136.
   Web of Science ®Google Scholar
• Xu PL., 1998. Mixed Integer Observation Models and Integer Programming in Geodesy. J. Geodetic Society of Japan, 44: 169–187.
   Google Scholar
• Xu PL., 1999. Spectral Theory of Constrained Second-Rank Symmetric Random Tensors. Geophysical Journal International., 138(1): 1–24.
   Web of Science ®Google Scholar
• Xu PL., 2001. Random Simulation and GPS Decorrelation. Journal of Geodesy, 75: 408–423.
   Web of Science ®Google Scholar
• Xu PL., 2002. Isotropic Probabilistic Models For Directions, Planes And Referential Systems. Royal Society of London Proceedings Series A, 458(2024): 2017–2038.
   Web of Science ®Google Scholar
• Xu PL., 2003. A Hybrid Global Optimization Method: The Multi-Dimensional Case. Journal of Computational and Applied Mathematics, 155, 423–446.
   Web of Science ®Google Scholar
• Xu PL., 2006. Voronoi Cells, Probabilistic Bounds and Hypothesis Testing in Mixed Integer Linear Models. IEEE Transactions on Information Theory, 52: 3122–3138.
   Web of Science ®Google Scholar
• Xu PL., 2012. Parallel Cholesky-Based Reduction for the Weighted Integer Least Squares Problem, Journal of Geodesy, 86: 35–52.
   Web of Science ®Google Scholar
• Xu PL, Cannon E, Lachapelle G., 1995. Mixed Integer Programming for the Resolution of GPS Carrier Phase Ambiguities. Paper presented at IUGG95 Assembly, 2–14 July, Boulder, CO.
   Google Scholar