Total least squares adjustment in inequality constrained partial errors-in-variables models: optimality conditions and algorithms

References

• Amiri-Simkooei, A.R. 2013. Weighted total least squares with weighted and hard constraints, Technical Report, No 101, Series on Mathematical Geodesy, Department of Geomatics Engineering, University of Isfahan, Isfahan, Iran.
   Google Scholar
• Amiri-Simkooei, A.R., 2013. Application of least squares variance component estimation to errors-in-variables models. Journal of geodesy, 87 (10–12), 935–944.
   Web of Science ®Google Scholar
• Amiri-Simkooei, A.R., 2016. Non-negative least-squares variance component estimation with application to GPS time series. Journal of geodesy, 90 (5), 451–466.
   Web of Science ®Google Scholar
• Amiri-Simkooei, A.R., 2017. Weighted total least squares with singular covariance matrices subject to weighted and hard constraints. Journal of surveying engineering, 143 (4), 04017018.
   Web of Science ®Google Scholar
• Amiri-Simkooei, A.R., and Jazaeri, S., 2012. Weighted total least squares formulated by standard least squares theory. Journal of geodetic science, 2 (2), 113–124.
   Google Scholar
• Armijo, L., 1966. Minimization of functions continuous first partial derivatives. Pacific journal of mathematics, 16 (1), 1–3.
   Web of Science ®Google Scholar
• De Moor, B. 1990. Total linear least squares with inequality constraints. In: Proceedings of ESAT-SISTA report 1990-2, Department of Electrical Engineering, Katholieke Universiteit Leuven, Belgium.
   Google Scholar
• Fang, X., 2013. Weighted total least squares: necessary and sufficient conditions, fixed and random parameters. Journal of geodesy, 87 (8), 733–749.
   Web of Science ®Google Scholar
• Fang, X., 2014. On non-combinatorial weighted total least squares with inequality constraints. Journal of geodesy, 88 (8), 805–816.
   Web of Science ®Google Scholar
• Fletcher, R., 1987. Practical methods of optimization. New York: Wiley.
   Google Scholar
• Gerhold, G.A., 1969. Least-squares adjustment of weighted data to a general linear equation. American journal of physics, 37 (2), 156–161.
   Web of Science ®Google Scholar
• Gleser, J.L., 1981. Estimation in a multivariate “errors in variables” regression model: large sample results. The annals of statistics, 9 (1), 24–44.
   Web of Science ®Google Scholar
• Golub, G.H., and Van Loan, C.F., 1980. An analysis of the total least squares problem. SIAM journal on numerical analysis, 17 (6), 883–893.
   Web of Science ®Google Scholar
• Jazaeri, S., Amiri-Simkooei, A.R., and Sharifi, M.A., 2014. Iterative algorithm for weighted total least squares adjustment. Survey review, 46 (334), 19–27.
   Web of Science ®Google Scholar
• Liew, C.K., 1976. Inequality constrained least-squares estimation. Journal of the American statistical association, 71 (355), 746–751.
   Web of Science ®Google Scholar
• Lu, G., Krakiwsky, E.J., and Lachapelle, G., 1993. Application of inequality constraint least squares to GPS navigation under selective availability. Manuscripta geodaetica, 18 (3), 124–130.
   Google Scholar
• Ma, C.F., 2010. Optimization method and its program design with MATLAB. Beijing: Science Press (in Chinese).
   Google Scholar
• Mahboub, V., 2012. On weighted total least-squares for geodetic transformation. Journal of geodesy, 86 (5), 359–367.
   Web of Science ®Google Scholar
• Moghtased-Azar, K., Tehraanchi, R., and Amiri-Simkooei, A.R., 2014. An alternative method for non-negative estimation of variance components. Journal of geodesy, 88 (5), 427–439.
   Web of Science ®Google Scholar
• Neitzel, F., 2010. Generalization of total least-squares on example of unweighted and weighted 2D similarity transformation. Journal of geodesy, 84 (12), 751–762.
   Web of Science ®Google Scholar
• Nocedal, J., and Wright, S.J., 2006. Numerical optimization. Berlin: Springer.
   Google Scholar
• Peng, J., Zhang, H., Shong, S. and Guo, C., 2006. An aggregate constraint method for inequality-constrained least squares problem. Journal of geodesy, 79 (12), 705–713.
   Web of Science ®Google Scholar
• Rao, C.R., 1999. Linear model: least squares and alternatives, second edition, Springer series in statistics. New York: Springer-Verlag.
   Google Scholar
• Remondi, B.W., 1992. Real-Time centimeter-accuracy GPS: initializing while in motion (warm start versus cold start). Journal of the institute of navigation, 40 (2), 199–208.
   Google Scholar
• Roese-Koerner, L., Devaraju, B., Sneeuw, N. and Schuh, W.D., 2012. A stochastic framework for inequality constrained estimation. Journal of geodesy, 86 (11), 1005–1018.
   Web of Science ®Google Scholar
• Schaffrin, B., 2006a. A note on constrained total least-squares estimation. Linear algebra and its applications, 417 (1), 245–258.
   Web of Science ®Google Scholar
• Schaffrin, B., Lee, I., Choi, Y. and Felus, Y., 2006b. Total least squares (TLS) for geodetic straight-line and plane adjustment. Bollettino di geodesia e scienze affini, 65 (3), 141–168.
   Google Scholar
• Shen, Y.Z., and Li, B.F., 2011. An iterative solution of weighted total least-squares adjustment. Journal of geodesy, 85 (4), 229–238.
   Web of Science ®Google Scholar
• Sjöberg, L.E., 1984. Non-negative variance component estimation in the Gauss-Helmert adjustment model. Manuscripta geodaetica, 9, 247–248.
   Google Scholar
• Song, Y.C., Zhu, J.J., and Li, Z.W., 2013. The least-squares estimation of adjustment model constrained by some non-negative constraints. Survey review, 42 (315), 62–71.
   Web of Science ®Google Scholar
• Van Huffel, V.J., 1989. Algebraic connections between the least squares and total least squares problems. Numerische Mathematik, 55 (4), 431–449.
   Web of Science ®Google Scholar
• Van Huffel, V.J., 1991. The total least squares problem: computational aspects and analysis. Philadelphia: SIAM.
   Google Scholar
• Xu, P.L., Liu, J.N., and Shi, C., 2012. Total least squares adjustment in partial errors-in-varibles models: algorithm and statistical analysis. Journal of geodesy, 86 (8), 661–675.
   Web of Science ®Google Scholar
• Yaron, A.F., and Robert, C.B., 2009. On symmetrical three-dimensional datum conversion. GPS solutions, 13 (1), 65–74.
   Web of Science ®Google Scholar
• Zeng, W.X., Fang, X., and Liu, J. N., 2014. Weighted total least squares algorithm with inequality constraints. Acta Geodaetica et Cartographica Sinica, 43 (10), 1013–1018. (in Chinese).
   Google Scholar
• Zeng, W., Liu, J., and Yao, Y., 2015. On partial errors-in-variables models with inequality constraints of parameters and variables. Journal of geodesy, 89 (2), 111–119.
   Web of Science ®Google Scholar
• Zhang, S.L., Tong, X.H., and Zhang, K., 2013. A solution to EIV model with inequality constraints and its geodetic applications. Journal of geodesy, 87 (1), 23–28.
   Web of Science ®Google Scholar
• Zhu, J.J., Santerre, R., and Chang, X.W., 2005. A Bayesian method for linear, inequality-constrained adjustment and its application to GPS positioning. Journal of geodesy, 78 (9), 528–534.
   Web of Science ®Google Scholar