Weighted and partial total least squares method for the EIV model with linear equality and inequality constraints

References

• Amiri-Simkooei, A.R., 2018. Weighted total least squares with constraints: alternative derivation without using Lagrange multipliers. Journal of surveying engineering, 144 (2), 06017005.
   Web of Science ®Google Scholar
• Bertsekas, D.P., 2016. Nonlinear programming. 3rd ed. Belmont: Athena Scientific.
   Google Scholar
• Boyd, S. and Vandenberghe, L., 2004. Convex optimization. Cambridge: Cambridge University Press.
   Google Scholar
• Britt, H.I. and Luecke, R.H., 1973. The estimation of parameters in nonlinear, implicit models. Technometrics, 15 (2), 233–247.
   Web of Science ®Google Scholar
• Dunn, W.L. and Shultis, J.K., 2012. Exploring Monte Carlo methods. Amsterdam: Elsevier.
   Google Scholar
• Engel, K. and Engel, S., 2015. Recursive least squares with linear inequality constraints. Optimization and engineering, 16 (1), 1–26.
   Web of Science ®Google Scholar
• Fang, X., 2014a. On non-combinatorial weighted total least squares with inequality constraints. Journal of geodesy, 88 (8), 805–816.
   Web of Science ®Google Scholar
• Fang, X., 2014b. A structured and constrained total least-squares solution with cross-covariances. Studia geophysica et geodaetica, 58 (1), 1–16.
   Web of Science ®Google Scholar
• Fang, X., et al., 2015. On total least squares for quadratic form estimation. Studia geophysica et geodaetica, 59 (3), 366–379.
   Web of Science ®Google Scholar
• Fang, X., 2015. Weighted total least-squares with constraints: a universal formula for geodetic symmetrical transformations. Journal of geodesy, 89 (5), 459–469.
   Web of Science ®Google Scholar
• Fang, X. and Wu, Y., 2016. On the errors-in-variables model with equality and inequality constraints for selected numerical examples. Acta geodaetica et geophysica, 51 (3), 515–525.
   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
• Jin, Y., et al., 2015. Total least L1- and L2-norm estimations of a coordinate transformation model with a structured parameter matrix. Studia geophysica et geodaetica, 59 (3), 345–365.
   Web of Science ®Google Scholar
• Jin, Y., et al., 2018. Partial total-least-squares adjustment of condition equations with application to a rectangular building adjustment in a GIS. Journal of surveying engineering, 144 (1), 04017021.
   Web of Science ®Google Scholar
• Judge, G.G. and Takayama, T., 1966. Inequality restrictions in regression analysis. Journal of the American Statistical Association, 61 (313), 166–181.
   Web of Science ®Google Scholar
• Li, X., 1991. An aggregate constraint method for Non-linear programming. Journal of the operational research society, 42, 1003–1010.
   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, 124–130.
   Google Scholar
• Mooney, C.Z., 1997. Monte carlo simulation. Thousand Oaks, CA: Sage.
   Google Scholar
• Peng, J., et al., 2006. An aggregate constraint method for inequality-constrained least squares problems. Journal of geodesy, 79 (12), 705–713.
   Web of Science ®Google Scholar
• Rosen, J.B., Park, H., and Glick, J., 1996. Total least norm formulation and solution for structured problems. SIAM journal on matrix analysis and applications, 17 (1), 110–126.
   Web of Science ®Google Scholar
• Schaffrin, B., 2006. A note on constrained total least-squares estimation. Linear algebra and its applications, 417 (1), 245–258.
   Web of Science ®Google Scholar
• Schaffrin, B. and Felus, Y.A., 2009. An algorithmic approach to the total least-squares problem with linear and quadratic constraints. Studia geophysica et geodaetica, 53 (1), 1–16.
   Web of Science ®Google Scholar
• Schaffrin, B. and Wieser, A., 2008. On weighted total least-squares adjustment for linear regression. Journal of geodesy, 82 (7), 415–421.
   Web of Science ®Google Scholar
• Shi, Y., et al., 2015. Alternative formulae for parameter estimation in partial errors-in-variables models. Journal of geodesy, 89 (1), 13–16.
   Web of Science ®Google Scholar
• Tukey, J.W., 1997. Exploratory data analysis. Reading: Addison-Wesley.
   Google Scholar
• Van Huffel, S. and Vandewalle, J., 1989. Analysis and properties of the generalized total least squares problem AX ≈ B when some or all columns in A are subject to error. SIAM journal on matrix analysis and applications, 10 (3), 294–315.
   Web of Science ®Google Scholar
• Van Huffel, S. and Vandewalle, J., 1991. The total least squares problems: computational aspects and analysis. Mathematics of computation, 59 (200), 724.
   Google Scholar
• Wang, L. and Xu, G., 2016. Variance component estimation for partial errors-in-variables models. Studia geophysica et geodaetica, 60 (1), 35–55.
   Web of Science ®Google Scholar
• Wang, L., et al., 2020. Jackknife method for variance components estimation of partial EIV model. Journal of surveying engineering, 146 (4), 04020016.
   Web of Science ®Google Scholar
• Wang, L., Wen, G., and Zhao, Y., 2019. Virtual observation method and precision estimation for ill-posed partial EIV model. Journal of surveying engineering, 145 (4), 04019010.
   Web of Science ®Google Scholar
• Wang, L. and Zou, C., 2021. Review of PEIV model parameter estimation theory and its applications. Geomatics and information science of Wuhan University, 46 (9), 1273–1283.
   Google Scholar
• Wolf, P.R. and Ghilani, C.D., 1997. Adjustment computations: statistics and least squares in surveying and GIS. New York: Wiley.
   Google Scholar
• Xu, P., 2016. The effect of errors-in-variables on variance component estimation. Journal of geodesy, 90 (8), 681–701.
   Web of Science ®Google Scholar
• Xu, P., Liu, J., and Shi, C., 2012. Total least squares adjustment in partial errors-in-variables models: algorithm and statistical analysis. Journal of geodesy, 86 (8), 661–675.
   Web of Science ®Google Scholar
• Zeng, W., et al., 2019. On the errors-in-variables model with inequality constraints of dependent variables for geodetic transformation. Survey review, 51 (365), 166–171.
   Web of Science ®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., Tong, X., 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., 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