Generalized total Kalman filter algorithm of nonlinear dynamic errors-in-variables model with application on indoor mobile robot positioning

Aftatah M, Lahrech A, Abounada A, Soulhi A (2016) GPS/INS/Odometer data fusion for land vehicle localization in GPS denied environment. Mod Appl Sci 11(1):62–75

Amiri-simkooei AR (2013) Application of least squares variance component estimation to errors-in-variables models. J Geod 87:935–944

Amiri-Simkooei AR (2016) Non-negative least-squares variance component estimation with application to GPS time series. J Geod 90:451–466

Amiri-simkooei AR, Jazaeri S (2012) Weighted total least squares formulated by standard least squares theory. J Geod Sci 2:113–124

Amiri-Simkooei AR, Jazaeri S (2013) Data-snooping procedure applied to errors-in-variables models. Stud Geophys Geod 57:426–441

Amiri-Simkooei AR, Zangeneh-Nejad F, Asgari J (2016) On the covariance matrix of weighted total least-squares estimates. J Surv Eng 142:04015014

Baheti RS (1986) Efficient approximation of Kalman filter for target tracking. IEEE Trans Aerosp Electron Syst. doi: 10.1109/TAES.1986.310687

Bell BM, Cathey FW (1993) The iterated Kalman filter update as a Gauss–Newton method. IEEE Trans Autom Control 38:294–297. doi: 10.1109/9.250476

Brown RG, Hwang PYC (2012) Introduction to random signals and applied Kalman filtering: with MATLAB exercises and solutions, 4th edn. Wiley, New York

Chang GB (2015) On least-squares solution to 3D similarity transformation problem under Gauss–Helmert model. J Geod 89:573–576

Chang GB, Xu TH, Wang QX, Zhang SB, Chen GL (2017) A generalization of the analytical least-squares solution to the 3D symmetric Helmert coordinate transformation problem with an approximate error analysis. Adv Space Res 59:2600–2610

Crassidis JL, Junkins JL (2011) Optimal estimation of dynamic systems, 2nd edn. Applied mathematics and nonlinear science series. Chapman & Hall/CRC, New York

Fan QG, Sun BW, Sun Y, Wu YH, Zhuang XP (2017) Data fusion for indoor mobile robot positioning based on tightly coupled INS/UWB. J Navig. doi: 10.1017/S0373463317000194

Fang X (2013) Weighted total least squares: necessary and sufficient conditions, fixed and random parameters. J Geod 87:733–749

Fang X (2014) On non-combinatorial weighted total least squares with inequality constraints. J Geod 88:805–816

Fang X (2015) Weighted total least-squares with constraints: a universal formula for geodetic symmetrical transformations. J Geod 89:459–469

Fang X, Wu Y (2016) On the errors-in-variables model with equality and inequality constraints for selected numerical examples. Acta Geod Geophys 51:515–525

Fang X, Wang J, Li BF, Zeng WX, Yao YB (2015) On total least squares for quadratic form estimation. Stud Geophys Geod 59(3):366–379

Fang X, Li BF, Alkhatib H, Zeng WX, Yao YB (2017) Bayesian inference for the errors-in-variables model. Stud Geophys Geod 61(1):35–52

Farrell J (2008) Aided navigation: GPS with high rate sensors. McGraw-Hill Inc, New York

Gelb A (1974) Applied optimal estimation. MIT Press, Cambridge

Golub G, van Loan C (1980) An analysis of the total least-squares problem. SIAM J Numer Anal 17:883–893

Han HZ, Wang J, Wang JL, Tan XL (2015) Performance analysis on carrier phase-based tightly-coupled GPS/BDS/INS integration in GNSS degraded and denied environments. Sensors 15:8685–8711

Han HZ, Wang J, Wang JL, Hernandez A (2017) Reliable partial ambiguity resolution for single-frequency GPS/BDS and INS integration. GPS Solut 21:251–264

Henderson HV, Searle SR (1981) On deriving the inverse of a sum of matrices. SIAM Rev 23:53–60

Julier SJ, Uhlmann JK, Durrant-Whyte HF (1995) A new approach for filtering nonlinear systems. In: Proceedings of the ACC’95, pp 1628–1632. doi: 10.1109/ACC.1995.529783

Li BF, Shen YZ, Li WX (2012) The seamless model for three-dimensional datum transformation. Sci China 55:2099–2108

Li ZK, Chang GB, Gao JX, Wang J, Hernandez A (2016) GPS/UWB/MEMS-IMU tightly coupled navigation with improved robust Kalman filter. Adv Space Res 58:2424–2434

Liu JN (1983) The equivalence of coordinate transformation models for the combination of satellite and terrestrial networks. J Wuhan Techn Univ Surv Mapp 8:37–50 (in Chinese with English abstract)

Liu J, Chen R (1998) Sequential Monte Carlo methods for dynamic systems. J Am Stat Assoc 93:1032–1044

Liu JN, Liu DJ (1985) The influence of the accuracy in geodetic and geocentric coordinates on combined adjustment. Acta Geod Cartogr Sin 14:133–144 (in Chinese with English abstract)

Liu JN, Liu DJ, Cui XZ (1987) Theory and applications of combined adjustment of satellite and terrestrial networks. J Wuhan Techn Univ Surv Mapp 12(4):1–9 (in Chinese with English abstract)

Lu J, Chen Y, Li BF, Fang X (2014) Robust total least squares with reweighting iteration for three-dimensional similarity transformation. Surv Rev 46:28–36

Mahboub V (2012) On weighted total least-squares for geodetic transformation. J Geod 86:359–367

Mahboub V, Sharifi MA (2013) On weighted total least-squares with linear and quadratic constraints. J Geod 87:279–286

Mahboub V, Ardalan AA, Ebrahimzadeh S (2015) Adjustment of non-typical errors-invariables models. Acta Geod Geophys 50:207–218

Mahboub V, Saadatseresht M, Ardalan AA (2016) A general weighted total Kalman filter algorithm with numerical evaluation. Stud Geophys Geod 61:19–34

Mahboub V, Saadatseresht M, Ardalan AA (2017a) A solution to dynamic errors-invariables within system equations. Acta Geod Geophys. doi: 10.1007/s40328-017-0201-0

Mahboub V, Saadatseresht M, Ardalan AA (2017b) On constrained integrated total Kalman filter for integrated direct geo-referencing. Surv Rev. doi: 10.1080/00396265.2017.1341736

Merwe R, Wan E (2001) The square-root unscented Kalman filter for state and parameter-estimation. Proc IEEE Int Conf Acoust Speech Signal Process (ICASSP) 6:3461–3464

Neitzel F (2010) Generalization of total least-squares on example of unweighted and weighted 2D similarity transformation. J Geod 84:751–762

Sage AP, Husa GW (1969) Adaptive filtering with unknown prior statistics. Joint Am Control Conf. doi: 10.1109/JACC.1969.4169325

Schaffrin B (2009) TLS collocation: the total least squares approach to EIV-models with stochastic prior information. In: 18th international, workshop on matrices and statistics, Solvakia

Schaffrin B, Iz HB (2008) Towards total Kalman filtering for mobile mapping. Intl Arch Photogr Rem Sens Spat Inf Sci 36:270–275

Schaffrin B, Uzun S (2011) Errors-In-Variables for mobile mapping algorithms. In: The presence of OutlIERS, archives of photogrammetry, cartography and remote sensing, vol 22. pp 377–387

Schaffrin B, Wieser A (2008) On weighted total least squares adjustment for linear regression. J Geod 82:415–421

Shen YZ, Li BF, Chen Y (2011) An iterative solution of weighted total least-squares adjustment. J Geod 85:229–238

Shi Y, Xu PL, Liu JN, Shi C (2015) Alternative formulae for parameter estimation in partial errors-in-variables models. J Geod 89:13–16

Teunissen PJG (1988) The nonlinear 2D symmetric Helmert transformation: an exact nonlinear least-squares solution. J Geod 62:1–15

Wang LY, Xu GY (2016) Variance component estimation for partial errors-in-variables models. Stud Geophys Geod 60:35–55

Wang LY, Zhao YW (2017) Unscented transformation with scaled symmetric sampling strategy for precision estimation of total least squares. Stud Geophys Geod. doi: 10.1007/s11200-11016-11113-11200

Wang B, Li JC, Liu C (2016) A robust weighted total least squares algorithm and its geodetic applications. Stud Geophys Geod 60:177–194

Wang B, Li JC, Liu C, Yu J (2017) Generalized total least squares prediction algorithm for universal 3D similarity transformation. Adv Space Res 59(3):815–823

Xu GC (2003) GPS-theory, algorithms and applications, 2nd edn. Springer, Berlin

Xu PL (2016) The effect of errors-in-variables on variance component estimation. J Geod 90(8):681–701

Xu PL, Liu JN (2013) Variance components in errors-in-variables models: estimability, stability and bias analysis. In: Invited talk, VIII Hotine-Marussi symposium on mathematical geodesy, Rome, 17–21 June 2013

Xu PL, Liu JN (2014) Variance components in errors-in-variables models: estimability, stability and bias analysis. J Geod 88:719–734

Xu PL, Liu JN, Shi C (2012) Total least squares adjustment in partial errors-in-variables models: algorithm and statistical analysis. J Geod 86:661–675

Zhou YJ, Kou XJ, Zhu JJ, LI J (2014) A newton algorithm for weighted total least-squares solution to a specific errors-in-variables model with correlated measurements. Stud Geophys Geod 58:349–375