Application of Total Least Squares for Spatial Point Process Analysis

By Y. Felus. 2004

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Total Least Squares Solution of Coordinate Transformation (2007, methodology): “where tr denotes the trace operation and [EA ; el] denotes the n×(m+1) augmented error matrix constructed by adding vector of observation errors el to the error matrix EA as a right most column [7], [4].”
Deformation analysis with Total Least Squares (2006, background): “…matrix H , which is defined by ‖H‖F = √√√√ n∑ i=1 m∑ j=1 h2ij = √ tr(H T H) (9) where tr denotes the trace operation and[EA; e`] denotes then×(m+1) augmented error matrix constructed by adding vector of observation errors el to the error matrixEA as a right most column (Leon, 2002; Felus, 2004).”
Weighted total least squares: necessary and sufficient conditions, fixed and random parameters (2013, methodology): “Schaffrin and Felus (2005, 2009) presented that the WTLS could be used as a promising tool to solve the constrained TLS problem. 2. Akyilmaz (2007) stated that the TLS solution with a general covariance matrix has not yet been achieved, even in mathematical science.”
An Improved Weighted Total Least Squares Method with Applications in Linear Fitting and Coordinate Transformation (2011, background): “However, this assumption is not the case in many adjustment systems where errors may exist in both the observation vector and the design matrix (Davis 1999; Felus 2004; Acar et al. 2006; Akyilmaz 2007; Schaffrin and Wieser 2008; Schaffrin and Uzun 2008).”