TY - JOUR

T1 - Application of total least squares for spatial point process analysis

AU - Felus, Yaron A.

PY - 2004/8

Y1 - 2004/8

N2 - The total-least-squares approach is a relatively new adjustment method of estimating parameters in linear models that include error in all variables. Specifically, given an overdetermined set of linear equations y≈ Aξ where y is the observation vector, A is a positive defined data matrix, and ξ is the vector of unknown parameters, the total-least-squares problem is concerned with estimating ξ providing that the number of observations n is larger than the number of parameters to be estimated and given that both the observation vector y and the data matrix A are subjected to errors and, need to be adjusted. This model is different from the classical least-squares model where only the observation vector y is subjected to errors. This paper starts with a brief summary of the least-squares approach and then explains how one can modify the approach to include error in all variables using the generalized least-squares technique. Then the total-least-squares problem is presented along with its formulas and the procedures used to solve it. Finally, the total-least-squares approach is used to determine the trend in a spatial point process.

AB - The total-least-squares approach is a relatively new adjustment method of estimating parameters in linear models that include error in all variables. Specifically, given an overdetermined set of linear equations y≈ Aξ where y is the observation vector, A is a positive defined data matrix, and ξ is the vector of unknown parameters, the total-least-squares problem is concerned with estimating ξ providing that the number of observations n is larger than the number of parameters to be estimated and given that both the observation vector y and the data matrix A are subjected to errors and, need to be adjusted. This model is different from the classical least-squares model where only the observation vector y is subjected to errors. This paper starts with a brief summary of the least-squares approach and then explains how one can modify the approach to include error in all variables using the generalized least-squares technique. Then the total-least-squares problem is presented along with its formulas and the procedures used to solve it. Finally, the total-least-squares approach is used to determine the trend in a spatial point process.

UR - http://www.scopus.com/inward/record.url?scp=4043083547&partnerID=8YFLogxK

U2 - 10.1061/(ASCE)0733-9453(2004)130:3(126)

DO - 10.1061/(ASCE)0733-9453(2004)130:3(126)

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AN - SCOPUS:4043083547

SN - 0733-9453

VL - 130

SP - 126

EP - 133

JO - Journal of Surveying Engineering, - ASCE

JF - Journal of Surveying Engineering, - ASCE

IS - 3

ER -