Complex Total Least Squares Adjustment

doi:10.11947/j.AGCS.2015.20130701

Abstract

Abstract: On the basis of complex least squares adjustment method (CLSAM), the theory of complex total least squares adjustment method (CTLSAM) is proposed. The algorithms of complex total least squares and complex LS-TLS method are derived. Through two examples, the complex LS method under the adjustment criterions that minimize the sum of squares of the module of observation vector residual (adjustment criterion 1) and the sum of squares of the real part and imaginary part of the observation vector (adjustment criterion 2), the complex TLS method under the adjustment criterions that minimize the sum of squares of the module of observation vector and coefficient matrix residual (adjustment criterion 3)and the sum of squares of the real part and imaginary part of the observation vector and coefficient matrix residual (adjustment criterion 4) are compared and analyzed respectively. The results of two examples show that the CLSAM under the adjustment criterion 1 is more reasonable than the adjustment criterion 2; the CTLSAM under the adjustment criterion 3 is more accurate than the adjustment criterion 4; the CTLSAM under the adjustment criterion 3 is better than the CLSAM under the adjustment criterion 1 when the coefficient matrix contains stochastic noise.

Key words: complex, total least squares, mixed total least squares, least squares, adjustment criterion

CLC Number:

P207

WANG Leyang, YU Dongdong, LÜ Kaiyun. Complex Total Least Squares Adjustment[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(8): 866-876.

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