IEICE TRANSACTIONS on Fundamentals
Cost-Effective Unbiased Straight-Line Fitting to Multi-Viewpoint Range Data
Summary :
The present paper clarifies that the variance of the maximum likelihood estimator (MLE) of a parameter does not reach the Cramer-Rao lower bound (CRLB) when fitting a straight-line to observed two-dimensional data. In addition, the variance of the MLE can be shown to be equal to the CRLB only if observed noise reduces to a one-dimensional Gaussian variable. For most practical applications, it can be assumed that noise is added only to the range direction. In this case, the MLE is clearly an asymptotically effective estimator. However, even if we assume such a noise model, ML line-fitting to the data from many points of view has a high computational cost. The present paper proposes an alternative fitting method in order to provide a cost-effective unbiased estimator. The reliability of this new method is analyzed statistically and by computer simulation.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E80-A No.3 pp.472-479
- Publication Date
- 1997/03/25
- Publicized
- Online ISSN
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- Type of Manuscript
- Special Section PAPER (Special Section of Selected Papers from the 9th Karuizawa Workshop on Circuits and Systems)
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Norio TAGAWA, Toshio SUZUKI, Tadashi MORIYA, "Cost-Effective Unbiased Straight-Line Fitting to Multi-Viewpoint Range Data" in IEICE TRANSACTIONS on Fundamentals,
vol. E80-A, no. 3, pp. 472-479, March 1997, doi: .
Abstract: The present paper clarifies that the variance of the maximum likelihood estimator (MLE) of a parameter does not reach the Cramer-Rao lower bound (CRLB) when fitting a straight-line to observed two-dimensional data. In addition, the variance of the MLE can be shown to be equal to the CRLB only if observed noise reduces to a one-dimensional Gaussian variable. For most practical applications, it can be assumed that noise is added only to the range direction. In this case, the MLE is clearly an asymptotically effective estimator. However, even if we assume such a noise model, ML line-fitting to the data from many points of view has a high computational cost. The present paper proposes an alternative fitting method in order to provide a cost-effective unbiased estimator. The reliability of this new method is analyzed statistically and by computer simulation.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e80-a_3_472/_p
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@ARTICLE{e80-a_3_472,
author={Norio TAGAWA, Toshio SUZUKI, Tadashi MORIYA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Cost-Effective Unbiased Straight-Line Fitting to Multi-Viewpoint Range Data},
year={1997},
volume={E80-A},
number={3},
pages={472-479},
abstract={The present paper clarifies that the variance of the maximum likelihood estimator (MLE) of a parameter does not reach the Cramer-Rao lower bound (CRLB) when fitting a straight-line to observed two-dimensional data. In addition, the variance of the MLE can be shown to be equal to the CRLB only if observed noise reduces to a one-dimensional Gaussian variable. For most practical applications, it can be assumed that noise is added only to the range direction. In this case, the MLE is clearly an asymptotically effective estimator. However, even if we assume such a noise model, ML line-fitting to the data from many points of view has a high computational cost. The present paper proposes an alternative fitting method in order to provide a cost-effective unbiased estimator. The reliability of this new method is analyzed statistically and by computer simulation.},
keywords={},
doi={},
ISSN={},
month={March},}
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TY - JOUR
TI - Cost-Effective Unbiased Straight-Line Fitting to Multi-Viewpoint Range Data
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 472
EP - 479
AU - Norio TAGAWA
AU - Toshio SUZUKI
AU - Tadashi MORIYA
PY - 1997
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E80-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 1997
AB - The present paper clarifies that the variance of the maximum likelihood estimator (MLE) of a parameter does not reach the Cramer-Rao lower bound (CRLB) when fitting a straight-line to observed two-dimensional data. In addition, the variance of the MLE can be shown to be equal to the CRLB only if observed noise reduces to a one-dimensional Gaussian variable. For most practical applications, it can be assumed that noise is added only to the range direction. In this case, the MLE is clearly an asymptotically effective estimator. However, even if we assume such a noise model, ML line-fitting to the data from many points of view has a high computational cost. The present paper proposes an alternative fitting method in order to provide a cost-effective unbiased estimator. The reliability of this new method is analyzed statistically and by computer simulation.
ER -
English
