Analysis of the Cramér-Rao Bound in the Joint Estimation of Astrometry and Photometry

Mendez, Rene A.; Silva, Jorge F.; Orostica, Rodrigo; Lobos, Rodrigo A.

doi:10.1086/678041

Cited by 13 publications

(25 citation statements)

References 15 publications

(23 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This array of figures ratifies the usefulness of a Bayesian strategy to mitigate the inevitable deterioration of astrometric precision as a function of flux (see Eq. (30) in Mendez et al 2014). Remarkably, this becomes particularly dramatic when the observations are performed under adverse conditions (panels d and e in Fig.…”

Section: Improvements In the Mean Errors Of Individual Positionsmentioning

confidence: 86%

“…Returning to the observational problem in Sect. 2.1, Mendez et al (2013Mendez et al ( , 2014 have characterized and analyzed the CR lower bound in Eq. (7) for the isolated problem of astrometry and photometry, respectively, as well as the joint problem of photometry and astrometry.…”

Section: Astrometric Cramér-rao Lower Boundmentioning

confidence: 99%

“…Concerning the observation distribution, we adopt some realistic design variables and astronomical observing conditions to model the problem, similar to those adopted in Mendez et al (2013Mendez et al ( , 2014. For the PSF (see Eq.…”

Section: Astrometric Observational Settingmentioning

confidence: 99%

“…One of the tools used to characterize this precision is the Cramér-Rao (CR) bound, which provides a lower bound for the variance that can be achieved to estimate (with an unbiased estimator) the position of a point source (Mendez et al 2013(Mendez et al , 2014Lobos et al 2015), given the properties of the source and the detector. In astrometry this CR bound offers meaningful closed-form expressions that can be used to analyze the complexity of the inference task in terms of key observational and design parameters, such as position of the object in the array, pixel resolution of the instrument, and background.…”

Section: Introductionmentioning

confidence: 99%

“…In astrometry this CR bound offers meaningful closed-form expressions that can be used to analyze the complexity of the inference task in terms of key observational and design parameters, such as position of the object in the array, pixel resolution of the instrument, and background. In particular, Mendez et al (2013Mendez et al ( , 2014 have developed closed-form expressions for this bound and have studied its structure and dependency with respect to important observational parameters. Furthermore, the analysis of the CR bound allows us to address the problem of optimal pixel resolution of the array for a given observational setting, and in general to evaluate the complexity of the astrometric task with respect to the signal-to-noise ratio (S/N) and different observational regimes.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Analysis of the Bayesian Cramér-Rao lower bound in astrometry

Echeverria

Silva

Mendez

et al. 2016

A&A

Self Cite

View full text Add to dashboard Cite

Context. The best precision that can be achieved to estimate the location of a stellar-like object is a topic of permanent interest in the astrometric community. Aims. We analyze bounds for the best position estimation of a stellar-like object on a CCD detector array in a Bayesian setting where the position is unknown, but where we have access to a prior distribution. In contrast to a parametric setting where we estimate a parameter from observations, the Bayesian approach estimates a random object (i.e., the position is a random variable) from observations that are statistically dependent on the position. Methods. We characterize the Bayesian Cramér-Rao (CR) that bounds the minimum mean square error (MMSE) of the best estimator of the position of a point source on a linear CCD-like detector, as a function of the properties of detector, the source, and the background.Results. We quantify and analyze the increase in astrometric performance from the use of a prior distribution of the object position, which is not available in the classical parametric setting. This gain is shown to be significant for various observational regimes, in particular in the case of faint objects or when the observations are taken under poor conditions. Furthermore, we present numerical evidence that the MMSE estimator of this problem tightly achieves the Bayesian CR bound. This is a remarkable result, demonstrating that all the performance gains presented in our analysis can be achieved with the MMSE estimator. Conclusions. The Bayesian CR bound can be used as a benchmark indicator of the expected maximum positional precision of a set of astrometric measurements in which prior information can be incorporated. This bound can be achieved through the conditional mean estimator, in contrast to the parametric case where no unbiased estimator precisely reaches the CR bound.

show abstract

Section: Improvements In the Mean Errors Of Individual Positionsmentioning

confidence: 86%

Section: Astrometric Cramér-rao Lower Boundmentioning

confidence: 99%

Section: Astrometric Observational Settingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Analysis of the Bayesian Cramér-Rao lower bound in astrometry

Echeverria

Silva

Mendez

et al. 2016

A&A

Self Cite

View full text Add to dashboard Cite

show abstract

Characterizing the astrometric precision limit for moving targets observed with digital-array detectors

Bouquillon

Mendez

Altmann

et al. 2017

A&A

View full text Add to dashboard Cite

Aims. We investigate the maximum astrometric precision that can be reached on moving targets observed with digital-sensor arrays, and provide an estimate for its ultimate lower limit based on the Cramér-Rao bound. Methods. We extend previous work on one-dimensional Gaussian point-spread functions (PSFs) focusing on moving objects and extending the scope to two-dimensional array detectors. In this study the PSF of a stationary point-source celestial body is replaced by its convolution with a linear motion, thus effectively modeling the spread function of a moving target. Results. The expressions of the Cramér-Rao lower bound deduced by this method allow us to study in great detail the limit of astrometric precision that can be reached for moving celestial objects, and to compute an optimal exposure time according to different observational parameters such as seeing, detector pixel size, decentering, and elongation of the source caused by its drift. Comparison to simulated and real data shows that the predictions of our simple model are consistent with observations.

show abstract

Theoretic Studies of Full Constraints on a Star Tracker's Influential Error Sources for In-orbit Calibration

Zhang¹,

Hao²,

Wang³

et al. 2016

PASP

View full text Add to dashboard Cite

To collect star transits data qualified for in-orbit calibration, this study derives the full error constraints to limit star trackerʼs influential error sources and computes their error boundaries from a theoretical perspective. The full constraints, including not only the minimum variance estimation of position but also the error bound prediction of scale and intensity of Gaussian-shaped starspots, are studied based on the Cramér-Rao Lower Bound (CRLB) theorem. By imposing these constraints on motion, drift in focal length, and other factors, their boundaries could be determined before launch. Therefore, the in-orbit correction accuracy is expected to be close to CRLB through suitable implementation of these constraints. The correctness of the theoretical position error of motion is demonstrated by the data-fitting procedure against test results of star tracker on dynamic performance. The simulation result shows that the drift in focal length can generate an error with the same magnitude as detector noise and thus might be the dominant error source when star tracker is working under stationary circumstance. Using the accuracy performance of some typical star trackers, this study shows that the CRLB constraint may be very effective to estimate the overall position error of a starspot or one axis, valuable data that can be used for online calibration. The overall position uncertainty analysis shows that a weighted method can be employed for calibration, a process where star data can be given a weight in inverse proportion to the CRLB value.

show abstract

Analysis of the Cramér-Rao Bound in the Joint Estimation of Astrometry and Photometry

Cited by 13 publications

References 15 publications

Analysis of the Bayesian Cramér-Rao lower bound in astrometry

Analysis of the Bayesian Cramér-Rao lower bound in astrometry

Characterizing the astrometric precision limit for moving targets observed with digital-array detectors

Theoretic Studies of Full Constraints on a Star Tracker's Influential Error Sources for In-orbit Calibration

Contact Info

Product

Resources

About