Bias-free Measurement of Giant Molecular Cloud Properties

(abridged) We review methods for measuring the sizes, line widths, and luminosities of giant molecular clouds (GMCs) in molecular-line data cubes with low resolution and sensitivity. We find that moment methods are robust and sensitive -- making full use of both position and intensity information -- and we recommend a standard method to measure the position angle, major and minor axis sizes, line width, and luminosity using moment methods. Without corrections for the effects of beam convolution and sensitivity to GMC properties, the resulting properties may be severely biased. This is particularly true for extragalactic observations, where resolution and sensitivity effects often bias measured values by 40% or more. We correct for finite spatial and spectral resolutions with a simple deconvolution and we correct for sensitivity biases by extrapolating properties of a GMC to those we would expect to measure with perfect sensitivity. The resulting method recovers the properties of a GMC to within 10% over a large range of resolutions and sensitivities, provided the clouds are marginally resolved with a peak signal-to-noise ratio greater than 10. We note that interferometers systematically underestimate cloud properties, particularly the flux from a cloud. The degree of bias depends on the sensitivity of the observations and the (u,v) coverage of the observations. In the Appendix to the paper we present a conservative, new decomposition algorithm for identifying GMCs in molecular-line observations. This algorithm treats the data in physical rather than observational units, does not produce spurious clouds in the presence of noise, and is sensitive to a range of morphologies. As a result, the output of this decomposition should be directly comparable among disparate data sets.Comment: Accepted to PASP (19 pgs., 12 figures). The submission describes an IDL software package available from http://cfa-www.harvard.edu/~erosolow/cprops

Probability-guaranteed set-membership state estimation for polynomially uncertain linear time-invariant systems

2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksConventional deterministic set-membership (SM) estimation is limited to unknown-but-bounded uncertainties. In order to exploit distributional information of probabilistic uncertainties, a probability-guaranteed SM state estimation approach is proposed for uncertain linear time-invariant systems. This approach takes into account polynomial dependence on probabilistic uncertain parameters as well as additive stochastic noises. The purpose is to compute, at each time instant, a bounded set that contains the actual state with a guaranteed probability. The proposed approach relies on the extended form of an observer representation over a sliding window. For the offline observer synthesis, a polynomial-chaos-based method is proposed to minimize the averaged H2 estimation performance with respect to probabilistic uncertain parameters. It explicitly accounts for the polynomial uncertainty structure, whilst most literature relies on conservative affine or polytopic overbounding. Online state estimation restructures the extended observer form, and constructs a Gaussian mixture model to approximate the state distribution. This enables computationally efficient ellipsoidal calculus to derive SM estimates with a predefined confidence level. The proposed approach preserves time invariance of the uncertain parameters and fully exploits the polynomial uncertainty structure, to achieve tighter SM bounds. This improvement is illustrated by a numerical example with a comparison to a deterministic zonotopic method.Peer ReviewedPostprint (author's final draft