Introduction

Surveying the Universe is the ultimate remote sensing problem. Inferring the intrinsic properties of the galaxy population, via analysis of survey-generated catalogues, is a major challenge for twenty-first century cosmology, but this challenge must be met without any prospect of measuring these properties in situ. Thus, for example, our knowledge of the intrinsic luminosity and spatial distribution of galaxies is filtered by imperfect distance information and by observational selection effects, issues which have come to be known generically in the literature as ‘Malmquist bias’. Figure 11.1 shows schematically how such effects may distort our inferences about the underlying population since, in general, these must be derived from a noisy, sparse and truncated sample of galaxies.

There is a long (and mostly honourable!) tradition in the astronomical literature of attempts to cast such remote surveying problems within a rigorous statistical framework. Indeed, it is interesting to note that seminal examples from the early twentieth century (Eddington 1913, 1940; Malmquist 1920, 1922) display, at least with hindsight, hints of a Bayesian formulation long before the recent renaissance of Bayesian methods in astronomy. Unfortunately, space does not permit us to review in detail that early literature, nor many of the more recent papers which evolved from it. A more thorough discussion of the literature on statistical analysis of survey data can be found in, e.g., Hendry and Simmons (1995), Strauss and Willick (1995), Teerikorpi (1997) and Loredo (2007).

This chapter is devoted to population orbit determination, that is not just computing the orbit for a single object, but compiling a catalog of orbits given a large number of observations. A survey is a project aiming at collecting observations of the largest and most representative sample of objects possible. We deal here only with the case in which the target population belongs to the Solar System; of course an astronomical survey may target simultaneously extrasolar populations. We deal with Earth satellites in Section 8.7. This chapter is based on our papers (Milani et al. 2005a, Milani et al. 2008, Milani et al. 2006) and ongoing research, in particular that in preparation for Pan-STARRS, a next-generation survey.

Operational constraints of Solar System surveys

The following three arguments should be taken into account in the definition of an identification/orbit determination procedure for a modern sky survey.

First, Moore's law tells us that the number of elements in an electronic chip grows exponentially with time; the doubling time has been around 18 months for more than 30 years. There is no indication that this trend might slow down; although in the last few years it has no longer been possible to increase the clock frequency, the increase in the complexity of the chips is now used to produce “multicore” CPUs. Assuming the multicores are used in an efficient parallelization procedure, the practical performance of computers continues to increase by a factor of 4 every three years.