  Ordered pivotal sampling is one of the simplest algorithm to perform
without-replacement unequal probability sampling. It has found uses in the
context of longitudinal surveys and spatial sampling, and enables in particular
a good spatial balance of the selected units. In this work, we follow the
approach proposed by Ohlsson~(1986), and apply a martingale central-limit
theorem to prove the asymptotic normality of the Horvitz-Thompson estimator
under a design-based approach, and under a model-assisted approach. In
particular, our model assumptions allow for correlations between values, which
is of particular interest for applications in spatial sampling.
