A calculation for estimating concentrations of long-lived airborne particulate radioactivity using fixed-filter continuous air monitors is given in an ISO standard. The method uses counts integrated over relatively long time intervals, rather than the "instantaneous" count rates that in digital systems are evaluated using much shorter time intervals and some form of variance-reduction filtering. This article presents three ways of deriving and interpreting this calculation, based on previously published mathematical models that were derived from first principles. The method is also extended here to apply for short-lived activity. Some statistical properties of the estimator are discussed, including its time-dependent variance and the presence of strong autocorrelation in the concentration estimates. An interactive simulation was used to examine the performance of the concentration estimation, using physically plausible concentration time-dependence profiles; example plots are provided. The conclusion of these studies is that the method, as modified herein, can perform remarkably well in providing periodic average-concentration estimates for both long- and short-lived activity, and it should be considered an appropriate method in those situations where the tracking of a time-dependent concentration is deemed necessary.