The temporal evolution of the gravitational wave background signal resulting from stellar-mass binary black hole (BBH) inspirals has a unique statistical signature. We describe the application of a new filter, based on the 'probability event horizon' (PEH) concept, that utilizes both the temporal and spatial source distribution to constrain the local rate density, r(0), of BBH inspiral events in the nearby Universe. Assuming advanced LIGO (Laser Interferometer Gravitational Wave Observatory) sensitivities and an upper rate of Galactic BBH inspirals of 30 Myr(-1), we simulate gravitational wave data and apply a fitting procedure to the PEH filtered data. To determine the accuracy of the PEH filter in constraining r(0), a comparison is made with a fit to the brightness distribution of events. We apply both methods to a data stream containing a background of Gaussian-distributed false alarms. We find that the brightness distribution yields lower standard errors, but is biased by the false alarms. In comparison, the PEH method is less prone to errors resulting from false alarms but has a lower resolution as fewer events contribute to the data. Used in combination, the PEH and brightness distribution methods provide an improved estimate of the rate density.