This article introduces a Rao-Blackwellised particle filtering (RBPF) approach in the finite set statistics (FISST) multitarget tracking framework. The RBPF approach is proposed in such a case, where each sensor is assumed to produce a sequence of detection reports each containing either one single-target measurement, or a "no detection" report. The tests cover two different measurement models: a linear-Gaussian measurement model, and a nonlinear model linearised in the extended Kalman filter (EKF) scheme. In the tests, Rao-Blackwellisation resulted in a significant reduction of the errors of the FISST estimators when compared with a previously proposed direct particle implementation. In addition, the RBPF approach was shown to be applicable in nonlinear bearings-only multitarget tracking.