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An extension is presented to the particle filtering toolbox that enables nonlinear/non-Gaussian filtering to be performed in the presence of out-of-sequence measurements (OOSMs) with arbitrary lag, without the need to adopt linearising approximations in the filter and without the degradation of performance that would occur if the OOSMs were simply discarded. An estimate of the performance of the OOSM particle filter (OOSM-PF) is obtained for bearings-only tracking scenarios with a single target and a small number of sensors. These performance estimates are then compared with the posterior Cramer-Rao lower bound (CRLB) for the state estimate rms error and similar performance estimates obtained from the oosm extended Kalman filter (OOSM-EKF) algorithms recently introduced in the literature. For a mildly nonlinear bearings-only tracking problem the OOSM-PF and OOSM-EKF are shown to achieve broadly similar performance.