  This paper derives the optimal Bayesian processing of an out-of-sequence
(OOS) set of measurements in continuous-time for multiple target tracking. We
consider a multi-target system modelled in continuous time that is discretised
at the time steps when we receive the measurements, which are distributed
according to the standard point target model. All information about this system
at the sampled time steps is provided by the posterior density on the set of
all trajectories. This density can be computed via the continuous-discrete
trajectory Poisson multi-Bernoulli mixture (TPMBM) filter. When we receive an
OOS measurement, the optimal Bayesian processing performs a retrodiction step
that adds trajectory information at the OOS measurement time stamp followed by
an update step. After the OOS measurement update, the posterior remains in
TPMBM form. We also provide a computationally lighter alternative based on a
trajectory Poisson multi-Bernoulli filter. The effectiveness of the two
approaches to handle OOS measurements is evaluated via simulations.
