The measurements produced by many sensing systems — such as GPS or IMU — are corrupted by coloured noises which can have significant time correlations. However, approximating these as white noises can significantly degrade the performance of an estimator. To overcome these difficulties, pre-whitening filters can be used. However, because of the number of sensors and complexities of the models, the number of states associated with these pre-whitening filters can become extremely large. In this paper, we consider how coloured noise models can be efficiently incorporated within graph-based formulations of filtering and estimation problems. We exploit the observation that a pose graph, unlike a conventional filtering algorithm, permits a high degree of flexibility in the temporal ordering and update rates of individual states. We show that implementing multi-rate filters is a special case of marginalising vertices in a graph. Exploiting the linear nature of many pre-whitening filters, we develop a closed form solution for the marginalisation scheme, and develop a covariance consistent approximation. We demonstrate the results in simulated examples.
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