CPHD filtering with unknown clutter rate and detection profile

In Bayesian multi-target filtering we have to contend with two notable sources of uncertainty, clutter and detection. Knowledge of parameters such as clutter rate and detection profile are of critical importance in multi-target filters such as the probability hypothesis density (PHD) and Cardinalized PHD (CPHD) filters. Naive application of the CPHD (and PHD) filter with mismatches in clutter and detection model parameters results in biased estimates. In this paper we show how to use the CPHD (and PHD) filter in unknown clutter rate and detection profile.