We consider the problem of controlling the precision of the multiple-model multiple-hypothesis filter with Gaussian mixture reduction. The controller adaptively chooses the number of hypotheses kept by the filter to (sub)optimally seek a tradeoff between filter precision and computational effort. In order to quantify the approximation error due to hypotheses truncation, the controller employs probability divergence measures such as f-divergences and the Wasserstein divergence. The proposed solution is tested on the problem of estimating the states of a networked control system with packet drops on the controller-actuator channel. Theoretical results demonstrate that our strategy leads to a divergence between the true Bayes posterior and the truncated one that remains bounded over time. Numerical results show a good improvement with respect to truncation with a constant number of hypotheses, specially as the number of modes increases and so does the problem dimensionality.