  Characterising the time over which quantum coherence survives is critical for
any implementation of quantum bits, memories and sensors. The usual method for
determining a quantum system's decoherence rate involves a suite of experiments
probing the entire expected range of this parameter, and extracting the
resulting estimation in post-processing. Here we present an adaptive
multi-parameter Bayesian approach, based on a simple analytical update rule, to
estimate the key decoherence timescales ($T_1$, $T_2^*$ and $T_2$) and the
corresponding decay exponent of a quantum system in real time, using
information gained in preceding experiments. This approach reduces the time
required to reach a given uncertainty by a factor up to an order of magnitude,
depending on the specific experiment, compared to the standard protocol of
curve fitting. A further speed-up of a factor $\sim 2$ can be realised by
performing our optimisation with respect to sensitivity as opposed to variance.
