We identify generic protocols achieving optimal power extraction from a
single active particle subject to continuous feedback control under the
assumption that the instantaneous velocity, but not the fluctuating
self-propulsion velocity, is accessible to direct observation. Our Bayesian
approach draws on the Onsager-Machlup path integral formalism and is
exemplified in the cases of free run-and-tumble and active Ornstein-Uhlenbeck
dynamics in one dimension. Such optimal protocols extract positive work even in
models characterised by time-symmetric positional trajectories and thus
vanishing informational entropy production rates. We argue that the theoretical
bounds derived in this work are those against which the performance of
realistic active matter engines should be compared.