In this work, we consider the problem of synchronising separately located transmitters and a staring array receiver that also has a local transmitter. The acknowledged benefits of using separate transmitters in active sensing are often undermined by the difficulty in accurate synchronisation of the receiver and the transmitters. In this work, we propose a solution that is based on measurements from non-cooperative objects in the illuminated region. We formulate the problem as parameter estimation in a state space model with individual transmitter channel data cubes as measurements. For maximum likelihood estimation, we use an expectation maximisation type iterative bound optimisation using distributions found by track-before-detect together with explicit formulae derived here for the related score function for chirp waveforms. We demonstrate that the proposed approach is capable of achieving very high accuracy with errors on the order of small fractions of the pulse width thereby enabling coherent processing in bi-static channels.