Determine instantaneous phase from two shifted periodic signals with unknown offset

Question

I have two periodic noisy signals which depend on a constantly increasing reference angle. The two signals are shifted by 90 degrees and one of them has an unknown varying offset. Two sample signals like this can be generated using a simple python code:

instantaneous_phase=np.linspace(0,6*np.pi,1000) % (2*np.pi)

unknown_offset=np.linspace(0,1,1000)

signal1=np.sin(instantaneous_phase) + ((np.random.rand(1000))-0.5)/10
signal2=np.cos(instantaneous_phase) + ((np.random.rand(1000))-0.5)/10 + unknown_offset

Giving something like:

I need to reconstruct instantaneous_phase, using only signal1 and signal2. Is this possible? I'd appreciate if someone can point me in the right direction.