Yes of course there is but the formula would be very complicated.
I would suggest the simplest method (which ignores phase shifts and residual capacitances/inductances but will give a reasonably accurate result) is to convert it to a resistor model and treat the antenna voltage, assuming that is the input, as DC. In reality it will be very frequency dependent.
So do this:
1. convert all the capacitors to equivalent resistances using the formula:
1/(2 * pi * f * C)
2. convert all the inductances to equivalent resistances using the formula:
2 * pi * f * L
3. for the diodes, subtract Vf from the voltage across them and calculate the power loss as Vf * I
Use the resistor as it is. The power loss in it is (V * V)/R
In the calculation, f is the frequency in Hz, C is in Farads, L is in Henries and R is in Ohms. When you have converted everything to it's equivalent resistance and calculated the total across the source, the power consumption is (source voltage * source voltage)/ total resistance.
As I said, the calculation is quite complex and will be inaccurate unless you also take into account the phase shifts and shape of the input waveform.
Brian.