By window I meant what values will "a" typically take? For instance, 0<a<1. Specifying this can simplify the problem greatly. You could then sample values of "a" in this interval, say 10 to 100 points in this interval, or even more depending on what you desire to analyze.
There might be a direct alternative by keeping "a" totally unknown, I do not know of a method to do so. I haven't got a chance to go through the equations you sent yet, I'll tell you if I figure something when I look at it.
Thanks,