There are two accepted ways to do this.
First, write a numerical simulation and just see what value it converges to.
Second, any of several textbooks will give you the procedure to compute it directly. I am not going to try to type several pages of instruction here, not the least because I am not solid on the theory itself. Crassidis' "Optimal Estimation of Dynamic Systems" gives the clearest presentation that I know of in section 5.3.4. Dan Simon's book talks about computing this for different filters (Crassidis is for a linear, discrete filter), and sites the research that discusses how to determine if your filter will converge or not.
Me, since I'm not sending rockets into space or doing other life-critical work, I just do the numerical simulation!