Kalman Filter Convergence Time

Question

For a time invariant system, is it possible to guarantee a convergence time that Kalman Filter error covariance reaches the steady state value. if it is possible, then how can we set that convergence time ?

Answer 1

What you can probably do is to look at the resulting error dynamics $\dot e(t)=Ae(t)$ ($A$ is the closed-loop matrix) and estimate its convergence to zero. The basic solution here is an exponential $e^{i Re\lambda_k t}$ where $\lambda_k$ is en eigenvalue of $A$. The slowest exponent (the largest negative Re$\lambda$) will affect the convergence the most.