An excellent introduction to Kalman Filters is the one by Welch Bishop (Google It)

Then i would suggest reading Van Der Merwe's thesis

At the end of the day, the KF, EKF, UKF etc are all stochastic observers that have the same structure as a Luenberger observer. In fact in the deterministic world the LQR control problem may be reformulated as a dual observer problem.

If the filter converges, the steady state Kalman gains will be as predicted by LQR theory

An aspect not covered usually is the closed loop behavior of KF + controller.

KF may have very low estimation error, but if it has poor frequency response there will be lag and possible instability in the closed loop.

An alternate approach is the Functional Observer architecture, which guarantees good robustness of the closed loop system, while maintaining the separation principle (Design of Observer and Controller should be separate).

My goal is to make a Functional UKF and develop methods to estimate the phase loss in the UKF

For INS-GPS integration i refer to "Strapdown Inertial Navigation" by "Titterton and Weston"