State Estimation by steady state Kalman Filter
I've just tried a toy example of doing what you're suggesting and it works fine. The plot below shows how the standard Kalman filter (red line) and the steady-state Kalman filter (green circles) outputs are the same, except for some minor differences at the beginning.

The bottom plot shows the evolution of the Kalman gain coefficients for the standard Kalman filter.

Without seeing more detail of what you're doing, I don't think I can help much.  Note that I'm using SISO example, which may not be what you're after... but I haven't ever seen reasons for MIMO models to work differently than expected.





R Code Below

#27879 and 29963

T &lt;- 100

#H = [3 -3 1]
H &lt;- matrix(c(1,0,0),c(1,3)) 

#F is just a tapped delay line
alpha &lt;- matrix(c(0.9,0,0,0,0.9,0,0,0,0.9),3,3)
A &lt;- matrix(c(3,1,0,-3,0,1,1,0,0),3,3)
B &lt;- matrix(c(1,0,0),c(3,1))

sigma_v &lt;- 1
v &lt;- rnorm(T,0,sigma_v)
sigma_w &lt;- 0.01
w &lt;- rnorm(T,0,sigma_w)

x &lt;- matrix(c(0,0,0),c(3,1))
z &lt;- rep(0,T)

for (t in 1:T)
{
  z[t] &lt;- H %*% x + w[t]
  x &lt;- A %*% x +v[t]
}
par(mfrow=c(2,1))
plot(z,type="l", col="blue", lwd=5)
title('Measurements and both Filtered Measurements')

Q &lt;- matrix(c(0,0,0,0,0,0,0,0,sigma_v^2),3,3)
R &lt;- sigma_w^2


library("MASS") # For pseudo inverse ginv()

xkm1km1 &lt;- matrix(rep(0,3*T+3),3,T+1)
xkkm1 &lt;- matrix(rep(0,3*T),3,T)
K &lt;- matrix(rep(0,3*T),3,T)
Pkm1km1 &lt;- matrix(c(1000,0,0 ,0,1000,0, 0,0,1000),3,3)
zhat &lt;- matrix(rep(0,T),c(T,1))

for (k in 1:T)
{
  xkkm1[,k] &lt;- A %*% xkm1km1[,k]
  Pkkm1 &lt;- A %*% Pkm1km1 %*% t(A) + Q
  K[,k] &lt;- Pkkm1 %*% t(H) %*% ginv( H %*% Pkkm1 %*% t(H) + R)
  xkm1km1[,k+1] &lt;- xkkm1[,k] + K[,k] %*% (z[k] - H %*% xkkm1[,k])
  Pkm1km1 &lt;- (matrix(c(1,0,0,0,1,0,0,0,1),3,3) - K[,k] %*% H) %*% Pkkm1  
  zhat[k] &lt;- as.numeric(H %*% xkkm1[,k])
}
lines(zhat, col="red")

xkm1km1 &lt;- matrix(rep(0,3*T+3),3,T+1)
xkkm1 &lt;- matrix(rep(0,3*T),3,T)
zhat &lt;- matrix(rep(0,T),c(T,1))

for (k in 1:T)
{
  xkkm1[,k] &lt;- A %*% xkm1km1[,k]
  K[,T] &lt;- Pkkm1 %*% t(H) %*% ginv( H %*% Pkkm1 %*% t(H) + R)
  xkm1km1[,k+1] &lt;- xkkm1[,k] + K[,T] %*% (z[k] - H %*% xkkm1[,k])
  zhat[k] &lt;- as.numeric(H %*% xkkm1[,k])
}
points(zhat, col="green")

plot(1:100, K[1,], type="l", ylim=c(-1,1))
title('Kalman Gain coefficients')
lines(1:100, K[2,], col="red")
lines(1:100, K[3,], col="green")