diff --git a/jsl/lds/kalman_filter.py b/jsl/lds/kalman_filter.py
index 81c6ad0..4982ec3 100644
--- a/jsl/lds/kalman_filter.py
+++ b/jsl/lds/kalman_filter.py
@@ -2,7 +2,7 @@
 # Author:  Gerardo Durán-Martín (@gerdm), Aleyna Kara(@karalleyna)
 from jax import config
 
-config.update('jax_default_matmul_precision', 'float32')
+config.update("jax_default_matmul_precision", "float32")
 
 import chex
 import jax.numpy as jnp
@@ -158,7 +158,9 @@ def kalman_step(state, obs, params):
     Sigma_cond = A @ Sigma @ A.T + Q
 
     # \mu_{t |t-1} and xn|{n-1}
-    mu_cond = A @ mu
+
+    mu_cond = A @ mu 
+    mu_cond = mu_cond + params.get_state_offset_of(t)
 
     Ct = params.get_obs_mat_of(t)
     R = params.get_observation_noise_of(t)
@@ -166,7 +168,9 @@ def kalman_step(state, obs, params):
     St = Ct @ Sigma_cond @ Ct.T + R
     Kt = solve(St, Ct @ Sigma_cond, sym_pos=True).T
 
-    mu = mu_cond + Kt @ (obs - Ct @ mu_cond)
+    innovation = Ct @ mu_cond 
+    innovation = innovation + params.get_obs_offset_of(t)
+    mu = mu_cond + Kt @ (obs - innovation)
 
     #  More stable solution is (I − KtCt)Σt|t−1(I − KtCt)T + KtRtKTt
     tmp = (I - Kt @ Ct)