<Dl> <Dd> x ^ (t 0) = E (x (t 0)), P (t 0) = V a r (x (t 0)) (\ displaystyle (\ hat (\ mathbf (x))) (t_ (0)) = E (\ bigl () \ mathbf (x) (t_ (0)) (\ bigr)) (\ text (,)) \ mathbf (P) (t_ (0)) = Var (\ bigl () \ mathbf (x) (t_ (0)) (\ bigr))) </Dd> </Dl> <Dd> x ^ (t 0) = E (x (t 0)), P (t 0) = V a r (x (t 0)) (\ displaystyle (\ hat (\ mathbf (x))) (t_ (0)) = E (\ bigl () \ mathbf (x) (t_ (0)) (\ bigr)) (\ text (,)) \ mathbf (P) (t_ (0)) = Var (\ bigl () \ mathbf (x) (t_ (0)) (\ bigr))) </Dd> <P> Predict - Update </P> <Dl> <Dd> x ^ _̇ (t) = f (x ^ (t), u (t)) + K (t) (z (t) − h (x ^ (t))) P _̇ (t) = F (t) P (t) + P (t) F (t) ⊤ − K (t) H (t) P (t) + Q (t) K (t) = P (t) H (t) ⊤ R (t) − 1 F (t) = ∂ f ∂ x x ^ (t), u (t) H (t) = ∂ h ∂ x x ^ (t) (\ displaystyle (\ begin (aligned) (\ dot (\ hat (\ mathbf (x)))) (t) & = f (\ bigl () (\ hat (\ mathbf (x))) (t), \ mathbf (u) (t) (\ bigr)) + \ mathbf (K) (t) (\ Bigl () \ mathbf (z) (t) - h (\ bigl () (\ hat (\ mathbf (x))) (t) (\ bigr)) (\ Bigr)) \ \ (\ dot (\ mathbf (P))) (t) & = \ mathbf (F) (t) \ mathbf (P) (t) + \ mathbf (P) (t) \ mathbf (F) (t) ^ (\ top) - \ mathbf (K) (t) \ mathbf (H) (t) \ mathbf (P) (t) + \ mathbf (Q) (t) \ \ \ mathbf (K) (t) & = \ mathbf (P) (t) \ mathbf (H) (t) ^ (\ top) \ mathbf (R) (t) ^ (- 1) \ \ \ mathbf (F) (t) & = \ left. (\ frac (\ partial f) (\ partial \ mathbf (x))) \ right \ vert _ ((\ hat (\ mathbf (x))) (t), \ mathbf (u) (t)) \ \ \ mathbf (H) (t) & = \ left. (\ frac (\ partial h) (\ partial \ mathbf (x))) \ right \ vert _ ((\ hat (\ mathbf (x))) (t)) \ end (aligned))) </Dd> </Dl>

Difference between extended kalman filter and kalman filter