\underline{1}

x̂_{k}^{−} = Ax̂_{k−1} + Bu_{k−1}  (0.0.1)
P_{k}^{−} = AP_{k−1}A^{T}+ BQB^{T}  (0.0.2)
K_{k} = P_{k}^{−} H^{T}(HP_{k}^{−} H^{T}+ R)^{−}  (0.0.3)
x̂^{k}= x̂_{k}^{−} + K_{k}(z_{k}− Hx̂_{k}^{−})  (0.0.4)
P_{k} = (I − K_{k}H)P_{k}^{−}  (0.0.5)

C_{v_{k}^{−}} = \frac{1}{N} ∑_{j=k−N+1}^{k} v_{j}^{−} (v_{j}^{−} )^{T}

(v_{j}^{−} = z_{j} − H_{j}x_{j}^{−} )  (0.0.6)
R̂_{k}= C_{v_{k}^{−}} − H_{k}P_{k}^{−} H_{k}^{T}  (0.0.7)

Q̂_{k}= \frac{1}{N} ∑_{j=k−N+1}^{k} Δx_{j}Δx_{j}^{T}+ P_{k}^{+} − ΦP_{k−1}^{+}Φ^{T}

(Δx_{j} = x_{j}^{−} − x_{j}^{+} )  (0.0.8)

f_{n}(z_{k}) = \frac{1}{\sqrt{(2π)^{m}|C_{v_{k}^{−}}|}}e^{− \frac{1}{2}v_{k}C_{v^{−}_{k}}^{−1} v_{k}^{T}}  (0.0.9)

p_{n}(k) = \frac{f_{n}(z_{k}) · p_{n}(k − 1)}{∑ _{j=1}^{N} f_{j}(z_{k}) · p_{j}(k − 1)}  (0.0.10)