UT变换UnscentedKalman Filter (UKF2那么，精确到2阶以上（泰勒级数）有2n(15)9=wiyii=02nPy =wi(yi-g)(yi-g)T(16)i=0其中，i=h(x,)，i=0,.,2n。10/37Dr.Yuan-LiCaiXi'an JiaotongUniversity
2 UT 变换 Unscented Kalman Filter (UKF) 那么，精确到 2 阶以上（泰勒级数）有 y¯ = X 2n i=0 wiyi (15) Py = X 2n i=0 wi(yi − y¯)(yi − y¯) T (16) 其中，yi= h(χi )，i = 0, · · · , 2n。 Dr. Yuan-Li Cai 10/37 Xi’an Jiaotong University
UnscentedKalmanFilter(UKF3SUT变换3.SUT 变换SUT:ScaledUnscentedTransformation(17)Xo=, i=0(18)Xi=+(V(n+)P)i,i=1,.-,n(19)Xi=-(V(n+^)P)i-n,i=n+l,...,2n11/37Dr.Yuan-Li CaiXian Jiaotong University
3 SUT 变换 Unscented Kalman Filter (UKF) 3. SUT 变换 SUT: Scaled Unscented Transformation χ0 = ¯x, i = 0 (17) χi = ¯x + (p (n + λ)Px)i , i = 1, · · · , n (18) χi = ¯x − ( p (n + λ)Px)i−n, i = n + 1, · · · , 2n (19) Dr. Yuan-Li Cai 11/37 Xi’an Jiaotong University
UnscentedKalmanFilter(UKF3SUT变换入/(n+),i=0(m)(20)301/2(n+^),i=1,2,...,2n入/(n +)+(1 -α2+β), i= 0,(c)(21)1/2(n +>),i=1,2,..,2n其中，可调参数0≤α≤1(一般可选α=10-3)，β根据先验知识选取(正态分布时，β=2为最优），k通常取为0.>=(n+k)α2-n12/37Dr. Yuan-Li CaiXi'an Jiaotong University
3 SUT 变换 Unscented Kalman Filter (UKF) w (m) i = λ/(n + λ), i = 0 1/2(n + λ), i = 1, 2, · · · , 2n (20) w (c) i = λ/(n + λ) + (1 − α 2 + β), i = 0 1/2(n + λ), i = 1, 2, · · · , 2n (21) 其中，可调参数 0 ≤ α ≤ 1(一般可选 α = 10−3 )，β 根据 x 先验知识选取 （正态分布时，β = 2 为最优），κ 通常取为 0，λ = (n + κ)α 2 − n. Dr. Yuan-Li Cai 12/37 Xi’an Jiaotong University