Mathematical Problems in Engineering

Research Article

Application of Improved Simplex Quadrature Cubature Kalman Filter in Nonlinear Dynamic System

Table 2

Points and weights for different degree of simplex cubature and higher-order Gauss–Laguerre rules for a second-order system.
2m + 1SCQ pointsWeights
31(1.4142, 0), (−0.7071, 1.2247), (−0.7071, −1.2247), (−1.4142, 0), (0.7071, −1.2247), (0.7071, 1.2247)1/6, 1/6, 1/6, 1/6, 1/6, 1/6
2(2.6131, 0), (−1.3066, 2.2630), (−1.3066, −2.2630), (−2.6131, 0), (1.3066, −2.2630), (1.3066, 2.2630), (1.0824, 0), (−0.5412, 0.9374), (−0.5412, −0.9374), (−1.0824, 0), (0.5412, −0.9374), (0.5412, 0.9374)0.0244,0.0244, 0.0244, 0.0244, 0.0244, 0.0244, 0.1423, 0.1423, 0.1423, 0.1423, 0.1423, 0.1423
3(3.5468, 0), (−1.7734, 3.0716), (−1.7734, −3.0716), (−3.5468, 0), (1.7734, −3.0716), (1.7734, 3.0716), (2.1421, 0), (−1.0710, 1.8551), (−1.0710, −1.8551), (−2.1421, 0), (1.0710, −1.8551), (1.0710, 1.8551), (0.9119, 0), (−0.4559, 0.7897), (−0.4559, −0.7897), (−0.9119, 0), (0.4559, −0.7897), (0.4559, 0.7897)0.0017, 0.0017, 0.0017, 0.0017, 0.0017, 0.0017, 0.0464, 0.0464, 0.0464, 0.0464, 0.0464, 0.0464, 0.1185, 0.1185, 0.1185, 0.1185, 0.1185, 0.1185
51(1.4142, 0), (−0.7071, 1.2247), (−0.7071, −1.2247), (−1.4142, 0), (0.7071, −1.2247), (0.7071, 1.2247), (0.7071, 1.2247), (0.7071, −1.2247), (−1.4142, 0), (−0.7071, −1.2247), (1.4142, 0)5/36, 5/36, 5/36, 5/36, 5/36, 5/36, 1/36, 1/36, 1/36, 1/36, 1/36, 1/36
2(2.6131, 0), (−1.3066, 2.2630), (−1.3066, −2.2630), (−2.6131, 0), (1.3066, −2.2630), (1.3066, 2.2630), (1.3066, 2.2630), (1.3066, −2.2630), (−2.6131, 0), (−1.3066, −2.2630), (−1.3066, 2.2630), (2.6131, 0), (1.0824, 0), (−0.5412, 0.9374), (−0.5412, −0.9374), (−1.0824, 0), (0.5412, −0.9374), (0.5412, 0.9374), (0.5412, 0.9374), (0.5412, −0.9374), (−1.0824, 0), (−0.5412, −0.9374), (−0.5412, 0.9374), (1.0824, 0)0.0203, 0.0203, 0.0203, 0.0203, 0.0203, 0.0203, 0.0041, 0.0041, 0.0041, 0.0041, 0.0041, 0.0041, 0.1185, 0.1185, 0.1185, 0.1185, 0.1185, 0.1185, 0.0237, 0.0237, 0.0237, 0.0237, 0.0237, 0.0237
3(3.5468, 0), (−1.7734, 3.0716), (−1.7734, −3.0716), (−3.5468, 0), (1.7734, −3.0716), (1.7734, 3.0716), (1.7734, 3.0716), (1.7734, −3.0716), (−3.5468, 0), (−1.7734, −3.0716), (−1.7734, 3.0716), (3.5468, 0), (2.1421, 0), (−1.0710, 1.8551), (−1.0710, −1.8551), (−2.1421, 0), (1.0710, −1.8551), (1.0710, 1.8551), (1.0710, 1.8551), (1.0710, −1.8551), (−2.1421, 0), (−1.0710, −1.8551), (−1.0710, 1.8551), (2.1421, 0), (0.9119, 0), (−0.4559, 0.7897), (−0.4559, 0.7897), (−0.9119, 0), (0.4559, −0.7897), (0.4559, 0.7897), (0.4559, 0.7897), (0.4559, −0.7897), (−0.9119, 0), (−0.4559, −0.7897), (−0.4559, 0.7897), (0.9119, 0)0.0014, 0.0014, 0.0014, 0.0014, 0.0014, 0.0014, 0.0003, 0.0003, 0.0003, 0.0003, 0.0003, 0.0003, 0.0387, 0.0387, 0.0387, 0.0387, 0.0387, 0.0387, 0.0077, 0.0077, 0.0077, 0.0077, 0.0077, 0.0077, 0.0988, 0.0988, 0.0988, 0.0988, 0.0988, 0.0988, 0.0198, 0.0198, 0.0198, 0.0198, 0.0198, 0.0198