The state of the system generally satisfies specific constraints imposed by material properties or physical laws, so the application of these constraints can improve the accuracy of state estimation. In this paper, a novel recursive filter referred as constrained high-degree cubature skew-Gaussian filter (CHCSGF) is proposed, which achieves soft-constrained state estimation by compressing the probability density of unconstrained states with constraint information. First, the probability density of the state under inequality soft constraints is modeled as a skew-Gaussian (SG) distribution, rather than truncated or single Gaussian distributions. Then, a recursive constrained SG filter is developed to handle inequality soft constraints in linear systems. Addressing nonlinear challenges, a 5th-degree spherical-radial cubature approximation method is presented to numerically calculate SG-weighted integrals for the nonlinear transformation of SG distribution. Finally, the CHCSGF algorithm is proposed using this method to tackle nonlinear filtering problems. The CHCSGF is applied to reentry trajectory tracking to improve estimation accuracy by dealing with heat flow, dynamic pressure and overload constraints during reentry flight. Simulation results demonstrate that the CHCSGF achieves higher estimation accuracy than unconstrained methods under nonlinear inequality soft constraints, and is robust to the constraints with a prior error. Compared to particle filter and moving horizon estimation, the computational complexity of CHCSGF is significantly reduced.

中文翻译：

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一种新型约束偏斜高斯滤波器及其在可机动再入飞行器跟踪中的应用


系统的状态通常满足材料属性或物理定律施加的特定约束，因此应用这些约束可以提高状态估计的准确性。该文提出了一种新型递归滤波器，称为约束高阶容积偏高斯滤波器（CHCSGF），它通过用约束信息压缩无约束态的概率密度来实现软约束状态估计。首先，在不等式软约束下状态的概率密度被建模为偏高斯 （SG） 分布，而不是截断或单一的高斯分布。然后，开发了一种递归约束 SG 滤波器来处理线性系统中的不等式软约束。为了应对非线性挑战，提出了一种 5 次球形-径向立方体近似方法，用于数值计算 SG 分布非线性变换的 SG 加权积分。最后，利用该方法提出CHCSGF算法来解决非线性滤波问题。CHCSGF 应用于再入轨迹跟踪，通过处理再入飞行期间的热流、动压和过载约束来提高估计精度。仿真结果表明，在非线性不等式软约束下，CHCSGF 的估计精度高于无约束方法，并且对先验误差的约束具有鲁棒性。与粒子滤波器和移动视界估计相比，CHCSGF 的计算复杂度显著降低。