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首页> 外文期刊>IEEE Transactions on Aerospace and Electronic Systems >Linear- and Linear-Matrix-Inequality-Constrained State Estimation for Nonlinear Systems
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Linear- and Linear-Matrix-Inequality-Constrained State Estimation for Nonlinear Systems

机译：非线性系统的线性和线性矩阵 - 不等式约束状态估计

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摘要

This paper considers nonlinear state estimation subject to inequality constraints in the form of linear and linear-matrix inequalities. Rewriting the standard maximum likelihood objective function used to derive the Kalman filter allows the Kalman gain to be found by solving a constrained optimization problem with a linear objective function subject to a linear-matrix-inequality constraint. Additional constraints, such as weighted-norm- or linear-inequality constraints, that the state estimate must satisfy are easily augmented to the constrained optimization problem. The proposed constrained estimation methodology is applied in the extended Kalman filter (EKF) and sigma point Kalman filter (SPKF) frameworks. Motivated by estimation problems involving a vehicle that can rotate and translate in space, multiplicative versions of the constrained EKF and SPKF formulations are discussed. Simulation results for a ground-based mobile robot operating in a constrained three-dimensional terrain are presented and are compared to results that use the traditional multiplicative EKF and SPKF, as well as filters that enforce inequality constraints by simply projecting the state estimate into the constrained domain along the shortest Euclidean distance.
机译：本文认为非线性状态估计对线性和线性矩阵不等式形式的不等式约束。重写用于导出Kalman滤波器的标准最大似然客观函数允许通过求解线性物镜函数来保护Kalman收益，以通过线性矩阵不等式约束来解决。诸如加权规范或线性不等式约束的附加约束，即状态估计必须满足，但容易增强到约束的优化问题。所提出的约束估计方法应用于扩展卡尔曼滤波器（EKF）和Sigma点卡尔曼滤波器（SPKF）框架。通过估计涉及可以在空间旋转和转换的车辆的估计问题，讨论了受约束的EKF和SPKF配方的乘法版本。介绍了在受约束的三维地形中操作的地面移动机器人的仿真结果，并与使用传统的乘法和SPKF的结果进行比较，以及通过简单地将状态估计投射到受约束的情况下强制执行不等式约束的过滤器领域沿着最短的欧几里德距离。

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