论文标题
等于受限的地图和最大似然估计中的不确定性估计，并应用于系统识别和状态估计
Uncertainty estimation in equality-constrained MAP and maximum likelihood estimation with applications to system identification and state estimation
论文作者
论文摘要
在无约束的最大后验（MAP）和最大似然估计中，减去功绩功能性Hessian矩阵的倒数是估计值协方差矩阵的近似值。在地图估计的贝叶斯语境中，它是模式周围后部正常近似的协方差。在最大似然估计中，它的近似渔民信息矩阵的近似值，有效估计器的协方差会融合。这些措施通常用于系统识别中，以评估估计不确定性和诊断问题，例如过度参数化，激发不当和无法识别。但是，系统和控制中的各种估计问题都可以作为相等约束的优化进行表述，并具有额外的决策变量，以利用计算机硬件中的并行性，简化实现并提高非线性程序求解器的收敛盆地和效率。但是，额外变量的引入使逆黑板与协方差矩阵分离。取而代之的是，必须使用受约束问题的拉格朗日式的逆黑板的子膜。在本文中，我们得出了这些关系，显示了如何直接从增强问题中估算的估计值的协方差。申请示例显示在系统识别中，使用输出错误方法和联合状态路径和参数估计。
In unconstrained maximum a posteriori (MAP) and maximum likelihood estimation, the inverse of minus the merit-function Hessian matrix is an approximation of the estimate covariance matrix. In the Bayesian context of MAP estimation, it is the covariance of a normal approximation of the posterior around the mode; while in maximum likelihood estimation, it an approximation of the inverse Fisher information matrix, to which the covariance of efficient estimators converge. These measures are routinely used in system identification to evaluate the estimate uncertainties and diagnose problems such as overparametrization, improper excitation and unidentifiability. A wide variety of estimation problems in systems and control, however, can be formulated as equality-constrained optimizations with additional decision variables to exploit parallelism in computer hardware, simplify implementation and increase the convergence basin and efficiency of the nonlinear program solver. The introduction of the extra variables, however, dissociates the inverse Hessian from the covariance matrix. Instead, submatrices of the inverse Hessian of the constrained-problem's Lagrangian must be used. In this paper, we derive these relationships, showing how the estimates' covariance can be estimated directly from the augmented problem. Application examples are shown in system identification with the output-error method and joint state-path and parameter estimation.
