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Reduced complexity dynamic programming solution for Kalman filtering of linear discrete time descriptor systems

机译：线性离散时间描述符系统的卡尔曼滤波的降低复杂度的动态规划解决方案

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We consider linear discrete time descriptor systems that are described by state and measurement equations that have both stochastic and purely deterministic components. We suggest an estimation algorithm that operates by decomposing the system into stochastic and deterministic parts, and processing each part separately. It solves the deterministic subsystem using the pseudo-inverse according to the Moore-Penrose definition [1], and then minimizes the Kalman filter objective function by exploiting the orthogonal subspace defined by the deterministic subsystem. A simulation example is given for estimating tray composition for a distillation column by linearization over a trajectory of a non-linear differential algebraic model. Compared to the method of R. Nikoukhah et.al [2], the reduction in time produced by our method for this example is 87%. The reason is that our algorithm requires only 1-block matrix inversion that does not involve any singular blocks, whereas the algorithm in [2] requires 3-block matrix inversions containing possibly singular matrix blocks arising from singular covariance matrices.
机译：我们考虑由状态和测量方程描述的线性离散时间描述符系统，这些方程具有随机和纯粹的确定性成分。我们建议一种估算算法，其工作原理是将系统分解为随机和确定性部分，然后分别处理每个部分。它根据Moore-Penrose定义[1]使用伪逆来求解确定性子系统，然后通过利用确定性子系统定义的正交子空间来最小化Kalman滤波目标函数。给出了用于通过在非线性微分代数模型的轨迹上进行线性化来估计蒸馏塔的塔板组成的模拟示例。与R. Nikoukhah等人的方法[2]相比，我们的方法在本示例中产生的时间减少了87％。原因是我们的算法只需要不涉及任何奇异块的1块矩阵求逆，而[2]中的算法则需要3块矩阵求逆，其中包含可能由奇异协方差矩阵引起的奇异矩阵块。

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