Mathematically Equivalent Approaches for Equality Constrained Kalman Filtering
Mathematically Equivalent Approaches for Equality Constrained Kalman Filtering
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发表时间：
2009-02
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通讯作者：
Nachi Gupta
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作者：
Nachi Gupta
卡尔曼滤波问题通常在物理动力学中具有固有的和已知的约束，尽管潜在地显著增益（例如，电机的固定速度）。在本文中，我们回顾了现有的方法，并提出了一些新的想法，过滤存在的等式约束。然后，我们表明，将状态空间等式约束的三种方法在数学上等价于更一般的“投影”方法，它允许不同的加权矩阵时，投影估计。尽管如此，不同的方法在实现中具有优势，可以使一种方法比另一种方法更适合于给定的应用。
Kalman Filtering problems often have inherent and known constraints in the physical dynamics that are not exploited despite potentially significant gains (e.g., fixed speed of a motor). In this paper, we review existing methods and propose some new ideas for filtering in the presence of equality constraints. We then show that three methods for incorporating state space equality constraints are mathematically equivalent to the more general "Projection" method, which allows different weighting matrices when projecting the estimate. Still, the different approaches have advantages in implementations that may make one better suited than another for a given application.