If a dynamic system has active constraints on the state vector and they are known, then taking them into account during modeling is often advantageous. Unfortunately, in the constrained discrete-time state-space estimation, the state equality constraint is defined for a parameter matrix and not on a parameter vector as commonly found in regression problems. To address this problem, firstly, we show how to rewrite the state equality constraints as equality constraints on the state matrices to be estimated. Then, we vectorise the matricial least squares problem defined for modeling state-space systems such that any method from the equality-constrained least squares framework may be employed. Both time-invariant and time-varying cases are considered as well as the case where the state equality constraint is not exactly known.

如果动态系统对状态向量具有主动约束并且它们是已知的，那么在建模期间将它们考虑在内通常是有利的。不幸的是，在受约束的离散时间状态空间估计中，状态等式约束是为参数矩阵定义的，而不是在回归问题中常见的参数向量上定义的。为了解决这个问题，首先，我们展示了如何将状态等式约束重写为待估计状态矩阵上的等式约束。然后，我们矢量化为建模状态空间系统而定义的矩阵最小二乘问题，以便可以采用来自等式约束最小二乘框架的任何方法。时不变和时变情况以及状态等式约束不完全知道的情况都被考虑。