In the context of control and estimation under information constraints, restoration entropy measures the minimal required data rate above which the state of a system can be estimated so that the estimation quality does not degrade over time and, conversely, can be improved. The remote observer here is assumed to receive its data through a communication channel of finite bit-rate capacity. In this paper, we provide a new characterization of the restoration entropy which does not require to compute any temporal limit, i.e., an asymptotic quantity. Our new formula is based on the idea of finding a specific Riemannian metric on the state space which makes the metric-dependent upper estimate of the restoration entropy as tight as one wishes.

在信息约束下进行控制和估计的情况下，恢复熵会测量所需的最小数据速率，在该数据速率之上可以估计系统的状态，以使估计质量不会随时间降低，反之则可以提高。这里假设远程观察者通过有限比特率容量的通信信道接收其数据。在本文中，我们提供了恢复熵的新特征，它不需要计算任何时间限制，即渐近量。我们的新公式基于以下想法：在状态空间上找到特定的黎曼度量，这使恢复熵的依赖于度量的上估计随心所欲。