论文标题
同时输入和状态估计,单数过滤和稳定性
Simultaneous input & state estimation, singular filtering and stability
论文作者
论文摘要
输入估计是一种信号处理技术,与已知动态系统过滤后测量信号的反卷积相关。 Kitanidis和其他人将其扩展到对输入信号和中间系统状态的同时估计。通常将其视为具有无偏见的特殊最小二乘估计问题。该方法在信号分析和控制中具有应用。尽管与最佳估计有联系,但标准算法不一定稳定,导致许多最近的论文具有足够的稳定性条件。在本文中,我们在时间不变的情况下以两种方式完成了这些稳定性:对于平方情况,测量值等于未知输入的数量,我们正好确定算法极点的位置;对于非方案,我们表明最佳的足够条件也是必要的。然后,我们利用先前的结果来解释这些算法,当稳定时,将这些算法作为单数Kalman过滤,以通过Kalman过滤提倡直接,保证稳定的实现。除稳定性外,这还具有清晰度和灵活性的优势。在途中,我们会根据系统反转和连续的单数过滤破译现有算法。稳定性结果直接扩展到时间变化的情况,以通过Riccati差异方程恢复早期的稳定条件。
Input estimation is a signal processing technique associated with deconvolution of measured signals after filtering through a known dynamic system. Kitanidis and others extended this to the simultaneous estimation of the input signal and the state of the intervening system. This is normally posed as a special least-squares estimation problem with unbiasedness. The approach has application in signal analysis and in control. Despite the connection to optimal estimation, the standard algorithms are not necessarily stable, leading to a number of recent papers which present sufficient conditions for stability. In this paper we complete these stability results in two ways in the time-invariant case: for the square case, where the number of measurements equals the number of unknown inputs, we establish exactly the location of the algorithm poles; for the non-square case, we show that the best sufficient conditions are also necessary. We then draw on our previous results interpreting these algorithms, when stable, as singular Kalman filters to advocate a direct, guaranteed stable implementation via Kalman filtering. This has the advantage of clarity and flexibility in addition to stability. En route, we decipher the existing algorithms in terms of system inversion and successive singular filtering. The stability results are extended to the time-varying case directly to recover the earlier sufficient conditions for stability via the Riccati difference equation.