英文:
Kalman Filter's Dynamic Shift matrix
问题
卡尔曼滤波器（KF）在预测步骤中使用所谓的动态转移矩阵。该矩阵有时被称为演变或传播矩阵，用D或M标记：
$ \mu_t = M_t \mu_{t-1} $
$ \Sigma_t = M_t \mu_{t-1} M_t' + Q_t $
在我了解的许多实现中，M通常只是一个单位矩阵。是否可以提供一个示例和解释，说明这个矩阵在更复杂的情况下有实际意义？
据说这个矩阵将前一时间步骤k-1的状态与当前时间步骤k的状态关联起来，在没有驱动函数或过程噪声的情况下，它可以在每个时间步骤中发生变化（参见Welch & Bishop 2001）。
英文:
Kalman Filter (KF) uses a so-called Dynamic Shift matrix in the forecast step. The matrix is sometimes called Evolution or Propagator matrix, and is marked with D or M:
$ \mu_t = M_t \mu_{t-1} $
$ \Sigma_t = M_t \mu_{t-1} M_t' + Q_t $
In many implementations that I know about, M is just an Identity matrix. Can anyone provide an example and explanation of when that matrix is meaningfully more complex?
It is said that this matrix relates the state at the previous time step k – 1 to the state at the current step, k, in the absence of either a driving function or process noise, as well as that it can change with each time step (see Welch & Bishop 2001).
答案1
得分: 1
这是一个很好的视频，用来解释位移操作矩阵的含义。希望这能澄清你的疑惑。由Khaisare教授制作的视频
卡尔曼滤波器的先验状态估计也可以通过物理信息的状态空间模型来实现。关于这点，你可以参考书籍：Grewal和Andrews编写的《卡尔曼滤波》。
英文:
Here is a good video to explain what the shift operator matrix means. Hopefully that clarifies your doubt.Video by Professor Khaisare
Kalman Filter a priori state estimates can also be made by physics informed State Space models. For that you can refer to the book: Kalman Filtering by Grewal and Andrews.
通过集体智慧和协作来改善编程学习和解决问题的方式。致力于成为全球开发者共同参与的知识库，让每个人都能够通过互相帮助和分享经验来进步。
评论