问个弱弱的问题－－kalman为什么能处理非平稳信号

netthief

kalman滤波到底滤掉了什么？

对于定常系统来讲，卡罗曼滤波到底滤掉了什么？
因为各种量都是定常了的话，你可以推导出来稳定后的kalman滤波到底是一种什么样的形式，应该与平常的滤波器有很大的相识之处（我以前推过，应该不难），这样，可能有助于理解其原理的推导。

个人观点，仅供参考

leojohn

卡尔曼滤波问题就是随机控制系统的状态估计问题。
如果是确定性系统，其状态无需估计，可直接计算。
详细情况请参照邓自立的大作《卡尔曼滤波与维纳滤波——现代时间序列分析》

netthief

leojohn wrote:
卡尔曼滤波问题就是随机控制系统的状态估计问题。
如果是确定性系统，其状态无需估计，可直接计算。
详细情况请参照邓自立的大作《卡尔曼滤波与维纳滤波——现代时间序列分析》

不能这么说吧，kalman滤波问题处理得是存在过程噪声和测量噪声时的状态估计问题，如果按你说的直接计算的话，你算出的量应该是没有什么意义的（噪声远远大于原信号）

cswbww

in my opinion, Kalman filter problem is 'state recovery' problem, which is as what leojohn said. But, the term "确定性系统" is not defined clearly so that netthief may misundertand the term "直接计算". Commonly, the system can be classified as
1. deterministic system (all plant parameters are known)
2. stochastic system (plant parameters are known but under random disturbance)
3. uncertain system (plant parameters are not fully know, neither is disturbance)

for the term "确定性系统", i guess it should be the 1st one "deterministic system". Therefore, plant state can be easily found by calculating suitable Riccati equation or other methodologies. It should be noticed that all filters are designed to solve problem that states of plant are not fully revealed.

cswbww

in my opinion, the function of "filter" is not exactly to filter something but to recover something valuable to the plant. Now, let's see the 4 problems.

1. 非平稳信号 can also be regulated signals. The key thing is that the ratio between the integration of this signal and the time is not constant whatever the integration time interval is. Well, you can just define this 非平稳信号 in matlab by a function varying with time.

2. why does kalman filter give the minimum? In my opinion, you'd better check how kalman filter is derived. Simply speaking, it just solves some equations in LQG problem. Since LQG is convex problem with a global or local minimum (global or local depends on the plant you are interested in), kalman filter must give the optimal solution.

3. why can kalman filter solve 非平稳信号 problem? Again, you need to check what the process it is. you cannot ask a problem of the thing before you really study it. Simply speaking, kalman filter imports 'noise' signals into the equations for calculation.

4. the same as above post.

cswbww

by the way,  for the problem "噪声远远大于原信号", there is no solution. If anybody knows, please help us. Thanks.

netthief

关于什么样的系统才是确定性系统的问题，我想我和你的想法是一样的，就是参数确定的系统，就是确定性系统，但是，什么是“plant parameters ”，如果cswbww觉得测量噪声和过程噪声等也可以称作系统参数的话，那我们的分歧可能在这里。我觉得，由于测量噪声和过程噪声的存在，使得确定性系统的状态本身也成为了随机信号（但是应该注意的是，状态之间的关系仍然是确定的，因此我还称它为确定性的系统），而Kalman Filter的意义正是在于处理这种随机信号，但是这样的系统到底还算不算确定性系统呢？

cswbww

i never think "plant parameters" include 'noise'. If you check with some paper titled with "uncertain system", no matter linear or nonlinear, 'noise' or disturbance is always regarded as exclusive to plant in the formula. I think it is fundalmental to tell difference from "plant" to "system".

"system" = "plant" + "controller" + "sensor" + "noise"

netthief

如果这么理解的话，显然你是对的

请问你所说的difference of "plant" to "system"是公认的说法，还是你个人的观点？

cswbww

it's classic definition.

netthief

哦，看来是我基础知识没有学好，多谢了