如何确定互补滤波器的参数α？ [英] How to determine the parameter alpha of a Complementary Filter?

问题描述

我知道互补滤波器同时具有LPF和HPF的功能。但是我认为我对于它背后的原理的理解还不清楚。

我在数字信号处理方面很新，也许一些非常基本的解释会有很大的帮助。 / p>

假设我有一个互补过滤器，如下所示：

$ p $ y = a * y +（1 - a）* x


然后我的参数 a 可以通过

a = time_constant /（time_constant + sample_period）来计算， >

其中 sample_period 仅仅是 sampling_frequency 的倒数。

time_constant 好像是由我自己选择的。

我的问题：

1. 这个计算背后的理论是什么？


2. 我们如何正确选择 time_constant ？
   
   
   

   _{注意：我也 pos在 robotics 上提出这个问题，因为答案在重点上可能略有不同。}
   

   解决方案

   
   

   这个计算背后的理论是什么？

   
   

   我会推荐：
   
   平衡过滤器：为平衡平台集成加速度计和陀螺仪测量的简单解决方案。
   
   

   
   

   我们如何正确选择time_constant？ / b>
   

   直观上， time_constant 是信任高通和低通滤波器部分。对于比 time_constant 更短的时间，您更相信高通滤波器部分，而长时间信任低通滤波器部分的时间更多。
   
   

   通常情况下，你有一些处理物理过程的经验，你可以猜测至少是 time_constant 。例如，如果您正在融合加速度计和陀螺仪数据（我假设您根据您的其他问题进行了测试），则0.5-1秒之间的数值是合理的首选猜测。然后，你开始调整你的过滤器，通过分析它在实际数据上的表现并相应地调整 a 。

   
   

   I know that the Complementary Filter has the functions of both LPF and HPF. But I think my understanding on the principal behind it is still unclear.

   I am quite new on digital signal processing, and maybe some very fundamental explanations will help a lot.

   Say I have a Complementary Filter as follows:

   y = a * y + (1 - a) * x
   

   Then my parameter a may be calculated by

   a = time_constant / (time_constant + sample_period),

   where the sample_period is simply the reciprocal of the sampling_frequency.

   The time_constant seems to be at my own choice.

   My Questions:

   1. What is the theory behind this calculation?
   2. How do we choose the time_constant properly?

   _{Note: I also} posted this question on robotics, as the answers there are likely to be slightly different in emphasis.

   解决方案

   What is the theory behind this calculation?

   For a human readable introduction I would recommend:
   The Balance Filter: A Simple Solution for Integrating Accelerometer and Gyroscope Measurements for a Balancing Platform.

   How do we choose the time_constant properly?

   Intuitively, the time_constant is the boundary between trusting the high-pass and the low-pass filter part. For shorter times than the time_constant you trust the high-pass filter part more, and for longer times you trust the low-pass part more.

   Usually, you have some experience with the physical process you are dealing with and you can guess at least the order of magnitude of the time_constant. For example, if you are fusing accelerometer and gyro data (which I assume you do based on your other question), something between 0.5-1 second is a reasonable first guess. Then, you start tuning your filter by analyzing its performance on actual data and adjusting a accordingly.

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