卡尔曼滤波器:如何在没有“状态转换模型"的情况下使用它? [英] Kalman filter: how to use it with no "state transition model"?

问题描述

我正在使用 Android 手机开发加速度计.我想过滤掉加速度计返回的可怕噪音，记录手机的移动.

I am working on accelerometer from an android phone. I wish to filter the horrible noise the accelerometer is returning recording the phone's moves.

我正在阅读卡尔曼滤波器，因为低通是不够的.

I was reading around on Kalman filter, because low pass are just not enough.

但是我没有从ACCELERATION(k-1)到ACCELERATION(k)的过渡模型，因为它是用户的动作.所以我没有状态转换矩阵(不同论文中的 H 或 F，在方程 Xk = HXk-1 + Bcommand+noise 中乘以 Xk-1 的矩阵)

But I don't have a model of the transition from ACCELERATION(k-1) to ACCELERATION(k) because it is the movements of the user. So I have no state transition matrix (H or F in different papers, the one that multiply Xk-1 in the equation Xk = HXk-1 + Bcommand+noise)

我看到一些人在简单的例子中使用单位矩阵.它如何用于动态加速?

I saw some people taking the identity matrix in simple examples. How can it work for dynamic acceleration?

我知道卡尔曼滤波器，人们总是会产生一些 H 矩阵，我只是不知道在我的情况下如何.

I know Kalman Filters, people always produce some H matrix, I just don't know how in my case.

推荐答案

卡尔曼滤波器通常被认为是一种线性滤波器，其中您拥有所有模型矩阵，但滤波器的概念及其第一个应用程序来自非线性模型.在这种情况下，您可以使用函数而不是矩阵.

Kalman Filter is often thought of as a linear filter where you have all model matrices but the idea of filter and its first applications come from non-linear models. In that case you use functions instead of matrices.

如果预测和更新函数是高度非线性的，您可以使用统计方法在线估计您的参数.您可以首先查看 无味卡尔曼滤波器，它可以恢复确定性采样技术的均值和协方差 - 无味转化.我认为就您而言，这可能是最好的开始.

If the functions for prediction and update are highly non-linear you can use statistical methods to estimate your parameters on-line. The first look what you can take is unscented kalman filter which recovers mean and covariance from deterministic sampling technique - unscented transformation. I think in your case this could be the best to start with.

卡尔曼滤波器还有其他变体.您可以从 wikipedia 开始，但如果您在谷歌上搜索自适应卡尔曼滤波器"，您可以看到各种主题.

There are other variants of Kalman Filter. You can start from wikipedia but if you google "adaptive kalman filter" you can see the variety of the subject.

如果您想更深入地了解该主题但没有必要从所有数学开始，我推荐非常好的 书籍:适用于初学者的卡尔曼滤波器，由 Phil Kim 开始.还有其他可能性作为传感器融合，但它是另一个广泛的主题.

If you want to get deeper into the subject but not necessary start with all maths I recommend very good book: Kalman Filter for Beginners to start with by Phil Kim . There are also other possibility as sensor fusion, but it is another broad subject.

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