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。我希望过滤掉加速度计返回的可怕噪音，以记录电话的移动情况。

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，因为低通还不够。

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

但是我没有从 ACCELERATION（k-1）到<$ c的过渡模型$ c> ACCELERATION（k），因为它是用户的动作。因此，我没有状态转移矩阵（在不同的论文中为H或F，是将等式Xk中的Xk-1乘以Xk = H Xk-1 + B command + noise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示例中使用了身份矩阵。它如何实现动态加速？

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，人们总是产生一些H矩阵，我只是不知道我的情况。

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

推荐答案

卡尔曼过滤器通常被认为是线性过滤器，其中拥有所有模型矩阵，但是过滤器及其最初的应用来自非线性模型。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，则可以使用统计方法在线估计参数。首先可以看到的是无味卡尔曼过滤器，它可以恢复确定性抽样技术的均值和协方差- unscented转变。我认为在您的情况下，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.

还有卡尔曼滤波器的其他变体。您可以从维基百科开始，但是如果您使用Google自适应卡尔曼过滤器，则可以看到各种

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.

如果您想更深入地学习该主题，但不必从所有数学入手，我建议您很好的本书：卡尔曼初学者过滤器由Phil Kim着手。传感器融合还有其他可能性，但这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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