传感器融合卡尔曼滤波器 [英] Sensor fusioning with Kalman filter
问题描述
你如何实际收获两个传感器的积极属性和最小化负面？
这是在观察模型矩阵（通常由大写字母H表示）中建模吗？
备注：这个问题在没有任何答案的情况下也被问到： math.stackexchange.com 通常，传感器融合问题是从贝叶斯定理推导出来的。其实你已经知道你的估算值（在这种情况下是水平面）将是你的传感器的加权总和，这是传感器模型的特征。对于双传感器，您有两种常见的选择：建立两个传感器系统，并为每个传感器（使用系统模型作为预测器）导出卡尔曼增益，或使用不同的观测模型运行两个校正阶段。给出两个不同的信息源，你应该看看贝叶斯预测器（比卡尔曼滤波器更通用一点），它是从最小化估计值的方差而得到的。如果你有一个加权和，并最小化总和的方差，对于两个传感器，那么你得到的卡尔曼增益。
传感器的属性可以看到在过滤器的两个部分。首先，你有你的观察的错误矩阵。这是表示传感器观测中的噪声的矩阵（假定为零均值高斯噪声，假定在校准期间，可以实现零均值噪声，这不是太大的假设）。另一个重要的矩阵是观测协方差矩阵。这个矩阵给你一个关于传感器给你信息有多好的信息（信息意思是新的，而不依赖于其他传感器的读数）。关于收获良好的特性，你应该做的是做一个很好的校准和噪音表征（是拼写好吗？）的传感器。让卡尔曼滤波器收敛的最好方法是为您的传感器建立一个良好的噪声模型，这是100％的实验。尝试确定你的系统的差异（不要总是信任数据表）。
希望有所帮助。
I'm interested, how is the dual input in a sensor fusioning setup in a Kalman filter modeled?
Say for instance that you have an accelerometer and a gyro and want to present the "horizon level", like in an airplane, a good demo of something like this here.
How do you actually harvest the two sensors positive properties and minimize the negative?
Is this modeled in the Observation Model matrix (usually symbolized by capital H)?
Remark: This question was also asked without any answers at math.stackexchange.com
Usually, the sensor fusion problem is derived from the bayes theorem. Actually you have that your estimate (in this case the horizon level) will be a weighted sum of your sensors, which is caracterized by the sensor model. For dual sensors, you have two common choices: Model a two sensor system and derive the kalman gain for each sensor (using the system model as the predictor), or run two correction stages using different observation models. You should take a look at Bayesian Predictors (a little more general than Kalman Filter) which is precisely derived from minimizing the variance of an estimate, given two different information sources. If you have a weighted sum, and minimize the variance of the sum, for two sensors, then you get the Kalman Gain.
The properties of the sensor can be "seen" in two parts of the filter. First, you have the error matrix for your observations. This is the matrix that represents the noise in the sensors observation (it is assumed to be zero mean gaussian noise, which isn't a too big assumption, given that during calibration, you can achieve a zero mean noise).
The other important matrix is the observation covariance matrix. This matrix gives you an insight about how good is the sensor at giving you information (information meaning something "new" and not dependent on the other sensors reading).
About "harvesting the good characteristics", what you should do is do a good calibration and noise characterization (is that spelled ok?) of the sensors. The best way to get a Kalman Filter to converge is to have a good noise model for your sensors, and that is 100% experimental. Try to determine the variance for your system (dont always trust datasheets).
Hope that helps a bit.
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