# Reflect data quality in Kalman filter

In a single stream of observations, I have some prior knowledge about the level of noiseness of the data that get feed into my Kalman filter. Some points are more noisy than the others.

To make use of this knowledge, I have two thoughts

(1) partition the data into two streams: low confidence and high confidence

(2) scale my confidence in data to a factor b/w 0 and 1, and multiply the kalman gain with this factor.

Can someone shed some light on this problem with some new thoughts or comment on my thoughts. Any comments would be appreciated.

• can you elaborate on this noise process you have prior knowledge about? Is it stationary? Is it binary (since you mention low and high regime)? Feb 1 '17 at 15:29
• @Memming it is stationary. The confidence level is more like a continuous spectrum. For example, if stock price is the measurement series, the associated volume could act as a confidence level. The higher the volume is, the higher confidence we have on this dat point. On the other hand, we may discretize the volume spectrum and separate the series based on that. Feb 1 '17 at 15:40

Kalman filter in principle supports variable noisiness of data, so you are good. Just encode the noisiness info as a sequence of observational (co)variance matrices, $\mathbf{R}_k$ in wikipedia notation.
• No, don't construct one R matrix based on average variance. Use different R matrices for each time step! That's why it is denoted $\mathbf{R}_k$, $k$ is the index for time step. Feb 1 '17 at 16:51