Assume I have 2 sensors capable of measuring distance to an object of known distance. If I apply a Kalman filter to these 2 sensors, I would have 2 correction and prediction equations. If I have 2 predicted distance values from this, what are some methods to return a final predicted value with this information? Or, in other words, is there a method in which I can return a more accurate predicted value using the two sensors instead of just one? There should be a better method than to just return an average of the two predicted values, especially in the case where 1 sensor may be potentially blocked.
This case is actually a great case for Kalman Filter.
Basically the Kalman Filter fuses data. In its classic form it fuses a prior data with a measurement.
In your case it will fuse data with 2 measurements. If all calibrated correctly it will actually yield even a better result.
Conceptually, assume you don't have the Kalman filter, but you have those 2 measurements. Moreover, assume they are done at the exact same time, how would you use them?
For the optimal answer, under the the assumption the measurement noise is Gaussian, you may have a look at:
- How to Linearly Combine Two Unbiased Estimators of One Parameter without Knowledge of Their CoVariance.
- MMSE Estimation - Fusion of 2 Measurements.
This is basically what the Kalman Filter would do, merge them according to the certainty level of each sensor which is modeled by the variance of the measurement noise.
In case the 2 sensors are not time aligned you just work using the regular Kalman Filter model with the difference of creating the model matrix online to calculate the actual time difference.
The most important parameter in your case is accurately define the noise measurement of each sensor.