Kalman filter with mixed frequency

[Plouffy]

Hi first post hoping for some advise or guidance.

Let's say I have GPS data on a robot every 10 Hz (every 0.1 second), I have accelerometer data every 40 Hz and steering wheel data every 80 Hz. I would like to use Kalman filter to produce estimates of where the robot is every 40 Hz given the previous data (e.g. interpolate the GPS data using Kalman). My question is what methodology should I use (if anyone knows a good paper on the subject I would be very grateful). My current thoughts are to either:

1. Apply a Kalman filter to each data series separately to interpolate to the highest frequency (i.e. only have lagged values of Y as its state variable) and then again with the entire datasets in our filter.

2. Have my Y (left hand side) be a vector of size [8*1] containing the GPS where the column vector is 0 everywhere but at 10Hz, and then apply Kalman filter (accelerometer vector would be treated the same but with two observations and NaN everywhere else).

Thanks a lot.

 

[Chuck Coleman]

Option 2 sounds like the appropriate one. The KF is robust wrt missing data. Set up your design for 80 Hz and read at any frequency you desire. I assume that the GPS data will benchmark the other data, so the filter will operate well. A good reference on the KF can be found at http://www.stat.pitt.edu/stoffer/tsa3/. Now, instead of "stealing" the PDF, you can download an earlier version of the book.

 

[docsxp]

I perform my KF at the highest rate that my sensor offers (100hz). When your GPS is not producing any data you can reflect that by modifying your H matrix accordingly. Note that IMU data shouldn't be dropped but should be averaged if you're going for a slower rate.