kalman filter multiple observations per time step

Question

I'm trying to use a Kalman Filter to estimate an online dynamic regression coefficient between two variables (e.g. http://www.thealgoengineer.com/2014/online_linear_regression_kalman_filter/)

In the example in the blog post, there is one new observation per time step, which is used to update the Kalman filter. What if you have N observations per time step - is there a generalized form of the Kalman filter you can use to update the filter with all N observations at once?

Or do you just do some type of averaging over the N observations and use the classic Kalman filter?

Edit: Let's say I have a universe of 3000 stocks and I have 2 alpha factors (value and momentum) computed for each stock in the universe at every time step

I want to use a Kalman filter to estimate FwdReturn = beta1 * momentum + beta2 * value + epsilon_i

Answer 1

Most of the time, implementing a Kalman filter with multiple observations falls under the data fusion or sensor fusion umbrella. In general, there is no single way to approach the problem. For a number of examples, check out this deck* from slide 144 onward.

*This link is from the Wayback Machine because the original link died and I couldn't find it anywhere else online.