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how i teach the kalman filter to 1st-year undergraduate engineering students @Penn : a thread 1/9
step 1 : when teaching multivariable calculus, i use matrices & linear transformations from the very beginning, with nice payoffs in derivatives & integrals. 2/9
step 2 : after doing triple integrals & moments of inertia, i introduce the "inertia matrix" to keep track of all the moments & show how to use it to compute the moment about any axis of rotation. 3/9
step 3 : after a brief foray into probability & random variables, i teach a simple version of the covariance matrix as a generalization of the inertia matrix for probability mass. 4/9
step 4 : what's the use of that? one (of many!) applications is to tracking, where you use probability densities to estimate the state of what you're trying to track. hmmmm... what happens over time as uncertainty grows? 5/9
step 5 : a simple version of the (extended) kalman filter uses prediction, measurement, & data fusion steps to track. it's a great application of derivatives, integrals, and matrices. 6/9
& that's it. my students like seeing *actual* applications of what they're learning, and this is great motivation to go deeper, since we only cover the basics of data fusion & filtering. 7/9
all of these lectures & animations are available in volume 3 of Calculus BLUE available on youtube: see, e.g., and 8/9
i taught this last semester for the 1st time & it went well. i'll be experimenting with it again in a few weeks using a flipped model. wish me luck! 9/9
