This is an example of the use of the Clark(1987) unobserved components model (Clark, “The Cyclical Component of U.S. Economic Activity,” Quarterly Journal of Economics, vol 102, pp 797–814), adapted from an example in Kim and Nelson. The Clark model is similar to the basic local trend model used in the Hodrick-Prescott filter, but with the deviation from trend (the "cycle") modeled as an AR(2) process rather than being assumed to be uncorrelated. The Clark model is often used as a building block in more complicated (that is, multivariate) models.
This is covered in detail in the 2nd Edition of the State-Space/DSGE e-course.