  COMPASS is a multi-purpose fixed-target experiment at CERN aimed at studying
the structure and spectrum of hadrons. It has collected the so far world's
largest data set on diffractive production of the $K^-\pi^-\pi^+$ decay, which
in principle gives access to all kaon states. We performed an elaborate
partial-wave analysis, using model-selection techniques to select the wave set
based on a large systematically constructed pool of allowed partial waves. The
partial-wave decomposition reveals signals in the mass region of well-known
states, such as $K_1(1270)$ and $K_1(1400)$. In addition, we observe potential
signals from excited states, such as $K_1(1650)$.
