In papers and textbooks and on Wikipedia, I regularly stumble upon so-called "lattice filters". They always look horribly more complex than their 'non-lattice counterpart' and I usually don't really understand what's going on (and why). I could not really find a useful introduction to lattice filters and the fundamental idea behind them. What I believe to have understood (please correct me if I'm wrong) is that they represent some form of very efficient implementation scheme for classical filters, e.g., RLS?
Can somebody explain the intuition behind lattice filters? What are they, which problem do they solve, and how do they solve it? References to readable introductions are also highly appreciated.
(Note that I have actually had a fair amount of DSP in my undergrad studies, but lattice filters were never even mentioned.)