State smoothing by sum-of-norms regularization

Henrik Ohlsson, Fredrik Gustafsson, Lennart Ljung, Stephen Boyd
2010 49th IEEE Conference on Decision and Control (CDC)  
The presence of abrupt changes, such as impulsive disturbances and load disturbances, make state estimation considerably more difficult than the standard setting with Gaussian process noise. Nevertheless, this type of disturbances is commonly occurring in applications which makes it an important problem. An abrupt change often introduces a jump in the state and the problem is therefore readily treated by change detection techniques. In this paper, we take a rather different approach. The state
more » ... moothing problem for linear state space models is here formulated as a least-squares problem with sum-of-norms regularization, a generalization of the 1regularization. A nice property of the suggested formulation is that it only has one tuning parameter, the regularization constant which is used to trade off fit and the number of jumps.
doi:10.1109/cdc.2010.5717386 dblp:conf/cdc/OhlssonGLB10a fatcat:2lqv53tkgndexbdy3letg4ouii