Training data reduction for nonlinear state estimator

In this paper, an approach for speeding up a kernel based nonlinear state estimator is proposed. The kernel based observer, which we are going to speed up in this paper, is one of the state estimator which employs a non-parametric structure. Although it shows high precision for nonlinear estimation due to its nonlinear nature, large amount of calculation makes it rather slow. In this paper, we propose some speeding up methods for a kernel based observer. Our speeding up methods are based on the data reduction of training data, which is stock in the memory of observer in a huge amount. By selecting and reducing those training data carefully, we show that we can reduce those training data with minimum degradations. We propose two types of data reduction strategies. First one is a method using a coefficient matrix which is easily induced from the kernel estimation method. In this method the coefficient matrix is processed to show that it is a mimic index of the likelihood which is indicating the importance of each training data. The second one is a method applying sparse algorithm. In this method the data reduction process is reduced to a multiplication of sparse diagonal matrix. The sparse diagonal matrix is calculated by a sparsification algorithm, where it is possible not only to avoid solving combinatorial optimization problems, but also to reduce the data in a deterministic way. Both strategies are tested in numerical simulations.