Minimal symmetric model-set design strategy on a hypersphere for multiple-model approach

The design of the model set used in a multiple-model algorithm is one of the most important problems in the application of the multiple-model approach. It is appealing for many applications in practice that the models used are symmetrically distributed. Furthermore, there is a strong incentive to reduce the computational costs which are proportional to the number of the models used. For this reason, we present a minimal symmetric model-set design strategy which defines a simplex of models that lie on a hypersphere by matching up to the 2th moment of the system mode. For an n-dimensional space, apart from the center model, only n+1 models are required. The probability mass applied to each model is proportional to 1/(n +1). Simulation results justifies that this model-set designed here outperforms the symmetric model-set on axes in estimation accuracy.