Observability and observable degree, which are derived from modern control theory and relative to control and estimation performances, are both important concepts for state estimation. For linear time-invariant systems, judgement of observability and evaluation of observable degree are irrelevant to filtering process and parameters. Thereby, it has limited application ability. Different from linear systems, observability and observable degree becomes more complex and are seldom studied deeply and integrally for nonlinear systems. Due to the complexity of nonlinear filtering, the observable degree depends strongly on filtering process, filter class and associated parameters. Thereby, we study the observable degree analysis of nonlinear estimation systems by using unscented information filter (UIF). A way to evaluate observable degree using singular value decomposition (SVD) of observability matrix is presented based on the UIF and the influencing factors are deeply analyzed. Moreover, differences of observable degree analysis are distinctly discussed between linear and nonlinear systems. The results reveal that evaluation of the observable degree for nonlinear systems can be affected by filtering estimate at last time, initial estimate and filter's parameters such as covariances of process and measurement noises. Some simulations are demonstrated to validate the results.

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In multi-objective particle swarm optimization (MOPSO), the selection of global guides for all partials is vital to improve the convergence and diversity of solutions. In this paper, the related work of global guides searching in MOPSO is introduced, and a new Pareto–based selecting strategy is proposed. Basing on the analysis of the structure and mapping relation of the particle swarm and the nondominated solutions archive, considering the density information, the global guides selecting frequency and other factors, a new gbest selecting strategy for each particle in the swam is presented. Experimental results of contrasting experiments of two typical MOPSO functions demonstrate that the proposed strategy is satisfying.