Abstract:

When boundary mismatch occurs in state-shifting models for nonlinear and non-Gaussian systems, it is often difficult to obtain accurate state estimates by particle filtering method. Considered constraints of boundary mismatch on particles, an extended set membership particle filtering method (MAP-ESMPF) was proposed on the basis of maximum a posteriori probability criterion. First, a feasible region for real states of particles was determined by extended set membership algorithm. Then, particles outside are projected into the feasible region by an optimization equation developed from the principle of maximum posteriori probability function. As a result, the accuracy of state estimate was ensured. Applications in a numerical simulation and process simulation of continuous stirred tank reactor (CSTR) showed effectiveness of the new method.

Key words: model-mismatch, extended set membership filtering, particle filter, MAP criterion

摘要：

在非线性非高斯系统中，当状态转移模型存在有界失配时，采用粒子滤波往往无法获得理想的状态估计值。考虑有界失配对粒子的约束条件，提出一种基于MAP准则的扩展集员粒子滤波算法（MAP-ESMPF）。该算法采用扩展集员求取真实状态的可信域，并基于MAP密度函数的准则，定义优化方程，从而将可信域外的粒子映射到可信域内，保证了状态估计的精度。在数值仿真和连续搅拌反应釜（CSTR）过程中的仿真应用，验证了该算法的有效性。

关键词: 模型失配, 扩展集员算法, 粒子滤波, MAP准则