In this technical note, a recursive set-membership filtering algorithm for discrete-time nonlinear dynamical systems subject to unknown but bounded process and measurement noises is proposed. The nonlinear dynamics is represented in a pseudo-linear form using the state dependent coefficient (SDC) parameterization. Matrix Taylor expansions are utilized to expand the state dependent matrices about the state estimates. Upper bounds on the norms of remainders in the matrix Taylor expansions are calculated on-line using a non-adaptive random search algorithm at each time step. Utilizing these upper bounds and the ellipsoidal set description of the uncertainties, a two-step filter is derived that utilizes the `correction-prediction' structure of the standard Kalman Filter variants. At each time step, correction and prediction ellipsoids are constructed that contain the true state of the system by solving the corresponding semi-definite programs (SDPs). Finally, a simulation example is included to illustrate the effectiveness of the proposed approach.

中文翻译：

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使用状态相关系数参数化的离散时间非线性系统的集合成员过滤器

在本技术说明中，提出了一种适用于受未知但有界过程和测量噪声影响的离散时间非线性动力系统的递归集合成员过滤算法。非线性动力学使用状态相关系数 (SDC) 参数化以伪线性形式表示。矩阵泰勒展开用于展开关于状态估计的状态相关矩阵。矩阵泰勒展开式中余数范数的上限是在每个时间步使用非自适应随机搜索算法在线计算的。利用这些上限和不确定性的椭球集描述，推导出利用标准卡尔曼滤波器变体的“校正-预测”结构的两步滤波器。在每个时间步，通过求解相应的半定规划 (SDP)，构建包含系统真实状态的校正和预测椭球。最后，包括一个仿真例子来说明所提出方法的有效性。