含未知输入不确定系统的扩展递归滤波算法

对一类具有未知输入、乘性噪声和量测丢失的不确定系统的扩展递归滤波问题进行研究。其中,实际系统存在时变性和不确定性的情形通过乘性噪声描述;量测丢失现象用服从伯努利分布且统计特性已知的随机序列表示;先验信息未知的外界干扰以未知输入的形式存在于系统方程和量测方程中。综合考虑上述因素,首先,利用传统的递归滤波性质和线性无偏最小方差估计准则,设计一种能同时估计系统状态和未知输入的扩展递归滤波器;然后,采用加权最小二乘优化理论和拉格朗日乘子法求取滤波器中待定的增益矩阵;最后,通过数值仿真实验验证了该算法的有效性。

线性系统未知输入和状态扩展递归滤波方法

在环境监测、导航与控制、故障检测等领域中,由于环境影响、模型参数选取不当、设备故障等原因,系统状态方程和测量方程中往往含有未知输入。针对未知输入直接馈通到测量方程的情况,研究同时估计线性系统状态和未知输入的问题。在没有未知输入先验知识的前提下,针对测量方程中未知输入系数矩阵不满秩时无法应用经典递归三步滤波器的问题,依据线性最小方差无偏估计准则,提出了一种新的扩展递归三步滤波器,并提炼汇总出具体递归迭代步骤。仿真结果表明,与以往系数矩阵不满秩情况下的无偏最小方差状态估计方法相比,新的滤波器能够有效降低状态估计误差。

Approach to estimation of vehicle-road longitudinal friction coefficient

According to the road adaptive requirements for the vehicle longitudinal safety assistant system an estimation method of the road longitudinal friction coefficient is proposed.The method can simultaneously be applied to both the high and the low slip ratio conditions. Based on the simplified magic formula tire model the road longitudinal friction coefficient is preliminarily estimated by the recursive least squares method.The estimated friction coefficient and the tires model parameters are considered as extended states. The extended Kalman filter algorithm is employed to filter out the noise and adaptively adjust the tire model parameters. Then the final road longitudinal friction coefficient is accurately and robustly estimated. The Carsim simulation results show that the proposed method is better than the conventional algorithm. The road longitudinal friction coefficient can be quickly and accurately estimated under both the high and the low slip ratio conditions.The error is less than 0.1 and the response time is less than 2 s which meets the requirements of the vehicle longitudinal safety assistant system.

滤波和有色背景噪声影响下细胞膜离子单通道信号的自适应恢复算法研究

为了克服反混叠滤波器和有色背景噪声的影响 ,本文提出了一种自适应算法 ,估计离子通道的动力学特征参数和背景噪声的统计特征 ,然后基于这些参数 ,运用统计技术从强噪声的膜片钳记录中恢复离子通道信号。这种算法交叉耦合了递归的 expectation- m axim ization(EM)算法和递归扩展最小二乘算法。递归 EM算法最优地估计隐Markov模型参数 ,递归扩展最小二乘算法最优地估计背景噪声的特征。仿真研究表明这种交叉耦合算法一致收敛 。