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Using a limited number of sampled-data of system output, a stochastic finite-memory model may be established to take the place of the system state equation used in the Kalman filter to perform one-step optimal prediction. On this basis, two sets of equations of the "minimum mean-square-error" discrete filter are derived. When the system state equation is unknown, the system state can be estimated with the method developed in this paper. 本文用对象输出信号的N个记忆量来构成随机限定记忆模型,去代替卡尔曼滤波器中所使用的对象状态方程模型,作为一步最优预测的依据。在此基础上推导出离散系统的最小均方误差的滤波公式组。在不能获得精确的对象状态方程的情况下,可用本文提出的滤波方法对对象的状态变量作出估计。 In this paper, formal derivation of the Kalman filter is made on the basis of an elementary knowledge of probability theory and matrix algebra. The structure of this filter formula and its application have also been illustrated through an example of estimating ship's position. 本文用较少的概率论和矩阵代数知识对卡尔曼滤波公式作了形式上的推导,并以船位估计问题为例介绍了滤波公式的结构和它的应用。 In this paper a simplified method of optimal design applied to semi-analyticinertial navigation system of marine(long-time operating)is discussed.When thesimulation is carried out on the digital computer DJS-6,in order to evaluate theperformance of the simplified optimal design approach,the square root algorithmis used for optimal recursive filter(Kalman filter),so as to reduce the effect ofcomputational error on filter;and a set of non-linear equation in the case of linearmotion with constant... In this paper a simplified method of optimal design applied to semi-analyticinertial navigation system of marine(long-time operating)is discussed.When thesimulation is carried out on the digital computer DJS-6,in order to evaluate theperformance of the simplified optimal design approach,the square root algorithmis used for optimal recursive filter(Kalman filter),so as to reduce the effect ofcomputational error on filter;and a set of non-linear equation in the case of linearmotion with constant velocity is employed for the equations of the inertial naviga-tion system.Thus,the above-mentioned method is close to the actual case.Thedetailed derivation of the principles of inertial navigation and optimal recursivefilter have not been made,and some conclusions concerning moder control theory areused directly in this paper. 本文讨论舰船(或长时间工作的)半解析式惯性导航系统最佳设计的一种简化方法。为了评定简化方法的性能,在DJS-6机上进行模拟试验时,最佳逆推过滤器(卡尔曼过滤器)采用了方根算法,以减少计算误差对过滤器性能的影响;而惯性导航系统方程组采用了一组在等速直线运动情况下的非线性方程组,这样做较为接近于真实情况。本文对惯导原理及最佳递推过滤器的设计,限于篇幅没有作详细推导。有关现代控制理论的一些问题,本文也只直接应用其结论。
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