卡尔曼-布西滤波的精细积分

Precise integration of Kalman-Buoy filtering problems

数值计算是卡尔曼－布西滤波不可缺少的一个方面．通常总是分解为黎卡提微分方程的离线积分以及在线执行的状态估计x（t）变系数微分方程组求解．采用变分、区段混合能等方法，推导了整套精细积分的公式与算法．适用于两端边值问题与黎卡提微分方程的求解，还可以用于x的变系数微分方程，数例表明了其高度精确性．

Numerical computation is one of the indispensable aspects of Kalman-Buoy filtering.It is usually to classify the computation into: (1) the off-line solution of the Riccati differentialequation; (2) the on-line integration of the state vector x(t) from a set of time-variantdifferential equations. The good solution methodology wants to be further explored. Thevariational approach with interval mixed energy is developed to derive the whole set of equationsand algorithm of precise integration in this paper. The present algorithms are not onlyappropriate to solve the two point boundary value problem and the corresponding Riccatidifferential equation, but also can be used to solve the estimated state i(t) from the time-variantdifferential equations. Numerical examples demonstrate the high precision and effectiveness of thealgorithm.