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在防空火控系统中,滤波器和预测器的输入信号来自对目标在空中的运动轨迹的测量。在设计滤波器和预测器时,首先要对目标运动规律做出决定。过去在飞机机动性能不高的情况下,曾把目标作等速直线运动做为常用的假设,效果还是比较好的。那时所用的计算工具主要是机电模拟式计算装置,所用的理论主要是维纳滤波理论。应用维纳理论设计滤波器的方法是根据输入信号误差的统计特性,找出滤波器的最佳重量函数,然后用实际装置逼近它。维纳理论比较适合于通讯系统,因为通讯系统的输入信息为语言或编码,较符合平稳随机过程,而火控系统的输入信息一般并不是平稳的,因而维纳理论对于火控系统来说,就不太合适,或者说不太理想。60年开始出现的卡尔曼滤波是递推式计算的,特别便于在数字计算机上进行。它计算的特点是边估计状态值,边估计误差的方差值,而且能随着误差的大小调整估计,提高估计精度。它的适应性是很强的。卡尔曼滤波器的这一特点,对于火控系统来说是非常宝贵的,因为实际的工作条件往往不是最佳的。上述对目标运动规律的决定,在卡尔曼滤波器设计中就是确定目标运动的数学模型。下边介绍适合现代空中目标运动特点的几种可用的数学模型,重点是随机加速度模型。
In air defense fire control systems, the input signals to the filters and predictors come from the measurement of the trajectory of the target in the air. When designing filters and predictors, first make a decision about the target’s motion law. In the past in the case of aircraft maneuver performance is not high, the goal has been used as a constant speed linear motion as a common assumption, the effect is still relatively good. The computational tools used at that time were mainly electromechanical analog computing devices. The theory used was mainly Wiener filter theory. The Wiener theory is used to design the filter based on the statistical characteristics of the error of the input signal to find the best weight function of the filter and then to approximate it with an actual device. Wiener theory is more suitable for communication systems, because the communication system input information for the language or coding, more in line with a stable random process, and fire control system input information is generally not stable, so Wiener theory for fire control system, It is not appropriate, or not ideal. Kalman filtering, which starts appearing in 60 years, is recursive and is especially convenient for digital computers. The characteristic of the calculation is that while estimating the state value, the variance of the error is estimated, and the estimation can be adjusted according to the size of the error so as to improve the estimation accuracy. Its adaptability is very strong. This feature of the Kalman filter is invaluable to the fire control system because the actual working conditions are often not optimal. The above decision on the target’s motion law is a mathematical model for determining the target’s motion in the Kalman filter design. The following describes several suitable mathematical models for the characteristics of modern airborne targets, with emphasis on stochastic acceleration models.