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本文研究卡尔曼滤波及其简化理论在近程低空边搜索边跟踪体制雷达中的应用。文章根据工程背景选定目标的运动模型和雷达的量测模型,认为前者在直角坐标系上是一阶线性的,扰动属高斯概型。后者在极坐标系上是线性的误差属高斯概型,由此模型出发,文章利用线性化处理方法,求出了极坐标系上的运动方程,从而得了极坐标系上的卡尔曼滤波算法,文章推广了K、C、wilsou的结果,利用最优控制论方法,在极坐标系上设计了最小平均位置予测方差为最佳准则的常系数滤波器,求出最佳参数α、β。为了比较,文章推导了上述模型在直角坐标上的卡尔曼滤波方程,文章还通过蒙特卡洛模拟和方差分析比较了上述各种算法的滤波效果,并从工程实践的角度提出作者在上述工程背景下对滤波算法的选用意见。
This paper studies the application of Kalman filter and its simplification theory in short-range search and tracking edge radar system. According to the engineering background, the article selects the target’s motion model and the radar’s measurement model, and considers that the former is first-order linear in Cartesian coordinate system and the perturbation belongs to the Gaussian model. The latter error in the polar coordinate system is Gaussian Gaussian error model, starting from the model, the article uses the linearization method, obtained the polar coordinates of the equation of motion, polar coordinates obtained Kalman filter algorithm , The article generalizes the results of K, C and Wilsou. Using the optimal control theory, a constant coefficient filter with the best criterion for the minimum average position variance is designed on the polar coordinate system. The optimal parameters α, β . For the sake of comparison, the paper derives the Kalman filter equation of the above model in Cartesian coordinates. The article also compares the filtering effects of the above algorithms by Monte Carlo simulation and analysis of variance, and from the engineering practice point of view, The choice of filtering algorithm under the views.