基于组合模型高精度预测弹丸径向速度的方法

利用连续波雷达测试弹丸径向速度时,会遇到弹丸、火炮、雷达及外界因素异常,测试的径向速度会出现缺失,导致递推出的炮口初速不准确。为此,选择建立合理的模型预测出缺失的径向速度对数据进行重构。雷达测试的径向速度属于一维数据,大口径弹丸的径向速度主要包含线性特征,小口径弹丸的径向速度既包含线性特征又包含非线性特征,都可以建立ARIMA模型、GM(1,1)灰色模型和回归模型进行预测。但是这些传统模型有时预测能力比较局限,预测精度不理想。为了充分整合所有模型的预测优势,提高预测精度,选择建立组合模型进行预测。针对大口径弹丸,建立由ARIMA、GM(1,1)和一阶线性回归方程构建的组合模型进行预测,针对小口径弹丸,建立由ARIMA、GM(1,1)和二次多项式回归方程构建的组合模型进行预测,为了保证预测精度,按照迭代的方式进行预测。实验结果表明,无论是大口径弹丸还是小口径弹丸,组合模型的预测精度始终高于单项模型,平均相对误差小于1‰,更加适合作为弹丸径向速度的预测模型。

A Method for High Precision Prediction of Radial Velocityof Projectile Based on Combined Model

While using continuous wave radar to measure the radial velocity of projectile,it will encounter anomalies of projectile,artillery,radar and external factors,and the measured radial-velocity will be missing,resulting in inaccurate muzzle velocity. Therefore,a reasonable model was built to predict the missing radial-velocity and reconstruct the data. The radial velocity measured by radar belongs to one-dimensional data. The radial velocity of large-caliber projectile mainly contains linear characteristics,while the radial velocity of small-caliber projectile contains both linear and nonlinear characteristics. The autoregressive integrated moving average(ARIMA)model,GM(1,1)grey model and regression model can be established for prediction. However,these traditional models sometimes have limited prediction ability and poor prediction accuracy. In order to fully integrate the prediction advantages of all models and improve the prediction accuracy,a combined model was selected for prediction. For large-caliber projectiles,a combined model constructed by ARIMA,GM(1,1)and first-order linear regression equation was established for prediction. For small-caliber projectiles,a combined model constructed by ARIMA,GM(1,1)and quadratic polynomial regression equation was established for prediction. In order to ensure the prediction accuracy,the prediction was carried out in an iterative manner. The experimental results show that the prediction accuracy of the combined model is always higher than that of the single model,and the average relative error is less than 1‰,which is more suitable for the prediction model of the radial velocity of the projectile.