Research on error compensation for dead reckoning based on SVM
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摘要: 一般在使用机器学习方法对航位推算进行误差补偿时, 常采用神经网络算法。但神经网络需要大量的训练样本才能达到稳定的训练结果。为了解决此问题, 对支持向量机(SVM)在航位推算的误差补偿问题进行研究。利用SVM训练出误差补偿模型, 对航位推算进行误差补偿, 提高了导航精度。误差补偿模型选取自主水下航行器的俯仰角、横滚角和航向角, 多普勒计程仪(DVL)对地的前向、右向和天向速度以及航位推算时间等7个参数作为输入参数, 以全球卫星定位系统(GPS)和惯导+DVL组合提供的经纬度与航位推算的经纬度差作为模型的输出, 训练出了误差补偿模型。对比神经网络算法, 在数据量较少的前提下, SVM训练模型的相对误差为0.28%, 神经网络训练模型的相对误差为0.93%。通过湖上试验得出, SVM训练模型能够将航位推算的相对误差控制在0.5%内。Abstract: In the use of machine learning methods for error compensation in dead reckoning, the commonly used algorithm is the neural network. However, neural networks require a large number of training samples to achieve stable training results. To solve this problem, research has been conducted on the application of support vector machine (SVM) for error compensation in dead reckoning. By utilizing SVM, an error compensation model was trained to correct the errors in dead reckoning, thereby improving navigational accuracy. The error compensation model takes seven parameters as input: pitch angle, roll angle, course angle, forward, right, and upward velocity of the Doppler velocity log(DVL) relative to the ground, and dead reckoning time of the autonomous underwater vehicle(AUV). The difference in latitude and longitude provided by the global positioning system(GPS) and inertial navigation system(INS) + DVL combination compared with the dead reckoning's latitude and longitude serves as the output of the model. The trained model shows a relative error of 0.28% with SVM and 0.93% with neural networks when the amount of data is limited. Through lake tests, it was concluded that the model trained by SVM could control the relative error of dead reckoning within 0.5%.
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表 1 SVM与BP误差补偿效果对比
Table 1. Comparison of error compensation effect between SVM and BP
模型 经度误差/(°) 纬度误差/(°) 距离偏差/m 补偿前 1.209×10−4 3.182×10−4 36.447 1 BP 4.904×10−5 7.210×10−5 8.334 4 SVM 2.386×10−5 1.684×10−5 2.489 0 表 2 样本增大前后BP与SVM误差补偿效果对比
Table 2. Comparison of error compensation effect between SVM and BP before and after increasing the sample size
模型 经度
误差/(°)纬度
误差/(°)距离
偏差/m样本量/组 SVM 2.386×10−5 1.684×10−5 2.489 0 2 331 BP 4.904×10−5 7.210×10−5 8.334 4 2 331 BP(增) 2.321×10−5 2.176×10−5 2.637 0 6 911 表 3 蛇形轨迹误差补偿前后对比
Table 3. Comparison of snake trajectory error before and after compensation
阶段 经度误差/(°) 纬度误差/(°) 距离偏差/m 补偿前 1.179×10−4 3.381×10−4 39.105 补偿后 2.416×10−5 2.086×10−5 2.894 表 4 AUV水下定深试验误差补偿前后对比
Table 4. Comparison of underwater fixed depth experiment error before and after compensation
阶段 经度误差/(°) 纬度误差/(°) 距离偏差/(m) 补偿前 1.126×10−4 2.869×10−4 31.9541 补偿后 9.742×10−5 6.751×10−5 10.2131 表 5 水下定深四边形试验误差补偿前后对比
Table 5. Comparison of underwater depth quadrilateral experiment error before and after compensation
阶段 经度误差/(°) 纬度误差/(°) 距离偏差/(m) 补偿前 9.648×10−4 3.486×10−4 38.7740 补偿后 1.542×10−5 2.004×10−5 2.2392 -
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