宇航学报 ›› 2012, Vol. 33 ›› Issue (8): 1048-1055.doi: 10.3873/j.issn.1000-1328.2012.08.008

• 制导、导航与控制 • 上一篇    下一篇

ARMA建模及其在Kalman滤波中的应用

王可东, 熊少锋   

  1. 北京航空航天大学宇航学院,北京 100191
  • 收稿日期:2011-06-14 修回日期:2011-11-01 出版日期:2012-08-15 发布日期:2012-08-22
  • 作者简介:10001328(2012)08104808
  • 基金资助:
    航空科学基金(20100851017,20100818015)

An ARMA Modeling Method and Its Application in Kalman Filtering

WANG Ke dong, XIONG Shai feng   

  1. School of Astronautics, Beihang University,Beijing 100191,China
  • Received:2011-06-14 Revised:2011-11-01 Online:2012-08-15 Published:2012-08-22

摘要: 提出了一种补偿惯性传感器随机误差的自回归滑动平均(ARMA)建模方法,在该方法中,首先,将时间序列平稳性检验的轮次法和样本方差变差系数相结合,以确定合适的建模样本长度;其次,将惯性传感器的随机误差看成是真实状态叠加白噪声,通过对观测数据做滤波处理,给出了求解模型参数的算法;随后,构建一组符合ARMA(6,4)模型分布的有色噪声,基于准确建立的ARMA(6,4)模型和AR(2)近似模型构建Kalman滤波器,以研究建模精度和Kalman滤波输出之间的关系;最后,探讨了基于状态可观测度分析的模型降阶方法,在保证精度情况下提高模型计算的实时性,便于建模方法在工程实际中的应用。通过对某型号加速度计的随机误差进行处理,高阶模型及降阶模型的滤波残差标准差分别降为原始随机误差标准差的1/66和1/28,说明方法是有效的。

关键词: 时间序列, 自回归滑动平均, Kalman滤波, 有色噪声

Abstract: An ARMA modeling method is proposed to compensate for the random errors of the inertial sensor’s output. In the method, the length of samples for modeling was determined by combining runs test method for ensuring the stationarity of the samples with coefficients of variation of sample variances firstly. Then, the random error of the inertial sensor is processed as the colored noise governed by an ARMA model and superimposes by a white noise. The ARMA model parameters are derived by filtering the samples. In the following, the colored noises governed by the ARMA(6,4) model are simulated to study the effect of the model accuracy on the Kalman filtering performance by comparing the Kalman filtering results of the derived ARMA(6,4) model with the ones of an approximated AR(2) model. Finally, the model reduction method based on the observability degree analysis is proposed to improve the real time performance of the modeling method with an acceptable accuracy degradation in applications. The modeling method is applied to process the random noise of an accelerometer. The standard deviations of the Kalman filtering residuals of the high\|order model and the reduced order model are just 1/66 and 1/28 of one of the unprocessed noise respectively, proving the effectiveness of the modeling method.

Key words: Time series, ARMA, Kalman filter, Colored noise

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