航空重力测量数据处理中基于频域的卡尔曼平滑滤波方法技术研究

    Technical research on frequency-domain-based Kalman smoothing filtering for airborne gravity data processing

    • 摘要: 卡尔曼滤波是一种基于模型的时域滤波方法,其在频率域上的实现方法是航空重力测量数据处理中的关键技术。笔者采用低阶泰勒级数展开近似的卡尔曼滤波模型,研究设计了一种基于频域的卡尔曼平滑滤波器。由泰勒级数公式出发,研究分析了信号幅值、信号频率、数据采样率和模型维数对模型误差的影响;根据一般卡尔曼平滑滤波算法,推导并给出平滑滤波器稳态条件下的频率响应函数 H(\texte^\textj\omega ) ;基于滤波器截止频率 f_c和幅频特性参数 \left| H(f_c)\right| ,提出一种用于确定系统噪声和量测噪声统计特性参数的方法,用于估算系统噪声序列和量测噪声序列方差。采用本文滤波器和重力异常解算方案,对某地实测数据进行重力异常解算及滤波处理,并与用GT-1A系统软件的处理结果进行对比研究,二者均方差值平均达0.47 mGal。

       

      Abstract: The Kalman filtering represents a time-domain filtering method based on dynamic models. Its frequency-domain implementation emerges as a key technique for airborne gravity data processing. In light of this, this study explored and designed a frequency-domain-based Kalman smoothing filter based on the Kalman filter model established previously by the authors through approximation using a low-order Taylor series expansion. First, using the Taylor series formula, the impacts of signal amplitude, signal frequency, data sampling rate, and model dimension on model errors were analyzed. The frequency response function H(\texte^\textj\omega ) of the Kalman smoothing filter under steady-state conditions was then derived using the general Kalman smoothing filtering algorithm. Subsequently, based on the cutoff frequency f_c and amplitude-frequency response parameter \left| H(f_c)\right| of the smoothing filter, a method was proposed to determine the statistical parameters of systematic and measurement noise. This method aims to estimate the variances of the systematic and measurement noise series. Measured data from a certain area were processed using the filter proposed in this study and the scheme for solving gravity anomalies. The results were compared with those derived using the GT-1A system software, yielding an average mean square error (MSE) of 0.47 mGal.

       

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