基于基函数逼近和卡尔曼滤波的温度场重建

为了提高声学CT复杂温度场重建能力,提出一种基于基函数逼近和卡尔曼滤波的温度场重建算法.利用Markov径向基函数的线性组合逼近被测区域内的声速分布,并使用卡尔曼滤波根据多路径声波飞行时间数据重建出声速分布,进而利用声速与温度的关系得到温度分布.分别采用Markov径向基函数Tikhonov正则化法、最小二乘法和BFAKF算法对4种典型的三维模型温度场进行了无噪声和有噪声仿真数据重建.重建结果表明,BFAKF算法的重建结果优势明显,具有更好的复杂温度场重建能力.

Reconstruction of temperature fields based on basis function approximation and Kalman filtering

In order to improve the reconstruction capacity of complex temperature fields of acoustic computer tomography(CT), a reconstruction algorithm for the temperature fields based on basis function approximation and Kalman filtering was proposed. The linear combination of Markov radial basis functions was used to approximate the sound speed distribution in the measured region, Kalman filtering was used to reconstruct the sound speed distribution with the acoustic time-of-flight data over multi-paths, and the temperature distribution was obtained by using the relationship between sound speed and temperature. Four typical three-dimension model temperature fields were reconstructed with both noise-free and noisy simulation data obtained by the Markov radial basis function Tikhonov regularization algorithm, the least square method and the BFAKF algorithm, respectively. The reconstruction results show that the advantages of BFAKF algorithm are obvious, and the BFAKF algorithm has better reconstruction capacity of complex temperature fields.