Dichotomy method for inversion of rainfall intensity by polarimetric phase shift of GNSS signal
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摘要: 降雨强度-极化相移模型的函数表达式较为复杂，难以导出反演降雨强度的解析式. 模拟退火法是一种反演降雨强度的有效方法，虽其能够较好地反演降雨强度，但计算耗时较长. 针对该问题，提出基于二分法的极化相移反演降雨强度算法. 首先将降雨强度反演问题转化为函数零点求解问题；然后采用二分法进行模型解算，并给出了基于二分法的降雨强度反演算法；最后通过仿真实验对新算法的效率进行了验证. 结果表明：与模拟退火算法相比，二分法能够在保证反演精度的前提下显著提升反演效率，将每次反演所需平均时间缩短约75%.Abstract: The function expression of the rain intensity- polarimetric phase shift model is complex, making it difficult to derive an analytical expression for inverting the rainfall intensity. Simulated annealing is an effective method for inverting rain intensity, but it is computationally time-consuming. In response to this problem, a rain intensity inversion algorithm based on the bisection method is proposed. Firstly, the rain intensity inversion problem is transformed into a function zero-point solving problem. Then, the bisection method is employed for model calculation, and a rain intensity inversion algorithm based on the bisection method is presented. Finally, the efficiency of the new algorithm is verified through simulation experiments. The results show that compared with the simulated annealing algorithm, the bisection method can significantly improve the inversion efficiency while ensuring the inversion accuracy, reducing the average required time for each inversion by about 75%.
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Key words:
- GNSS /
- polarimetric phase shift /
- rainfall intensity /
- simulated annealing algorithm /
- bisection method
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表 2 实验3反演雨强结果表
编号 雨强 仿真极化相移 观测极化相移 模拟退火算法 二分法 1 6.060 6 0.790 5 3.575 1 21.941 9 21.940 9 2 14.141 4 2.144 6 0.683 0 5.361 4 5.351 2 3 22.222 2 3.628 1 2.833 5 17.960 7 17.959 5 4 30.303 0 5.194 4 4.676 4 27.669 5 27.669 7 5 38.383 8 6.823 0 6.707 3 37.818 6 37.819 4 6 46.464 6 8.501 7 7.917 6 43.677 9 43.678 2 7 54.545 5 10.222 6 9.001 0 48.828 5 48.828 5 8 62.626 3 11.980 1 12.752 3 66.130 0 66.129 5 9 70.707 1 13.769 8 10.054 6 53.764 7 53.764 3 10 78.787 9 15.588 5 12.996 4 67.231 8 67.231 6 11 86.868 7 17.433 4 17.772 9 88.344 0 88.343 5 12 94.949 5 19.302 2 19.073 1 93.963 7 93.963 4 13 103.030 3 21.193 2 19.313 3 94.996 8 94.996 0 14 111.111 1 23.104 5 21.551 7 104.552 6 104.552 2 15 119.191 9 25.034 9 24.774 0 118.104 3 118.102 3 16 127.272 7 26.983 1 25.762 0 122.216 4 122.218 6 17 135.353 5 28.947 9 23.218 4 111.589 9 111.589 9 18 143.434 3 30.928 5 27.682 5 130.157 0 130.156 9 19 151.515 2 32.923 9 28.609 3 133.965 5 133.966 0 20 159.596 0 34.933 3 31.223 6 144.633 1 144.632 6 21 167.676 8 36.956 1 37.150 6 168.451 4 168.451 5 22 175.757 6 38.991 5 41.936 8 187.368 1 187.366 3 23 183.838 4 41.038 9 37.563 5 170.093 6 170.095 5 24 191.919 2 43.097 8 41.289 1 184.823 0 184.809 7 25 200.000 0 45.167 6 43.964 0 195.306 1 195.305 2 
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表 3 两种算法反演结果的RMSE
mm/h 算法 实验1 实验2 实验3 实验4 模拟退火算法 2.215 4 5.264 1 8.706 3 13.878 9 二分法 2.215 9 5.274 6 8.706 5 13.878 1
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表 4 两种算法平均耗时
实验 模拟退火算法/s 二分法/s 百分比/% 实验1 0.426 1 0.104 0 75.68 实验2 0.428 0 0.100 0 76.53 实验3 0.429 2 0.105 0 75.42 实验4 0.432 8 0.101 0 76.75
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