Weight-Function Notch Filter Algorithm for Narrow-band Interference in eLORAN System
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摘要: 针对增强型罗兰(eLORAN)系统的带内干扰问题，该文基于陷波滤波器(NF)原理提出一种抗带内窄带干扰的自适应权函数陷波算法(WF-NF)。首先，该文分析讨论了NF算法在eLORAN系统中的适用性及检测频差引起的伪收敛问题；之后通过增加频差权函数，推导出新的WF-NF算法，解决了固有频差导致的陷波逻辑缺陷；随后，提出梯度跳跃收敛优化技术，改进了权系数收敛速度过慢的问题；最后，通过多种环境下的实验验证了算法的稳定性、多元适用性及实用性。分析结果表明，WF-NF算法能够克服检测频差的实际问题，实现高效的干扰跟踪及滤除，同时也可以补偿干扰检测精度，进而为后续的信号处理流程提供保障。Abstract: In order to solve the problem of in-band interference of enhanced LOng RAnge Navigation (eLORAN) system, an adaptive Weight-Function Notch Filter (WF-NF) algorithm is proposed based on the principle of Notch Filter (NF) to resist narrow-band interference. Firstly, the applicability of NF algorithm in eLORAN system and the pseudo convergence caused by detection frequency difference are analyzed. Then, by adding the weight function of frequency difference, a new WF-NF algorithm is derived to solve the notch logic flaw caused by the inherent frequency difference. Next, a gradient-jump optimization technique is designed to improve the convergence speed of weight coefficients. Finally, the stability, multiple applicability and practicability of the new algorithm are verified by simulation experiments in various environments. The analysis results show that the WF-NF algorithm can overcome the practical problem of detection frequency difference, realize efficient interference tracking and filtering, and compensate the accuracy of interference detection, so as to provide guarantee for the subsequent signal processing process.
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表 1 无噪声环境6个干扰及WF-NF滤波统计(360 ms处)
干扰频率(kHz) 干扰幅度 检测频率(kHz) 频差(Hz) 频差权系数(Hz) 频差误差(Hz) 幅-相权系数 跟踪幅度 幅度误差 97 0.5 97.1 –100 –100.00001887 1.887e-5 0.48757903–0.11075511 0.50000000 <1e-8 106 0.42 105.95 50 50.00004769 4.769e-5 0.40969754–0.09245514 0.42000003 <3e-8 93 1.1 92.808 192 192.00001730 1.730e-5 1.093862170.11604118 1.10000000 <1e-8 112.3 0.73 112.7 –400 –400.00000267 2.67e-6 0.70671391–0.18290832 0.73000000 <1e-8 87.2 0.57 87.232 –32 –31.99998525 1.475e-5 0.569164820.03084474 0.57000000 <1e-8 102.5 1.35 102.435 65 64.99996204 3.796e-5 1.348538100.06280919 1.35000000 <1e-8 
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表 2 6个干扰+10 dB白噪声环境WF-NF滤波统计(360 ms处)
干扰频率(kHz) 干扰幅度 检测频率(kHz) 频差(Hz) 频差权系数(Hz) 频差误差(Hz) 幅-相权系数 跟踪幅度 幅度误差 97 0.5 97.1 –100 –99.92467515 0.07532485 0.49562550
–0.047870830.49793197 0.00206803 106 0.42 105.95 50 49.97971179 0.02028821 0.39140512
0.138242630.41510118 0.00489882 93 1.1 92.808 192 192.05701743 0.05701743 1.07620635
0.197662201.09420768 0.00579232 112.3 0.73 112.7 –400 –399.91977736 0.08022264 0.69925836
–0.199050530.72703739 0.00296261 87.2 0.57 87.232 –32 –31.89363265 0.10636735 0.56605044
–0.020301290.56641438 0.00358562 102.5 1.35 102.435 65 64.92559131 0.07440869 1.33417085
0.190344511.34768056 0.00231944
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