A Multi-Station Emitter TDOA Deinterleaving Method for Severe Pulse-Loss Environments
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摘要: 针对高脉冲丢失环境下多站辐射源时差分选中真实峰难以累积、高重频条件下脉冲重复间隔模糊易诱发伴生伪峰、大量孤立脉冲难归并以及跨片轨迹易断裂的问题，提出一种以到达时间序列为核心观测量的多站辐射源闭环时差分选方法。首先，对候选脉冲对构造多尺度核密度估计(Kernel Density Estimation, KDE)，重构稀疏时差分布并自适应提取候选到达时间差(Time Difference of Arrival, TDOA)峰；其次，利用主峰提取后伪峰显著坍塌的特性，构建动态记忆矩阵，对候选峰进行坍塌率校验与伪峰屏蔽；然后，针对未配对孤立脉冲，采用动态时间规整(Dynamic Time Warping, DTW)度量残缺序列与已提取序列的间隔相似性，实现孤立脉冲归并；最后，利用卡尔曼滤波对多基线TDOA轨迹进行跨片关联与平滑，降低高丢失场景下的身份标识切换。构建高重频、参数混叠、消融实验和10部多体制混合四组测试场景，并与现有方法进行对比。结果表明，在10部多体制混合且整体丢失率为50%的场景下，所提方法的脉冲提取正确率达到92.72%，TDOA检测虚警率控制在8%以内，且身份标识切换均值低于对比方法。Abstract:
Objective Modern electronic reconnaissance systems must deinterleave dense and overlapping radar pulse streams in non-cooperative environments. As radar emitters increasingly employ agile waveforms, similar pulse descriptor words, and low-intercept-probability strategies, conventional single-station methods based on carrier frequency, pulse width, and Pulse Repetition Interval (PRI) become less reliable. Multi-station deinterleaving based on Time Difference of Arrival (TDOA) provides a more stable geometric observable, but severe pulse loss still causes sparse cross-station pairing, weak true TDOA peaks, ambiguity-induced spurious peaks, isolated pulses, and fragmented trajectories across time slices. These effects increase false alarms and weaken track continuity. To address these issues, a closed-loop multi-station emitter TDOA deinterleaving method is proposed for severe pulse-loss environments, with Time of Arrival (TOA) sequences used as the core observables. Methods A slice-based framework is developed for continuous reconnaissance. Residual unmatched pulses are carried forward by a sliding window to alleviate cross-slice misalignment. First, candidate pulse pairs satisfying geometric TDOA constraints are generated, and pulse descriptor word constraints on carrier frequency and pulse width are used to remove inconsistent pairs. To reduce the sparsity and binning sensitivity of conventional histograms, multiscale Kernel Density Estimation (KDE) is introduced to reconstruct the TDOA density from sparse candidate differences. Gaussian kernels with different bandwidths are fused, and candidate peaks are adaptively extracted using local statistics and peak widths. Second, a dynamic memory matrix is designed to suppress ambiguity-induced spurious peaks in high pulse repetition frequency scenarios. Since dependent spurious peaks collapse after the dominant peak is extracted and removed, a collapse-rate criterion is defined, and the spurious regions are recorded in a memory mask for subsequent iterations. Third, Dynamic Time Warping (DTW) is used to compare incomplete TOA sequences of isolated pulses with extracted pulse sequences, enabling reassignment of unequal-length and incomplete sequences. Finally, a Kalman-filter-based state-space model tracks multi-baseline TDOA trajectories across successive slices. Predicted and observed TDOA residuals are jointly used for association, so intermittent observations can still be linked to the correct track. In this way, the proposed method forms a closed-loop processing chain that links weak-peak reconstruction, spurious-peak suppression, isolated-pulse reassignment, and trajectory association ( Fig. 3 ).Results and Discussions Four simulation scenarios are designed: a high pulse repetition frequency scenario dominated by ambiguity-induced spurious peaks, a parameter-overlapping scenario dominated by isolated pulse reassignment, an ablation scenario for evaluating the memory matrix and DTW modules, and a 10-emitter mixed-regime scenario including fixed PRI, staggered, jittered, frequency-agile, pulse-group frequency-agile, frequency-agile jittered-PRI, linear-sliding, and sinusoidal-sliding PRI signals. In the mixed-regime scenario, the total reconnaissance duration is 1 s and the slice duration is 0.1 s. The environmental pulse loss rate is fixed at 10%, and the receiver-specific loss rate increases from 0% to 40%. Both loss rates are calculated with respect to the initial theoretical number of transmitted pulses; therefore, the total loss rate is their sum, ranging from 10% to 50%. The proposed method is compared with an extended TDOA histogram method under constrained criteria, a cloud-model-based multi-station sorting method, and a Dirichlet Process Mixture Model (DPMM)-based method ( Table 5 ). In the high pulse repetition frequency scenario, the proposed method maintains near-zero false alarms by identifying the collapse of dependent spurious peaks and suppressing them through the memory matrix, whereas the comparison methods show severe false alarms (Figs. 4 and5 ). In the parameter-overlapping scenario, DTW-based reassignment improves isolated-pulse recovery, while the memory matrix suppresses spurious TDOA peaks. Their combination improves extraction reliability and reduces false alarms (Figs. 6 and7 ). The ablation results verify their complementary roles: at a 50% loss rate, the memory matrix reduces the TDOA false alarm rate from 29.92% to 3.32%, DTW increases pulse extraction accuracy from 66.71% to 91.99%, and the complete method achieves a TDOA detection rate of 99.25% with a false alarm rate of 0.88% (Fig. 8 ). In the 10-emitter mixed-regime scenario, the proposed method achieves a favorable overall trade-off. At an overall pulse loss rate of 50%, its pulse extraction accuracy remains 92.72%, and the TDOA false alarm rate is limited to 7.75%, lower than 35.39%, 35.05%, and 37.58% for the DPMM, cloud-model, and constrained recursive histogram methods, respectively. After cross-slice trajectory association, the mean number of identity switches decreases to 3.83, compared with 10.64, 9.85, and 12.64 for the three comparison methods (Fig. 9 andTable 5 ).Conclusions A closed-loop multi-station emitter TDOA deinterleaving method is proposed for severe pulse-loss environments. By integrating multiscale KDE-based weak peak reconstruction, dynamic memory-matrix-based spurious peak suppression, DTW-based isolated pulse reassignment, and Kalman-filter-based trajectory association, the method addresses the coupled failure mechanisms caused by severe pulse loss. Simulation results demonstrate high extraction accuracy, low TDOA false alarm rates, and strong trajectory continuity in high-loss and mixed-regime scenarios. These results demonstrate the effectiveness of the method under the simulated conditions and indicate its application potential for persistent multi-station passive reconnaissance. -
表 1 高重频辐射源信号参数设置
辐射源 载频类型 载频/MHz 脉宽/$ \text{μs} $ PRI类型 PRI/$ \text{μs} $ 幅度 脉冲个数
(理论/实际)MS1之间真实
时差/$ \text{μs} $MS2之间真实
时差/$ \text{μs} $E1 定频 2500 6 固定 100 1.0 995 / 485 – 130.7615 – 34.6091 E2 定频 2600 10 抖动 80 ± 30% 1.9 1240 / 639– 71.6453 – 124.0738 E3 脉组捷变 2620 –2680 5 固定 87 1.0 1149 / 54025.2821 – 106.5098 E4 定频 2700 5 锯齿滑变 90～120(步长2) 1.3 987 / 477 86.7675 – 36.3207 
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表 2 参数混叠辐射源信号参数设置
辐射源 载频类型 载频/MHz 脉宽/$ \text{μs} $ PRI类型 PRI/$ \text{μs} $ 幅度 脉冲个数
(理论/实际)MS1之间真实
时差/$ \text{μs} $MS2之间真实
时差/$ \text{μs} $E1 定频 2500 6 固定 300 1.0 332 / 192 – 130.7615 – 34.6091 E2 定频 2500 6 参差 140,180,220 1.0 551 / 335 – 71.6453 – 124.0738 E3 定频 2600 10 抖动 350 ± 30% 1.9 284 / 148 25.2821 – 106.5098 E4 定频 2600 10 线性滑变 750～800(步长5) 1.8 129 / 68 86.7675 – 36.3207
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表 3 消融实验信号参数设置
辐射源 载频类型 载频/MHz 脉宽/$ \text{μs} $ PRI类型 PRI/$ \text{μs} $ 幅度 脉冲个数
(理论/实际)MS1之间真实
时差/$ \text{μs} $MS2之间真实
时差/$ \text{μs} $E1 定频 2500 6 固定 30 1.0 3334 /1466 – 130.7615 – 34.6092 E2 定频 2500 6 参差 130,170,210 1.1 589 / 290 – 71.6453 – 124.0738 E3 定频 2500 6.2 抖动 70 ± 20% 0.9 1429 / 58525.2823 – 106.5097 E4 脉组捷变 2970 –3030 5 固定 55 1.5 1818 / 769 86.7675 - 36.3206 E5 定频 3000 5 驻留转换 85,115,145 1.2 851 / 327 132.4057 73.6684 E6 定频 3000 4.8 锯齿滑变 90～120(步长2) 1.2 990 / 389 115.9916 125.0508
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表 4 复杂多体制辐射源混合场景信号参数设置
辐射源 载频类型 载频/MHz 脉宽/$ \text{μs} $ PRI类型 PRI/$ \text{μs} $ 幅度 脉冲个数
(理论/实际)MS1之间真实
时差/$ \text{μs} $MS2之间真实
时差/$ \text{μs} $E1 定频 2500 6 固定 100 1.0 10000 /4669 – 130.7567 – 34.5839 E2 定频 2300 14 固定 10000 1.0 100 / 32 – 71.6405 – 124.0702 E3 定频 2400 13 参差 150,190,210 1.0 5453 /2918 25.3029 – 106.4937 E4 定频 2600 10 抖动 350 ± 30% 1.9 2856 /1305 86.7705 – 36.3135 E5 捷变频 2450 –2550 11 固定 550 1.3 1818 / 987 132.4053 73.6711 E6 捷变频 2110 –2190 9 固定 480 1.6 2083 /1007 115.9921 125.0526 E7 脉组捷变 2620 –2680 5 固定 87 1.0 11484 /5426 8.0822 111.0895 E8 捷变频 2170 –2230 10 抖动 589 ± 10% 2.0 1697 / 7800.0354 105.5237 E9 定频 2400 13 线性滑变 750～800(步长5) 1.5 1291 / 553– 46.6987 – 128.9768 E10 定频 2700 17 正弦滑变 $ 1000+100\text{sin}(2\text{π} \dfrac{n}{50}) $ 1.0 1000 / 446126.7155 113.1280
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表 5 复杂多体制辐射源混合场景下的各算法性能指标
整体
丢失率/%算法 提取
正确率/%提取
虚警率/%TDOA
MAE/$ \text{μs} $TDOA
RMSE/$ \text{μs} $检测率/% 漏检率/% 虚警率/% ID切换
(无跟踪)ID切换
(有跟踪)10 本文 98.84 0.00 0.0028 0.0034 91.66 8.34 0.18 80.90 0.30 文献[7] 99.41 0.00 0.0038 0.0063 97.91 2.09 16.56 106.24 4.26 文献[9] 99.73 0.04 0.0036 0.0059 97.78 2.22 13.15 101.55 3.64 文献[13] 99.68 0.00 0.0034 0.0050 97.86 2.14 14.77 103.76 4.01 20 本文 97.44 0.00 0.0029 0.0035 91.04 8.96 0.29 80.39 0.33 文献[7] 89.68 0.00 0.0191 0.1906 96.25 3.75 22.00 112.23 6.84 文献[9] 97.66 2.41 0.0062 0.0420 95.22 4.78 13.44 98.99 4.06 文献[13] 97.40 0.02 0.0034 0.0048 95.99 4.01 15.87 103.03 4.93 30 本文 96.82 0.00 0.0030 0.0037 90.85 9.15 0.37 80.27 0.36 文献[7] 80.95 0.00 0.1003 0.7953 92.91 7.09 31.34 124.08 10.82 文献[9] 95.43 4.29 0.0980 0.7724 91.79 8.21 25.31 111.85 8.14 文献[13] 95.09 0.03 0.0033 0.0046 93.07 6.93 26.56 115.66 8.48 40 本文 95.06 0.00 0.0030 0.0038 89.94 10.06 2.44 81.28 2.13 文献[7] 72.94 0.00 0.1778 1.1122 92.42 7.58 35.45 131.84 12.34 文献[9] 93.07 5.78 0.2251 1.2346 89.70 10.30 32.97 122.59 10.02 文献[13] 92.58 0.03 0.0034 0.0045 90.55 9.45 33.85 125.63 10.08 50 本文 92.72 0.00 0.0030 0.0039 87.63 12.37 7.75 84.07 3.83 文献[7] 65.87 0.00 0.2276 1.2646 90.95 9.05 37.58 134.38 12.64 文献[9] 90.99 7.03 0.2897 1.4026 88.26 11.74 35.05 124.61 9.85 文献[13] 90.55 0.06 0.0034 0.0046 89.77 10.23 35.39 127.62 10.64
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