在多域协同与目标态势感知任务中，传统高精度波达方向（Direction of Arrival，DOA）估计方法通常依赖已知且固定的信源数。然而在持续跟踪过程中，目标数量可能随时间发生变化，导致基于固定信源数的模型失效；同时，被动阵列观测中多目标信号往往以叠加形式出现，难以直接构建对单目标有效的似然函数，从而限制了随机有限集（Random Finite Set, RFS）滤波方法在DOA跟踪中的应用。为解决上述问题，本文提出一种基于泰勒展开的投影相消DOA连续跟踪方法。该方法通过将预测角度附近的导向矢量进行泰勒展开，构造扩展信号子空间，并利用逐源投影算子消除其它目标的干扰分量，从而获得与单信源等价的伪谱，实现多源叠加观测的分解与稳健的单目标似然构建。同时，基于投影相消谱的能量结构与粒子权重分布特征，提出了一种无需预先估计信源数的生灭检测机制，可在概率假设密度滤波器(Probability hypothesis density，PHD)滤波中自适应调整似然维度。仿真结果表明，该方法在低信噪比及信源动态变化条件下相较于传统方法具有较好的DOA跟踪性能。
In multi-domain collaborative sensing and target situation awareness tasks, traditional high-accuracy direction-of-arrival (DOA) estimation methods typically rely on a known and fixed number of sources. However, during continuous tracking, the number of targets may vary over time, causing fixed-source-number models to become invalid. Meanwhile, in passive array sensing, multi-target signals often appear in a superimposed form, making it difficult to construct effective single-target like-lihood functions and thus limiting the applicability of Random Finite Set (RFS)–based filters in DOA tracking. To address these challenges, this paper proposes a continuous DOA tracking method based on a Taylor-expanded projection-cancellation model. By performing a Taylor expansion of the steering vector around the predicted angle, an extended signal subspace is constructed, and interference from other sources is eliminated using sequential projection operators, resulting in a single-source–equivalent pseudo-spectrum. This enables robust decomposition of multi-source superimposed observations and relia-ble construction of single-target likelihoods. Furthermore, based on the energy characteristics of the projection-cancellation spectrum and the particle-weight distribution, a birth–death detection mechanism is introduced, which adaptively adjusts the likelihood dimension in the PHD filter without requiring prior source-number estimation. Simulation results demonstrate that the proposed method achieves superior DOA tracking performance compared with conventional approaches, particularly under low SNR conditions and dynamically varying source scenarios.
[1]陈开源, 李嘉琪, 张小飞.圆与非圆信号混合入射下的低复杂度分布式信源估计算法[J].信号处理, 2025, 41(05):958-966
[2]Zhang X, Xu L, Xu L, et al.Direction of departure (DOD) and direction of arrival (DOA) estimation in MIMO radar with reduced-dimension MUSIC[J].IEEE communications letters, 2010, 14(12):1161-1163
[3]周静, 鲍长春, 段海威.基于滤波与频率聚焦的单声源到达方向实时估计与跟踪方法[J].清华大学学报自然科学版, 2024, 64(11):1902-1910
[4]Schmidt R.Multiple emitter location and signal pa-rameter estimation[J].IEEE transactions on antennas and propagation, 1986, 34(3):276-280
[5]Li J, Jiang D, Zhang X.DOA estimation based on combined unitary ESPRIT for coprime MIMO radar[J].IEEE Communications Letters, 2016, 21(1):96-99
[6]李天成, 谢昱昕, 李固冲, 等.面向多目标跟踪的数据关联方法研究综述[J].雷达科学与技术, 2025, 23(01):10-31
[7]Wan L, Han G, Shu L, et al.The application of DOA estimation approach in patient tracking systems with high patient density[J].IEEE Transactions on Industrial Informatics, 2016, 12(6):2353-2364
[8]Yang B.Projection approximation subspace track-ing[J].IEEE Transactions on Signal processing, 1995, 43(1):95-107
[9]Yang B.Convergence analysis of the subspace track-ing algorithms PAST and PASTd[C]//1996 IEEE Inter-national Conference on Acoustics, Speech, and Signal Processing Conference Proceedings. IEEE, 1996, 3: 1759-1762.
[10]Rissanen J.Modeling by shortest data description[J].Automatica, 1978, 14(5):465-471
[11]Akaike H.A new look at the statistical model identifi-cation[J].IEEE transactions on automatic control, 2003, 19(6):716-723
[12]高一丁, 吴敏, 郝程鹏, 等.无需信源数先验的快速稀疏增强估计方法[J].海军航空大学学报, 2024, 39(05):515-522
[13]Dong F, Xu L, Li X.Particle filter algorithm for DOA tracking using co-prime array[J].IEEE Communica-tions Letters, 2020, 24(11):2493-2497
[14]Tang Z, Manikas A.Multi direction-of-arrival tracking using rigid and flexible antenna arrays[J].IEEE Trans-actions on Wireless Communications, 2021, 20(11):7568-7580
[15]Tang Z, Manikas A.Direction-of-arrival tracking of multiple fast-moving sources in antenna array based ac-cess networks[C]//ICC 2020-2020 IEEE International Conference on Communications (ICC). IEEE, 2020: 1-6.
[16]Cao J, You M, Li D, et al.Multi-source DOA tracking with an adaptive superposition model for sparse array[J]. Signal Processing, 2025, 230: 109877.[J].Signal Processing, 2025, 230(1):109877-109877.
[17]Vo B N, Singh S, Doucet A.Random finite sets and sequential Monte Carlo methods in multi-target track-ing[C]//2003 Proceedings of the International Confer-ence on Radar (IEEE Cat. No. 03EX695). IEEE, 2003: 486-491.
[18]柴雷.基于随机有限集的分布式多传感器分治融合算法研究[D].电子科技大学, 2023.
[19]钟展鸣, 宋强, 张月, 等.基于带标签滤波器的低慢小群目标跟踪改进方法[J].信号处理, 2025, 41(05):906-923
[20]Reifler B L, Jones B A.Improving labeled random finite set-based filtering with limited fields of view[J]. IEEE Transactions on Aerospace and Electronic Sys-tems, 2024.[J].IEEE Transactions on Aerospace and Electronic Systems, 2024, 60(6):9275-9290
[21]Zhao J, Gui R, Dong X.A new measurement associa-tion mapping strategy for DOA tracking[J]. Digital Sig-nal Processing, 2021, 118: 103228.[J].Digital Sig-nal Processing, 2021, 118(1):103228-103228
[22]Dong X, Sun M, Zhao J, et al.An improved PHD filtering for DOA tracking with sparse array via un-scented transform strategy[J].IEEE Transactions on Circuits and Systems II: Express Briefs, 2023, 70(8):3174-3178
[23]陈雨轩, 赵宏宇, 张博轩, 等.基于自适应波束形成的水下目标高稳健跟踪技术[J].无人系统技术, 2024, 7(02):82-91
[24]Cao J, Yang M, You M, et al.Passive Multisource Tracking via Distributed Sparse Arrays: Homogene-ous Data Fusion and Multivariate Adaptation[J]. IEEE Transactions on Intelligent Transportation Systems, 2025.[J].IEEE Transactions on Intelligent Transportation Systems, 2025, 26(5):6570-6586
[25]Mahler R.PHD filters of higher order in target num-ber[J].IEEE Transactions on Aerospace and Electronic systems, 2008, 43(4):1523-1543
[26]Vo B N, Singh S, Doucet A.Sequential Monte Carlo methods for multitarget filtering with random finite sets[J].IEEE Transactions on Aerospace and electronic systems, 2005, 41(4):1224-1245
[27]张小飞, 曾浩威, 郑旺, 等.多阵列中非圆信号借助于降维搜索和子空间数据融合的直接定位算法[J].数据采集与处理, 2020, 35(06):1022-1032
[28]Rahmathullah A S, García-Fernández á F, Svensson L.Generalized optimal sub-pattern assignment met-ric[C]//2017 20th International Conference on Infor-mation Fusion (Fusion). IEEE, 2017: 1-8.
CJA