時變來源數和方向下的稀疏陣列來源追蹤

Sparse Array Source Tracking under Time-Varying Source Numbers and Directions

劉又嘉(Yu-Chia Liu)

指導教授 ： 劉俊麟

國立臺灣大學/電機資訊學院/電信工程學研究所/碩士(2024年)

https://doi.org/10.6342/NTU202401715

摘要

偵測無人機是訊號處理中的熱門主題，而追蹤無人機的數量和位置至關重要。在訊號處理中，通常將無人機視為訊號來源。在來源數列舉和訊號子空間追蹤的領域中有許多現有方法。子空間追蹤可以追蹤來向角，而來源數列舉可以估計不動的來源數量。然而，無人機的數量和位置可能同時變化。各個領域中的方法都無法應對這樣的困難情況。也有一些處理困難情況的新方法，但它們只能應用於均勻線性陣列。在來向角估計與來源數列舉的領域中，稀疏陣列比均勻線性陣列的表現更好。稀疏陣列可以更準確地列舉源的數量和估計來向角。我們想要為稀疏陣列設計一種新方法。

本論文提出了「時變來源數和方向下的稀疏陣列來源追蹤」（SAST-TVSND）方法。SAST-TVSND 演算法包含兩個部分。一個是來源數列舉的部分，另一個是訊號子空間追蹤的部分。為了在稀疏陣列上執行 SAST-TVSND 演算法，我們使用「透過協同子空間最佳的稀疏陣列來源數列舉」（SASE-CSO）演算法進行來源數列舉，並使用「空間平滑化之投影近似子空間追蹤」（SS-PAST）演算法進行訊號子空間追蹤。我們設計了一個用於快照的分配器，分配器會追蹤 SS-PAST 演算法中的參數。一旦達到特定的條件，分配器將快照提供給 SASE-CSO 演算法。當分配器從 SASE-CSO 切換到 SS-PAST 時，SASE-CSO 中與訊號子空間相關的一些參數會傳遞給 SS-PAST，反之亦然。這讓演算法能在較少的時間內收斂到正確的值。

在模擬部分，我們選擇「PASTd-AIC」作為我們的競爭對手。與 PASTd-AIC相比，SAST-TVSND 演算法在估計來源數量和來向角方面具有更高的準確性。SAST-TVSND 演算法的正確列舉率超過 0.8，而 PASTd-AIC 的正確列舉率低於 0.8。SAST-TVSND 的方均根誤差小於 10^−2，而 PASTd-AIC 的誤差則超過 10^−2。SAST-TVSND 演算法擅長處理來源移動快速，例如在相鄰離散時間點改變 0.05 度，或當兩個來源角度差只有 2 度時的情況。

關鍵字

來源數列舉 ； 訊號子空間追蹤 ； 稀疏陣列 ； 來向角估計

並列摘要

Detecting unmanned aerial vehicles (UAVs) has been a popular topic in signal processing. Tracking the number and the location of the UAVs becomes important. The UAVs are commonly assumed as sources in signal processing. There are many existing methods in source enumeration and subspace tracking. Subspace tracking can track the Directions of Arrivals (DOAs). Source enumeration can count the number of fixed sources. However, the number and the location of the UAVs may change at the same time. The methods in each field cannot deal with such difficult scenario. There are also some new methods dealing with the difficult scenario, but they can only be used on uniform linear arrays (ULA). In DOA estimation and source enumeration, sparse arrays perform better than ULAs do. Sparse arrays can enumerate the number of sources and estimate the DOAs more accurately. It is desirable to design a new method for sparse arrays.

This thesis proposes Sparse Array Source Tracking under Time-Varying Source Numbers and Directions (SAST-TVSND). The SAST-TVSND algorithm contains two sections. One is the source enumeration part, and the other is subspace tracking part. To perform SAST-TVSND algorithm on sparse arrays, we use Sparse Array Source Enumeration via Coarray Subspace Optimization (SASE-CSO) algorithm for enumeration, and Spatial Smoothing Projection Approximation Subspace Tracking (SS-PAST) algorithm for subspace tracking. We design an allocator for the snapshots. The allocator traces the parameters in SS-PAST algorithm. Once some criterions are achieved, the allocator would give the snapshots to the SASE-CSO algorithm. When the allocator switches from SASECSO to SS-PAST, some parameters related to the signal subspace in SASE-CSO will be passed to SS-PAST, and vice versa. It makes the algorithm converges to a correct value in fewer time indices.

In our simulations, we chose “PASTd-AIC” as the competitor. The SAST-TVSND algorithm outperforms PASTd-AIC in estimating the number of sources and DOAs. SAST-TVSND has a correct enumeration fraction above 0.8, while PASTd-AIC's is below 0.8. The root-mean-square error of SAST-TVSND is less than 10^−2, whereas PASTd-AIC's error exceeds 10^−2. The SAST-TVSND algorithm also performs well in scenarios with rapidly moving sources (changing by 0.05 degrees per discrete-time index) and closely spaced sources (2-degree angle difference).

並列關鍵字

Source Enumeration ； Subspace Tracking ； Sparse Array ； DOA Estimation

參考文獻

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