摘要 數據處理的速度不但取決于計算機本身，而且在一定程度上取決于的算法復雜程度，算法運算量的大小直接影響到設備運行的質量。文中通過對分布式Zigbee多節點傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" 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title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" 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title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器" title="傳感器">傳感器數據融合中的軌跡關聯問題進行探討，對節點狀態估算進行推導，形成節點狀態估算算法，提供了簡單、方便、實用的軌跡關聯算法。
關鍵詞: Zigbee；傳感器；軌跡關聯；目標跟蹤

    分布式Zigbee多節點傳感器結構，以用較低的費用獲得較高的可靠性和實用性，可以減少數據總線的頻寬和數據處理的要求；當一個傳感器的性能降低時，其觀察結果對整個傳感器的信息融合性能和結果的影響較小；同時，可以逐步增加數據采集節點的數量，使系統的結構適應控制中心的操作要求，并有與集中式結構相同或類似的精度。設計新的多傳感器數據交換系統時，分布式結構已成為優先選擇的方案。分布式結構在交通管制、監視系統和多平臺數據融合系統有著廣泛的應用前景。在分布式多傳感器壞境中，每個傳感器都有自己的信息處理系統，并且各系統中都收集了大量的目標信息。那么，一個重要的問題是Zigbee路由節點，如何判斷來自不同節點的兩個信息是否表示同一個目標信息，也就是軌跡關聯問題；解決了軌跡關聯問題，實際上也就解決了Zigbee多節點傳感器覆蓋區域中的重復跟蹤問題。
    對于Zigbee節點N>2的多節點情況，所有節點不僅存在著共同的公共監視區，而且各節點間也可能存在局部公共監視區，如圖1給出了Zi-gbee節點N=3情況下的公共監視區平面示意圖。其中，I區為3個節點的公共監視區；Ⅱ區為節點N1和N2間的公共區；Ⅲ區為節點N2和N3間的公共區；Ⅳ區為節點N3和N1間的公共區。從示意圖中不難看出，可以通過N1分別和N2、N3進行數據關聯校驗，然后再進行N2和N3數據關聯校驗，這樣I區的軌跡多關聯了二次；由于關聯在數學上是等價關系，即對I區的軌跡而言，N1與N2關聯校驗一次之后，再對N2和N3進行一次關聯校驗即可。因此，N1與N3關聯校驗時可不考慮I區的軌跡，而只考慮他們之間的監視公共區(Ⅳ區)軌跡；對I區各節點公共區的軌跡也可以單獨處理，有兩種方法：一種是N1和N2關聯，然后N3和N2關聯，再運用等價關系的可傳遞性形成N個節點的共同關聯軌跡。另一種方法是將其化成多節點分配問題，共同監視區軌跡處理完后，再分別處理兩個節點間的重疊區的軌跡。這兩種方法的優點是直觀、簡單、容易理解、工程上容易實現，當節點N較少時處理速度較快；但當節點N較多時處理速度成倒指數規律衰減，同時，這種處理方式缺乏嚴格的數學描述。所以，為提高分析軌跡關聯的科學性、嚴密性，下面采用多節點分配方法探討Zigbee多節點傳感器數據融合中的軌跡關聯問題。

1 多節點關聯問題的求解
    對于多節點關聯問題的求解，其復雜程度隨著節點數量的增大成指數規律增長。基于測量的多節點分配方法可以形成一套完整的算法。下面先討論傳感器測量的劃分。
    考慮有3個Zigbee節點傳感器形成的觀察量是來自j1、j2和j3Zigbee節點傳感器測量的集合；針對劃分測量，假定測量，n=1，2，3的引入可以是在測量單個和兩個節點傳感器的檢測目標交互中，把觀測量看作是由3個傳感器形成的觀測量。若傳感器j1在位置丟失目標，而傳感器j2和j3的測量源于目標t，則這一情況的似然函數可表示為
   
    式中，Z0j2j3是3個傳感器對位于目標真實位置向量處的同一目標的測量集合；PDs是傳感器s的檢測概率；表示傳感器s的第js測量值。這一事件的似然函數為
   
    式中，u(js)為二值示性函數，當js=0時，u(js)=0；否則，u(js)=1。
    這樣一來，一個可能的劃分是把集合Z劃分成兩個與目標互聯的測量子集Zt和沒有與其他目標互聯的虛擬測量子集Zf，表示為γ={Zt，Zf}，其中，Zt={Zj1j2j3}，ji=1，2，3，…，ni，i=1，2，3；Zf={Ziji}，ji=1，2，3，…，ni，i=1，2，3；γ={Zt，Zf}表示集合Z劃分成子集Zt，Zf的可能，把集合分成測量子集和虛擬測量子集；在靜態傳感器測量數據互聯中，對一個位置進行全面測量估計至少需要兩個傳感器；否則就是認為虛擬測量子集。因此，測量集合Z的最佳關聯劃分是把Z劃分為來源于目標的測量子集Zt和虛警子集Zf，這時只需求解γ與γ0的最大聯合似然函數比，即

    真實目標位置ωt近似于極大化廣義似然比的極大似然估算值，所以式(4)中的ωt可用代替，該估算值可從3個傳感器測量獲得，即
   

2 近似測量
    近似測量算法采用節點狀態估算推導形成，節點狀態估算算法為

    式中，為局部節點s用于更新第i個局部軌跡的近似測量；Ksis(k)是局部節點s的第is個局部軌跡的濾波增益。根據式(6)求解有

    式中，(k)是Ksij(k)的逆陣或偽逆陣。局部節點僅向融合中心傳送狀態估計值，不傳送近似測量值，通過式(7)可以在融合中心獲得局部Zigbee節點的近似測量值。近似測量構造要求信息融合中心已知軌跡狀態值(k|k-1)、狀態估計值(k|k)。增益矩陣Ksij(k)和測量矩陣Hs(k)之所以可作為近似測量，是因為構造的結果可能不是實際測量值，這取決于局部節點使用的數據關聯算法。當局部節點使用最近鄰域互聯算法時，所構成的測量值是局部近似算法中使用的實際測量值；但當局部節點使用聯合概率數據為互聯算法(JPDA)或混合歸并(MR)算法時，重新構成的算法結果不產生實際測量值；因而原測量值需要加權平均。N≥3時多節點分配方法適用于各節點公共監視區的軌跡關聯校驗。對各局部節點間的局部公共區則要利用N=2時的各種軌跡關聯算法或使用二維分配模型求解。

3 結束語
    在多數目標跟蹤的應用中，獲得大量精確的傳感器數據較困難。例如：Zigbee無線車輛門禁控制系統中，只能每幾秒鐘測量一次小區門前內外機動車的位置，當獲取的信息不足時，所采用的模型的精度就顯得尤為重要。原因有二：第一如果控制系統對目標狀態的采集頻率高于Zigbee傳感器的頻率，那么就要用到跟蹤器對位置的預測值，不同的模型對這個預測值的質量影響很大；第二是為了優化Zigbee傳感器的性能，必須最大限度地利用來自傳感器的有限數據，在多數近似測量算法中，只能通過開發一些精度的實用模型來實現。上述節點狀態估算算法有效地改善了Zigbee傳感器的性能，提高了跟蹤精度。