摘要 數(shù)據(jù)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(fù)雜程度，算法運算量的大小直接影響到設(shè)備運行的質(zhì)量。文中通過對分布式Zigbee多節(jié)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" 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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" title="傳感器">傳感器" title="傳感器">傳感器數(shù)據(jù)融合中的軌跡關(guān)聯(lián)問題進行探討，對節(jié)點狀態(tài)估算進行推導(dǎo)，形成節(jié)點狀態(tài)估算算法，提供了簡單、方便、實用的軌跡關(guān)聯(lián)算法。
關(guān)鍵詞: Zigbee；傳感器；軌跡關(guān)聯(lián)；目標(biāo)跟蹤

    分布式Zigbee多節(jié)點傳感器結(jié)構(gòu)，以用較低的費用獲得較高的可靠性和實用性，可以減少數(shù)據(jù)總線的頻寬和數(shù)據(jù)處理的要求；當(dāng)一個傳感器的性能降低時，其觀察結(jié)果對整個傳感器的信息融合性能和結(jié)果的影響較?。煌瑫r，可以逐步增加數(shù)據(jù)采集節(jié)點的數(shù)量，使系統(tǒng)的結(jié)構(gòu)適應(yīng)控制中心的操作要求，并有與集中式結(jié)構(gòu)相同或類似的精度。設(shè)計新的多傳感器數(shù)據(jù)交換系統(tǒng)時，分布式結(jié)構(gòu)已成為優(yōu)先選擇的方案。分布式結(jié)構(gòu)在交通管制、監(jiān)視系統(tǒng)和多平臺數(shù)據(jù)融合系統(tǒng)有著廣泛的應(yīng)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(tǒng)，并且各系統(tǒng)中都收集了大量的目標(biāo)信息。那么，一個重要的問題是Zigbee路由節(jié)點，如何判斷來自不同節(jié)點的兩個信息是否表示同一個目標(biāo)信息，也就是軌跡關(guān)聯(lián)問題；解決了軌跡關(guān)聯(lián)問題，實際上也就解決了Zigbee多節(jié)點傳感器覆蓋區(qū)域中的重復(fù)跟蹤問題。
    對于Zigbee節(jié)點N>2的多節(jié)點情況，所有節(jié)點不僅存在著共同的公共監(jiān)視區(qū)，而且各節(jié)點間也可能存在局部公共監(jiān)視區(qū)，如圖1給出了Zi-gbee節(jié)點N=3情況下的公共監(jiān)視區(qū)平面示意圖。其中，I區(qū)為3個節(jié)點的公共監(jiān)視區(qū)；Ⅱ區(qū)為節(jié)點N1和N2間的公共區(qū)；Ⅲ區(qū)為節(jié)點N2和N3間的公共區(qū)；Ⅳ區(qū)為節(jié)點N3和N1間的公共區(qū)。從示意圖中不難看出，可以通過N1分別和N2、N3進行數(shù)據(jù)關(guān)聯(lián)校驗，然后再進行N2和N3數(shù)據(jù)關(guān)聯(lián)校驗，這樣I區(qū)的軌跡多關(guān)聯(lián)了二次；由于關(guān)聯(lián)在數(shù)學(xué)上是等價關(guān)系，即對I區(qū)的軌跡而言，N1與N2關(guān)聯(lián)校驗一次之后，再對N2和N3進行一次關(guān)聯(lián)校驗即可。因此，N1與N3關(guān)聯(lián)校驗時可不考慮I區(qū)的軌跡，而只考慮他們之間的監(jiān)視公共區(qū)(Ⅳ區(qū))軌跡；對I區(qū)各節(jié)點公共區(qū)的軌跡也可以單獨處理，有兩種方法：一種是N1和N2關(guān)聯(lián)，然后N3和N2關(guān)聯(lián)，再運用等價關(guān)系的可傳遞性形成N個節(jié)點的共同關(guān)聯(lián)軌跡。另一種方法是將其化成多節(jié)點分配問題，共同監(jiān)視區(qū)軌跡處理完后，再分別處理兩個節(jié)點間的重疊區(qū)的軌跡。這兩種方法的優(yōu)點是直觀、簡單、容易理解、工程上容易實現(xiàn)，當(dāng)節(jié)點N較少時處理速度較快；但當(dāng)節(jié)點N較多時處理速度成倒指數(shù)規(guī)律衰減，同時，這種處理方式缺乏嚴(yán)格的數(shù)學(xué)描述。所以，為提高分析軌跡關(guān)聯(lián)的科學(xué)性、嚴(yán)密性，下面采用多節(jié)點分配方法探討Zigbee多節(jié)點傳感器數(shù)據(jù)融合中的軌跡關(guān)聯(lián)問題。

1 多節(jié)點關(guān)聯(lián)問題的求解
    對于多節(jié)點關(guān)聯(lián)問題的求解，其復(fù)雜程度隨著節(jié)點數(shù)量的增大成指數(shù)規(guī)律增長。基于測量的多節(jié)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(jié)點傳感器形成的觀察量是來自j1、j2和j3Zigbee節(jié)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(jié)點傳感器的檢測目標(biāo)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(biāo)，而傳感器j2和j3的測量源于目標(biāo)t，則這一情況的似然函數(shù)可表示為
   
    式中，Z0j2j3是3個傳感器對位于目標(biāo)真實位置向量處的同一目標(biāo)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(shù)為
   
    式中，u(js)為二值示性函數(shù)，當(dāng)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(biāo)互聯(lián)的測量子集Zt和沒有與其他目標(biāo)互聯(lián)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(tài)傳感器測量數(shù)據(jù)互聯(lián)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(rèn)為虛擬測量子集。因此，測量集合Z的最佳關(guān)聯(lián)劃分是把Z劃分為來源于目標(biāo)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(lián)合似然函數(shù)比，即

    真實目標(biāo)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(jié)點狀態(tài)估算推導(dǎo)形成，節(jié)點狀態(tài)估算算法為

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

    式中，(k)是Ksij(k)的逆陣或偽逆陣。局部節(jié)點僅向融合中心傳送狀態(tài)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(jié)點的近似測量值。近似測量構(gòu)造要求信息融合中心已知軌跡狀態(tài)值(k|k-1)、狀態(tài)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(gòu)造的結(jié)果可能不是實際測量值，這取決于局部節(jié)點使用的數(shù)據(jù)關(guān)聯(lián)算法。當(dāng)局部節(jié)點使用最近鄰域互聯(lián)算法時，所構(gòu)成的測量值是局部近似算法中使用的實際測量值；但當(dāng)局部節(jié)點使用聯(lián)合概率數(shù)據(jù)為互聯(lián)算法(JPDA)或混合歸并(MR)算法時，重新構(gòu)成的算法結(jié)果不產(chǎn)生實際測量值；因而原測量值需要加權(quán)平均。N≥3時多節(jié)點分配方法適用于各節(jié)點公共監(jiān)視區(qū)的軌跡關(guān)聯(lián)校驗。對各局部節(jié)點間的局部公共區(qū)則要利用N=2時的各種軌跡關(guān)聯(lián)算法或使用二維分配模型求解。

3 結(jié)束語
    在多數(shù)目標(biāo)跟蹤的應(yīng)用中，獲得大量精確的傳感器數(shù)據(jù)較困難。例如：Zigbee無線車輛門禁控制系統(tǒng)中，只能每幾秒鐘測量一次小區(qū)門前內(nèi)外機動車的位置，當(dāng)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(tǒng)對目標(biāo)狀態(tài)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(yù)測值，不同的模型對這個預(yù)測值的質(zhì)量影響很大；第二是為了優(yōu)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(shù)據(jù)，在多數(shù)近似測量算法中，只能通過開發(fā)一些精度的實用模型來實現(xiàn)。上述節(jié)點狀態(tài)估算算法有效地改善了Zigbee傳感器的性能，提高了跟蹤精度。