第四章 調整通訊半徑以降低最大定位誤差之研究
4.5 每一次區塊合併後調整通訊半徑
4.5.3. 例子
4.5.3.2. 只有 A 調整通訊半徑 L sec 會被影響
當只有 Beacon Node A 調整通訊半徑時會影響 L
sec
線段，此時不會影響 Lsec
線段的 Beacon Node B 可以做較多的調整空間，所以我們先讓 Beacon Node B 先 行調整，若有不足的才讓 Beacon Node A 補充調整。下面 Case1 舉例說明調整的 過程，Case2 至 Case5 由於決策過程相似所以只以圖例簡單說明。
Case1:
圖 4.15 為一個只有 Beacon Node A 調整通訊半徑時會影響 L
sec
線段的例子，圖中長條為 Beacon Node 所在的一維區域，藍色區域為 Beacon Node A 所在的小 區塊，黃色為 Beacon Node B 所在的小區塊。假設 Beacon Node A 以左的區塊及 Beacon Node B 以右的區塊合併，那麼我們依據節 4.5.1 先求出 L
Max
等十個線段，如圖 4.15 上方所示，接著依據節 4.5.2 的表 4.2 來調整通訊半徑。此例中，Beacon Node B 需要縮小通訊半徑，所以會執行公式(9)。
如 Step1 所示我們求出調整後 Beacon Node B 的半徑為 R
B
，Beacon Node B 調整半徑後的各線段需重新計算新值，且 LSec
需要重新從十個線段參數中重新挑0 1 2 3 4 5 6
LA l in = LsecLA l out = 3.5 LA r in = Lmax
LA r out = 5
LB l in = Lmax
LB l out = Lsec LB r in = 5 LB r out = 2 Lsec = 6
A B
Lmax = 12.5
RA = 9.5 RB = 9 DAB = 6
選，調整過後十個線段參數值與圖形如圖 4.16。接著執行 Step2，我們使用了公 式(10)計算出了調整後的 Beacon Node A 的半行行為 R
A
，結果如圖 4.17 所示。圖 4.15: 4.5.3.2 節的 Case1，調通訊半徑整前。
Step1:如果 B 需縮小通訊半徑，就使用公式(9)
R B
= Max (8, 6.5 + 6– 11.5 = 1, 6.5 + (((15.5 + 1.5)/2) – 11.5 = 3.5, 6.5 + (((15.5 + 2.5)/2) – 11.5 = 4)圖 4.16: 4.5.3.2 節的 Case1，Beacon Node B 調整通訊半徑後。
LA l in = Lsec
LA l out = 4 LA r in = Lmax
LA r out = 2
LB l in = Lmax
LB l out = 4 LB r in = 1 LB r out = 5 Lsec = 6
Lmax = 13
A
B
0 1 2 3 4 5 6
RA = 11.5 RB = 8 DAB = 6.5
LA l in = Lsec
LA l out = 4 LA r in = Lmax
LA r out = 2
LB l in = Lmax
LB l out = 1.5 LB r in = 3.5 LB r out = 2.5 Lsec = 6
Lmax = 15.5
A B
0 1 2 3 4 5 6
RA = 11.5 RB = 10.5 DAB = 6.5
Step2:如果 A 需縮小通訊半徑，就使用公式(10)
R A
= Max (6.5, 6.5 + (((13 + 4)/2) – 8 = 7, 6.5 + (((13 + 2)/2) – 8 = 6)圖 4.17: 4.5.3.2 節的 Case1，Beacon Node A 調整通訊半徑後。
Case2:
圖 4.18: 4.5.3.2 節的 Case2，調整通訊半徑前。
Step1:如果 B 需縮小通訊半徑，就使用公式(9)
R B
= Max (7.5, 7 + 9.5 – 12 = 4.5, 7 + (((16 + 2)/2) – 12 = 4, 7 + (((16 + 1)/2) – 12 = 3.5)0 1 2 3 4 5 6
LA l in = 6 LA l out = Lsec
LA r in = Lmax
LA r out = 1
LB l in = Lmax
LB l out = 2 LB r in = 5 LB r out = 1 Lsec = 9.5
Lmax = 16
A
B
RA = 12RB = 11 DAB = 7
LA l in = 1.5 LA l out = Lsec
LA r in = Lmax
LA r out = 6.5
LB l in = Lmax
LB l out = 4 LB r in = 1 LB r out = 5 Lsec = 8.5
Lmax = 8.5
A B
0 1 2 3 4 5 6
RA = 7 RB = 8 DAB = 6.5
圖 4.19: 4.5.3.2 節的 Case2，Beacon Node B 調整通訊半徑後。
Step2:如果 A 需縮小通訊半徑，就使用公式(10)
R A
= Max (7, 7 + (((12.5 + 9.5)/2) – 7.5 = 10.5, 7 + (((12.5 + 1)/2) – 7.5 = 6.25)圖 4.20: 4.5.3.2 節的 Case2，Beacon Node A 調整通訊半徑後。
0 1 2 3 4 5 6
LA l in = 4.5 LA l out = Lsec
LA r in = Lmax
LA r out = 2.5
LB l in = Lmax
LB l out = 5.5 LB r in = 1.5 LB r out = 4.5 Lsec = 11
Lmax = 11
A
B
RA = 10.5RB = 7.5 DAB = 7
0 1 2 3 4 5 6
LA l in = 6 LA l out = Lsec
LA r in = Lmax
LA r out = 1
LB l in = Lmax
LB l out = 5.5 LB r in = 1.5 LB r out = 4.5 Lsec = 9.5
Lmax = 12.5
A
B
RA = 12RB = 7.5 DAB = 7
Case3:
圖 4.21: 4.5.3.2 節的 Case3，調整通訊半徑前。
Step1:如果 B 需縮小通訊半徑，就使用公式(9)
R B
= Max (10.5, 8 + 6– 12 = 2, 8 + (((15 + 2)/2) –12 = 4.5, 8 + (((15 + 4.5)/2) –12 = 5.75)圖 4.22: 4.5.3.2 節的 Case3，Beacon Node B 調整通訊半徑後。
LA l in = 3 LA l out = 1
LA r in = Lmax
LA r out = Lsec
LB l in = Lmax
LB l out = 2.5 LB r in = 0.5 LB r out = 5
Lsec =6
Lmax = 14.5
A B
RA = 12 RB = 10.5 DAB = 8
0 1 2 3 4 5 6
LA l in = 3 LA l out = 1
LA r in = Lmax
LA r out = Lsec
LB l in = Lmax
LB l out = 2 LB r in = 1 LB r out = 4.5
Lsec =6
Lmax = 15
A B
RA = 12 RB = 11 DAB = 8
0 1 2 3 4 5 6
Step2:如果 A 需縮小通訊半徑，就使用公式(10)
R A
= Max (5.5, 8 + (((14.5 + 1)/2) – 10.5 = 5.25, 8 + (((14.5 + 6)/2) – 10.5 =7.75)
圖 4.23: 4.5.3.2 節的 Case3，Beacon Node A 調整通訊半徑後。
Case4:
圖 4.24: 4.5.3.2 節的 Case4，調整通訊半徑前。
LA l in = Lsec
LA l out = 0 LA r in = 2 LA r out = Lmax
LB l in = 1 LB l out = Lmax
LB r in = 5 LB r out = 2 Lsec = 17.5
Lmax = 21
A B
RA = 10 RB = 8 DAB = 39
0 1 2 3 4 5 6
LA l in = 0.75 LA l out = 1.25 LA r in = Lmax
LA r out = Lsec
LB l in = Lmax
LB l out = 2.5 LB r in = Lsec
LB r out = 5 Lsec =10.25
Lmax = 10.25
A
B
RA = 7.75RB = 10.5 DAB = 8
0 1 2 3 4 5 6
Step1:如果 B 需放大通訊半徑，就使用公式(8)
R B
= Min (15, 8 + 21 – 17.5 = 11.5, 39 – 10 – ((21 + 1)/2) = 18, 39 – 10 – (21 + 5)/2 = 16, 8 + 21 = 29, 8 + 2 = 10)圖 4.25: 4.5.3.2 節的 Case4，Beacon Node B 調整通訊半徑後。
Step2:如果 A 需放大通訊半徑，就使用公式(11)
R A
= Min (15, 39 – 10 – ((19 + 17.5)/2) = 10.75, 39 – 10 – (19 + 2)/2 = 18.5, 10 + 0 = 10, 10 + 19 = 29)圖 4.26: 4.5.3.2 節的 Case4，Beacon Node A 調整通訊半徑後。
LA l in = Lsec
LA l out = 0 LA r in = 2.75 LA r out = Lmax
LB l in = 3 LB l out = Lmax
LB r in = 7 LB r out = 0 Lsec = 17.5
Lmax = 18.25
A B
RA = 10.75 RB = 10 DAB = 39
0 1 2 3 4 5 6
LA l in = Lsec
LA l out = 0 LA r in = 2 LA r out = Lmax
LB l in = 3 LB l out = Lmax
LB r in = 7 LB r out = 0 Lsec = 17.5
Lmax = 19
A B
RA = 10 RB = 10 DAB = 39
0 1 2 3 4 5 6
Case5:
圖 4.27: 4.5.3.2 節的 Case5，調整通訊半徑前。
Step1:如果 B 需放大通訊半徑，就使用公式(8)
R B
= Min (10, 6 + 14 – 11 = 9, 27 – 7 – ((14 + 2)/2) = 10, 27 – 7 – (14 + 4)/2 =11, 6 + 14 = 20, 6 + 2 = 8)
圖 4.28: 4.5.3.2 節的 Case5，Beacon Node B 調整通訊半徑後。
LA l in = Lsec
LA l out = 2.5 LA r in = 2 LA r out = Lmax
LB l in = 4 LB l out = Lmax
LB r in = 6 LB r out = 0 Lsec = 11
Lmax = 12
A
B
RA = 7RB = 8 DAB = 27
0 1 2 3 4 5 6
LA l in = LsecLA l out = 2.5 LA r in = 2 LA r out = Lmax
LB l in = 2 LB l out = Lmax
LB r in = 4 LB r out = 2 Lsec = 11
Lmax = 14
A
B
RA = 7RB = 6 DAB = 27
0 1 2 3 4 5 6
Step2:如果 A 需放大通訊半徑，就使用公式(11)
R A
= Min (10, 27 – 8 – ((12 + 11)/2) = 7.5, 27 – 8 – ((12 + 2)/2) = 12, 7 + 2.5 =9.5, 7 + 12 = 19)
圖 4.29: 4.5.3.2 節的 Case5，Beacon Node A 調整通訊半徑後。