As the name suggests, TDOA estimation requires the measurement of the difference in time between the signals arriving at two base nodes. Similar to TOA estimation, this method assumes that the positions of base nodes are known [5] .

The TOA difference at the base nodes can be represented by a hyperbola. A hyperbola is the locus of a point in a plane such that the difference of distances from two fi xed points(called the foci) is a constant.

顧名思義，TDOA估計需要測量到達兩個基節點的訊號之間的時間差。 與TOA估計類似，該方法假設基節點的位置是已知的[5]。

基節點處的TOA差可以用雙曲線表示。雙曲線是平面中點的軌跡，使得距兩個固定點（稱為焦點）的距離差是常數。

關於雙曲線的基礎知識，可自行充電： Hyperbola

Assuming known positions of base nodes and a coplanar scenario, three base nodes and two TDOA measurements are required to localize a target node (see Fig. 1.2 b).

Fig. 1.2 b

As shown in the figure, the base station that first receives the signal from the target node is considered as the reference base station . The TDOA measurements are made with respect to the reference base station. For a non - coplanar case, the positions of four base nodes and three TDOA measurements are required.

如圖所示，首先從目標節點接收訊號的基站被認為是參考基站。 TDOA測量是相對於參考基站進行的。 對於非共面情況，需要四個基節點的位置和三個TDOA測量。

TDOA addresses the first drawback of TOA by removing the requirement of synchronizing the target node clock with base node clocks. In TDOA, all base nodes receive the same signal transmitted by the target node. Therefore, as long as base node clocks are synchronized, the error in the arrival time at each base node due to unsynchronized clocks is the same.

TDOA通過消除將目標節點時鐘與基節點時鐘同步的要求來解決TOA的第一個缺點。 在TDOA中，所有基節點接收由目標節點發送的相同訊號。 因此，只要基節點時鐘同步，由於不同步的時鐘，每個基節點的到達時間的誤差是相同的。

意思是TOA的測量需要知道目標什麼時候傳送訊號，這樣我才能計算出來目標訊號到達測量站之間的到達時間，用一句話總結就是目標節點和基節點時鐘同步。然而，這在很多情況下是不現實的，例如，你對敵方目標進行偵察定位，你還要求對方告訴你什麼時候傳送訊號嗎？哈哈。。。

至於TDOA，我不需要知道對方什麼時候傳送訊號，我只需要我的測量平臺上的時鐘同步即可，我的參考節點接收到訊號的時間與其他基節點接收到訊號的時間是同步的，我們之間有一個差值，通過這個差值可以實現定位。一個差值可以確定一個雙曲線，在共面的情況下，兩個差值就可以確定兩個雙曲線，這兩個雙曲線可以有一個交點，即為目標。如果不共面，則需要三個差值，那就是4個測量站。

As shown in Figure 1.2 c, TOA is the time duration (or the relative time) between the start time ( t  s ) of the signal at the transmitter (target node) and the end time ( t  i ) of the transmitted signal at the receiver (base node B  i ). However, as shown in Figure 1.2 c, TDOA is the time difference between the end times ( t  i and t  j ) of the transmitted signal at two receivers (base nodes B  i and B  j ). Thus, in the TDOA technique, only base nodes ’ clocks need to be synchronized to ensure minimum measurement error.

如圖1.2c所示，TOA是發射機（目標節點）處的訊號的起始時間（t s）與發射機訊號的結束時間（t i）之間的持續時間（或相對時間）。 但是，如圖1.2c所示，TDOA是兩個接收機（基站節點B i和B j）的傳送訊號的結束時間（t i和t j）之間的時間差。 因此，在TDOA技術中，只需要同步基節點的時鐘以確保最小的測量誤差。

In general, the complexity of target node clock synchronization is higher compared with base node clock synchronization. This is mainly due to the use of quartz clocks at target nodes, which are not as precise as atomic clocks that are generally used for timing at base nodes [5] . Target node clock synchronization is further explained later in this chapter.

The base node clock can be synchronized externally by using a backbone network or internally using timing standards provided at the nodes. The fact that synchronization of target nodes is not required enables many applications for TDOA -based systems. For example, in battlefield applications, a rescue team may localize the position of a soldier using its beacon signal without the need of synchronization of rescue team clocks with that of the soldier.

基節點時鐘可以通過使用骨幹網在外部同步，也可以在內部使用節點提供的時序標準進行同步。 不需要同步目標節點的事實使得基於TDOA的系統的許多應用成為可能。 例如，在戰場應用中，救援隊可以使用其信標訊號來定位士兵的位置而無需同步 救援隊的時鐘與士兵的時鐘。

With respect to the second drawback of TOA, the transmitted signal from the target node in TDOA need not contain a time stamp, since a single TDOA measurement is the difference in the arrival time at the respective base nodes. This simplifies the structure of transmitted signals and removes potential sources of error. This advantage of TDOA is again exploited by many applications such as emergency call localization on highways [6] and sound source localization by an artificially intelligent humanoid robot [7] .

關於TOA的第二個缺點，來自TDOA中的目標節點的傳送訊號不需要包含時間戳，因為單個TDOA測量是各個基節點處的到達時間的差異。 這簡化了傳輸訊號的結構並消除了潛在的錯誤源。 TDOA的這一優勢再次被許多應用所利用，例如高速公路上的緊急呼叫定位[6]和人工智慧人形機器人的聲源定位[7]。