快速定位GPS軟體接收機之設計

Abstract

傳統的全球衛星定位系統(Global Positioning System; GPS)定位演算法中包含了三個程序：訊號擷取(Signal acquisition)、訊號追蹤(Signal tracking)及定位解算(Positioning)，在訊號追蹤的程序中，為了收集完整的導航訊息(navigation message)，至少需要30秒以上的取樣資料長度，因此，該程序成為定位演算法中最耗時的部分，我們利用了軟體接收機(software receiver)，具備著彈性架構的優點，設計了一種適用於軟體接收機的定位演算法，透過外部來源(external source)提供的衛星位置資訊，省略訊號追蹤程序，以達到快速定位的效果。 本論文提出的設計包含兩部分：都卜勒定位演算法以及碼相位定位演算法。第一部分中，應用都卜勒定位演算法，配合先驗時間(a priori time)與在訊號擷取程序中所獲得的都卜勒測量值來計算出接收機粗略的位置，此位置便成為碼相位定位演算法的先驗位置(a priori position)，在第二部分，使用碼相位定位演算法，利用先驗時間和位置以及在訊號擷取所獲得的碼相位測量值，求得精確的時間與接收機位置，在文獻中，有類似的合併定位演算法，被稱為都卜勒/碼相位定位演算法，但其仍有著需要較長取樣資料長度以得到穩定測量值的追蹤程序，本論文所提出的無追蹤程序(tracking-free)的設計，可以使得所需要的取樣資料長度在10 毫秒以下，初次定位時間(time to first fix, TTFF)便可以大幅降低。 本論文中使用的取樣資料長度分為兩種：10毫秒以及1毫秒，先驗時間的準確度則分為極端的兩種：1 秒以及12 小時，即有以下四種情況：1秒-10毫秒、1秒-1毫秒、12小時- 10毫秒以及 12小時-1毫秒，都卜勒/碼相位定位演算法只能在第一種情況求得正確的接收機位置，我們利用在都卜勒定位演算法中使用所提出的幾何約束條件(geometric constraint)，可以在第三種情況下求得正確的定位結果。第二種狀況因為取樣資料長度較短，會產生整數未定值(integer ambiguity)問題，因此，我們使用時間準確度為1毫秒的約束條件(time accuracy constraint)，有效率地搜尋正確的整數設定值以求得正確的定位結果。除此之外，在文獻中提到了當接收機速度超過80-100 km/h，最後定位結果誤差為數百公里，此動態問題亦可經由此約束條件解決。 換而言之，使用所提出的約束條件，放寬了定位演算法所需的限制，原本無法得到正確定位結果的第二和第三種情況，可以使用本論文所設計的定位演算法配合約束條件來得到定位結果。當擁有10毫秒的取樣資料長度，透過在都卜勒定位演算法中使用的幾何約束條件，需要的先驗時間準確度可以放寬至12小時，當先驗時間的準確度為1秒時，應用時間準確度約束條件於碼相位定位演算法，只需要1毫秒的取樣資料長度，便可以進行定位。當使用1毫秒的資料，其定位準確度大約為20-30公尺，要是將長度拉長至10毫秒，該演算法的定位準確度表現便相似於傳統包含追蹤程序的定位演算法，大約在10-20公尺的誤差。我們設計了數種靜態以及動態實驗，利用模擬和實際訊號來驗證所設計的定位演算法。

There are three processes in traditional GPS positioning algorithm: Signal acquisition, signal tracking and positioning. At least 30 seconds sampled data length are required to complete the reception of navigation messages in the tracking process which is the most time consuming part of positioning. Using the advantage of a software receiver which is flexible architecture of positioning algorithm, we design a new positioning algorithm to achieve fast positioning without the tracking process. In the proposed design, the information of satellite positions is provided by an external source. The proposed design is divided to two parts: Doppler positioning algorithm and code-phase positioning algorithm. In the first part, we apply the Doppler positioning algorithm with a priori time and the Doppler measurements obtained from signal acquisition process to derive coarse position of receiver which is used as a priori position in the code-phase positioning algorithm. In the second part, the a priori time and position are then used in the code-phase positioning algorithm with the code-phase measurements obtained from signal acquisition process to calculate precise time and position solution. There is a similar combined positioning algorithm named Doppler/code-phase positioning algorithm with tracking process which requires longer length of sampled data for stable measurements addressed in the literature. Using proposed tracking-free design, the required sampled data length can be less than 10 milliseconds. Therefore, time to first fix (TTFF) can be greatly reduced. There are two different lengths of sampled data used in the dissertation :10 milliseconds(ms) and 1 millisecond. Two extreme time accuracy of a priori time are used: 1 second(s) and 12 hours(h). Therefore, there are four cases which are 1s-10ms, 1s-1ms ,12h-10ms and 12h-1ms. algorithm. Using Doppler/code-phase positioning algorithm, we can only derive the correct receiver position in the first case. The correct position can be obtained using proposed geometric constraint in the Doppler positioning algorithm for the third case. Because of short sampled data length used in the second case, there will be an integer ambiguity problem. Therefore, the time accuracy constraint of 1 ms is introduced in the code-phase positioning algorithm to efficiently search correct integers for deriving correct receiver position. Besides, a dynamic problem was addressed in the literature. If the speed of receiver is over 80-100 km/h, error of positioning results will be several hundreds of kilometers which can also be resolved by the time accuracy constraint. In other words, the limitations are reduced using the proposed constraints. We can derive the receiver position in the second and third case using the designed algorithm. When the sampled data length is 10ms, the required time accuracy of a priori time can be relaxed to 12 hours with geometric constraint used in the Doppler positioning algorithm. If the time accuracy of a priori time is 1 second, the sampled data length of signal can be as short as 1 ms by using the time accuracy constraint in the code-phase positioning algorithm. The positioning accuracy is about few tens of meters with 1 ms sampled data . However, with 10 ms sampled data, the positioning accuracy can be improved to 10-20 meters which is similar to traditional positioning algorithm with tracking. We set up several static and dynamic experiments using both simulated and real signals to verify the proposed design.