適用於GPS衛星不足時之定位演算法

Positioning Algorithm for Insufficient GPS Satellites

陳志偉(Chih-Wei Chen)

指導教授 ： 張帆人

共同指導教授 ： 王立昇

國立臺灣大學/電機資訊學院/電機工程學研究所/碩士(2005年)

https://doi.org/10.6342/NTU.2005.02988

摘要

GPS系統定位的最低需求是接收機至少能夠觀測到四顆衛星，但在都市環境中，卻不易達成此條件。本文討論的主題就是在接收機無法觀測到足夠的衛星之時，如何利用有限的衛星數目及先前成功定位的資訊，在這種環境之中達成定位的工作。
當接收機觀測到三顆衛星時，本文使用了限制高度變化的方式來進行定位。由於在道路上行駛時，使用者的高度通常是呈現緩慢變化的情形。利用地球為橢球的模型，配合先前正常定位所獲得資訊，限制使用者的高度為最近十秒內的平均高度值，便可以在接收機僅觀測到三顆衛星時進行定位。
當接收機觀測到二顆衛星時，配合限制高度的作法，以及預估接收機時鐘偏差的方式，依然可以進行定位一段時間，但較易產生定位誤差，配合檢查DOP值的方式仍可以提供有效的定位解。
本文另外提出了虛擬距離預估器，利用衛星的虛擬距離呈現線性變化的假設，可由現在所解出來的使用者的位置以及速度配合衛星的位置和速度，來估算出下一秒時衛星的虛擬距離值。當某顆衛星恰好被遮蔽時，便可利用所估算出的虛擬距離值來進行定位。但在連續預估同一顆衛星時，會有誤差累計的現象，不適合長時間利用。
利用虛擬距離預估器配合不同衛星數目的定位演算法，便可大幅的改善以往GPS系統僅能在接收機觀測四顆衛星以上定位的限制。

關鍵字

衛星不足 ； 高度 ； 鐘差 ； 虛擬距離 ； 預估

並列摘要

The minimum positioning requirement of the GPS is that the GPS receiver can observer at least four satellites. However, it is difficult to reach the minimum requirement in city environment. The theme of this text is how to utilize the insufficient satellites information and previous positioning result to position in such environment.
When the receiver observes three satellites, the altitude constraint method is used to positioning. Because driving on the road, the user’s altitude is usually changed slowly. Restricting the user's altitude to average height in recent ten seconds, the receiver can position in three satellites environment with the model that the earth is ellipsoid.
When the receiver observes two satellites, it can position by combining the altitude constraint method and the receiver clock bias estimation method. This approach is easy to produce positioning error but it can offer effective positioning result with the DOP check.
In addition, this article proposes a pseudorange predictor, which utilizes the current user and satellite’s positions and velocities to estimate the next time satellite’s pseudorange. When the satellite is blocked by with buildings or shelters, the GPS receiver can utilize the estimated pseudorange to position. While estimating the same satellites a few seconds, there is error accumulation phenomenon. It is unsuitable to utilize this predictor estimates the same satellites for a long time.
Utilizing the pseudorange predictor and the different satellites number positioning algorithm, it can release the restriction that the GPS receiver only works when at least four satellites are observable.

並列關鍵字

GPS ； insufficient satellites ； altitude constraint ； receiver clock bias ； pseudorange ； predict

參考文獻

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