基于卡爾曼濾波器的gps近實時定位時鐘估計畢業(yè)論文外文翻譯

1、<p><b>　　中文5030字</b></p><p>　　出處： GPS solutions, 2009, 13(3): 173-182</p><p><b>　　外文原文</b></p><p>　　Kalman-filter-based GPS clock estimation for ne

2、ar real-time positioning</p><p>　　Andre´ Hauschild . Oliver Montenbruck</p><p>　　Abstract： In this article, an algorithm for clock offset estimation of the GPS satellites is presented. The

3、algorithm is based on a Kalman-filter and processes undifferenced code and carrier-phase measurements of a global tracking network. The clock offset and drift of the satellite clocks are estimated along with tracking sta

4、tion clock offsets, troposphericzenith path delay and carrier-phase ambiguities. The article provides a brief overview of already existing nearreal-time and real-time clock</p><p>　　Keyword :Clock estimatio

5、n Precise orbit determination Real-time Kalman filter</p><p>　　Introduction</p><p>　　A growing number of near real-time precise point positioning (PPP) applications raise the need for precise

6、GPS orbit and clock products with short latency. One of these applications is the precise orbit determination (POD) of remote-sensing satellites, which is to be performed shortly after a ground station pass. The observat

7、ions of the satellite’s GPS receiver are available immediately after the download to the ground station. For processing these data,the user requires precise orbit and clock </p><p>　　The Astronomical Institu

8、te of University Berne (AIUB) has also computed near-real-time clock and orbit products for the test period used in this article. AIBU generates orbit- and clock-data by post-processing of short 100-min batches of GPS ob

9、servations (Bock et al. 2008).</p><p>　　A real-time system for clock estimation is currently under development at the German Space Operations Center of DLR. The generated orbit/clock-products will be used to

10、 support orbit determination of low-earth-orbit satellites (LEO satellites) for up-coming space missions, which require near real-time orbit determination accuracies downto 8–10 cm. The software is based on a Kalman-filt

11、er, which processes undifferenced code and carrier phase observations from a worldwide network of GPS stations. T</p><p>　　Filter algorithm</p><p>　　The clock-estimation algorithm is based on a

12、Kalman-filter,which can be used as a conventional Kalman-filter as well as a forward-/backward-filter with smoother. The filter</p><p>　　processes ionosphere-free linear data combinations of code and carrier

13、 phase measurements on the L1- and L2-frequency.The filter state includes the satellite clock error and the clock drift for the complete constellation of 32 satellites.</p><p>　　The state vector additionally

14、 comprises the receiver clock offset, a differential tropospheric zenith delay as well as the float carrier phase ambiguities of all satellites in view of each station. The station positions are extracted from recent IGS

15、 Sinex-files (IGS 2008) and held fixed in the filter. The current GPS constellation has 32 active satellites and typical tracking network size for the filter is about 20 stations. Assuming that each station tracks on ave

16、rage 10 GPS satellites leads to</p><p>　　Some of the state vector elements require further explanation: the estimated receiver clock offsets for the tracking stations do not represent the offset of the real

17、receiver clocks, since the observation data has been preprocessed before being used in the filter. The pseudo range observations are used together with the a priori orbits and known station position to compute a coarse e

18、stimation of the receiver’s clock error. All observations and the measurement epoch are then corrected by the esti</p><p>　　carrier phase ambiguities in the filter state are estimated as float values and are

19、 not fixed.</p><p>　　In order to be able to perform the Kalman-filter time update, the state vector must be predicted towards the next update epoch using a system model. For this algorithm,the GPS satellite

20、clocks are predicted linearly in time. The clock drift and all other state parameters are assumed to be constant. Of course, the satellite clock drift is not strictly constant but it undergoes slow variations.These varia

21、tions are due to the characteristics of the individual satellite clocks and are driven by hard</p><p>　　Figure 1 depicts a flowchart of the complete filter algorithm. At the beginning, the forward filter is

22、initialized.The coarse values from the IGS ultra-rapid product are used as a priori values for the satellite clock offset and drift. All other elements of the state vector are set to zero.Additionally the process noise f

23、or the filter state and the measurement noise are set during this step.</p><p>　　The selection of the process noise and measurement noise determines whether the filter adds more weight to the propagated stat

24、e based on the system model or to the actual measurements. That is, if the process noise is low compared to the measurement noise, the filter will rely more on the system model and will only gradually correct the filter

25、state during the measurement update. Meaningful settings for the noise of the observables can easily be found from an assessment of the measurement precis</p><p>　　The process noise of the state vector eleme

26、nts is in general more difficult to determine. For simplicity, it is assumed to result from an integrated white noise process,which means that the process noise increases linear in time. It is denoted qi for the filter s

27、tate element i and is characterized with the standard deviation σ and τ time constant s. The process noise matrix has diagonal structure and the elements of the main diagonal are found from</p><p>　　qi =σi2Δ

28、t/τi.</p><p>　　The time difference Δt denotes the time between the consecutive epochs.</p><p>　　For the process noise settings of the satellite clock states, no distinction is made between the i

29、ndividual clock types. Instead, the process noise settings are the same for all GPS satellites. The clock offsets have a process noise with a standard deviation of 3 cm and a time-constant of 600 s. The clock drift proce

30、ss noise has a standard deviation of 0.0005 m/s (&10-12 s/s) over 900 s. Though these simplified assumptions do not strictly reflect the selected two-state clock-model, they are favo</p><p>　　The differe

31、ntial zenith path delay of the ground stations are assumed to vary only marginally over time. Consequently,only a small amount of process noise with a standard deviation of 2 mm over 1 h is assigned. On the contrary, the

32、 ground station clock offset will exhibit noiselike behavior with deviations in the order of tens of meters due to the ‘‘clock-jump’’ elimination procedure mentioned previously. Therefore, the comparably large process no

33、ise has been chosen to compensate for these devia</p><p>　　In the next step, the filter state is propagated towards the first epoch where measurements are available. During preprocessing in the following ste

34、p, the ground station clock jumps are eliminated from the data as previously explained. Additionally, the observables are screened for missing data and satellites, which have dropped below an elevation cutoff angle of 10

35、. The core part of the data screening is an integrity monitoring which is performed on the pseudo range and the carrier phase measur</p><p>　　Afterwards, the ambiguities in the state vector are examined. If

36、satellites have dropped below the elevation limit of the filter or are no longer tracked, their ambiguities are deleted and the space in the filter state is freed. If satellites are newly acquired, their ambiguities are

37、initialized using code-carrier differences to provide their initial values. In addition, ambiguities of satellites, which have been rejected during the data screening, are removed from the filter and initialized aga</

38、p><p>　　Prior to the measurement update the filter applies a clock constraint, since the mean of all GPS satellite clocks is unobservable in the system. The clock constraint is applied as a ‘‘pseudo’’-measureme

39、nt update, which treats the mean of all clock offsets in the IGU clock product as observation of the mean clock offset in the filter state.Therefore, the filter clock estimates are tied to the predicted mean IGU clock, w

40、hich is serves as a virtual referenceclock.</p><p>　　Special care has been taken in modeling the pseudo range and carrier phase observations in the measurement update. Table 2 summarizes the used models and

41、conventions.After the measurement update of the filter, the state vector and the associated covariance matrix are stored for potential usage in the smoother. The procedure is iterated until all epochs have been processed

42、. If smoothing of the results is not desired, they are stored in an SP3-file, which consists of the ultra-rapid orbit interpol</p><p>　　If the smoother shall be used, the filter is again initialized to proce

43、ss the complete data arc backwards in time starting at the end. The processing scheme is identical to the forward filter. After the backward run is finished, the smoother computes the mean of the forward and backward res

44、ults of the filter state weighted according to theircovariance. The filter requires some time after initialization during which the filter state converges and the computed covariance decreases. Consequently, a</p>

45、<p>　　The capabilities of this clock filter algorithm are twofold: it can be used to compute clock solutions for a given orbit product based on recorded global GPS observations for long and short data arcs. It can

46、also be used to demonstrate the expected performance of a real-time clock estimation filter, by using it as a standard forward Kalman filter. The typical processing time of the algorithm with a 20 station network and clo

47、ck solutions at 30 s epochs is about 1 h on a recent office PC for a for</p><p>　　Clock product assessment strategy</p><p>　　Having computed an orbit- and clock-product immediately poses the que

48、stion how its performance in a position application can best be assessed. The Signal In Space Range Error (SISRE) has often been used to gain a coarse estimate of the expected positioning accuracy (Warren and Raquet 2003

49、). The SISRE equation has been modified for the analysis of this article to avoid, that radial orbit errors or clock errors, which are common to all satellites, affect the computed SISRE. In a navigation solutio</p>

50、;<p><b>　　中文翻譯</b></p><p>　　基于卡爾曼濾波器的GPS近實時定位時鐘估計</p><p>　　摘要：本文提出了一種全球定位系統(tǒng)時鐘偏移估計的算法。該算法基于卡爾曼濾波及非差進程代碼和一個全球性的跟蹤載波相位測量網(wǎng)絡(luò)。時鐘偏移和漂移的衛(wèi)星時鐘預(yù)計隨著時鐘偏移跟蹤站，對流層天頂路徑延遲和載波相位的變化而變化。本文提供了一個對現(xiàn)有

51、近實時和實時時鐘產(chǎn)品的簡要的概述。并提出該過濾器算法和數(shù)據(jù)處理方案。最后，軌道和時鐘產(chǎn)品的精確度是根據(jù)METOP衛(wèi)星的精密定軌而來的，并與其他實時產(chǎn)品的結(jié)果相比較。</p><p>　　關(guān)鍵詞：時鐘估計精密定軌實時卡爾曼濾波器</p><p>　　近實時精密單點定位越來越多的應(yīng)用擴大了對高精度全球定位系統(tǒng)和短延時時鐘產(chǎn)品的需要。其中一個應(yīng)用方面，就是遙感衛(wèi)星的精密定軌，它的執(zhí)行緊接著地面接

52、收站的數(shù)據(jù)傳送。數(shù)據(jù)下載到地面站后，全球定位系統(tǒng)接收器的觀測可立即投入使用。為了處理這些數(shù)據(jù)，用戶需要完整的全球定位系統(tǒng)星座的精確軌道和時鐘數(shù)據(jù)。銣和銫的原子的GPS衛(wèi)星時鐘標準是受噪聲和頻率的變化，它可以來自一個各種各樣的影響，很難預(yù)測。對時鐘偏移和漂移的預(yù)計，例如由鈊象電子提供的超快速軌道預(yù)測的一部分或廣播星歷所提出的，將很快從其真值偏離出數(shù)分米甚至幾米。因此，這些軌道/時鐘產(chǎn)品便無法購買力平價的應(yīng)用中使用，因為在這個應(yīng)用中，載波相

53、位的定位精確到厘米級。對這個問題的解決辦法是時鐘偏移，它的估計來源于GPS測量傳感器站的網(wǎng)絡(luò)。目前，只有少數(shù)的提供精確的（近）實時軌道/時鐘產(chǎn)品可用。其中有三個是IGS的分析中心：噴氣推進實驗室（(Bar-Sever等。2003年），加拿大自然資源部和歐空局（Perez等人。2006年）。噴氣推進實驗室的結(jié)果轉(zhuǎn)交給用戶擁有約5秒的延遲，并且可以通過多種方式獲取這些數(shù)據(jù)，例如，通過互聯(lián)網(wǎng)數(shù)據(jù)和衛(wèi)星廣播（即通過網(wǎng)絡(luò)和</p>

54、<p>　　德國航天中心的德國空間發(fā)展中心正在研發(fā)一個時鐘估計的實時系統(tǒng)。研發(fā)的軌道/時鐘產(chǎn)品將用于支持低地球軌道衛(wèi)星定軌低地球軌道衛(wèi)星）用于即將到來的太空飛行任務(wù)，其中需要近實時定軌精度精確到8-10厘米。該軟件是基于卡爾曼濾波器，它所處理的無差代碼和載波相位觀測都是從GPS全球網(wǎng)絡(luò)所獲得的。該濾波器所使用的軌道信息來自于最新的IGS超快速產(chǎn)品的預(yù)測部分，它還能預(yù)測完整的全球定位系統(tǒng)星座的時鐘偏移和漂移。在這篇文章中，對完整

55、的濾波算法進行了介紹，其中也包括對原始數(shù)據(jù)的預(yù)處理。使用該濾波算法的軌道和時鐘產(chǎn)品用于精密定軌，其中結(jié)合了全球定位系統(tǒng)的數(shù)據(jù)處理，它是基于全球衛(wèi)星導(dǎo)航系統(tǒng)接收機的數(shù)據(jù)。IGS的超快速，噴氣推進實驗室，歐洲航天局和AIUB也都對同樣的分析進行了計算和估計，并且對他們的結(jié)果和產(chǎn)品進行比較和討論。</p><p><b>　　濾波算法</b></p><p>　　該時鐘估計

56、算法是基于卡爾曼濾波器，它可以被用來作為一個傳統(tǒng)的卡爾曼濾波器，也可以作為一個具有平滑器的超前/滯后濾波器。這個濾波器處理無電離層的代碼和載波相位數(shù)據(jù)的線性數(shù)據(jù)組合時的頻率是L1和L2。該濾波器狀態(tài)包括星座中所有32顆衛(wèi)星的衛(wèi)星時鐘誤差和時鐘漂移。狀態(tài)向量包括接收機的時鐘偏移，對流層天頂延遲和載波相位的誤差。他媽包括所有的衛(wèi)星，并且通過每個站都可見。該站的位置從最近IGS的辛克斯-文件（IGS 2008年）種提取，然后輸入到濾波器中?，F(xiàn)

57、有的全球定位系統(tǒng)星座共有32顆衛(wèi)星，可供濾波器用的典型跟蹤網(wǎng)絡(luò)有20個。假設(shè)每個站平均跟蹤10顆衛(wèi)星，這樣總共會產(chǎn)生大約300個的狀態(tài)向量元素。</p><p>　　有些狀態(tài)向量元素需要進一步說明：跟蹤站接收機的時鐘偏移的估計量并不代表實際的接收器時鐘偏移量，由于在濾波器使用這些數(shù)據(jù)前，觀測數(shù)據(jù)已經(jīng)進行了預(yù)處理。偽范圍的觀測和先驗軌道是結(jié)合在一塊兒使用的，用已知站的位置來大體估計接收器的時鐘誤差。已估計的時鐘偏移

58、對所有的觀察和測量進行修正。這種預(yù)處理可以減少大的時鐘跳躍，是非常有益的，原因有二：第一，時鐘接收機的該進程的噪音可以減少幾個數(shù)量級，作為地面站時鐘跳躍不須補償。人們已經(jīng)發(fā)現(xiàn)，這一程序在更新測量中改進了濾波器的穩(wěn)定性。第二，預(yù)處理中的消除緩解了后面步驟的執(zhí)行，因為沒有進一步的措施對地面站時鐘的處理是必要的。此外，也避免了個別過程中對每個地面站的噪聲設(shè)置，因為它在地面站的設(shè)置改變時，也要保持不變。微分對流層天頂延遲也應(yīng)在這里進一步詳細解釋

59、。該模型的非電離層代碼和載波相位觀測值已包括標準大氣層中對流層延遲的修改，在本節(jié)后面將進行進一步介紹。真正的對流層延遲會因為不同的實驗?zāi)Ｐ吞峁┑闹档牟煌煌耶數(shù)靥鞖馇闆r也與給出的不同。為了彌補這些偏差，每個站都有一個差分天頂?shù)穆窂窖舆t估計，然后這種映射到一個微分對流層斜坡延遲，使用了海拔獨立測繪功能。</p><p>　　為了能夠執(zhí)行卡爾曼濾波器時間更新，在系統(tǒng)模型中對狀態(tài)向量的預(yù)測必須指向下一個時刻。在

60、這個算法中，GPS衛(wèi)星時鐘的預(yù)測在時間上是線性的。時鐘漂移和所有其他狀態(tài)參數(shù)都假定不變，設(shè)為常數(shù)。當然，衛(wèi)星時鐘漂移并不是嚴格不變，但是它的變化非常緩慢。這些變化是由于不同衛(wèi)星時鐘的特點和一些難以預(yù)測的因素引起的。此外，地面站的時鐘偏移和微分對流層延遲收到這些變化的影響。為了從真值補償該系統(tǒng)的偏差，狀態(tài)向量中引入了過程噪聲這一元素。沒有過程噪聲，狀態(tài)向量協(xié)方差將隨時間而減少。作為結(jié)果，測量值的權(quán)重在濾波器的更新中減少，從而導(dǎo)致了濾波器的

61、分歧。</p><p>　　描述了一個完整的過濾器的流程圖算法。在開始的時候，前置過濾器初始化。從IGS的超快速的產(chǎn)品獲得的粗值用于作為衛(wèi)星的時鐘偏移和漂移的先驗值。狀態(tài)向量的所有其他元素都設(shè)置為0。此外，過濾器狀態(tài)的過程噪聲和測量噪聲也在這一步種設(shè)置。</p><p>　　這一個過程噪聲和測量噪聲的選擇決定了濾波器是否對基于系統(tǒng)的基礎(chǔ)上在增加更多的權(quán)重，還是增加到實際測量上。也就是說，如

62、果過程噪聲比測量噪聲低，該過濾器將更多地依賴于系統(tǒng)模型，并且會隨著測量的進行不斷慢慢的改正濾波器的狀態(tài)。對測量精度的評估中可以輕易的發(fā)現(xiàn)對觀測量噪聲有意義的設(shè)置。在我們的例子中，載波相位觀測值已經(jīng)精確到了2厘米測量噪聲。</p><p>　　狀態(tài)向量元素的過程噪聲一般更難以確定。為簡單起見，假定它是從一個綜合的白噪聲過程中產(chǎn)生的，也就是說，這個過程噪聲隨時間的推移而增加。把濾波器第i個元素的過程噪聲記為qi，通過

63、標準差σ和時間常數(shù)τ的關(guān)系表達出來。過程噪聲矩陣的結(jié)構(gòu)是對角線矩陣，主對角線元素符合以下關(guān)系:</p><p>　　qi =σi2Δt/τi</p><p>　　時間差Δt指連續(xù)時刻之間的時間間隔。</p><p>　　對于衛(wèi)星時鐘狀態(tài)的過程噪聲的設(shè)定，并沒有因為時鐘類型的不同而有所差異。相反，所有的GPS衛(wèi)星的過程噪聲設(shè)置都是一樣的。時鐘偏移的過程噪聲的偏差為3厘

64、米，時間常數(shù)是600秒。時鐘漂移的過程噪聲的偏差為0.005米/秒。雖然這些簡化假設(shè)沒有嚴格反映所選定的二態(tài)時鐘模型，但是它們和其他模型相比，更有實時性。使用過程噪聲根據(jù)不同衛(wèi)星類型(Senior et al.2008)或不同衛(wèi)星時鐘(Hutsell1996)而設(shè)置的時鐘模型，會更加復(fù)雜，因為標準時鐘頻率的變化和非典型時鐘的動作都要與過程噪聲的設(shè)置相適應(yīng)。另外，這種模型的好處不會得到充分體現(xiàn)。在實時系統(tǒng)中使最近的數(shù)據(jù)和這些設(shè)置相適應(yīng)大大

65、增加了計算量，因此并沒有投入使用。然而，對不同的時鐘模型優(yōu)缺點的評估對于它們的改進有很大的幫助。</p><p>　　假設(shè)地面站的差分天頂延遲隨時間變化很小，那么過程噪聲每個小時只會產(chǎn)生2毫米的偏差。相反，地面站的時鐘偏移將會由于前面所提到的時鐘跳躍消除程序的原因而產(chǎn)生數(shù)十米的偏移，同時會有相應(yīng)的大的過程噪聲來抵消這些偏差。假設(shè)載波相位測量的為常數(shù)，并且沒有引入過程噪聲。濾波器初始化后，最初的協(xié)方差矩陣是一個對角

66、陣，它對角線上的元素是最初的標準差的平方。表1提供了過濾器設(shè)置概述。</p><p>　　在下一步中，濾波器的狀態(tài)將會指向第一時刻，該時刻的測量數(shù)據(jù)是已知的。在下一步的預(yù)處理中，以上所進一步說明的幾個參數(shù)消除了地面站的時鐘跳躍。此外海拔仰角低于10度的數(shù)據(jù)也可以觀測得到。該數(shù)據(jù)篩選的核心部分是一個完整的監(jiān)視過程，它通過測量偽距和載波相位測量來檢測和刪除異常值。在此監(jiān)測過程中，通過IGU先發(fā)產(chǎn)品的軌道和時鐘與已知站

67、的位置來計算每個衛(wèi)星的非電離層的殘差。站的位置是已知的，時鐘偏移在所有的測量中都一樣，它必須從殘差中計算出或者刪除掉。如果偽距的RMS幅度超過預(yù)定的閾值，殘差會以遞歸的方式根據(jù)某顆衛(wèi)星重新計算出來。在偽距的測量中，這種具有最小殘差的組合，指出了具有差異性的衛(wèi)星。在這個時刻，這顆衛(wèi)星被濾波器排除在外。如果剩余的殘差仍然超出已知閾值，那么排除衛(wèi)星這個過程將繼續(xù)重復(fù)進行，直到殘差達到要求或者只有兩顆有效衛(wèi)星。在后一種情況下，所有剩余的衛(wèi)星仍然

68、達不到要求的話，那么監(jiān)督程序不能再進一步執(zhí)行。在載波相位的監(jiān)視和篩選過程中，也用到了類似的方法，但是當前時刻和前一時刻載波相位的時間差異避免了在這一步中粗略估計所帶來的混亂。通過這個監(jiān)控程序，可以檢測出來異常的測量和周期性跳躍，數(shù)據(jù)的</p><p>　　之后，檢查狀態(tài)向量的歧義性。如果衛(wèi)星低于了濾波器所規(guī)定的還把最低極限或者不再被跟蹤，那么它們的將被刪除，同時在濾波器狀態(tài)中的空間也被釋放。如果衛(wèi)星第一次被使用，

69、則通過代碼載波差來對它們的進行初始化，以提供一個初始值。此外，在數(shù)據(jù)篩選中被篩選調(diào)的衛(wèi)星的非單性值從濾波器中刪除并且在衛(wèi)星能夠有效測量后立即重新進行初始化。</p><p>　　因為系統(tǒng)中所有衛(wèi)星時鐘的平均值都是不可觀測的，所以在濾波器在測量校正前有一個時鐘約束。該時鐘約束作為一個偽測量校正，它吧IGU時鐘產(chǎn)品的所有時鐘偏移的平均值當做濾波狀態(tài)平均時鐘偏移的觀測值。因此，濾波器時鐘估計值作為一個虛擬的參考時鐘，它

70、是和預(yù)計IGU時鐘的平均值聯(lián)系在一起的。</p><p>　　在測量校正中，測量偽距和載波相位的觀測值時需要進行特殊處理，表格2中總結(jié)了所用到的模型和定理。在濾波器的測量校正之后，狀態(tài)向量和相關(guān)的協(xié)方差矩陣存儲在校平器中以備后用。這是一個迭代的過程，直到所有的時刻都完成。如果經(jīng)過平滑之后結(jié)果仍然不是所期望的，它們將被存在一個SP3文件里面，它包括了超快速軌道每30秒超一次的插值?？焖傥募械某跏紩r鐘參數(shù)被將被濾波

71、器的結(jié)果取代。</p><p>　　如果需要使用校平器的話，濾波器應(yīng)該重新進行初始化以及時完成數(shù)據(jù)從上次運算結(jié)尾開始的運算。這個運算方案和前置濾波器是一樣的。濾波器狀態(tài)的權(quán)重是由它們的協(xié)方差所決定的，當向后的這個運程完成后，校平器將會計算超前和滯后結(jié)果的平均值。在濾波器初始化之后的一段時間內(nèi)，濾波器狀態(tài)是收斂的，而且協(xié)方差會減小。因此，在插入數(shù)據(jù)開始是，正向濾波器的不良估計的加權(quán)值低于后向濾波器的更優(yōu)估計值，反之

72、亦然。正向/后向平滑減弱了濾波器對收斂誤差的敏感性，特別是對短弧數(shù)據(jù)，因為在短數(shù)據(jù)弧中，濾波器的收斂時間是整個數(shù)據(jù)弧中很重要的一部分。</p><p>　　該時鐘濾波算法的功能是雙重的：它可以用來計算基于已錄在庫的全球定位系統(tǒng)的觀測值的時鐘產(chǎn)品的時鐘方案。如果把它作為一個標準的前向卡爾曼濾波器來看，它還可以用來推算實時時鐘估計濾波器的預(yù)期效果。假如每30秒作為一個時刻，利用這個算法，在一臺辦公室的計算機上，完成2

73、0個站的網(wǎng)絡(luò)和時鐘解決方案需要一個小時的時間。用于這些分析計算的數(shù)據(jù)都是從IGU每天更新的數(shù)據(jù)庫中下載得到的。</p><p><b>　　時鐘產(chǎn)品的評估策略</b></p><p>　　在生產(chǎn)出軌道時鐘產(chǎn)品之后，隨之就產(chǎn)生了一個問題，就是怎樣確定這樣一個產(chǎn)品在應(yīng)用中是否取得最優(yōu)的效果，也就是對產(chǎn)品的評價。為了得到對預(yù)期定位精度的粗略估計，用到了空間范圍誤差信號（SI

74、SRE） (Warren and Raquet 2003).。徑向軌道誤差或時鐘誤差對所有的衛(wèi)星來說都是一樣的，為了計算它們，建立了空間范圍誤差信號方程，它將會影響到已計算出的空間范圍誤差信號。在導(dǎo)航解決方案中，這些常見的誤差會進入到用戶時鐘校正中，并且不會影響其位置。因此在每個時刻，都必須通過SISRE消除掉這些誤差。對于單個衛(wèi)星i的SISRE的計算，是基于交軌誤差和沿軌誤差以及它們結(jié)合后的徑向軌道和時鐘誤差，分別記為eC，eA和eR