基于卡爾曼濾波器的gps近實(shí)時(shí)定位時(shí)鐘估計(jì)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(shí)時(shí)定位時(shí)鐘估計(jì)</p><p>　　摘要：本文提出了一種全球定位系統(tǒng)時(shí)鐘偏移估計(jì)的算法。該算法基于卡爾曼濾波及非差進(jìn)程代碼和一個(gè)全球性的跟蹤載波相位測量網(wǎng)絡(luò)。時(shí)鐘偏移和漂移的衛(wèi)星時(shí)鐘預(yù)計(jì)隨著時(shí)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(gè)對現(xiàn)有

51、近實(shí)時(shí)和實(shí)時(shí)時(shí)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(shí)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(shí)時(shí)產(chǎn)品的結(jié)果相比較。</p><p>　　關(guān)鍵詞：時(shí)鐘估計(jì)精密定軌實(shí)時(shí)卡爾曼濾波器</p><p>　　近實(shí)時(shí)精密單點(diǎn)定位越來越多的應(yīng)用擴(kuò)大了對高精度全球定位系統(tǒng)和短延時(shí)時(shí)鐘產(chǎn)品的需要。其中一個(gè)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(shí)鐘數(shù)據(jù)。銣和銫的原子的GPS衛(wèi)星時(shí)鐘標(biāo)準(zhǔn)是受噪聲和頻率的變化，它可以來自一個(gè)各種各樣的影響，很難預(yù)測。對時(shí)鐘偏移和漂移的預(yù)計(jì)，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(shí)鐘產(chǎn)品便無法購買力平價(jià)的應(yīng)用中使用，因?yàn)樵谶@個(gè)應(yīng)用中，載波相

53、位的定位精確到厘米級(jí)。對這個(gè)問題的解決辦法是時(shí)鐘偏移，它的估計(jì)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(shí)時(shí)軌道/時(shí)鐘產(chǎn)品可用。其中有三個(gè)是IGS的分析中心：噴氣推進(jìn)實(shí)驗(yàn)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(jìn)實(shí)驗(yàn)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(gè)時(shí)鐘估計(jì)的實(shí)時(shí)系統(tǒng)。研發(fā)的軌道/時(shí)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(shí)時(shí)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(shí)鐘偏移和漂移。在這篇文章中，對完整

55、的濾波算法進(jìn)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(shí)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(jī)的數(shù)據(jù)。IGS的超快速，噴氣推進(jìn)實(shí)驗(yàn)室，歐洲航天局和AIUB也都對同樣的分析進(jìn)行了計(jì)算和估計(jì)，并且對他們的結(jié)果和產(chǎn)品進(jìn)行比較和討論。</p><p><b>　　濾波算法</b></p><p>　　該時(shí)鐘估計(jì)

56、算法是基于卡爾曼濾波器，它可以被用來作為一個(gè)傳統(tǒng)的卡爾曼濾波器，也可以作為一個(gè)具有平滑器的超前/滯后濾波器。這個(gè)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(shí)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(shí)鐘誤差和時(shí)鐘漂移。狀態(tài)向量包括接收機(jī)的時(shí)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(gè)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(gè)。假設(shè)每個(gè)站平均跟蹤10顆衛(wèi)星，這樣總共會(huì)產(chǎn)生大約300個(gè)的狀態(tài)向量元素。</p><p>　　有些狀態(tài)向量元素需要進(jìn)一步說明：跟蹤站接收機(jī)的時(shí)鐘偏移的估計(jì)量并不代表實(shí)際的接收器時(shí)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(jìn)行了預(yù)處理。偽范圍的觀測和先驗(yàn)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(jì)接收器的時(shí)鐘誤差。已估計(jì)的時(shí)鐘偏移

58、對所有的觀察和測量進(jìn)行修正。這種預(yù)處理可以減少大的時(shí)鐘跳躍，是非常有益的，原因有二：第一，時(shí)鐘接收機(jī)的該進(jìn)程的噪音可以減少幾個(gè)數(shù)量級(jí)，作為地面站時(shí)鐘跳躍不須補(bǔ)償。人們已經(jīng)發(fā)現(xiàn)，這一程序在更新測量中改進(jìn)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?yàn)闆]有進(jìn)一步的措施對地面站時(shí)鐘的處理是必要的。此外，也避免了個(gè)別過程中對每個(gè)地面站的噪聲設(shè)置，因?yàn)樗诘孛嬲镜脑O(shè)置改變時(shí)，也要保持不變。微分對流層天頂延遲也應(yīng)在這里進(jìn)一步詳細(xì)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(biāo)準(zhǔn)大氣層中對流層延遲的修改，在本節(jié)后面將進(jìn)行進(jìn)一步介紹。真正的對流層延遲會(huì)因?yàn)椴煌膶?shí)驗(yàn)?zāi)Ｐ吞峁┑闹档牟煌煌耶?dāng)?shù)靥鞖馇闆r也與給出的不同。為了彌補(bǔ)這些偏差，每個(gè)站都有一個(gè)差分天頂?shù)穆窂窖舆t估計(jì)，然后這種映射到一個(gè)微分對流層斜坡延遲，使用了海拔獨(dú)立測繪功能。</p><p>　　為了能夠執(zhí)行卡爾曼濾波器時(shí)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(gè)時(shí)刻。在

60、這個(gè)算法中，GPS衛(wèi)星時(shí)鐘的預(yù)測在時(shí)間上是線性的。時(shí)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(dāng)然，衛(wèi)星時(shí)鐘漂移并不是嚴(yán)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(shí)鐘的特點(diǎn)和一些難以預(yù)測的因素引起的。此外，地面站的時(shí)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(bǔ)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(shí)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(gè)完整的過濾器的流程圖算法。在開始的時(shí)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(shí)鐘偏移和漂移的先驗(yàn)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(gè)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(shí)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(huì)隨著測量的進(jìn)行不斷慢慢的改正濾波器的狀態(tài)。對測量精度的評(píng)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(gè)綜合的白噪聲過程中產(chǎn)生的，也就是說，這個(gè)過程噪聲隨時(shí)間的推移而增加。把濾波器第i個(gè)元素的過程噪聲記為qi，通過

63、標(biāo)準(zhǔn)差σ和時(shí)間常數(shù)τ的關(guān)系表達(dá)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(shí)間差Δt指連續(xù)時(shí)刻之間的時(shí)間間隔。</p><p>　　對于衛(wèi)星時(shí)鐘狀態(tài)的過程噪聲的設(shè)定，并沒有因?yàn)闀r(shí)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(shí)鐘偏移的過程噪聲的偏差為3厘

64、米，時(shí)間常數(shù)是600秒。時(shí)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(yán)格反映所選定的二態(tài)時(shí)鐘模型，但是它們和其他模型相比，更有實(shí)時(shí)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(shí)鐘(Hutsell1996)而設(shè)置的時(shí)鐘模型，會(huì)更加復(fù)雜，因?yàn)闃?biāo)準(zhǔn)時(shí)鐘頻率的變化和非典型時(shí)鐘的動(dòng)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(huì)得到充分體現(xiàn)。在實(shí)時(shí)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(jì)算量，因此并沒有投入使用。然而，對不同的時(shí)鐘模型優(yōu)缺點(diǎn)的評(píng)估對于它們的改進(jìn)有很大的幫助。</p><p>　　假設(shè)地面站的差分天頂延遲隨時(shí)間變化很小，那么過程噪聲每個(gè)小時(shí)只會(huì)產(chǎn)生2毫米的偏差。相反，地面站的時(shí)鐘偏移將會(huì)由于前面所提到的時(shí)鐘跳躍消除程序的原因而產(chǎn)生數(shù)十米的偏移，同時(shí)會(huì)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(gè)對角

66、陣，它對角線上的元素是最初的標(biāo)準(zhǔn)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(huì)指向第一時(shí)刻，該時(shí)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(jìn)一步說明的幾個(gè)參數(shù)消除了地面站的時(shí)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(gè)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(shí)鐘與已知站

67、的位置來計(jì)算每個(gè)衛(wèi)星的非電離層的殘差。站的位置是已知的，時(shí)鐘偏移在所有的測量中都一樣，它必須從殘差中計(jì)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(huì)以遞歸的方式根據(jù)某顆衛(wèi)星重新計(jì)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(gè)時(shí)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(gè)過程將繼續(xù)重復(fù)進(jìn)行，直到殘差達(dá)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(dá)不到要求的話，那么監(jiān)督程序不能再進(jìn)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(dāng)前時(shí)刻和前一時(shí)刻載波相位的時(shí)間差異避免了在這一步中粗略估計(jì)所帶來的混亂。通過這個(gè)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(shí)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(jìn)行初始化，以提供一個(gè)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(jìn)行初始化。</p><p>　　因?yàn)橄到y(tǒng)中所有衛(wèi)星時(shí)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(gè)時(shí)鐘約束。該時(shí)鐘約束作為一個(gè)偽測量校正，它吧IGU時(shí)鐘產(chǎn)品的所有時(shí)鐘偏移的平均值當(dāng)做濾波狀態(tài)平均時(shí)鐘偏移的觀測值。因此，濾波器時(shí)鐘估計(jì)值作為一個(gè)虛擬的參考時(shí)鐘，它

70、是和預(yù)計(jì)IGU時(shí)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(shí)需要進(jìn)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(chǔ)在校平器中以備后用。這是一個(gè)迭代的過程，直到所有的時(shí)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(gè)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(shí)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(jìn)行初始化以及時(shí)完成數(shù)據(jù)從上次運(yùn)算結(jié)尾開始的運(yùn)算。這個(gè)運(yùn)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(dāng)向后的這個(gè)運(yùn)程完成后，校平器將會(huì)計(jì)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(shí)間內(nèi)，濾波器狀態(tài)是收斂的，而且協(xié)方差會(huì)減小。因此，在插入數(shù)據(jù)開始是，正向?yàn)V波器的不良估計(jì)的加權(quán)值低于后向?yàn)V波器的更優(yōu)估計(jì)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?yàn)樵诙虜?shù)據(jù)弧中，濾波器的收斂時(shí)間是整個(gè)數(shù)據(jù)弧中很重要的一部分。</p><p>　　該時(shí)鐘濾波算法的功能是雙重的：它可以用來計(jì)算基于已錄在庫的全球定位系統(tǒng)的觀測值的時(shí)鐘產(chǎn)品的時(shí)鐘方案。如果把它作為一個(gè)標(biāo)準(zhǔn)的前向卡爾曼濾波器來看，它還可以用來推算實(shí)時(shí)時(shí)鐘估計(jì)濾波器的預(yù)期效果。假如每30秒作為一個(gè)時(shí)刻，利用這個(gè)算法，在一臺(tái)辦公室的計(jì)算機(jī)上，完成2

73、0個(gè)站的網(wǎng)絡(luò)和時(shí)鐘解決方案需要一個(gè)小時(shí)的時(shí)間。用于這些分析計(jì)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(shí)鐘產(chǎn)品的評(píng)估策略</b></p><p>　　在生產(chǎn)出軌道時(shí)鐘產(chǎn)品之后，隨之就產(chǎn)生了一個(gè)問題，就是怎樣確定這樣一個(gè)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(píng)價(jià)。為了得到對預(yù)期定位精度的粗略估計(jì)，用到了空間范圍誤差信號(hào)（SI

74、SRE） (Warren and Raquet 2003).。徑向軌道誤差或時(shí)鐘誤差對所有的衛(wèi)星來說都是一樣的，為了計(jì)算它們，建立了空間范圍誤差信號(hào)方程，它將會(huì)影響到已計(jì)算出的空間范圍誤差信號(hào)。在導(dǎo)航解決方案中，這些常見的誤差會(huì)進(jìn)入到用戶時(shí)鐘校正中，并且不會(huì)影響其位置。因此在每個(gè)時(shí)刻，都必須通過SISRE消除掉這些誤差。對于單個(gè)衛(wèi)星i的SISRE的計(jì)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(shí)鐘誤差，分別記為eC，eA和eR