【正文】 它也就是每個時刻應(yīng)該消除的誤差。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。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(jī)上，完成20個站的網(wǎng)絡(luò)和時鐘解決方案需要一個小時的時間。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，反之亦然。如果需要使用校平器的話，濾波器應(yīng)該重新進(jìn)行初始化以及時完成數(shù)據(jù)從上次運(yùn)算結(jié)尾開始的運(yùn)算。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。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。之后，檢查狀態(tài)向量的歧義性。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(jìn)行，直到殘差達(dá)到要求或者只有兩顆有效衛(wèi)星。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。在下一步的預(yù)處理中，以上所進(jìn)一步說明的幾個參數(shù)消除了地面站的時鐘跳躍。假設(shè)載波相位測量的為常數(shù)，并且沒有引入過程噪聲。在實(shí)時系統(tǒng)中使最近的數(shù)據(jù)和這些設(shè)置相適應(yīng)大大增加了計算量，因此并沒有投入使用。時鐘偏移的過程噪聲的偏差為3厘米，時間常數(shù)是600秒。把濾波器第i個元素的過程噪聲記為qi，通過標(biāo)準(zhǔn)差σ和時間常數(shù)τ的關(guān)系表達(dá)出來。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。狀態(tài)向量的所有其他元素都設(shè)置為0。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)致了濾波器的分歧。這些變化是由于不同衛(wèi)星時鐘的特點(diǎn)和一些難以預(yù)測的因素引起的。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。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。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。有些狀態(tài)向量元素需要進(jìn)一步說明：跟蹤站接收機(jī)的時鐘偏移的估計量并不代表實(shí)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(jìn)行了預(yù)處理。他媽包括所有的衛(wèi)星，并且通過每個站都可見。濾波算法該時鐘估計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。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。AIBU通過分批預(yù)處理一百分鐘的計算來生成軌道和時鐘數(shù)據(jù)（Bock 等人，2008年）。相應(yīng)的時鐘從較短的23分鐘的數(shù)據(jù)計算，包括一弧8分鐘重疊到以前的批處理（Zandbergen等，2006年）。噴氣推進(jìn)實(shí)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)和電視）。目前，只有少數(shù)的提供精確的（近）實(shí)時軌道/時鐘產(chǎn)品可用。銣和銫的原子的GPS衛(wèi)星時鐘標(biāo)準(zhǔn)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。關(guān)鍵詞：時鐘估計 精密定軌 實(shí)時 卡爾曼濾波器簡介 近實(shí)時精密單點(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)和短延時時鐘產(chǎn)品的需要。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。 Hauschild . Oliver MontenbruckAbstract In this article, an algorithm for clock offset estimation of the GPS satellites is presented. The algorithm is based on a Kalmanfilter and processes undifferenced code and carrierphase measurements of a global tracking network. The clock offset and drift of the satellite clocks are estimated along with tracking station clock offsets, troposphericzenith path delay and carrierphase ambiguities. The article provides a brief overview of already existing nearrealtime and realtime clock products. The filter algorithm and data processing scheme is presented. Finally, theaccuracy of the orbit and clock product is assessed with aprecise orbit determination of the MetOp satellite andpared to results gained with other realtime products.Keyword Clock estimation Precise orbit determination Realtime Kalman filterIntroduction A growing number of near realtime precise point positioning (PPP) applications raise the need for precise GPS orbit and clock products with short latency. One of these applications is the precise orbit determination (POD) of remotesensing satellites, which is to be performed shortly after a ground station pass. The observations 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 data for theplete GPS constellation. The rubidium and cesium atomic standards of the GPS satellites are subject to clock noise and frequency variations, which can originate from a variety of effects and are hard to forecast. Predictions of clock offset and drift, which are provided for example in the predicted part of the ultrarapid orbits provided by IGS or the broadcast ephemerides, will deviate quickly from the true values by several decimeters or even meters. Thus,these orbit/clockproducts bee unusable for PPP applications, where a carrierphase based positioning accuracy down to centimeter level is desired. The solution to this problem is the use of clock offsets, which have been estimated from GPS measurements originating from a network of sensor stations. Currently, only a limited set of providers for precise (near) realtime orbit/clockproducts is available. Among them are three of the IGS Analysis Centers: JPL (BarSever et al. 2003), NRCan and ESA (Pe180。rez et al. 2006). The JPL products are transmitted to the user with a latency of about 5 s and can be accessed in various ways, for example, internet data streams and satellite broadcast. The realtime orbit and clock product generation at ESA is currently under development and not publicly available. For our article, however, near realtime orbit and clock products dedicated for the support of the MetOpMission have been used. A batch algorithm has been used to generate these products by processing a 2day data arc for the satellite orbits. The corresponding clocks are puted from shorter data arcs of 23 min including an overlap of 8 min to the previous batch (Zandbergen et ). The realtime orbits and clocks from NRCan are based on data from a global realtime station network. The products are not publicly available.The Astronomical Institute of University Berne (AIUB) has also puted nearrealtime clock and orbit products for the test period used