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 Jan 22, 2014, 4:15:39 PM (8 years ago)
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 trunk/BNC/txt
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trunk/BNC/txt/frankfurt.tex
r5622 r5623 509 509 510 510 \begin{frame} 511 \frametitle{Combination using Kalman filtering} 512 The combination is performed in two steps 513 \begin{itemize} 514 \item[1.] The satellite clock corrections that refer to different broadcast 515 messages (different IODs) are modified in such a way that they all refer 516 to common broadcast clock value (common IOD is that of the selected 517 ``master'' analysis center). 518 \item[2.] The corrections are used as pseudoobservations for Kalman filter 519 using the following model (observation equation): 520 \begin{displaymath} 521 c_a^s = c^s + o_a + o_a^s 522 \end{displaymath} 523 where 524 \begin{tabbing} 525 $c_a^s$ ~~ \= is the clock correction for satellite s estimated by \\ 526 \> the analysis center a, \\ 527 $c^s$ \> is the resulting (combined) clock correction for 528 satellite s, \\ 529 $o_a$ \> is the ACspecific offset 530 (common for all satellites), and \\ 531 $o_a^s$ \> is the satellite and ACspecific offset. 532 \end{tabbing} 533 \end{itemize} 534 The three types of unknown parameters $c^s$, $o_a$, $o_a^s$ differ in their 535 stochastic properties: the parameters $c^s$ and $o_a$ are considered to be 536 epochspecific while the satellite and ACspecific offset $o_a^s$ is assumed 537 to be a static parameter. 538 \end{frame} 539 540 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 541 542 \begin{frame} 511 543 \frametitle{PPP  ServerSide} 512 544 \begin{center} … … 562 594 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 563 595 564 \section{PPP AR} 565 \subsection{Principles} 566 567 \begin{frame} 568 \frametitle{Principles of PPP with Ambiguity Resolution} 569 \framesubtitle{Observation Equations} 570 571 The PPPAR is in principle based on the processing the following two types of singledifference 572 observations: \\ 573 The ionospherefree linear combination 574 \be\label{obs_IF} 575 L^{ij}_3 = \varrho^{ij}  c\delta^{ij} + T^{ij} + \bar{N}^{ij}_3 ~, 576 \ee 577 where the ambiguity term is given by 578 \be\label{amb_N3} 579 \bar{N}^{ij}_3 = N^{ij}_3  l^{ij}_3 580 = \frac{c\;f_2}{f^2_1f^2_2}\;(n^{ij}_1n^{ij}_2) + \lambda_3\;n^{ij}_1  l^{ij}_3 581 \ee 582 and the MelbourneW\"{u}bbena linear combination 583 \be\label{obs_MW} 584 L^{ij}_w = \lambda_5\;n^{ij}_5  l^{ij}_w 585 \ee 586 the uncalibrated bias $l^{ij}_3$ is the corresponding linear combination of biases 587 $l^{ij}_1,l^{ij}_2$, the uncalibrated bias $l^{ij}_w$ is the corresponding linear combination of 588 biases $p^{ij}_1,p^{ij}_2,l^{ij}_1,l^{ij}_2$. 589 \end{frame} 590 591 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 592 593 \subsection{Parameters provided by Server} 594 595 \begin{frame} 596 \frametitle{Principles of PPP with Ambiguity Resolution} 597 \framesubtitle{Parameters provided by Server} 598 In addition to orbit corrections, the server(s) has(have) to provide the values 599 \bdm 600 c\delta^{ij} ~,~ l^{ij}_w ~,~ l^{ij}_3 ~~~ \mb{or} ~~~~ (c\delta^{ij} + l^{ij}_3) ~,~ l^{ij}_w 601 \edm 602 Corrections $l^{ij}_w,l^{ij}_3$ depend on the set of fixed singledifference ambiguities on the 603 serverside. This set of fixed ambiguities is not unique  it depends on the constraints applied on 604 the ambiguities. 605 606 There is a difference between correction $l^{ij}_w$ and the narrowlane correction $l^{ij}_3$. The 607 widelane correction $l^{ij}_w$ depends {\em only} on the ambiguities estimated at the 608 serverside. The narrowlane correction $l^{ij}_3$ depends on the ambiguities and {\em also} on the 609 satellite clock corrections $\delta^{ij}$ estimated at the serverside. 610 611 \end{frame} 612 613 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 614 615 \begin{frame} 616 \frametitle{Principles of PPP with Ambiguity Resolution} 617 \framesubtitle{How many servers?} 618 All three corrections 619 \bdm 620 c\delta^{ij} ~~~ l^{ij}_w ~~~ l^{ij}_3 621 \edm 622 may be estimated together by a single server run (in which case the $c\delta^{ij}$ and $l^{ij}_3$ 623 are indistinguishable and are combined into $c\delta^{ij}+l^{ij}_3$) Or, each of them may be 624 estimated by a separate server run. 625 626 \vspace*{2mm} 627 Current approach: 628 \begin{itemize} 629 \item PPPNB server: estimates $c\delta^{ij}$ 630 \item PPPAR server: uses $c\delta^{ij}$ from PPPNB server and estimates $l^{ij}_w,l^{ij}_3$ 631 \end{itemize} 632 633 \vspace*{2mm} 634 Advantages: PPPAR corrections are compatible with PPPNB corrections (the client may decide between 635 PPP and PPPAR). 636 637 \vspace*{2mm} 638 Disadvantages: additional delay 639 640 \vspace*{2mm} 641 An alternative approach to consider: separate server run for $l^{ij}_w$. 642 643 \end{frame} 644 645 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 646 647 \begin{frame} 648 \frametitle{Principles of PPP with Ambiguity Resolution} 649 \framesubtitle{How to disseminate the corrections?} 650 651 \begin{enumerate} 652 \item The corrections are valid (accurate) on the single (between satellites) difference 653 level but it is more practical to send the zerodifference (satellitespecific) corrections. 654 \item The corrections are specific for the observation types used for their estimation  e.g. if 655 the C/A code on the first carrier and the Pcode on the second carrier have been used at the 656 server side, the client can use the $l^{ij}_w$ correction only if it uses the same two types of 657 code observations. 658 \end{enumerate} 659 660 The corrections $l^{ij}_w,l^{ij}_3$ are actually the combinations of the phase (and in case of 661 $l^{ij}_w$ also code) biases: 662 \begin{eqnarray*} 663 l^{ij}_w & = & \frac{1}{f_1f_2} \bigl( f_1~l^{ij}_1  f_2~l^{ij}_2 \bigr)  664 \frac{1}{f_1+f_2} \bigl( f_1~p^{ij}_1 + f_2~p^{ij}_2 \bigr) ~ 665 \\ 666 l^{ij}_3 & = & \frac{1}{f^2_1f^2_2} \bigl( f^2_1~l^{ij}_1  f^2_2~l^{ij}_2 \bigr) 667 \end{eqnarray*} 668 RTCM suggests to send $p^{ij}_1,p^{ij}_2,l^{ij}_1,l^{ij}_2$ directly ... 669 670 \end{frame} 671 672 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 673 674 \begin{frame} 675 \frametitle{Principles of PPP with Ambiguity Resolution} 676 \framesubtitle{How to disseminate the corrections (continuation)?} 677 678 In principle there are altogether 5 values which can be sent by server(s): 679 \bdm 680 c\delta^{ij},p^{ij}_1,p^{ij}_2,l^{ij}_1,l^{ij}_2 681 \edm 682 PPPNB server estimates the $c\delta^{ij}$ and the ionospherefree 683 linear combination of the code biases 684 \bdm 685 p^{ij}_3 = \frac{1}{f^2_1f^2_2} \bigl( f^2_1~p^{ij}_1  f^2_2~p^{ij}_2 \bigr) 686 \edm 687 PPPAR server estimates the $l^{ij}_w$ and $l^{ij}_3$. Assuming that we know the differential code 688 bias 689 \bdm 690 d^{ij}_{p1p2} = p^{ij}_1  p^{ij}_2 691 \edm 692 The four values 693 \bdm 694 p^{ij}_3 ~~~ l^{ij}_w ~~~~ l^{ij}_3 ~~~~ d^{ij}_{p1p2} 695 \edm 696 can be converted into four biases 697 $p^{ij}_1,p^{ij}_2,l^{ij}_1,l^{ij}_2$. 698 699 \end{frame} 700 701 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 702 703 \begin{frame} 704 \frametitle{Precise Point Positioning with PPP (cont.)} 705 BNC provides a good framework for the PPP client (observations, orbits, and 706 corrections stand for disposal). 707 708 Main reasons for the PPP module in BNC have been: 709 \begin{itemize} 710 \item monitoring the quality of incoming data streams (primarily the PPP 711 corrections) 712 \item providing a simple easytouse tool for the basic PPP positioning 713 \end{itemize} 714 715 The PPP facility in BNC is provided in the hope that it will be useful. 716 \begin{itemize} 717 \item The mathematical model of observations and the adjustment algorithm are 718 implemented in such a way that they are (according to our best knowledge) 719 correct without any shortcomings, however, 720 \item we have preferred simplicity to transcendence, and 721 \item the list of options the BNC users can select is limited. 722 \item[$\Rightarrow$] Commercial PPP clients may outperform BNC in some 723 aspects. 724 \end{itemize} 725 We believe in a possible good coexistence of the commercial software and 726 open source software. 727 \end {frame} 596 \begin{frame} 597 \frametitle{Principle of our PPPRTK Algorithm} 598 For a dualband GPS receiver, the observation equations may read as 599 \begin{eqnarray*} 600 P^i & = & \varrho^i + c\;\delta  c\;\delta^i + T^i + b_P \\ 601 L^i & = & \varrho^i + c\;\delta  c\;\delta^i + T^i + b^i 602 \end{eqnarray*} 603 where 604 \begin{tabbing} 605 $P^i$, $L^i$ ~~~~~~~ \= are the ionospherefree code and phase measurements, \\ 606 $\varrho^i$ \> is the travel distance between the satellite 607 and the receiver, \\ 608 $\delta$, $\delta^i$ \> are the receiver and satellite clock errors, \\ 609 $T^i$ \> is the tropospheric delay, \\ 610 $b_P$ \> is the code bias, and \\ 611 $b^i$ \> is the phase bias (including initial 612 phase ambiguity). 613 \end{tabbing} 614 The singledifference bias $b^{ij} = b^i  b^j$ is given by 615 \begin{displaymath} 616 b^{ij} = \displaystyle\frac{\lambda_5\lambda_3}{2}\;(n_5^{ij} + b_5^{ij}) 617 + \lambda_3\;(n_1^{ij} + b_1^{ij}) 618 \end{displaymath} 619 where 620 \begin{tabbing} 621 $n_1^{ij}$, $n_5^{ij}$ ~~~~ \= are the narrowlane and widelane integer ambiguities \\ 622 $b_1^{ij}$ \> is the narrowlane (receiverindependent) SD bias \\ 623 $b_5^{ij}$ \> is the widelane (receiverindependent) SD bias 624 \end{tabbing} 625 \end{frame} 626 627 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 628 629 \begin{frame} 630 \frametitle{Principle of our PPPRTK Algorithm (cont.)} 631 Receiverindependent singledifference biases $b_1^{ij}$ and $b_5^{ij}$ have 632 to be estimated on the serverside. 633 \begin{itemize} 634 \item Narrowlane bias $b_1^{ij}$ may be combined with satellite clock 635 corrections $\Longrightarrow$ \textbf{modified satellite clock corrections.} 636 \item Widelane bias have to be transmitted from the server to the client 637 (this bias is stable in time and can thus be transmitted in lower rate). 638 \end{itemize} 639 640 On the clientside the biases $b_1^{ij}$ and $b_5^{ij}$ are used as known 641 quantities. It allows fixing the integer ambiguities $n_5^{ij}$ and 642 $n_1^{ij}$. The technique is called Precise Point Positioning with Ambiguity 643 Resolution (PPP~AR) or PPP~RTK, or zerodifference ambiguity 644 fixing (the latter term not fully correct because the ambiguities are 645 actually being fixed on singledifference level). 646 \end{frame} 647 648 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 649 650 \begin{frame} 651 \frametitle{Performance} 652 \begin{center} 653 \includegraphics[width=0.75\textwidth]{kir0.png} 654 \end{center} 655 \vspace*{5mm} 656 \begin{block}{Standard deviations (N,E,U)} 657 \vspace*{3mm} 658 \begin{small} 659 \hspace*{2cm} 660 \begin{tabular}{lcccccc} 661 \mbox{} & \multicolumn{3}{c}{1060 min} & \multicolumn{3}{c}{3060 min} \\ 662 float & 0.034 & 0.026 & 0.026 & 0.010 & 0.009 & 0.011 \\ 663 fix & 0.007 & 0.003 & 0.016 & 0.007 & 0.003 & 0.012 664 \end{tabular} 665 \end{small} 666 \end{block} 667 \end{frame} 668 669 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 670 671 \begin{frame} 672 \frametitle{Challenges} 673 PPP~RTK works and provides mmaccuracy results, what is this symposium 674 about? 675 676 \pause 677 There are still both principal and technical problems and challenges: 678 \begin{itemize} 679 \item Principal problems: 680 \begin{itemize} 681 \item Convergence time: PPP~RTK in the form outlined above provides 682 accuracy similar (or even slightly better) to RTK but the convergence 683 time is longer. 684 \item There is a degradation in accuracy with the age of corrections. 685 \item Glonass ambiguity resolution: is it possible to resolve Glonass 686 ambiguities? (yes, it is possible but it implicates introducing new 687 parameters  does it really improve the results?) 688 \item ... 689 \end{itemize} 690 \item Technical problems: 691 \begin{itemize} 692 \item Availability of data in real time (reference network, highprecision 693 satellite orbits). 694 \item Very high CPU requirements on the serverside. 695 \item Solution robustness on the serverside 696 (problems with reliable DD ambiguity resolution). 697 \item ... 698 \end{itemize} 699 \end{itemize} 700 \end{frame} 701 702 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 703 704 \begin{frame} 705 \frametitle{Challenges (cont.)} 706 \begin{block}{Longer convergence time} 707 In case of a standard RTK the very short convergence time is being achieved 708 thanks to the combined DD ambiguity resolution on both $L_1$ and $L_2$ when 709 the differential ionospheric bias can either be neglected (short baselines) 710 or its influence is mitigated (stochastic ionosphere estimation with 711 constraints). 712 713 On the contrary, the outlined PPP~RTK algorithm is in principle based on 714 processing single (ionospherefree) linear combination and resolving only 715 one set of (narrowlane) initial phase ambiguities. 716 \end{block} 717 \begin{block}{Possible solutions} 718 \begin{itemize} 719 \item third carrier 720 \item multiple GNSS (Glonass ambiguity resolution?) 721 \item processing original carriers (instead of ionospherefree linear 722 combination) and modeling the ionosphere? 723 \item ? 724 \end{itemize} 725 \end{block} 726 \end{frame} 727 728 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 729 730 \begin{frame} 731 \frametitle{Challenges (cont.)} 732 \begin{block}{Age of corrections 0 s} 733 \begin{center} 734 \includegraphics[width=0.6\textwidth]{age1.png} 735 \end{center} 736 \end{block} 737 \end{frame} 738 739 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 740 741 \begin{frame} 742 \frametitle{Challenges (cont.)} 743 \begin{block}{Age of corrections up to 35 s} 744 \begin{center} 745 \includegraphics[width=0.6\textwidth]{age2.png} 746 \end{center} 747 \end{block} 748 \end{frame} 749 750 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 751 752 \begin{frame} 753 \frametitle{RealTime Data Availability} 754 \framesubtitle{IGS network: very good global coverage:} 755 \vspace*{5.5cm} 756 \begin{center} 757 \includegraphics[width=0.9\textwidth]{map.pdf} 758 \end{center} 759 \end{frame} 760 761 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 762 763 \begin{frame} 764 \frametitle{RealTime Data Availability (cont.)} 765 \begin{tabular}{cc} 766 \includegraphics[width=0.4\textwidth]{100A_lat.png} & 767 \includegraphics[width=0.4\textwidth]{101A_lat.png} \\ 768 \includegraphics[width=0.4\textwidth]{102A_lat.png} & 769 \includegraphics[width=0.4\textwidth]{104A_lat.png} 770 \end{tabular} 771 772 Gaps in reference network data may degrade the PPP~RTK server performance 773 considerably! 774 \end{frame} 775 776 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 777 778 \begin{frame} 779 \frametitle{Technical issues} 780 \begin{block}{CPUrequirements on the serverside} 781 Processing a global reference network is a very CPUintensive 782 task. Numerically stable forms of the Kalman filter (squareroot, UDU 783 factorization etc.) require very fast hardware. 784 785 Possible solutions: 786 \begin{itemize} 787 \item Processing optimization (estimating various kinds of parameters in 788 different rates) 789 \item Parallel processing 790 \item Advanced hardware (GPS Solutions uses GPUaccelerated library) 791 \end{itemize} 792 \end{block} 793 \begin{block}{Reliable DD ambiguity resolution on the serverside} 794 Reliable doubledifference ambiguity resolution on the serverside remains 795 the crucial issue of the PPP~RTK technique. 796 \end{block} 797 \begin{block}{Dissemination of PPP~RTK corrections} 798 \begin{itemize} 799 \item data links 800 \item formats (standardization?) 801 \item optimization of correction rates (bandwidth) 802 \end{itemize} 803 \end{block} 804 \end{frame} 805 806 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 807 808 \begin{frame} 809 \frametitle{Satellite orbits} 810 811 Predicted part of the IGS ultrarapid orbits (available in realtime) is 812 sometimes not sufficient for the processing of a global reference network 813 (with narrowlane ambiguity resolution). We have been forced to implement 814 the realtime orbit determination capability in our main processing tool 815 RTNet (RealTime Network software). 816 \begin{center} 817 \includegraphics[width=0.75\textwidth]{rtnet_pod.png} 818 \end{center} 819 \end{frame} 820 821 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 822 823 \begin{frame} 824 \frametitle{Regional versus global PPP~RTK services} 825 Currently we are routinely running both regional and global PPP~RTK service 826 demonstrators in realtime (some of the results will be shown below). 827 \begin{itemize} 828 \item in principal there is no difference between a global and regional 829 service as far as the data processing, algorithms etc. is concerned 830 \item global PPP~RTK service has at least the following two advantages 831 \begin{itemize} 832 \item[1.] a single correction stream can serve all users 833 \item[2.] all satellites are tracked permanently (helps ambiguity 834 resolution) 835 \end{itemize} 836 \item global PPP~RTK service is much more challenging (data availability, 837 CPUrequirements on the serverside, DD ambiguity resolution on long 838 baselines, the highest requirements for the accuracy of the satellite 839 orbits) 840 \end{itemize} 841 842 \end{frame} 843 844 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 845 846 \begin{frame} 847 \frametitle{Services monitoring} 848 Reliable, productionquality PPP~RTK service requires sophisticated 849 monitoring tools. 850 \begin{tabular}{cc} 851 \includegraphics[width=0.6\textwidth]{monitor1.png} & \\[1.5cm] 852 & \hspace*{3cm} \includegraphics[width=0.6\textwidth]{monitor2.png} 853 \end{tabular} 854 855 \end{frame} 856 857 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 858 859 \begin{frame} 860 \frametitle{Results} 861 \begin{center} 862 \includegraphics[width=0.9\textwidth]{tsunami.pdf} 863 \end{center} 864 \end{frame} 865 866 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 867 868 \begin{frame} 869 \frametitle{Results (cont.)} 870 \begin{center} 871 \includegraphics[width=0.9\textwidth]{nrcan.png} 872 \end{center} 873 \end{frame} 874 728 875 729 876 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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