Ready to Navigate!
A Methodology for the Estimation of the Time-to-First-Fix
Working Papers explore the technical and scientific themes that underpin GNSS programs and applications. This regular column is coordinated by Prof. Dr.-Ing. Günter Hein. Contact Prof. Hein at Guenter.Hein@unibw-muenchen.de
Estimating and comparing the various GNSS signals’ time-to-first-fix is an excellent tool for evaluating the design trades made on GNSS signal structures and a particularly important feature for general users in the mass market. This column describes the various factors that contribute to delays in a receiver’s initial position fix and proposes a methodology for estimating time-to-first-fix for various signals and receiver start conditions.
After three decades of increasingly widespread use, satellite navigation-based services have changed significantly, especially for general users in the mass market. New technology enablers such as assisted GPS (A-GPS), the use of massively parallel correlation, and the application of advanced positioning techniques have significantly enhanced the time-to-first-fix (TTFF) and sensitivity of today’s receivers.
Although these techniques have increased satisfaction for end users, they could partially mask many particular differences expressed among the various GNSS signals, today and in the future.
These new signals contain many innovations, including the use of longer spreading codes, new modulation techniques, and new navigation message structures using channel-coding techniques.
With such a wide variety of signals, it is essential to define criteria that enable us to understand the main differences among the signals, as well as under which conditions one would perform better than others and their relative suitability for particular applications.
Among the different performance metrics, estimating and comparing the various signals’ TTFF is an excellent tool for evaluating the design trades made on GNSS signal structures, especially those concerning spreading codes and navigation messages.
In this article we propose a methodology to account for and evaluate what happens in a conventional receiver “behind the scenes,” from the very first moment the receiver is switched on, until it is “ready to navigate”.
After presenting a theory that may be applied to any GNSS signal, we discuss simulation results obtained with some GPS and Galileo signals. Our proposed approach can be seen as an extension of the methodology described in the article by J. K. Holmes et alia, listed in the Additional Resources section near the end of this column, where the results are computed for a confidence level of 95 percent.
Definition of TTFF
Usually we distinguish among three different TTFF scenarios, depending on the particular status of the receiver when it is started. We refer to cold, warm, or hot starts according to the availability and validity of the data required for computing the navigation solution (satellite almanac and ephemeris parameters, send time of the received signal, previously stored PVT solutions). These three cases can be described as follows:
In addition to the availability of navigation data, TTFF performance depends on the number of visible satellites and the strength of the received signals.
In this study, we performed all our analyses with three baseline assumptions: (1) received signals have high enough C/N0 (e.g. no bit errors), (2) the number of visible satellites is always sufficient to allow the receiver to perform a first position fix within the standard accuracy requirements; and (3) the receiver uses parallel processing on all the signals coming from the different satellites, as is common in a state-of-the-art receiver today. Under these three conditions the TTFF equals the time needed to process one of the signals coming from the different satellites.
In the following sections we present a methodology for the computation of a 95 percent probability of TTFF. This method may be applied to any GNSS signal.
The approach also may be seen as a generalization of J. K. Holmes’ method, where the TTFF is subdivided into different contributions, each of which may be estimated separately and the combination of which produces the final result.
Contributions to the TTFF
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We treat the acquisition process as a detection problem, usually performed in a navigation receiver by measuring the complex amplitude of the correlator’s output. The test statistic is thus defined and compared with a predefined fixed threshold, indicating whether the signal sought is present.
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The acquisition time for a 95 percent confidence level has been calculated for the five GNSS signals, applying the three different search techniques discussed earlier to each of the cold, warm and hot start cases. Thus, we considered nine different simulation scenarios for each signal.
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Initialization of Tracking Loops
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A common feature of the various types of messages is that, after retrieving the navigation bits, a validity check, such as a cyclic redundancy check (CRC), is performed. Considering the number of bits to which this check applies, together with the field containing the checksum, the block of navigation symbols obtained by encoding these bits is called a page.
Usually the page contains also a known sequence of symbols located at the beginning and called the synchronization — or synch — word. For example all the Galileo I/NAV message pages begin with the sequence 0101100000.
The search process leading to the identification of the starting point of a valid page is called frame synchronization. This is generally achieved by the identification of a valid synch word.
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Navigation Data Read Time
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Reading a GNSS Nav Message
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Key Notes: Navigation Data Delivery Versus Retrieval
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The very low data rate of the Galileo E5a-I signal results in a quite long data read time and, as a consequence, its TTFF performance is the worst for the cold and warm start cases, where data from the message needs to be retrieved.
For the GPS L1C signal, we can see how the poor performance of the acquisition time, due to the long coherent integration and the length of the PRN codes, is counterbalanced by a very short data read time. The GPS L1C signal is, indeed, presenting the shortest data read time because of its particular navigation message structure, which allows for a very short ephemeris repetition time.
Because the contribution of acquisition time to total TTFF can be substantially decreased by employing new algorithms and technologies, a key factor for a good TTFF performance turns out to be the design of the navigation message structure itself.
The estimates presented in the article were made under the assumption that signals were received with a high enough carrier-to-noise ratio density, such that no bit errors occurred.
We extended our analysis to consider the behavior of the TTFF in low C/N0 environments. A detailed discussion of these results can be found in the article by M. Paonni et alia (Additional Resources).
Individuals who wish to further investigate the TTFF metric can easily implement our proposed method using GNSS performance simulation tools. We also suggest that this method could be incorporated into GNSS theoretical studies, especially those regarding next-generation systems.
For the complete story, including figures, graphs, and images, please download the PDF of the article, above.
ManufacturersThe data presented in this article was plotted using MATLAB from The Mathworks, Inc., Natick, Massachusetts, USA.
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