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30 InsideGNSS N O V E M B E R / D E C E M B E R 2 0 1 8 www.insidegnss.com e standard steps in Signal Pro- cessing to search, acquire, and wait for tracking loops to converge are inap- plicable in snapshot positioning. ese steps must be replaced with an iterative approach to generate code phase and Doppler frequency measurements (the short sampling times mean that carrier phase data is not available). e Signal Processing block can be computation- ally complex so the sampling frequency and bit resolution of the digital samples must be carefully chosen for the trade- off between computation time (there- fore power consumption) and, sensitiv- ity and measurement quality. e implications for the Position Estimation arise because there is not enough time to decode navigation data from the received signal. All GNSS receivers require the use of ephem- eris information to compute satellite information and, by extension, the receiver position. For conventional receivers, the ephemeris can typically be obtained either directly by decoding the broadcast ephemeris or through alternative means via a communication network; this approach is commonly referred to as Assisted GNSS (AGNSS) technology. In contrast, a state of the art snapshot receiver does not attempt to download/decode the incoming sat- ellite ephemeris information; instead, it takes advantage of utilizing extended ephemeris technology to enable the snapshot receiver to the predict ephem- eris autonomously for up to 28 days between ephemeris updates. Even with the ephemeris obtained by means of broadcast, network assis- tance, prediction, or post-processing; conventional GNSS processing must still derive the transmit time from the satellite broadcast data. As a result, a pseudorange measurement cannot be obtained without reconstructing the transmit time or using a broader set of techniques also known as Coarse Time Positioning. Along with the requirement to obtain ephemerides from an alterna- tive source, snapshot receivers can- not estimate receiver position from pseudoranges without an approxi- mate initial time and position of the receiver. In contrast to snapshot receivers of the past, a state of the art snapshot positioning process described below, has these initial time and receiver posi- tion requirements either eliminated or greatly relaxed. Some techniques for coarse time positioning require an a priori time within a few seconds and position within a few km. However, with more recent techniques, the initial position requirement can be relaxed to 75 km, and the initial time to 60 sec- onds. is wider requirement can be met using Doppler-based positioning so that, ultimately, there is no initial position requirement at all and the initial time requirement is 30 minutes, which can be easily achieved using a Real Time Clock (RTC) that is widely available in most low-cost consumer electronics. Further details are pro- vided below. Snapshot Position Estimation As described above, the satellite signal transmit time cannot be decoded in snapshot GNSS receivers. In the exam- ple of a conventional GPS receiver, the integer component of transmit time in milliseconds can be derived from the Z-count time of week (TOW) and an integer count of elapsed C/A code epochs. e fractional component of transmit time is the measured code phase. en, the pseudorange (ρ) can be calculated as Where c is the speed of light, t r is the received time of the signal, and t t is the transmit time with an integer millisec- ond component , and the code phase τ t as the fractional component. Because the integer component of transmit time (τ t ) is unknown in a snapshot receiver because TOW can- not be extracted, the full pseudorange must be generated by other means. Broadly, for any coarse time position- ing method, the pseudorange is cal- culated using an estimated range that comes from the initial approximation of receiver time and position, with careful handling of the receiver clock offset. In particular, using advanced techniques, the transmit time is recon- structed relative to the received time such that pseudorange can be calcu- lated in the standard method of equa- tion 1. A common representation of pseu- dorange, ignoring noise and propaga- tion errors, is where r is the geometric range to the satellite, Δt sv is the satellite clock cor- rection, and b is the sub-millisecond receiver clock bias. Combining equations 1 and 2, the integer component of the transmit time is solved as where and here represent the fact that the initial received time in a snapshot receiver may have an error of multiple seconds. is error in absolute time ( ) can be considered to be an integer number of milliseconds (rang- ing code periods) since the fractional component is absorbed by the receiver clock bias. us the error in approxi- mated integer transmit time will be identical . When and are applied in equation 1, will cancel out: e geometric range r in equation 3 is approximated from the ephemeris and the initial estimates of position and received time. e satellite clock correction Δt sv is known and the code phase p is measured. So all that remains to calculate an approximate integer transmit time is the clock bias b, which is unknown. An approximate clock bias can be determined by searching for a value that minimizes how far off is from an integer value for all satellites. When the best clock bias is found, then all values of can be rounded to integers. From these reconstructed transmit GNSS SOLUTIONS

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