On stochastic modeling of the modernized global positioning system (GPS) L2C signal

Abstract

In order to take full advantage of the modernized GPS L2C signal, it is essential that its stochastic characteristics and code bias be rigorously determined. In this paper, long sessions of GPS measurements are used to study the stochastic characteristics of the modernized GPS L2C signal. As a byproduct, the stochastic characteristics of the legacy GPS signals, namely C/A and P2 codes, are also determined, which are used to verify the developed stochastic model of the modernized signal. The differential code biases between P2 and C2, DCBP2-C2, are also estimated using the Bernese GPS software. It is shown that the developed models improved the precise point positioning (PPP) solution and convergence time.

Stochastic Analysis of Low-Cost Single-Frequency GPS Receivers

“…Figure 3 shows that the standard deviation of C/A code is about 0.5 m and 1.5 m at 90° and 05° elevation angles, respectively. These results makes sense for single-frequency receiver if Trimble R7 GNSS receiver's model has corresponding values of 0.2 m and 0.7 m at elevation angles of 90° and 05°, respectively [5]. To test the developed model, new raw data are collected using the same single-frequency receivers in addition to dual-frequency data of the base station which is used as a reference.…”

“…Alternatively, the GPS system noise can be tested by differencing pseudorange and the carrier phase measurements [5]. The noise level of the carrier phase measurements is approximately 1% of that of the pseudorange measurements.…”

“…PPP was first introduced by researchers at the Jet Propulsion Laboratory [4]. However, to achieve such accuracy all errors and biases must be rigorously modelled [5]. Few millimeters accuracy is achievable if precise orbit and clock corrections are applied [6].…”

Precise Point Positioning using Triple-Frequency GPS Measurements

“…Typically, a geometry-free linear combination of P1 and P2 codes is used to estimate the ionospheric delay, while DCB is obtained as a by-product of the estimation process. Similar geometry-free linear combinations could be formed using L2C modernized signal to estimate C1-C2 differential code bias, (Elsobeiey and El-Rabbany, 2010). The same criteria could be applied for C1-C5 geometry-free combination to estimate as follows: where P 4 ,C 4 are geometry-free linear combination of P1, P2, and C1, C5, respectively (m), I 1 is the ionospheric delay of L1 (m), is the receiver hardware delay difference of C1 and C5 observables (s) and is the receiver hardware delay difference of P1 and P2 observables (s).…”

“…Typically, a geometry-free linear combination of P1 and P2 codes is used to estimate the ionospheric delay, while DCB is obtained as a by-product of the estimation process. Similar geometry-free linear combinations could be formed using L2C modernized signal to estimate C1-C2 differential code bias, DCB s C1ÀC2 (Elsobeiey and El-Rabbany, 2010). The same criteria could be applied for C1-C5 geometry-free combination to estimate DCB s P1ÀC5 as follows:…”