Alternative Characterization of Analog Signal Deformation for GNSS‐GPS Satellites

Currently, analog signal deformation is described using individual-chip step response curves for each GPS/WAAS-GEO satellite. Such a set of curves is helpful – it allows us to have an overall idea of the distortions for all satellites as well as identify possibly anomalous satellite signals. However, the step response curves do not convey the severity of the distortions to the user in a metric he/ she can intuitively grasp. In addition, there is no current specification for nominal analog deformation. The ICAO model describes only the faulted mode. In this paper, we propose an alternative method of characterizing nominal analog distortion: using the change in behavior of early-minus-late (EML) tracking errors across different correlator spacings. Such a measurement metric is more user-intuitive, and is directly related to user-domain parameters of interest such as pseudorange and position errors. In turn, these errors are of great importance to the performance and integrity of satellite-based augmentation systems (SBAS) and groundbased augmentation systems (GBAS). Two different methods to obtain such tracking error curves are described and compared – processing of satellite dish antenna raw data and hardware GPS receiver outputs. Error sources affect the accuracy of our tracking error plots; for the satellite dish method these error sources and mitigation procedures are illustrative and discussed. The results from the two methods are presented and compared. The predicted inter-satellite tracking error plots are also compared to those observed from actual hardware receivers. For additional verification, results from the tracking error plots for particular correlator spacings are also compared to errors from actual hardware receiver pseudoranges with the same correlator spacings. Future work for both these methods is also proposed. INTRODUCTION Signal deformations for GNSS-GPS satellites have previously been classified based on the ICAO secondorder step fault model[1]. This model has 3 parameters: 1. Δ: the amount of lead or lag in the falling edges of the distorted C/A code with respect to the expected position of those edges. 2. fd: the ringing frequency associated with the edges of the distorted C/A code. 3. σ: the damping coefficient associated with that ringing. [Δ pertains to digital distortion and fd and σ pertain to analog distortion.] The digital distortion parameter, Δ, is easily measured and its effects are well-understood. Thus, it is a convenient parameter to use in characterizing digital distortions of the GNSS-GPS satellite constellation. There is even a nominal range of values specified for Δ: between -10ns and +10ns. Currently, analog signal deformation is described using individual-chip step response curves for each GPS/WAAS-GEO satellite (Figure 1). 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Time [sec] L1 : N or m al iz ed S te p R es po ns e [  se c] GPS-L1 Normalized Step Response vs Time [sec] Ideal Actual (Multi-SVN) Figure 1: Analog distortion for all PRN satellites. Data collected in Aug 2008, Jul 2009, Aug 2010. Such a set of curves is helpful – it allows us to have an overall idea of the distortions for all satellites as well as identify possibly anomalous satellite signals. However, the step response curves do not convey to the user how he/ she would be affected by the severity of the distortions. In addition, there is no current specification for nominal analog deformation; the ICAO model describes only the faulted mode. In this paper, we propose an alternative method of characterizing analog distortion: using the change in behavior of early-minus-late (EML) tracking errors across different correlator spacings. Examples of such plots are presented in Figure 2. The figure shows the differential pseudorange errors a mobile user would experience at various correlator spacings, for different GPS satellite signals, given a reference receiver correlator spacing of 1 chip. 0 0.2 0.4 0.6 0.8 1 1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Reference correlator spacing (Early‐minus‐Late): 1 chip Figure 2: Example plot of tracking errors across different tracking loop Early-minus-Late (EML) correlator spacings, for different satellite signals. Such a measurement metric is more intuitive, and is directly related to user-domain parameters of interest such as pseudo-range and position errors. In turn, these errors are of great importance to the performance and integrity of satellite-based augmentation systems (SBAS) and ground-based augmentation systems (GBAS). In this paper, the new process(es) to obtain these curves will be described. These are based on data collected two different ways: 1. Data collection campaign of all GNSS-GPS and WAAS satellite signals using a 46m satellite dish antenna over a continuous 24-hour period. 2. All-in-view hardware GPS receivers with limited correlator outputs, over a 24-hour period. We will begin by describing the processing for the satellite dish data as this is more involved. The measured curves depend on the analog distortion caused by the measurement equipment. The effects of the ground equipment may change over time due to thermal changes or due to changes in equipment. The use of reference GNSS-GPS and WAAS satellite signals can remove these temporal changes and allow meaningful comparisons between satellite signals collected in different time periods. This process is described for the satellite dish data approach. It is also important to note that common effects across all satellites affect only the timing accuracy and not the positioning accuracy. It is the satellite to satellite differences that are of greatest interest. Thus, we will also estimate and remove a common mode analog deformation caused by the measuring equipment and similar behavior of the satellite filters. These curves estimate what user receivers would experience in the absence of errors. The process for estimating some of these errors is presented, for the satellite dish data approach. The hardware receiver approach contains some similarities and differences. The idea to obtain the tracking error plots is the same but the method is simpler as we do not have access to raw pre-correlation data. Instead, we only have correlator outputs at certain limited number of correlator spacings (typically less than 10). We use these outputs to obtain the tracking error plots and compare them with those from the satellite dish data. The hardware receiver approach also allows us to configure a differential setup with specific correlator spacings and measure the double-difference pseudo-range errors. From these we derive the measured inter-satellite errors and compare them against the results from the tracking error plots. This serves as a simple verification of our tracking error plots. Future work for both the satellite dish data approach and the hardware receiver approach will also be suggested. SATELLITE DISH DATA PROCESSING METHOD The tracking error plots are obtained by processing data from two different sources – satellite dish antenna and hardware. The method for processing satellite dish antenna data is as follows: 1. Data collection campaign. This has been described previously[4]. 2. Data processing procedure This has also been described previously [4] and is briefly mentioned here: a. Use of high gain antenna b. Signal acquisition and tracking c. Multiple C/A code epoch averaging and interpolation for noise reduction d. Additional filtering for either noise reduction and/ or interpolation The output of this process is an estimate of the actual received code chip waveform for all chips, for all GPS and WAAS-GEO satellite signals. The difference here is that zero crossing locations for the formation of individual chips are not required; thus zero crossing determination methods are not applied unlike before. 3. Form points on correlation triangle by correlating received code chip waveform with ideal replicas at various delays and advances Ideal replicas of various delays and advances of up to 1 chip are formed to correlate with the actual code chip waveform, for both GPS and WAAS-GEO satellite signals, to form correlator outputs. (In practice, given the large number of correlator output points available for our interpolated code chip waveform, the correlation is performed using the Fast Fourier Transform method). In the example below in Figure 3, we use ideal replicas advanced and delayed by 0.1, 0.2, 0.3 and 0.4 chips to form early and late correlator outputs E1 and L1, E2 and L2, E3 and L3 and E4 and L4 at these chip spacings. Correlating the ideal replica without advances or delays with the received signal gives us the P (Prompt) correlator output. P, E1-E4 and L1-L4 form discrete points on the correlation triangle (Figure 4). Using more finely spaced advanced and delayed ideal replica chip spacings produces the entire correlation triangle. The ideal correlation triangle, formed by correlating an ideal replica code (without advances or delays) with itself, is shown in blue. An example error-injected correlation “triangle”, with artificially injected errors for illustration, is shown in red. 6 6.5 7 7.5 8 8.5 9 9.5 10 chips Chip Sequence for PRN 14 Actual Early‐4 Early‐3 Early‐2 Early‐1 Late‐1 Late‐2 Late‐3 Late‐4 Prompt Figure 3: Form early, prompt and late replicas at different delays/ advances and correlate with actual code-sequence. -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 Correlation Triangle Points Ideal, Erroneous Signal User Correlator Spacing [Chips] N or m al iz ed U ni ts Ideal Erroneous E1 E2 E3 E4 L1 P L2 L3 L4 Figure 4: Points on correlation triangle for each different delay/ advance. 4. Subtract corresponding points, scale and plot with respect to horizontal separation (chips) between these points With the points on the correlation triangle (Figure 4), we take differences of corresponding points (eg. E1 – L1, E2 – L2, E3 – L3 etc). Next we normalize and scale the differences. The scale factor K used to scale the normalized differences is computed as follows: ----------------------------------(1) where fCA: frequency of GPS-L1C/A Code c: speed of light P: value of prompt (P) correlation Finally we plot the normalized and scaled differences against the absolute horizontal distance (chips) between the points. For instance, the absolute horizontal distance between E1 and L1 is abs(-0.1 – (+0.1)) chips = 0.2 chips. This produces the tracking error plots we are looking for. Figure 5 shows the tracking error plot obtained using our ideal signal and signal with artificially injected errors. 0 0.2 0.4 0.6 0.8 1 1.2 -50 -40 -30 -20 -10 0 10 20 30 40 50 User Correlator Spacing [Chips] Tr ac ki ng E rro r [ m ] Tracking Error Plot Ideal Erroneous (E1‐L1)*K (E3‐L3)*K