This paper discusses some anomalies that afect the reliability and accuracy of GNSS data. In this paper we study patterns in the Common Generic GNSS Timing Transfer Standard (CGGTTS) data. The pseudorange residuals in this data appear to include patterns that repeat every day. We discuss in this paper more the diferent factors on these patterns, like satellite age and position on the sky. Ability to detect these anomalies will help to identify the satellites with unreliable timing behavior for an improved time solution on the receiver side.
We use in our study the pseudorange residuals of CGGTTS generated from VTT MIKES time-transfer
GNSS receiver (receiver code MI05, Septentrio PolaRx5TR), available in the IDA data storage [
This chapter discusses the method of processing the measurements by modifying the CGGTTS data (Sec. 2.1). Results of long-term observations are presented in Sec. 2.2, and Sec. 2.3 discusses the satellite age on predictability of its modified data, which is at the core of the presented method. The efect of satellite position in the sky is briefly discussed in Sec. 2.4. We present a result of detecting anomalies by observing the biases and slopes of the cycles in Sec. 2.5.
The reported pseudorange residuals were averaged over 16-minute periods, when the satellite was
visible. In our method, the data set from each cycle is made zero-mean by allowing each cycle to have
their individual bias, and subtracting it. We denote this with modification #1. Secondly, only cycles of
most common, mode length are shown, and we denote this with modification #2. The resulting data set,
illustrated in [
However, for some satellites, subtracting the bias from the data is not suficient, because each cycle
has its individual slope as well. This statement was supported by looking at the measurements of GPS12
during morning cycles [
If the measurements are drifting away or towards the GPS system time, the modified data set spreads out towards the edge periods of low elevation. This was seen as lower standard deviations than 1.5. However, if each cycle is allowed to have its own slope, and it is subtracted, the modified data set is grouped together more tightly. Subtraction of the slope yielded modification #3. The standard deviation of modified data set still increased toward the edge periods, but now less distinctly. This indicates that knowing the bias and slope of the cycle allows us to make more accurate predictions about the pseudorange residuals.
Previous day’s bias could be hypothetically used in predicting the following day’s morning cycle bias. We aim to verify this by plotting a histogram of their diferences. We perform a similar analysis in order to predict the same days evening cycle bias based on the morning cycle bias. The results shown in Fig. 1 indicate that in addition to the morning bias time history, prediction of the bias of a next morning cycle could potentially be more accurate if the previous evening cycle bias was set as a precursor. Adding also the evening cycle’s time history enables to obtain a more stable estimate. The diference between the cycle biases are centered around 3 ns in Fig. 1. Compared to biases, slopes behave in a diferent manner, with the longer evening cycles being more centered around zero, whereas the morning cycle slopes have a higher variance. The regression lines in Fig. 2 reveal a positive correlation between the slope of the next evening cycle and that of the known morning cycle. That is, a higher morning slope is associated with a higher evening slope, and vice versa. An outlying evening cycle slope would be easy to spot.
The pseudorange residuals of satellites can be predicted more accurately when we shift to the estimated constellation system time. With the goal being able to make a predictive model for tomorrow’s data sets based on the data set time history, we can make comparisons between simplistic models and use those to study if the age of the satellite afects its residual error. The simplistic models that we use to study this are 1. no pooling model, where we simply duplicate yesterday’s modified data set and use that to make a prediction about the new value, 2. complete pooling model, where we take the mean of all the modified data sets and use that to make a prediction about the new value, and
3. partial pooling model, where we make a compromise between these two models, and give 70% of the weight to no pooling-model and 30% of the weight to complete pooling-model.
The 70%/30% ratio was selected because its predictions had the smallest standard error of the ratios for each period. The example results are shown in Fig. 3. The partial pooling-model is the best predictor, suggesting some regularization should be used in the prediction models. Only cycles of mode length are analyzed, resulting in some days not present, such as late yellow days in evening cycles. We also see that the predictions are less certain around the edge periods, possibly due to errors from low elevation angles. Both this pattern and the partial pooling being the best predictor hold for all other GPS satellites also.
Next, we take the mean of the residual standard errors across periods for all satellites to see if older satellites have higher residual errors, or in other words, if new satellites have more predictable modified data sets. The results are shown in Fig. 4. Contrary to expectations, the older satellites do not have less predictable modified data sets, and the highest scatter in the modified data sets is for a relatively new GPS8.
Looking at the modified data set for consecutive days in Fig. 3 (of similar colors, for example yellow) reveals that the similar colors are more grouped than being random draws from the distribution based on where the satellite is in the sky. Fig. 5 demonstrates a more subtle pattern and adds to the prediction accuracy of the modified data set as a function of where the satellite is positioned in the sky. Thus, we can obtain a prediction with an even smaller standard deviation based on how the modified data set has behaved in the previous several days. This latter observation is also better visible with another perspective on the data, where we plot the modified data set for each period separately as a function of their sidereal day. The drawback of this graph shown in Fig. 5 is that the cycles must be restricted to be of a specific length, leading the modified data from cycles of other lengths to be removed. The residual error appears to be around 1 ns for the central periods and higher for the edge periods.
If we assume that the bias and slope of the cycle are changing slowly across diferent days, we can
detect anomalies by looking at the biases and slopes of the cycles. Two cases were presented in [
We have studied satellite aging, elevation as well as slope and bias of measurements as a precursor for further studies in extracting atmospheric efects from the data sets, in particular discerning ionospheric efects from other intentional interference like jamming and spoofing. More accurate bias and slope estimation will enable improved prediction of the measurements. As we gather more measurements from the cycle, the accuracy of the bias and slope estimates improves. At the final periods of the cycle, we have a very accurate estimate of both the bias and the slope and the uncertainty only comes from the uncertainty of the modified data set. This uncertainty comes from the filtering step that excludes data from some cycles. The method includes subtracting the bias from the CGGTTS data, but each cycle has its individual slope as well. The modified data set is constrained in that it might not be comparable to a diferent data set obtained at a diferent operational condition: the method is afected by measurement uncertainties when gathering the CGGTTS data. Most importantly, the stability of the receiver is an essential factor. If the antenna is moved intentionally or unintentionally, or some changes occur around, say, a new tall building is built, the efect on the CGGTTS data is significant. Namely, the system would need recalibration from time to time. In addition, the method is not really scalable to be comparable to diferent locations without a suitable calibration method, which has not yet been discussed in the framework of this work. Therefore, developing a suitable calibration method in order to improve the scalability of the method would be imperative.
The patterns for each of the satellites are dependent on the environment around the antenna of the
GNSS receiver used in generating the CGGTTS files. Collecting the data from the entire track enables
us to find the anomalous satellites sooner than the geodetic time transfer method [
This paper presented results of ongoing work to detect anomalies in satellites’ timing solutions. In the future work, a predictive model should be built. Utilizing past data in the manner described in this paper, the expected behavior of each satellite can be modeled. The model can predict plausible intervals for the bias and slope based on historical data and integrate that uncertainty with the modified data set uncertainty, allowing us to quantify the now descriptive anomaly identification. If the actual data doesn’t agree with the prediction interval at any period, it would be possible to warn the user from using the time solutions from this satellite. In SURI project, we intend to gather large data sets of GNSS data that contains both ionospheric scintillation and intentional interference, and apply machine learning methods in order to be able to gain a situational awareness of quality of GNSS signals in a larger scale. We will use the supercomputer LUMI for modeling the efect of ionosphere very accurately on the PNT solution.
This work was supported by the Research Council of Finland under Grant 338042 (REASON) and Grant 364761 (SURI).
The author(s) have not employed any Generative AI tools.