Discussion

Given the specifications of the coarse star tracker used in the simulations, we can confidently state that all cases of very severe attitude errors (errors larger than 30°) result from misidentifications, whereas in the severe class (errors between 1° and 30°), some of these could be the result of a partial misidentification (where some stars are correctly identified and others are incorrectly identified) or a correct identification where each star had an extremely large measurement error in their position, since many cases of attitude errors between 1° a 5° seem to be at the tail of attitude error distribution. Further analysis will be needed to understand exactly what is happening in these cases.

Figure 5.10 summarizes the reduction in the frequency of severely incorrect attitude determinations versus the modifications tested in this section. This frequency of incorrect attitude determinations serves as a proxy for the misidentification rate of the algorithm.

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Figure 5.10 – Reduction of the rate of incorrect attitude determination versus each new added feature.

Source: Drawn by the author.

It can be seen that, proportionally, the most significant reduction of the mis-ID rate was obtained with the inclusion of the magnitude filter (reduction by a factor of 6.2 in the rate of incorrect attitudes), followed by the inclusion of the first color index filter (reduction by a factor of 3.8 in the rate of mis-ID) and pre-sorting the list of observed stars by magnitude (reduction by a factor of 3.7 in the rate of misidentifications). Removing all mirror triangles in the triangle identification step (Section 5.3.4) reduced the misidentification rate by 2. Addition of a secondary color index reduced the misidentification rate by 2, at a cost of a slight decrease in the success rate. The effect of adding a limit of maximum 15 kernels to be tested was very small in the misidentification rate. The original version of Pyramid was not tested, since to test it in PTASE would demand many modifications in the original code to make it compatible with the program. But judging from its code and from the fact that it checks mirror condition for most triangles, but not in every case, it is expected that its misidentification rate would be intermediate between the “baseline version” and the test configuration labeled “discarding all mirror triangles” (numbers 1 and 2 in Figure 5.10).

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Taken in isolation, each of these new features don’t seem to provide a significant increase in the star identification reliability, but when all these modifications are taken into account, they lead to a reduction of more than 2 orders of magnitude in the misidentification rate.

5.4.11.1 Use of additional bands

As shown by the simulations, the verification of additional spectral bands can give further gains for stellar identification, but with diminishing returns for each new spectral band included, since each new spectral band introduced becomes more and more correlated with the previous ones. This becomes clear in the color-color diagram shown in Figure 5.11. From this diagram, it is evident that there is a significant correlation between the V−I and B−V color indexes. Therefore, when designing a color star tracker, a balance on the number of spectral bands added must be made considering the benefits of additional color information and the drawbacks of increased system complexity and cost. These considerations would probably favor monochrome star trackers. However, when we consider that color information enables to diagnose optics degradation caused by ionizing radiation (usually manifested as a reddening in the lenses), and enables a better correction of chromatic aberration, the possibility of measuring color becomes more interesting. Another consideration in support for using a hardware capable of color discrimination is that with the need to reduce mass, volume and power consumption, instruments aboard future spacecraft will tend to accumulate more functions. Thus, the same hardware used for star tracking might also be used for target recognition, optical navigation, and other uses in other phases of the mission. Some of these uses may require color information.

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Figure 5.11 – B−V and V−I plot for the 5000 brightest stars in the Hipparcos catalog.

Source: Drawn by the author.

5.4.11.2 Timing measurements

Timing measurements were the most difficult ones, also being the least reliable type of measurement presented in this work. In modern computers, running modern operating systems, many times it is not possible to disable all background processes, such as antivirus, system processes, etc. Hence, it is not possible to predict when a background process will request CPU resources, robbing CPU time from the algorithm under test. To work around this limitation, we have adopted a number of tactics, besides performing multiple Monte Carlo simulations using the same configuration.

As the tests were performed in a Windows machine, the first measure taken was to close all network connections to avoid unwanted downloads and update processes running concurrently with our tests. This was done by allowing all updates to complete and disconnecting the test machine from the Internet before performing the tests.

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Another tactic that was used was to interleave test configurations, as can be inferred from the first column shown in Table 5.7, Table 5.8 and Table 5.9. For example, in one of PTASE runs (log file ptase_20170727_05.log), the results from the first Monte Carlo simulation were used in Table 5.7, the results from the second simulation were used in Table 5.8, the results from the third in Table 5.9, and so on. By interleaving test configurations, we can reduce the probability that a background process, running for a relatively large amount of time, would go unnoticed, affecting all measurements with a given configuration and biasing conclusions.

Unfortunately, all the measures adopted here are not failproof. The best solution to this problem would be to run the Monte Carlo simulations in an environment where the user has complete control over all the processes (including interrupt service routines) running on the test machine, such as a dedicated hardware or an emulator simulating a target processor. In cases this is not possible, an alternative would be to perform Monte Carlo simulations using an operating system where the user has better control of background tasks, such as Linux.

A final remark to this section is that the fastest algorithm or implementation in a given machine (e.g., the test computer used to evaluate them) might not be the fastest on a different machine (e.g., in the STR hardware). Hence when selecting algorithms based on speed, decisions should be made preferably on tests conducted in the target hardware.

5.4.11.3 Conclusion

Simulations have shown that magnitude and color indexes can be successfully used to reduce the misidentification rate, improve success rate and in many cases to speed up star identification. Even with the relatively large errors in magnitude and color index measurement considered in this simulation, we have obtained a significant reduction in misidentification rate by including magnitude and color indexes as additional filters in the star identification process. Had we

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used the values obtained by the preliminary experimental work described in Section 3.6 in our simulations, results would be even better.

Monte Carlo simulations have shown that even for monochrome star trackers, the use of magnitude information as an additional check for star identification leads to a significant reduction in misidentification rate, therefore improving attitude determination reliability without the need of additional hardware. If color information is available, it should be used to further reduce the probability of a misidentification occurring.

An important evaluation which was not performed in this work is to verify how the tested star-ID algorithms behave in the presence of false stars (spikes). This verification is very important in real applications. Future work should evaluate how star-ID algorithms behave with the presence of false stars, using a model that attempts to mimic in a realistic way the distribution of false stars with magnitude and color indices.

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