## 4 Performance Evaluation
### Positioning Accuracy Test  
In this section, the ACSA-OLTA based positioning accuracy is evaluated by the off-line processing with the help of the GPS satellite signals. Since few satellites send new GNSS signals, the GPS L1 CA signal is used in the test. In order to clearly confirm the experiment condition, also to correctly obtain the navigation message in the signal to eliminate the phase inversion and lengthen the coherent integration length as the pilot signal, all of the origin satellite signals with a relatively high \(C/N_{0}\) are collected in the open air in the Beijing Institute of Technology campus. The constellation and \(C/N_{0}\) are showed in Figure 9. The \(C/N_{0}\) is gained from a NovAtel navigation receiver. The Geometric Dilution of Precision (GDOP), which is a geometry factor, representing the amplification of the standard deviation of the measurement errors onto the solution [21], is less than 2.0 during the collection. In the first place of the test, the navigation message is collected by processing the original satellite data. The evaluation is carried out after the message in the GPS L1 CA signal is demodulated based on the collected one. The coherent integration length of open-loop tracking in the test is 300 ms. The frequency search step is 5 Hz. For other feasible values, the comparison results are more or less the same so that they are not listed for simplicity. In this case, as the tests of the open loop tracking methods with different measurement extraction strategies are based on the same data, at any time during the test, the satellites that can be detected and used for positioning are all the same among these methods. Hence, the satellite constellation, ephemeris error, atmosphere error and \(C/N_{0}\) are all identical in the test. The pseudo range based Least square (LS) positioning algorithm is used to test the accuracy for the reason that there is no  
Figure 8: The standard deviation of the code phase measuring error for different \(C/N_{0}\). filter in the process of LS and it can better reveal the variation of the measurement [21]. Accordingly, the positioning accuracy can remarkably indicate the code phase measuring performance. In consideration of the fact that satellite signal power may be attenuated by sheltering, inappropriate antenna direction, _etc_. in an urban area, extra AGWN is added to change the \(C/N_{0}\) of the received signal. Three tests are conducted in which the signal is attenuated by 10 dB, 20 dB and 30 dB. When it is 10 dB attenuated, for all the satellites, ACSA-OLTA computes the pseudo range with the discriminator based method. As a consequence, the three-Dimension (3-D) positioning error of DET with the fixed code search grid sizes of 0.1 chip and 0.05 chip is computed to compare with that of ACSA-OLTA. When \(C/N_{0}\) is 20 dB and 30 dB attenuated, ACSA-OLTA changes the measurement extraction strategy and the 3-D positioning error of ACSA-OLTA is compared with DET and DIS in which the grid sizes are both 0.1 code chip. The 3-D position error cumulative distribution of the three tests is showed in Figure 10. The position error cumulative distribution is a statistic result of the position error. It calculates the percentage of position results with the 3-D error less than the given value in all positioning results. The expression of the position error cumulative distribution (PECD) is  
\[E_{PECD}(E_{g})=\frac{1}{N_{p}}CNT(\{E_{n};E_{n}<E_{g},n=1,2,...,N_{p}\}) \tag{37}\]  
where \(E_{g}\) is the given position error and \(E_{n}\) is the 3-D error of the \(nth\) position result. \(N_{p}\) is the total number of the position results. \(CNT(\{\mathbf{x}\})\) is the number of the elements in the set \(\{\mathbf{x}\}\). When \(C/N_{0}\) is 10 dB attenuated, the lowest \(C/N_{0}\) of these satellites is 30 dBHz. For ASCA-OLTA and other open loop tracking methods with the fixed grid sizes, all of the satellites shown in Figure 9 can be detected and used for position.