Self-Aiding in GPS Signal Tracking Qin Zhengdi, Research & Technology Access, Nokia Corporation, Finland

BIOGRAPHY Dr. Qin Zhengdi graduated from the Department of Physics, Hunan Normal University, China in 1981. He received his M. Sc in Applied Physics from the Chinese Academy of Science in 1985 and his Ph. D. in Biomedical Engineering from Zhejiang University, China in 1988. He worked as a post-Ph. D. scholar in the Department of Electronic Engineering, Oulu University and the Computer Department of the State Technology Research Center of Finland (VTT) during the years from 1988 to 1993. He has been with Nokia Corporation since 1993. His current interests include CDMA technologies, the mobile signal processing and positioning and navigation technologies. ABSTRACT In the GPS C/A signal tracking process, the longest coherent integration time is 20 milliseconds that are limited by the 50 Hz navigation data on top of the base band CDMA signal. To improve the sensitivity for weak signal tracking, such as indoor applications, external aiding is a good option. The aiding resources can be, for example, from a local mobile network. With the aiding of the binary navigation data sequence, the integration time for the tracking loop can be extended for a better tracking performance. But in the cases when the external aiding is not available, the navigation data can be estimated at the same time when the tracking process is going on. The estimated binary data can be then used in a feedback scheme for the self-aiding to extend the coherent integration time of the tracking loop. In this report, some feedback principles are discussed for the GPS signal tracking. It ranges from a simple hard binary estimation feedback and a softer decision feedback based on the signal quality, or the likelihood of the signal power level. The experiment results show that the self-aiding can improve the tracking behavior. The improvement can be as high as +5 dB. The premises are that the satellite signal acquisition has been set up and the data bit synchronization has been achieved. So, the method cannot be used alone in a deep low signal level environment at the beginning. But the improvement of the tracking

performance gives a better pseudo range measurement in a normal situation. The tracking process is getting more stable in most of the cases when the coherent integration time increases. On the other hand, the scheme can be applied when a GPS receiver is moving, for example, from outdoor to indoor or from highway to tunnel. The already tracked signal can be continually tracked in a deeper low signal level environment. The sensitivity of the receiver is somehow improved. The technique is quite simple for the implementation in practice. INTRODUCTION The principle of the decision feedback is often applied to improve the performance of a receiver. In the technique, after the income signal has passed through the detection channel and the decision has been made, the estimated message from the signal is fed back to the input of the detection channel and used for later processes in order to improve the performance of the system. In the GPS tracking process, the sensitivity of the tracking loop to the satellite signal is mostly decided by the coherent integration time of the input signal. Due to the data modulation on top of the CDMA signals, the longest coherent integration time is limited by the bit length of the binary navigation data. That is 20 ms for the C/A code. The original design of the C/A code is not meant for such as indoor applications. The 20 milliseconds can only give the receiver a minimum sensitivity around –150 dBm, while the satellite signals inside a building could be as low as –155 dBm. In order to track the satellite signal for indoor applications, the sensitivity of the tracking process should be improved. This can only be done by wiping off the binary data modulation and extending the coherent integration time for the tracking loop. The navigation data wipe-off technique is generally realized when an external aiding is available, for example, in a cellular system. The information about the GPS signal is estimated in a fixed station under a good condition. Then demodulated navigation binary data is sent to the mobile terminal through the mobile network. Normally, it

results a delayed or an off-line process for the mobile receiver. With the aiding information about the navigation data, the coherent integration time can be extended for the tracking loop as long as to satisfy the sensitivity requirement for the weak signal and the signal can keep its coherency as well. It is true that the satellite signal to the mobile receiver is relatively more stable for the indoor than for the outdoor environment. It means that it is acceptable for a longer coherent integration time in cases that the aiding is available or the data modulation can be wiped off. In many cases, the aiding information is not available, or the real-time processing is essential. So, the external aiding is not possible. In this report, a self-aiding technique is introduced in which the decision feedback principle is applied that the aiding message is estimated by the tracking process itself. In a GPS receiver, after the satellite signal acquisition and the navigation data bit synchronization, the data estimation is performed. The estimated data bit can then be fed back to the input of the tracking loop for wiping off the effect of the data modulation. The coherent integration time can be extended to improve the sensitivity of the tracking loop for weak signal applications. HARD DECISION FEEDBACK The easiest way for the decision feedback is to use the estimated binary value directly as the feedback message. The navigation data message is estimated for every 20 milliseconds. The sampling data within each 20 ms are dumped together coherently and the sign of the output is the estimation result. Then the sign or the binary value (+1 or –1) is fed back to the input for the purpose of removing the data modulation. It is done by multiplying the original coherently dumped signal with the estimated binary value. After the data removing, several dumped periods can be integrated together coherently for a better signal-to-noise ratio. In the tracking process, the coherent integration time can then be extended to be the multiple of 20 ms. In a zero degree tracking process for the BPSK signal, the modulated navigation data information is considered to be mainly in the real part (I) of the signal while the noise is mainly in the imaginary part (Q). Depending on the system response and the required tracking loop bandwidth, the integration process can be done sequentially or in a moving window manner. If the moving window is used, the coherent integration time is the length of the moving window; while the NCOs updating time interval in the tracking loop can be shorter than the coherent integration time for a faster response. For example, the length of the moving window can be a multiple of 20 ms while the NCOs updating time interval can be 20 ms or less. In this way, the original tracking loop structure does not have to be changed much.

Figure 1 shows the actual implementation for the hard decision feedback with a multiple of 20 ms moving window. The coherent integration time is M * 20 ms. The dumped signal y (n) with an extended coherent integration time is then used as the reference for calculating the tracking errors (DLL, PLL, FLL,). The calculation is performed for each 20 ms as well as for the NCOs updating.

20 ms integrated signal

Z- 1

x(n)

i=0

Data bit estimation

Z -1 1

M-1

Dn (+1 or –1)

y(n)

Fig 1. The hard decision feedback with a moving window.

y ( n) =

M−1

∑

Dn − i x ( n − i )

i= 0

(1)

Dn = sign[real ( xn )]

The process is just like what an external aiding process does for removing the navigation data modulation. The difference for the self-aiding technique is that the aiding resources for the navigation data message is coming from the tracking loop itself. SOFTER DECISION FEEDBACK Like all other signal combining techniques, the reliabilities of the components participated should be take into account for a better estimation. It is more important especially for weak signals. To make the combination more reliable, the components participated should be weighted before the combining process. If one component has a higher quality, a better weighting factor is given to the component in the process; while if a component is poorer, a small weighting factor is used for the component. To apply this principle to the combination process for the decision feedback scheme, it is called the soft decision feedback. It would be nice if the probability estimation (priori as well as posterior probabilities) could be done for the incoming signal of the receiver. The probability (0 – 1) of the received signal estimated could be directly used as the weighting factor for the components. In practice, the probability of the received GPS signal is difficult to estimate. And also it is not feasible for a real time processing. In order to give a quality measure for the signal, some other methods can be used to present the incoming signal reliability. For examples, the likelihood or the signal-to-noise ratio of the received signal can be used as the approximation.

In our practice, we found that the relationship between the real part (I) and the imaginary part (Q) of the 20 ms dumped signal can be used as an indicator for monitoring the tracking behavior. It is also somehow related to the signal-to-noise ratio level when the tracking is in progress. Based on the relation between I and Q the likelihood of the signal can then be draw, for example, as:

 0  w=  I − Q I + Q 

( if I < Q ) ( others)

(2)

Here we refer to a zero phase tracking process and also a BPSK modulation. If the tracking phase is not zero, it is not difficult to rotate the phase angle by adding a constant phase. The range of the likelihood for the weighting factor w is from 0 – 1. When w = 0, it means that the signal is too noisy to be used while if w = 1, the signal looks like pure. In the formula, if |I| < |Q|, it means that the phase lock of the signal is more than 45 degree away from its tracking phase. The component is not worth to be used in the coherent combination process. On the other hand, if the signal to be tracked is 45 degree away from its desired tracking phase direction, we might say that it is already lost tracking. Another approach for the likelihood is to use the phase angle of the dumped data to linearly represent the reliability of the signal. It can be calculated as: w = 1−

2 angle{I + jQ} π

(3)

In the expression, the range of w is also from 0 – 1. Combining the data bit decision and the weighting factor, the softer decision feedback can be expressed as: y ( n) =

M−1

∑

wn Dn − i x(n − i)

i= 0

(4)

Dn = sign[real( xn )]

EXPERIMENTAL RESULTS The experiments with a prototype GPS receiver have been performed. The signal source is produced by a WelNavigate GS1010 GPS constellation simulator with a variable attenuator. The scenario is that the receiver is moving constantly in a direction with a speed of 10 km per hour. In order to be used for weak signal tracking, the receiver is first acquired and synchronized with the GPS satellite under a relatively strong signal situation. Then the GPS signal power level is adjusted with the attenuator at the rate of –1 dB / 2-5 seconds. Let the receiver track the

satellite signal continually when the signal is getting weaker and weaker. The results are compared with those by using 20 ms coherent integration time for a normal tracking without decision feedback. The output of the carrier phase lock detector PLL is used as the indicator to represent the tracking performance. The tracking performance indicator is expressed as:

2  atan Q I  (I ≠ 0) 1 − PLL =  π    0 (I = 0)

(5)

Both the hard decision feedback and the softer decision feedback with a moving window are used in the tracking process. The window size, or the coherent integration time is extended to 40 ms, 60 ms and 80 ms respectively. The NCOs in the tracking loop are updating for each 20 ms. Figure 2 on the next page shows the results by using the hard decision feedback. It clearly shows the improvement by using the decision feedback. If we consider that 50% of the PLL lock detector is the lower limit for the successfully tracking, without decision feedback, the tracking process can track the signal down to about -148 dBm and then lost tracking. With the decision feedback, the PLL lock indicator is getting better and better when the coherent integration time is getting longer. We can see that when the signal level is lower than –152 dBm, the receiver is still tracking the signal with the coherent integration time over 60 ms. From the figure we can also see that the curves of the phase lock are getting flatter when the integration time increases. It means that with the decision feedback and the increase of the coherent integration time, the stability of the tracking process is improved for both the strong and the weak signals. If the coherent integration time is longer than 60 ms in this case, the improvement is not much. It tells us that the coherent integration time is also limited by the coherence of the signal itself. Figure 3 shows the results by using the softer decision feedback. We can see that the tracking behavior is getting slicely better compared with the hard decision feedback, especially when the signal power level is less than –150 dBm. With the 80 ms window size or the coherent integration time, the tracking process can track the signal down to about -153 dBm or even weaker in this case. CONCLUSIONS With the decision feedback technique, the navigation data modulation of the GPS signal can be wiped off by the tracking process itself under certain circumstances. It is called self-aiding. The coherent integration time can then be extended for a better signal to noise ratio in the tracking process. In our report, a moving window is applied in order to maintain the original NCOs updating

is suitable for weak signal tracking especially for indoor applications where the GPS signal is relatively stable.

speed for a desired tracking loop bandwidth. The implementation is then very simple in practice. For the coherent combination, a hard combination as well as a softer combining principles are presented. For the hard combining, each of the 20 ms dumped signals is directly added together coherently after the data wipe off. For the softer combination, each of the 20 ms dumped signals is weighted before the combination.

REFERENCES [1] Parkinson, B. W. and J. J. Spilker Jr., Global Positioning System: Theory and Applications, AIAA, 1996. [2] Elliot D. Kaplan, Understanding GPS: Principles and Applications, 1996

The technique is simple but the benefits are evident. Based on our experiments, the tracking behavior can be improved by around +5 dB. The tracking process is getting more robust when the coherent integration time increases, as long as the signal can keep its coherency. It

[3] Don H. Johnson and Dan E. Dudgeon, Array Signal Processing, PTR, 1993

PLL lock detector (%)

90 80 70 60 50

---- 80 ms window for coherent integration

40

---- 60 ms window for coherent integration

30

---- 40 ms window for coherent integration 20

---- 20 ms window for coherent integration

10 0

-152

-150

-148

-146

-144

-142

-140

dBm

Figure 2, Weak signal tracking with hard decision feedback. 90

PLL lock detector (%)

80 70 60 50

---- 80 ms window for coherent integration

40

---- 60 ms window for coherent integration 30

---- 40 ms window for coherent integration

20

---- 20 ms window for coherent integration

10 0

dBm

-152

-150

-148

-146

Figure 3, Weak signal tracking with softer decision feedback.

-144

-142

-140

-138