An Enhancement Coherent Code Discriminator for Tracking GPS Signal

Tracking the global positioning system (GPS) signals is a more important process in hardware/software GPS receivers. Any error leads to either provide inaccurate location fixing/measurement or lose signal lock in the tracking process. Delay lock loop and phase lock loop are responsible for synchronising with receiving code and wiping off the carrier frequency with Doppler frequency shift receptively. Code discriminator and code loop filter are characterised the delay lock loop, which is utilised to synchronise the generated code with received signal’s code. In this work, an enhanced coherent code discriminator is designed in order to enhance the tracking process. Our discriminator has been analysed and compared with the coherent and non-coherent discriminators. Also, real GPS data is employed for different GPS satellites situations, in these comparisons. The processing results showed that our design has better performance than the coherent and non-coherent code discriminators for the strong and weaker GPS signals in terms of reducing errors of discriminator output. Moreover, a standard deviation and root mean square is also utilised to evaluate our design, and the results revealed that all obtained values are less than the coherent and non-coherent code discriminators.


Introduction
Tracking GPS signal considers the main challenge for the GPS receiver's designer, due to having various receiving scenarios (outdoors and/or indoors) [1]. Consequently, the tracking process will define the ability of the GPS receiver among these scenarios. The tracking process is accomplished by integrating the process of delay lock loop (DLL) and the phase lock loop (PLL) [2]. Basically, the PLL consists of carrier loop discriminator and carrier loop filter, while, the DLL comprises code loop discriminator and code loop filter [3]. The main function of PLL is to reduce the frequency error obtained by the acquisition process for adjusting the generated frequency of local oscillator to match the received frequency signal (carrier frequency + Doppler frequency shift). On the other hand, the DLL is used to improve the code phase accuracy and also maintaining the generated code alignment with the received code [4]. Usually, these frequency and code phase values can be adjusted by using the discriminators in the PLL and DLL, and there are various types of discriminators for carrier and code phase [5]. Moreover, there are several algorithms have been developed for estimating the carrier frequency and code phase delay to improve tracking process based on Kalman filter. However, these algorithms would help to reduce tracking error depending on pre-filtering, but this will add more complexity and processing time to the tracking process  [6]. The present work focuses on enhancing the performance of DLL code discriminator. The code discriminator can be categorised into two groups: the coherent and non-coherent code discriminators. The coherent code discriminator utilises only the in-phase (Ix) outputs correlators, while the noncoherent discriminator uses both the in-phase and quadrate-phase (Qx) outputs correlators [7]. Practically, a coherent code discriminator is designed to enhance the GPS signals tracking in outdoors and indoors environments, which mean only the Ix correlators, are employed. The idea behind choosing Ix or coherent correlators is that the correlated signal has little amount of noise and all the noise will be located in Qx correlators. Moreover, the designed discriminator has been normalised to reduce the amplitude sensitivity and to be more efficient in dynamic environment.
This paper is organized as follows: Section 2 summarizes previous designed tracking methods; Section 3 explains methodology of the tracking process and mathematical model of the enhanced coherent discriminator. The results and discussion are illustrated in Section 4 to demonstrate the performance of this work with the coherent and non-coherent code discriminators. Finally, Section 5 concludes this work.

Previous works
As mention earlier, the main parameters of the tracking process are DLL and PLL. Consequently, most of the researchers are focused on either developed their methods according to these lock loops or by employing the Kalman filter to their proposal design. However, some of these solutions are used another way to enhance the tracking process, such as increasing the integration time. An FFT tracking solution for GPS signal is designed to enhance the accuracy of weak GPS signal [8]. This solution is based on increasing the integration time in order to increase the power of the weak GPS signal. The computational complicity is overcome by making the integration to the results of the in-phase and the quadrature-phase correlators. In the same vein, another solution based on extending the integration time (post-processing) to 100 ms and/or 20 ms in order to accommodate the power of five/one bit of the navigation message [9]. This post-processing will help the receiver's sensitivity and add about 3 dB gain to the received GPS signal in harsh environments. Furthermore, a code and carrier tracking for planed GPS and Galileo signals are implemented based on exciting discriminators [10]. Such implementation is to evaluate the future signals, where the signals based binary offset carrier are tracked using single side lobe to overcome the ambiguity issue. The authors conclude it necessitates designing a new tracking method to assess these binary offset carrier signals in real-time kinematic and multipath environments. In addition, a new design to enhance the tracking and estimating the error of the GPS signal depending on prefiltering is proposed [11]. The pre-filtering process is accomplished by using non-coherent integration to estimate the carrier phase error. The authors are recommended that the use of coherent and noncoherent integration time would improve the estimation of code and carrier errors and can be applied for weak and strong GPS signals.
On other hand, a joint code and carrier tracking based on Kalman filter is designed [12]. The proposed algorithm used grid mechanism to combined code, phase and carrier discriminators that would enable the Kalman filter for tracking GPS signal. This achieved by generating three replicas of code and carrier frequency to allow receipt wide area of GPS signal in indoors. Similarly, for a dynamic scenario, a tracking method has been proposed based on adaptive four-state Kalman filter [13]. The four states are the DLL, PLL, frequency lock loop with an adaptive Kalman filter. The method is using assistance from an inertial navigation system in order to prevent the losing lock of the PLL. The results showed the use of the Kalman filter can provide a particular code phase delay and Doppler frequency shift.
In contrast, another solution based on memory discriminator is proposed to improve tracking GPS signals in outdoors and indoors scenario [14]. The proposed discriminator is extended the integration time to increase noise rejection and increase the chance to accommodate weak GPS signals. In addition, an enhancing weak global navigation satellite system signal method is designed based on carrier/phase discriminator [15]. Actually, this method is proposed for the receiver that used for pedestrian navigation application due to having different scenarios, i.e. moving for outdoors to indoors or vice versa. The method is used pre-processing in order to compensate for the power of the received (weak) GNSS IOP Publishing doi:10.1088/1757-899X/1076/1/012050 3 signals, particularly when having a dynamic scenario. Another solution to overcome the dynamic scene is achieved by adjusting the space of the DLL loop [16]. Such solution is based on changing the chip distance between the early and the late correlators according to the receiver localization. On other word, the space getting wider when the receiver placed in harsh environment and this space become smaller in outdoors.
It is noteworthy, that most of these works have offered a better way to overcome the dynamic situation, but at the expense of increasing the computational complexity and/or the processing time. In this work, an enhancement for tracking process is accomplished by enhancing coherent code discriminator for the strong and weaker GPS signals. This will lead to reduce the errors of discriminator output and resultant an efficient performance in dynamic environments.

The enhancement discriminator
Practically, the tracking process comprises four units: two units are responsible for the code and carrier tracking (DLL and PLL), while the others are signal generator and decoding unit [17]. This section will demonstrate the process of DLL code tracking, the code discriminators types and the mathematical representation of the enhanced coherent discriminator.

DLL code tracking
DLL and PLL functions are obtained rough values of code phase delay and frequency Doppler shift from the acquisition process before starting the tracking signal. The goal of DLL is to keep synchronising with the received GPS signal's code. In addition, DLL is determining the code phase errors, then filtering these errors and regenerate new replica codes, as shown in Figure 1. In the tracking process, practically the received GPS signal is converted to baseband to remove carrier plus Doppler frequency shift. This accomplished by multiplying the received signal with a locally generated carrier frequency. Next, the resultant baseband signal is correlated with three replicas codes (E, P and L), where E refers to the early code, P is the prompt code and L means the late code. Moreover, the space chip between (E & P and P & L) is 0.5 chip and might be smaller (i.e. ≥0.1) or larger (i.e. ≤1) according to the receiver design.
As shown in Figure 2, the six correlation outputs determine the matching between the generated and received codes. The resultant outputs are then fed to the code discriminator for comparing and deciding which correlator has the highest correlation. Eventually, these outputs are directly provided to the code loop filter. The parameters of the loop filter are set with noise bandwidth is equal to 2 Hz off, in order to reduce the amount of noise level as much as possible, and the damping ratio is 0.7 to overcome the high overshoot.

DLL code discriminator
The code discriminator determines the number of correlators that employed in the DLL (the coherent and non-coherent code discriminators). The standard illustrations of the coherent & non-coherent code discriminators [7] are shown in Table 1.  It is worthwhile to mention that only the dot product discriminator has used the six correlators. Furthermore, it is clearly seen that all discriminators (coherent and non-coherent) are based on a specific IOP Publishing doi:10.1088/1757-899X/1076/1/012050 5 idea which is "early correlator minus late correlator" outputs. Consequently, in this work, the enhanced coherent discriminator is also based on this particular idea, but the prompt correlator is involved with the early and late correlators. In addition, the enhanced coherent discriminator has been normalised to improve the tracking performance when having a dynamic reception, i.e. when changing the location of GPS receiver from open sky to harsh environment or vice versa. Mathematical representation of the proposed discriminator is expressed below in Table 2. Table 2. The enhanced code discriminator.

Enhanced coherent discriminator
As shown above, the use of (IP) with both early (IE) and late (IL) correlators will reduce the code discriminator errors. Figure 3. depicts the response of each discriminator, where the enhanced coherent proposed has the lowest value of 0.5 chip delay and even lower than the dot product discriminator. Nevertheless, the normalised early minus late (EML) power and the suggested enhanced discriminators have the highest value of 1 chip delay. Actually, this is not applicable because currently all the DLL are designed based on 0.5 chip or less space between E and L correlators to have accurate tracking and good performance.

Experimental results and discussion
To evaluate the presented design performance, two standard types of code discriminators ("coherent EML" and the "non-coherent normalised EML power") have been utilised in the comparison. All experiments are based on real recorded GPS signals obtained from [7]. This recorded signal has sampling frequency of 38.192 MHz with intermediate frequency 9.55 MHz and the tracking time is set to 10 sec. The PLL is based on the Costas loop and the type of PLL discriminator is = −1 ( ⁄ ) for all experiments.

Discriminators outputs
The following results are illustrating the performance of the present enhanced coherent discriminator and highlight the discriminator outputs. Figures (4 & 5) show the discriminator outputs, which represents the amount of the code error, for strong GPS satellites signals of 15 and 29 respectively. It is clearly seen that the proposed discriminator is outperforming by more than half than the standard coherent and non-coherent discriminators.  On other hand, Figures (6 & 7) depict the discriminator outputs of GPS satellites 3 and 6 respectively. Although these signals have weak power, the performance is still better than the coherent EML by (1/2) and the non-coherent normalised EML power discriminators by (1/3). This achieved due to using (Ip) together with IE and IL and because the proposed discriminator has been normalised which reduces the noise signals comes with the received GPS signals.

Zero crossing and the in-phase correlators outputs
This section focuses on the zero crossing from -1 to 1, also shows IP (blue line), IE (red line) and IL (yellow line) which represents outputs of the in-phase correlators. As shown in Figure 8, signal of satellite 22, the enhanced discriminator has preserved the synchronisation with the received (strong) GPS signal by keeping the zero crossing in the in-phase correlator. Moreover, the behaviour of the enhanced discriminator is much similar to the behaviour of coherent discriminator for all three correlators' outputs (IP, IE and IL). The other experiments that also employed for this part of the comparison are testing low-power reception of GPS signal. Similarly, Figure 9 represents the behaviour of the output's correlators for signal of satellite 3, which have the same performance of enhanced coherent as testing strong GPS signal. This conclude that the proposed discriminator able to preserve the synchronisation with the received GPS signal (the low-power and high-power signals).  Figure 9. Zero crossing and the in-phase correlators' outputs from strong signal of satellite 3 (top left "Coherent EML", top right "Noncoherent normalised EML power", bottom left "Enhanced coherent").

Bit transition
After determining the zero crossing a bit transition can be located, in this comparison "1 sec" is tested to represent 50 bits of the navigation data. As shown in Figure 10, the power of the strong signal is double than the power of the weaker signal. Also, the Figure depicts that the proposed enhanced discriminator has maintained the bit transition in the tracking output from satellite 21. Moreover, Figure  11 is illustrated the bit transition of weaker GPS signal, where clearly seen that the proposed enhanced coherent discriminators have successfully extracted the navigation data by preserving the bit transition.

Standard Deviation and root mean square evaluation
Additional comparison to assess the discriminator performance is by using the standard deviation. Table  3 demonstrates all standard deviation (STD) values for the enhanced coherent discriminator and the coherent and non-coherent discriminators. It is clearly seen that the proposed discriminator has smaller values than the non-coherent discriminator. Also, the STD values obtained are almost equal or less than the STD values of a coherent discriminator for weak and strong GPS signals. In addition, it is worthwhile to mention that the STD values for satellites 9 and 29 of our discriminator are much smaller than the coherent discriminator value. The reason of obtaining this highest discriminator output for the coherent discriminator is the high level of error at the beginning of the tracking process as shown previously in Figure 5. Similarly, the root mean square (RMS) is also utilised to evaluate the performance of proposed solution for estimating error. Table 4 illustrates the RMS results obtained from testing discriminators. The results confirm that the enhanced discriminator has the lowest values than other standard discriminators. This confirmation is based on high convergence between STD and RMS values, which have tiny differences between them and follow their basic formulas.

Conclusions
This work presents an enhanced coherent code discriminator to improve the tracking of GPS signals. The response and mathematical representation are demonstrated and compared with the standard discriminators. Also, other comparisons, such as DLL discriminator outputs, in-phase correlation outputs, the zero crossing and bit transition, have been processed with different GPS signal receptions. A standard deviation and root mean square measurements are also utilised to evaluate the proposal design, although the tiny differences between obtained results. The results are confirming that the enhanced coherent discriminator is outperforming with more than 35% as average of the standard coherent and non-coherent discriminators in terms of reducing the noise level. These leads, as a result, to reduce the correlators code error by 50% in various receptions scenarios. Moreover, the authors believe that the enhanced coherent discriminator can be added to the standard coherent discriminators and can be implemented in the GPS receivers.