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Conclusions
In the result of the conducted research were developed blocks for Galileo E5 GNSS signals acquisition and tracking. These blocks were developed in Matlab software and tested on the real samples of data. Also, the comparison with GPS signals acquisition results was conducted. It was shown that Galileo E5 signals perform better in the higher noise conditions and it is more reliable than GPS signal. Galileo E5 signal may be used, for example, in urban conditions and give more accurate results of object positioning. Testing on real samples of data, recorded by the research group, showed that the developed blocks perform well - the satellites that present in data record are acquired and tracked properly.
Figure 3 - Time-frequency meshes
Figure 4
output of DLL correlator; (b) output of PLL correlator
On the next stage of the research it is necessary to develop navigation solution block in order to have operational Galileo E5 receiver.
After that it is supposed to optimize the algorithm of the receiver operation for its faster work and to implement it on FPGA.
REFERENCES
1. Galileo Open Service Signal In Space Interface Control Document (OS SIS ICD), Issue 1.2, November 2015. European Union 2015.
2. European GNSS Service Centre. Constellation Information. [Online] Available from: http://www.gsc-europa.eu/system-status/Constellation-Information [Accessed: 5th November 2015].
3. Ionospheric Correction Algorithm for Galileo Single Frequency Users, Issue 1.1, June 2015. European Union 2015.
4. Borre, K. A Software-Defined GPS and Galileo Receiver/K. Borre.- Boston: Birkhauser, 2007. -
176 p.
5. Shivaramaiah, N. C., Dempster A. G. The Galileo E5 AltBOC: Understanding the Signal Structure/ N. C. Shivaramaiah. - International Global Navigation Satellite Systems Society. IGNSS Symposium 2009. Holiday Inn Surfers Paradise, Qld, Australia 1 - 3 December, 2009.
6. Simsky A., Mertens D., Sleewaegen J., Hollreiser M., Crisci M. (2008) Experimental Results for the Multipath Performance of Galileo Signals Transmitted by GIOVE-A Satellite. International Journal of Navigation and Observation Volume 2008, Article ID 416380
7. Shivaramaiah, N. C., Dempster A. G. An Analysis of Galileo E5 Signal Acquisition Strategies/ N. C. Shivaramaiah. - Proc. of the European Nav. Conf., ENC GNSS 2008, April 23-25, 2008, Toulouse, France.
8. Tawk, Y., Bollerun, C., Jovanovic, A., Farinc, P. Analysis of Galileo E5 and E5ab code tracking./ Y. Tawk. - Springer-Verlag 2011.
9. MathWorks. [Online] Available from: http://www.mathworks.com. [Accessed: 10th October 2015].
10. Самарский университет. Материальная база. НИЛ-98. [Online] URL: http://www.ssau.ru/mat-baza/11/ [Accessed: 25th December 2015]
УДК 621.396
Tabatabaei1 A. , Mosavi1 И. R., Khavari1 A., Shahhoseini1 H.Sh., Shafran2 S.V.
1Iran University of Science and Technology, Narmak, Iran
2Samara National Research University, Samara, Russia
RELIABILITY ADVANTAGES OF IMPROVED FUZZY WLS METHOD FOR GPS AND GLONASS COMBINED RECEIVER IN JAMMING SCENARIOS
One of the important concerns in Global Positioning System (GPS) receivers is interference and jamming. Received signals in GPS receivers are very weak. So, they are vulnerable to interference which cause losing the satellite signals and thus impairs the positioning availability and accuracy. In this paper, the integration of GPS with Russian Global Navigation Satellite System (GLONASS) as the second world-wide satellite-based navigation system is proposed to overcome this problem. Increasing the number of visible satellites is a significant benefit of this compound system. We also introduce an improved fuzzy weighted least-square method to weight the information according to its system reliability and its satellite properties such as its impress on positioning and horizontal dilution oof precision. Experimental results show that the final solution has been improved to 32% in defined figure of merit parameter.
Key words:
GPS, GLONASS, Integrated Receiver, Jamming, Reliability, Fuzzy Weighted Least Square
1. Introduction
An important threat for positioning is jamming that is a form of intentional interference that prevents Global Positioning System (GPS) signal acquisition and tracking. There are different methods for jamming mitigation in GPS receivers. These methods are mainly in three groups: adaptive antennas based methods, adaptive filtering based methods and time-frequency filtering based methods that mainly utilized in acquisition unit to eliminate jamming signals. For example, adaptive antennas based methods are suitable for both wideband and narrowband jamming mitigation and adaptive filtering based methods are suitable for low power applications.
Also, the Discrete Wavelet Transform (DWT) method splits a signal into an approximation part and a detail part so provides detailed signal decomposition and is useful for interference rejection applications [1,2].
Another proposed method to overcome the interference signals is integrated receiver which can receive and analyze at least two kinds of Global Navigation Satellite System (GNSS) signals. This solution increases the number of satellites, availability and reliability of the output results and unlike the previous effort to mitigate effect of jamming on signal acquisition and tracking of GPS receiver, mitigates jamming effect in navigation solution and improves accuracy of positioning [3].
The combination of GPS as the first satellite navigation system with Russian fully operational Global Navigation Satellite System (GLONASS) is one of the possible integrated system utilized in difficult scenarios [4].
The basis of GNSS positioning is the estimation of unknown coordinate of receiver by means of distance between receiver and each satellite. This distance is calculated in two ways: pseudorange and carrier phase measurements.
The best known estimation tool is Least Square (LS) that makes the sum of the squares of the errors as small as possible to find the best estimation. Some paper used pseudo-range or carrier phase separately and some of them such as Ref. [5] utilized both of them and reached to an acceptable RMS error and more than 45% improvement in specifying receiver position.
Improving the accuracy of LS method is an important target possible by weighting data that known as Weighted Least Square (WLS) method. Its performance is giving larger weights to high quality signals and reducing the influence of weak signal in positioning.
Ref. [6] utilizes Signal-to-Noise (C/N0) ratio and elevation angle for weighting and has an improvement of 76.89% on the standard deviation value rather than LS method. Ref. [7] also uses elevation angle and C/N0 for decision making about quality of signals and introduces eight ways for estimating variance of observation based on these quality factors. So, weight of observation is inversely proportional to variance which improves the accuracy of the positioning results more than 50%.
Selecting an appropriate weighting matrix is an important step in WLS algorithm. A balance among all parameters should exist for finding suitable weights. So a fuzzy system can help us in this situation. Fuzzy inputs are the specific parameters of signal. The main step in designing a suitable system is defining good rules and membership functions. For example, Ref. [8] reduces the position error to less than 1.5 meters using fuzzy system, while it was about 60 meters before.
The rest of this paper is organized as follows. In section 2, the basic principles of the paper are briefly reviewed. The proposed method is described in section 3 and section 4, reports the experimental results. Finally, section 5 provides us with the conclusion.
2. Basic principles
In this part, basic principles of the paper are reviewed.
2.1. GPS and GLONASS Integration
Satellite-based navigation is a tool to determine position, velocity and precise time. Currently, the generic GNSS includes two worldwide operative navigation systems. One is U.S GPS and the other is Russian GLONASS.
The multi-constellation approach provides improvements in terms of solution availability and accuracy, but with a needing to an extra observation to introduce an additional unknown, because of GLONASS time offset. The most important advantage is the increased immunity to interference and jamming [9-11].
In the most cases, GPS and GLONASS are the same, but with some differences. These differences are in constellation, signal and reference which should be noticed in integrated system design. Another important point discussed by many papers theoretically and practically is the fact that GLONASS performance is not comparable to GPS and sometimes can make deviation in the integrated receiver solution with the incorrect information [12].
2.2. Jamming and Interference
Despite increasing the developments in data collections and navigation solutions in new receivers, the main drawback of the satellite navigation systems are its high sensitivity to different interferences including multi-path, jamming and spoofing. The effect of interference on the GNSS receiver is to reduce the Signal to Noise Ratio (SNR) and decrease the availability of satellite information and as the result, increase the navigation solution error.
GPS signals are transmitted from the satellites orbiting 20,000 km above the earth and can become weaker as they approach the receiver. This weakness makes the signals so sensitive to different interferences. Jammers are the devices deliberately transmit troublemaker signals in the space and as the result, preventing the receivers from determining and reporting the accurate results [13,14].
2.3. Least Square for GNSS Navigation Solution using Pseudo-Range Measurement
A major step in positioning using satellite navigation systems is measuring the distance between the satellites and receiver. This distance can be calculated by multiplying the travelling time of the GNSS signal by the signal propagation speed. The measured range is called pseudorange. Because of the inaccuracy of the receiver clock and another error sources such as multi-path effects and atmospheric delays, this measurement is not accurate. By taking into account the main errors, the pseudo-range measurement can be defined as:
Ri = ri + cAti - cAt + T +1 + M + e (1)
Where T and 1 are ionospheric and tropospheric delays, M is multi-path error, e is an unmolded error and r represents the actual range between the satellite and receiver position that is expressed as:
= ^(x - x )2 + (yJ - y )2 + (^ - z )2
2)
In which j and i belong to the satellites and receiver, respectively. The calculated pseudoranges are used as known parameters to estimate receiver position by means of an appropriate method. The LS method is one of the most widely used methods for estimation. If the initial position of receiver (Xo,yo,Zo) is known, then actual receiver position will be shown as Eq. (3):
x = x0 + Ax , Yi = y + Ay , Zi = Zq + Azt (3) Where (AXj,Ayj,AZj)are the position deviations defined as unknown parameters. If we write
r
(Xj,yj,Zj) as Eq. (4) and use Taylor's series, Eq. (5) will be obtained.
f (xi, y,, z,) = f (x0 + Ax,, yo + 4y, zo + Az,)
f( xi, yt, z, ) = f (xo, yû, zo) +
, Sf(xQ,y0,za) ^ 1 d2f
Sf (xo
, yo, zû) Ax + Sf ( xo, yo, z0)
9x„
^o
Ay,.
9z,
^ Az,. + - ^ +... ' 2! S x
5)
For linearization the higher order terms will be ignored. Linear expression coefficients are obtained by Eq. (6):
Sf ( ^ Уo, zo) Sxn
xj - xo Sf (xo,yo,zo)_ yj - yo
Sf ( xo, Уo, zo^ zj - z0
dzn
0 '0
By refraining from unmolded errors, we can rewrite the pseudo-range equation in form of Eq.
(7)
RJ = roj - xj-xo
Ax -
-Ay--
-Az + cAt,
7)
After simplifying, we can relate GNSS pseudorange measurements to the unknown user position by Eq. (8):
l = hx (8)
Where L is an observation vector, H is a design matrix and X is the state vector. The receiver clock offset for GPS and GLONASS are different. So, an additional unknown parameter is needed in the state vector of combined system and at least five satellites are required for positioning. The state vector for a combined system is expressed as Eq. (9):
X=[Ar Ay Az AtGPS AtGLO ]
(9)
Where At^p^ the receiver clock is offset with
respect to GPS time and At^^Q is the receiver
clock offset with respect to GLONASS time. The design matrix of a combined system is shown in Eq. (10):
h =
hgps1 xi
hgps2
l,gps2
"yi
hgpsN "gPsN
hgla1 yi
hg'a1
hgps1 hgps 2
hgpsN hgla1
1 0 1 0
1 0 0 1
Where hj
hgloM hg'oM hg'oM 0 1 xi yi zi
, hj. = -
(10)
„J y,
z. - z0
and h =--:— . The observation vector is:
zi rJ
r0
L =
lJ
That V = RJ -' . The solution of Eq. be obtained by Eq. (12) [15]:
X =(HTH )-1 HT L
2.4. Weighted Least Square Method
(11)
(12)
In order to achieve more accurate response in positioning, it is essential that satellites have coefficients chosen intelligently. This is due to the difference in properties of satellite signals which some of them have high quality and should be weighted more than others. In other words, unlike the ordinary LS that all satellite have the same influence in positioning, in this method each satellite is weighted according to their signal specifications. Therefore, poor signals have less efficiency in positioning [16]. The user position in WLS method is given by:
x = (HTWH) 1HTW L
(13)
Where W is the weighting matrix with n*n dimension.
2.5. Geometric and Authenticity Factors
Satellite geometry in receiver view as an important factor in precision and accuracy of the final result can be described by a parameter called Geometric Dilution of Precision (GDOP). In other words, GDOP provides a simple interpretation of positioning precision. Lower GDOP value usually causes better accuracy in GNSS positioning.
Horizontal Dilution of Precision (HDOP) is a parameter for solution evaluation horizontally which is related to whole satellite geometry and cannot be used to evaluate a special satellite, particularly. Hence, Ref. [17] defines a factor called Residual HDOP (RHDOP) which indicates each satellite effect on the position accuracy. The larger the RHDOP, the more effective the satellite in final result calculation.
HDOP for set of satellite without satellite number n
rhdopn =
(14)
HDOP for set of all satellite
3. Proposed Fuzzy System
The combination of fuzzy logic and fuzzy set is a fuzzy system and its main components are fuzzy rules, fuzzy inference engine, fuzzifier and defuzzifier. The rules are the main part of a fuzzy system that specify relationship between inputs and outputs. Fuzzifer and defuzzifer are the first and last part of fuzzy system respectively with opposite task. First one converts crisp input value to the fuzzy value and the second one converts the fuzzy output to crisp value [18].
The fuzzy system used in this paper is shown in Figure 1. Two inputs are defined for this system: RHDOP and authenticity factor. This means that the proper weight for each satellite will be determined according to the RHDOP and authenticity factor values based on proposed fuzzy rules. Signal with higher RHDOP and authenticity factor has more valuable information. So, it should be weighted more than others. The Mamdani and the centroid methods are used for the inference process and the defuzzification, respectively. It should be noted that the number of membership function, the shapes of them and the rules are specified by try and error.
Figure 2 shows the MFs for inputs of fuzzy system. Three subsets defined for RHDOP: Small, Medium and large and authenticity factor with four subsets: very small, small, medium and large.
The membership function for weight as an output is shown in Figure 3.
According to the number of input subsets, 12 proposed rules are needed for this system. The mentioned rules are summarized in Table 1.
According to this fact that the reliability and accuracy of GPS signals are more than GLONASS, it is better that the coefficient of GPS signal is higher than GLONASS in WLS method. So, we introduce a new parameter called system factor that attributes two different coefficients to GPS and GLONASS signals. The complete system is shown in Figure 4.
r
0
an
Figure 2 - Input membership functions
0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.9 1 Weight
Figure 3 - Output membership function The proposed fuzzy rule base
Table 1
RHDOP Authenticity Factor
Very small Small Medium Large
Small NS S PS NM
Medium S M PM NL
Large PS PM L PL
Figure 4 - The proposed FWLS system
4. Experimental Results and Discussions
In this part we compare the result of proposed method and ordinary LS in presence of jamming. An open-source MATLAB-based GNSS Software-Defined Receiver (SDR) is used to analyze the results.
Firstly satellite constellation compared to prove the superiority of integrated GNSS system
to only GPS. Figure 5 shows the sky plot of available GPS satellite before jamming. There are five satellites in receiver view that decreased to three after jamming. As we know, at least four satellites are needed for positioning, so in this situation there are not sufficient satellites.
Figure 5 - Sky plot of GPS in jamming situation
As reported in Table 2, GLONASS aided GPS to increase the number of satellites. The comparison of GDOP also illustrated in this table. Satellite geometry of GLONASS in our data is not good, so the integrated GDOP is higher than GPS
GDOP, but it is obvious that satellite geometry of GPS+GLONASS is better than GPS only in presence of jamming. Also the sky plot of integrated system is shown in Figure 6.
Comparison of number of satellites in GPS and GPS+GLONASS
Table 2
System Number of Satellites GDOP
GPS without jamming 5 3.74
GPS with jamming 3 ---
GPS+GLONASS with jamming 7 8.88
Figure 6 - Sky plot of GPS+ GLONASS in jamming situation
A primary comparison of X error for navigation solution using proposed method and LS presented in Figures 7. These figures show that in most of the times, error for proposed method is less than LS. In order to compare the results of proposed method and ordinary LS, three parameters are selected and reported in Table 3. The
Root Mean Square (RMS) value shows the precision of results and the values of Standard Division (STD) and Maximum (Max) error present stability of accuracy. RMS error can also be calculated as:
1
Where M shows the number of data-base epochs. In order to simplify the comparison, a new Figure of Merit (FOM) parameter is defined as:
FOM -
j M
RMS = y M^1 [(xpredicted ~ xreal ) + (ypredicted ~ yreal ) + (z predicted ~ zreal ) ]
(15)
Where STDAvg and MaxAvg are the average of the STD and Max error in 3 dimention, respectively
106
RMS x STDAvg x MaxAvg
16
Figure 7 - Proposed method and LS for comparison of X error LS and proposed method result comparison for GNSS
Table 3
Parameter LS Proposed method
RMS Error 37.72 34.16
STD Error 25.89 22.34
Max. Error 89.80 86.88
FOM 11.40 15.08
Based on FOM parameter reported in Table 2, accuracy and precision in this method are improved more than 32.28%.
5. Conclusion
Jamming as an intentional interference is one of the most important troubles of new receivers. Jamming makes the satellite information weaker or unavailable and as the result deviates or stops the receiver navigation solution process. So, adding new satellites belong to other constellations can increase the availability and
accuracy of the outputs. The fact that information provided by other constellations is not comparable with U. S. GPS tended us to propose an improved fuzzy weighted least square method which can weigh the satellite information according to its effect in the compound system geometry and final solution. The experimental result showed that defined FOM parameter had been improved for more than 32%.
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