A Comprehensive Study of Linear Kalman Filter ... - Science Direct

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ScienceDirect Procedia Technology 25 (2016) 427 – 434

Global Colloquium in Recent Advancement and Effectual Researches in Engineering, Science and Technology (RAEREST 2016)

A Comprehensive Study of Linear Kalman filter based Tracking Techniques under Ionosphere Scintillation Manjula T Ra* Dr. G Rajub a

Research scholar Jain University, Karnataka, Bangalore-562112, India b Professor,Jain University,Karnataka Bangalore-562112, India

Abstract To accurately determine the position of the user, the navigation systems, GPS/IRNSS play a significant role. The integrity, reliability and continuity of these systems depend on the performance of the receiver which uses carrier tracking loop to maintain synchronization with the received signal. Under harsh conditions such as ionosphere scintillation and multipath effects, the performance of these loops deteriorates leading to loss of phase lock and also causes signal outages. Recursive and time varying nature of Kalman filter perform better in such harsh conditions as it continuously adapt the loop bandwidth to the changing signal parameters. This paper analyses the limitations of the traditional carrier tracking technique and provides a survey of linear Kalman filter based carrier tracking techniques and investigates its robustness when tracking the signals under ionosphere scintillation conditions © Published by by Elsevier Ltd. Ltd. This is an open access article under the CC BY-NC-ND license ©2016 2015The TheAuthors. Authors.Published Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of RAEREST 2016. Peer-review under responsibility of the organizing committee of RAEREST 2016 Keywords:Ionosphere

scintillation; Kalman filter; PLL;GPS; IRNSS; tracking loop;

I. Introduction The Indian Regional Navigation Satellite System (IRNSS) similar to a Global Positioning System (GPS) is an independent navigation system to be a constellation of seven satellites. Presently satellites in geosynchronous * Corresponding author. Tel.:+919900460100. E-mail address:[email protected]

2212-0173 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of RAEREST 2016 doi:10.1016/j.protcy.2016.08.128

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T.R. Manjula and G. Raju / Procedia Technology 25 (2016) 427 – 434

orbits are IRNSS-1A/B/E and in geostationary Earth orbit, IRNSS-1C. Its primary service area will cover the Indian sub-continent extended by about 1500 km.A number of environmental factors are known to affect the performance of IRNSS/GPS, includingelectromagnetic interference, multipath effects, vegetation attenuation, and atmospheric delays and with ionosphere scintillations events being the most severe.The charged particles in the ionosphere creates plasma layer of irregular density of electrons, the propagation of RF signal from the satellite when traverses through the density of electrons of the ionosphere undergoes refraction and diffraction and the process of constructive and destructive interference will give rise to rapid fluctuations in the amplitude and phase of the signal known as ionosphere scintillation. The rate of scintillation depends on several factors including space weather, the current Total Electron Count (TEC) [1], the time of day, geomagnetic activity, and solar activity. Under certain conditions, the signal is completely reflected off resulting in abrupt and significant fades.

Fig.1. Plot of C/N0 v/s time for IRNSS L5 signals experiencing rapid fluctuation with amplitude fades up to 20dBHz

Scintillations are detrimental to the performance of IRNSS/GPS system as they affect the reliability and continuity of GPS/IRNSS systems by degrading the performance of the code and carrier tracking loops of a receiver. Ionosphere Scintillation generates rapid fluctuations in the amplitude and phase of the signal. Reducing the amplitude of a radio signal reduces its power level which directly affects the signal to noise ratio, thus hindering a base station's ability to detect and receive the signal while Phase fluctuations increases the phase error which when exceeds tracking threshold leads to loss of phase lock. During normal atmospheric conditions, a nominal Carrier to Noise Ratio (C/N0) value acquired by a commercial GPS receiver is about 44 dB-Hz [11] and 50 dB-Hz for IRNSS. However during ionosphere scintillation events, power fades up to 20 dB or more can occur in IRNSS as shown in the Fig.1. When theRF carrier signal undergoes deep power fades, accompanied with rapid fluctuations in phase, the carrier tracking loop fails to track accurately the carrier phase which causes phase error to build up and when it exceeds pull in range of the Phase Locked Loop (PLL), leads to loss of phase lock [11]. When the phase unlock occurs, it may be necessary for the GPS receiver to reacquire the signal to regain the lock that can take several seconds or minutes, this delay poses a serious risk to navigation systems onboard vehicles such as aircraft, guidance systems, and missiles that require current and precise coordinates. From Kalman Filter (KF)theory [12], its adaptive nature and optimal approach of estimation has made it suitable for tracking signals under ionosphere scintillation conditions. KF based carrier tracking techniques are broadly classified into two methods based on the observations [2]: Extended KF which directly uses correlator outputs as observation, has limitation of increased computation load compared to linear KF which directly uses discriminator output as measurement In this paper, a review of linear KF based carrier tracking techniques are presented beginning with traditional

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PLL carrier tracking loop, its limitations, followed by Kalman filter based tracking technique, its benefits and the suitability of KF to operate under various working conditions. Lastly the qualitative comparison of all techniques is presented and conclusions are drawn 1.1. Traditional carrier tracking loop The carrier tracking loop in GPS/IRNSS is realized using PLL [14] is as shown in Fig.2. PLL is used as a carrier tracking loop to maintain synchronization with the received signal by generating the carrier replica which matches in phase and frequency of the received signal. It uses Costas version of PLL where the incoming Intermediate Frequency (IF) signal is first multiplied by code replica to wipe off the Pseudo Random Noise (PRN)code [11]and then by in phase and Quadrature phase carrier replica to wipe off the carrier to demodulate the signal to baseband signal.

Fig.2.Block diagram of traditional carrier tracking loop

The phase of the carrier is modified by several error sources such as relative motion between satellite and receiver, ionosphere scintillation, receiver clock instability. The received and sampled IF signal of GPS/IRNSS system is given by equation (1) [13] ܵሺ‫ݐ‬௞ ሻ ൌ ‫ܦܽߜܣ‬ሺ‫ݐ‬௞ ሻ‫ܥ‬ሺ‫ݐ‬௞ ሻ ሺ‫ݓ‬ூி ‫ݐ‬௞ ൅ ߮଴ ൅ ߮௜ ൅ ߮ௗ ሻ ൅ ݊ሺ‫ݐ‬௞ ሻ

(1)

Whereܵሺ‫ݐ‬௞ ሻ is the sampled signal at sample time ‫ݐ‬௞ A is the signal amplitude, ߜܽ is the variation in amplitude, D is the navigation data stream, C is the C/A code, ‫ݓ‬ூி isthe IF signal frequency߮଴ initial phase of the carrier, ߮௜ is the phase variation due to ionosphere scintillations, ߮ௗ is the phase due relative motion between satellite and receiver, ݊ሺ‫ݐ‬௞ ሻ is additive white Gaussian noise. The problem under consideration is tracking carrier phase variations in harsh conditions. Tracking the carrier phase involves generating the phase error between received signal and replicated signal by using discriminator function and accordingly steering the Numerically Controlled Oscillator (NCO) frequency towards the received signal frequency with the aim of minimizing the phase error to zero. 1.2. Limitations One of the limitations of the traditional carrier tracking loop is the constant bandwidth of the loop filter and its inability to adapt the bandwidth to changing signal parameters such as C/N0 and phase variations associated with ionosphere scintillation. The loop filter in the PLL tracking loop plays a significant role as its bandwidth controls the amount of noise as well as track the dynamics of the signal. The smaller bandwidth is required to reduce the thermal

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noise while larger bandwidth is required to follow the high signal dynamics. Hence there are always tradeoffs in achieving both the objectives.Moreover the loop filter with fixed bandwidth performs poorly when it is required to track both a weak signal characterized by low C/N0 and a high signal dynamics characterized by large Doppler frequency rate. Hence adaptive bandwidth filtering is preferred over the constant bandwidth when tracking signals under dynamic condition. 2. Kalman filter based strategies KF offers adaptive bandwidth filtering and can serve as a better substitute for loop filter in carrier tracking loop due to its optimal, systematic and recursive nature of estimating the time varying Parameters in dynamic conditions. The desirable features of KF in tracking the scintillated signal are many. First it weighs the quality of the prediction against that of a measurement and hence it optimally estimates the parameters. Second, the dynamic and measurement models offer a unique opportunity to utilize any prior information about the operating environment of the receiver and thus increase the performance of the filter. Third, the parameters estimated by the KF represents optimal as it is determined by minimizing phase error in additive white Gaussian noise(AWGN) operating conditions. 2.1. Fundamentals of KF The kalman filter estimates the process using a feedback control: the filter estimates the process state at some time and then updates the estimates using feedback in the form of measurements. As such, the algorithm of Kalman filter is performed in 2 steps: time update and measurement update. The time update is responsible ି ି ି ෟ forprojecting forward the current state‫ݔ‬ෞ ௞ and error covariance estimates‫݌‬௞ to obtain the a priori estimates‫ݔ‬௞ାଵ and ି ‫݌‬௞ାଵ for the next time step. The measurement update equations are responsible for incorporating new measurement‫ݖ‬௞ into the a priori estimate to obtain an improved a posterior estimate‫ݔ‬ෞ௞ and‫݌‬௞ Ǥ The equations for the time update and measurement update are given in equations (2) to (6).

Ak x k Bu k wk

(2)

Ak p k A Qk

(3)

x k 1 k 1

P

Kk

xk Pk

T k

Pk H kT ( H k Pk H kT Rk ) 1

(4)

x K ( z k H k xk ) k

(I K k H k )P

(5) (6)

The limitations posed by the loop filter in tracking scintillated signals is overcome by adopting Kalman filter (KF) and the carrier tracking loop is referred as Kalman filter based PLL and block diagram is shown in the Fig.3. KF is data recursive algorithm which estimates the parameters of interest provided it has the knowledge of the process noise and the measurement noise. The sources of noise that contribute to the modification and variation of carrier phase comes under the process noise such as ionosphere scintillation, receiver clock instability errors, line of sight acceleration changes. The probability density functions of noise sources are expressed in the form of matrix called process noise covariance matrix Q [13] given in equation (7) The noise at the output of measurement device such as phase discriminator is referred to as measurement noise matrix R.


Fig.3. Block diagram of Kalman filter based Carrier tracking

3. The linear KF based carrier tracking techniques The comparison of the performance of second order PLL with 2 state KF based tracking loop is presented in [2]. KF exhibits some desirable features which is suitable to track dynamic signal. First and foremost is noise equivalent bandwidth is smaller than traditional PLL and hence has more noise rejection capability. Though its tracking sensitivity is same as traditional PLL but it has better dynamic adaptability and tracking accuracy In the context of adaptive KF, the approach in [3] focuses on increasing the robustness of KF in tracking the signal under ionosphere scintillation. The KF is self-tuned to the detected scintillation level by updating the process noise covariance matrix (Q) with scintillation parameters. The scintillation parameters are computed in real time from the phase scintillation spectrum. This technique improves the accuracy of carrier phase tracking with allowing less noise in the carrier Doppler and minimized phase error (jitter).The performance of KF in terms of avoiding cycle slips and loss of phase lock occurring during scintillation is ignored. The proposed tracking scheme is only suitable for ionosphere scintillation monitors. Three different carrier techniques are investigated in [4]: advanced closed loop, open loop scalar techniques and vector tracking techniques. The performance is assessed in harsh environments, including fading, ionosphere scintillation and high dynamics. Closed loop techniques uses Kalman filter based tracking as they are able to adapt to the changing signal conditions. Open loop techniques are able to cope up with loss of lock conditions. Vector architectures allow tracking of signal with low C/N0 and avoiding loss of lock. observations show that KF based approaches are more robust as it exhibits small phase estimation error but its effectiveness in avoiding loss of phase lock by maintaining lock on to the signal is ignored. Open loop scalar techniques show same benefits at lower C/N0 ranges. Vector based tracking techniques provide a better position based solution. The tracking approach in [5] replaces the conventional PLL loop filter by Kalman filter as KF provide the optimal filter gain when the noise models defined are closed to realistic values. The potentiality of KF is analyzed for tracking GPS L1 signal in the presence of Scintillations. This method uses 3 state 2 equations KF with Kalman gain fixed and hence ignores the process noise covariance matrix Q and measurement noise covariance matrix R. An approach is initiated to predict the value of the current bit of the navigation message in order to use four quadrant arctangent discriminator which extends the phase detection capability of the loop. The observations shows that the estimated phase tracking errors are lower for KF based PLL than the conventional method and KFP has smaller number of reacquisition compared to conventional methods. The work presented in [6] compares 3 carrier tracking loops: the conventional PLL, a Frequency locked loop (FLL) assisted PLL and Kalman filter based PLL (KFP). The tracking performance of the above stated methods is evaluated in the scintillation conditions for parameters such as loop bandwidth and Discriminator types such as atan

431

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and atan2. KFP uses 3 state 2 equations with fixed gain matrix. The observation shows that all 3 methods exhibit similar tracking loop errors. The KFP has the most robust performance in terms of minimum loss of lock and cycle slips. The equivalent noise bandwidth of KF is comparatively small. The approach adopted in [7] is to increase the robustness of KF based PLL when tracking the scintillated signal. The idea is that the loop bandwidth is varied as function of C/N0 and focuses on avoiding the loss of phase lock by reducing the phase error updation to next iteration level in Kalman filter. Accordingly KF is operated in 3 regions: In the region where C/N0 is above some upper threshold the KF operates in normal mode. In the region where C/N0 between lower and upper threshold of C/N0, error updation to next level is reduced as a function of C/N0. In the region where C/N0 is below lower threshold, phase error is discarded and the loop is maintained atthe previous iteration. [8] Analyses the performance of the GPS carrier tracking loops in the presence of severe ionosphere scintillation. A comparison of the behaviour of PLL in the presence and absence of scintillation indicates that Phase discriminator (PD) plays a significant role in avoiding cycle slips during ionosphere scintillations. Performance of the PLL is studied using different types of PDs such as arctangent, conventional Costas, Decision Direct and Dot Product Arctangent (DPAT).DPAT is shown to experience fewer cycle slips than other detectors. Observations show that average mean time between cycle slips is longer in DPAT compare to other detectors which is a desirable feature in avoiding loss of phase locks Reference [9] demonstrates the architecture of Kalman filter based carrier tracking loop to enhance the robustness of tracking the signal subjected to fading in urban environments by increasing its sensitivity. The sensitivity of the loop is increased by extending the integration time which increases the signal to noise of the detected signal and thus allowing tracking of a weak signal. The approach is suitable to track weak signals with steady dynamics. The approach in[10]proposes KF based carrier tracking loop designed to track low C/N0 signals. The design of KF is based on decorrelating the process and measurement noise models 4. Investigating the performance of KF in tracking scintillated signal The performance of the Kalman filter depends on its tuning parameter Q and R given in equations (7) and (8) [13] respectively.

Q

ª S GM « «0 «0 ¬

0 S Gf 0

0º » 0 » S Ga »¼

(7)

‫ݏ‬ఋఝ ,‫ݏ‬ఋ௙ , are power spectral densities (PSDs) [13] of the clock bias and clock drift respectively and ‫ݏ‬ఋ௔ is the PSD of line of sight acceleration changes

R

§ · ¨ ¸ 1 ¨ 1 ¸ 1 c ¨ c ¸ 2 T¨ 2 T¸ n0 © n0 ¹

(8)

c/n0, is the Signal to noise ratio of the signal and T is the integration time of the correlator. The Kalman gain which represents the loop bandwidth is varied as a function of Q and R to continuously adapt the bandwidth to changing signal dynamics. In order to track the signal under normal signal conditions, the KF is operated with fixed Q and R matrices and hence the bandwidth offered by KF based PLL is constant With the changing signal acceleration /conditions, the difference between the fixed Kalman filter model and actual signal is becoming larger and hence the phase error increases. This can be overcome by using adaptive bandwidth KF where Q and R matrices are updated in real time. This mode of operation of Kalman filter is suitable to track the signal in dynamic condition When phase scintillations are not accompanied by amplitude fades as is typically the case for auroral scintillations [4], the PLL bandwidth must be wide enough to accurately track the phase scintillations. To handle this

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scenario Kalman filter gain representing the loop bandwidth is no longer a constant value but is made a function of real time estimated scintillation parameters (T and p) [13] i.e., measurement noise covariance matrix Q is not fixed but is real time updated to the changing signal phase conditions. This mode of KF is referred to as scintillation mode. Lowering the loop bandwidth enables the PLL to track/ maintain lock on a weak signal .So when tracking the signals affected with amplitude scintillations and not accompanied by phase scintillations, bandwidth of the loop has to be small enough to reject the noise and track a weak signal. In this situation Kalman filter gain representing the loop bandwidth is varied as a function of real time estimated C/N0 i.e., measurement noise covariance matrix R is not fixed but is real time updated to the changing C/N0 of the signal. This mode of operation of KF is referred to as C/N0 mode. Accordingly Kalman filter can be operated in normal mode, C/N0 mode and scintillation mode by tuning the filter’sQ and R parameters according to signal conditions. Kalman filter offers optimal solution when tracking signal under different ionosphere scintillation conditions [4] by providing adaptive bandwidth. It is capable of tracking weak and dynamic signal with minimum phase error at a given bandwidth. 5. Qualitative comparison In the previous sections, we have given the description of linear KF based carrier techniques highlighting the advantages and disadvantages. As far as the performance is concerned, it is difficult to compare all these techniques, since there is not a single technique that performs best in all working conditions. Some techniques perform better than others in certain scenarios. Therefore it is not possible to make a decision on the best that can be used under all conditions for a given application. Nevertheless, it is possible to provide some guidelines to choose the technique that can be considered for a specific problem. In this context there are three main problems that we encounter in carrier tracking applications: random thermal noise, Amplitude scintillation and phase scintillation due to ionosphere scintillation events. These three threat parameters are taken as base for comparison of different carrier tracking techniques, depicted in the first row of the Table. 1. First column categories different techniques based on bandwidth. While the second and subsequent rows correspond to different modes of Kalman filter capable of combating specified threat parameters. The last column indicates the merit of each technique in the respective area of tracking. Table.1. Comparison of different linear KF based carrier tracking techniques Thermal noise

Amplitude scintillation

phase scintillation Scintillation mode of KF

To track auroral scintillations

C/N0 mode of KF Adaptive bandwidth

Avoids loss of phase lock

Variable gain KF

Minimum phase error

Normal mode of KF Scintillation updated KF Constant bandwidth

Conventional PLL

To track high signal dynamics

Improved accuracy of phase tracking Less complexity

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6. Conclusions In this Survey, beginning with overview of conventional PLL based carrier tracking loop, the different methods to combat the problems of carrier tracking under ionosphere scintillation conditions are discussed broadly giving the reader the detailed overview of existing linear Kalman filter based techniques available in literature. This study analysis the robustness of Kalman filterand different modes of Kalman filter suitable for tracking the signal under different signal conditions. Acknowledgements The authors would like to thank ISRO for providing data sets and Jain University for providing an opportunity to work and publish this paper. This work is carried out at project laboratory department of Electronics and Communication Engineering, School of Engineering & Technology, Jain University References [1 ] Norsuzila, Wan Muhammad Faizhaqimi Wan Hasbullah, “GPS ionosphere Scintillation and Total Electron Content during Partial Solar Eclipse in Malaysia “, 2014 IEEE 10th International Colloquium on Signal Processing & its Applications (CSPA2014),. 2014 [2] Xingli sun, Hongleiqin, and Jjingyiniu, “Comparison and analysis of GNSS signal tracking performance based on Kalman filter and traditional loop”, WSEAS TRANSACTIONS on SIGNAL PROCESSING, Issue3, Volume 9, July 2013 [3] Melania Susi, Marcio Aquino, “Design of robust receiver architecture for scintillation monitoring” in Proceedings of IEEE PLANS, California, 5-8 May 2014 [4] Christophe Macabiau, Lina Deambrogio, Valentin Barreau, “Kalman Filter Based Robust GNSS Signal Tracking Algorithm in Presence of Ionospheric Scintillations”, Proceedings of the 25th International Technical Meeting of the Satellite Division of the Institute of Navigation September 17 - 21, 2012 [5] Todd E. Humphreys, Mark L. Psiaki, “Tracking L1 C/A and L2C signals through Ionosphere scintillations”, Proceedings of the 20th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2007). [6] Lei Zhang, ’’Tracking GPS signals under Ionosphere Scintillation conditions’’, 22nd International Meeting of the satellite division of the institute, September 22-25,2009 [7] Lei Zhang“A variable gain Adaptive Kalman filter based GPS carrier tracking Algorithm for Ionosphere Scintillation signals”, Proceedings of the 23rd International Technical meeting of the satellite division of the institute of Navigation, September 21-24,2010 [8] Todd E. Humphreys, Mark L.Psiaki, Paul M, “Modelling the effects of Ionosphere Scintillation on GPS carrier Phase tracking”, IEEE Transactions on aerospace and electronic systems Vol. 46 No. 4 October 2010 [9]Jose A Del Peral-Rosado, Jose A, Del Peral-Rosado, and Gonzalo Seco-Granados, “Kalman filter based Architecture for robust and high sensitivity tracking in GNSS receivers”, Satellite navigation Technologies And European Workshop on GNSS Signals and Signal Processing (NAVITEC), 2010 5th ESA Workshop on IEEE, 2010 [10] Miao Jianfeng, Chen Wu, Sun Yon Grong, Liu Jianye, “Low C/N0 Carrier Tracking Loop Based on Optimal Estimation Algorithm in GPSSoftware Receivers”, Science Direct, Chinese Journal of Aeronautics, Elsevier, February 2010, Pages 109–116 [11]Nathan Olivarez (2013), “Mitigating the effects of ionosphere scintillation on GPS carrier recovery”, A Thesis, WORCESTER POLYTECHNIC INSTITUTE [12] Greg Welch, Gary Bishop. “An introduction to the Kalman filters”, Technical report, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA, 1995 [13] Melania Susi, Marcus Andreotti and Marcio Aquino, “Kalman filter based PLL robust against ionosphere Scintillation”,Mitigation of Ionosphere Threats to GNSS: An Appraisal of the Scientific and Technological Outputs of theTRANSMIT Project, July 17, 2014 [14] Kwang-hoon Kim, Gyu-In Jee,Jong-Hwa Song, “Carrier Tracking Loop using the adaptive two stage Kalman filter for High dynamicssituations”, International Journal of control automation and systems, vol. 6, No.6, pp. 948-953, December 2008.