Syed Fairuz Syed Dardin 1, Vincent Calmettes 1, Benoit Priot 1, Jean-Yves Tourneret 2 1 ISAE, University of Toulouse, France

Transcription

1 Adaptive GNSS signal tracking techniques in the context of a deeply integrated GNSS/INS navigation system designed for tackling multipath in urban environment Syed Fairuz Syed Dardin 1, Vincent Calmettes 1, Benoit Priot 1, Jean-Yves Tourneret 1 ISAE, University of Toulouse, France s.syed@isae.fr, vincent.calmettes@isae.fr, benoit.priot@isae.fr ENSEEIHT-IRIT, University of Toulouse, France jean-yves.tourneret@enseeiht.fr Abstract This study is part of a project which proposes deep fusion of GNSS signals with data provided by MEMS inertial sensors by using vector-tracking methods. The main drawback of this implementation is that tracking errors occurring in a given receiver channel can potentially affect other channels and lead to significantly reduced navigation performance. Therefore, providing reliable delay and Doppler estimates at the tracking loop output is crucial in order to achieve an accurate estimate of the vehicle position and velocity. The main idea of this paper is to improve the reliability and the availability of the signal tracking module by taking advantage of the integrated navigation solution to mitigate efficiently multipath effects. A specific processing approach inside the tracking loop is revisited in order to improve the estimation of the received direct-path signal parameters. This is done by introducing a set of indicators which make possible an adaptive robust tracking control. Simulations are carried out to assess the performance of the designed tracking loop. BIOGRAPHIES Syed Mohd Fairuz Bin SYED MOHD DARDIN is a PhD student at Institut Supérieur de l'aéronautique et de l'espace (ISAE) since 11. He received Bachelor of Engineering in electronics from Multimedia University, Malaysia in and a Master of Engineering in telecommunication from University Technology of Malaysia in 5. He worked as an engineer for a telecommunication company until 7 and later became a teaching assistant in National Defense University of Malaysia until 1. He later received a Master of Science in aeronautical and space system from ISAE in 11. His research interest includes GNSS receiver tracking algorithm and GNSS/INS integration. Vincent CALMETTES received a Ph.D. degree in signal processing from ISAE (French Institute of Aeronautics and Space, Toulouse, France). He is a training and research scientist at the signal, communications, antenna and navigation laboratory of ISAE. His research interests include Bayesian filtering and multi-sensors data fusion, with applications to tracking and navigation in harsh environments. He is also working on new Galileo signal processing and GNSS receiver architectures and is involved in several projects devoted to the development of embedded navigation system based on DSP and programmable logic devices. Benoit PRIOT received the Engineering Diploma from Ecole Nationale Supérieure d Ingénieur de Limoges (ENSIL), Limoges, France specializes in Electronic, Telecommunications and Instrumentation, in 4. Since 7, he is working as an Engineer on INS and GNSS navigation systems at the Institut Supérieur de l'aéronautique et de l'espace (ISAE), Toulouse, France. Jean-Yves TOURNERET received the ingénieur degree in electrical engineering from the Ecole Nationale Supérieure d Electronique, d Electrotechnique, d Informatique, d Hydraulique et des Télécommunications (ENSEEIHT) de Toulouse in 1989 and the Ph.D. degree from the National Polytechnic Institute from Toulouse in 199. He is currently a professor in the University of Toulouse (ENSEEIHT) and a member of the IRIT laboratory (UMR 555 of the CNRS). His research activities are centered around statistical signal and image processing with a particular interest to Bayesian and Markov chain Monte Carlo (MCMC) methods. He has been involved in the organization of several conferences including the European conference on signal processing (EUSIPCO) in (as the program chair), the international conference ICASSP 6 (in charge of plenaries) and the statistical signal processing workshops SSP 1 (for

2 international liaisons). He has been a member of different technical committees including the Signal Processing Theory and Methods (SPTM) committee of the IEEE Signal Processing Society (1-7, 1- present). He has been serving as an associate editor for the IEEE Transactions on Signal Processing (8-11). I. INTRODUCTION Multipath (MP) propagation remains a dominant source of errors in GNSS. Indeed, multipath produces noises and biases which can lead to large errors in position estimates, especially in challenging environments such as urban canyons. Different techniques have been proposed to mitigate MP effects within the receiver tracking loops. The most efficient methods exploit high resolution timefrequency decomposition [1], or channel deconvolution []. However, these blind techniques have a high computation complexity. In the context of adaptive vector tracking loop, the integrated navigation solution (which can also benefit from the use of other complementary sensors) can be harnessed to improve GNSS signal tracking in the presence of MP. This study considers slow fading channels for which MP effects can be classified in two main categories depending on the value of the MP frequency with respect to that of the line of sight (LOS) signal. When the vehicle moves with an inclination with respect to the reflecting surfaces, we can observe that the support of the Doppler spectrum is broadened. In this case, signal decorrelation can be performed in frequency domain. On the contrary, when the vehicle is stationary or moves in the direction of the reflecting surfaces, MP frequency and direct path (DP) frequency have the same value. Thus the signal decorrelation must be addressed in time domain. The major idea is to introduce a set of monitoring indicators which are necessary for controlling efficiently the signal tracking module. These indicators are identified to detect errors induced by MP and to determine their origin. Test Statistics based on the knowledge of the vehicle state, time and frequency analysis applied to the correlator outputs are performed for detecting the presence of MP and describing the state of the tracking module. In a nominal condition, conventional tracking loops as in [3] are considered in order to estimate the propagation delay and the Doppler frequency (which are translated into pseudorange (PR) and delta-range (DR)) of the received signal. These estimates are then used as inputs for the navigation algorithm. In presence of MP, signal decorrelation is first carried out in the frequency domain to mitigate non-coherent signals. A frequency locked loop (FLL)-assisted phase locked loop (PLL) which uses an FFT-based discriminator for separating non coherent MP is designed. This technique allows MP frequency-dependent selection of the integration time and of the PLL noise bandwidth in order to track efficiently the LOS signal that is potentially contaminated by coherent MP signals. In that case the issue is to consider temporal diversity in order to allow an accurate tracking of the LOS signal. Here decorrelation in the time domain is obtained by using the outputs of coherent correlators to construct a multiple double delta ( ) structure. This structure is used for coherent MP detection and to reduce delay discriminator errors. This processing allows us to provide reliable PR and DR measurements when the LOS signal in a given channel is available. Conversely, the measurements associated with channels without LOS signals are discarded. This paper is organized as follows: section II describes the signal model and the architecture of the system which has been specifically designed for addressing the navigation problem in harsh environments. The MP context is described in section III. Section IV focuses on the adaptive FLL-assisted PLL whereas the section V details the structure of the adaptive delay locked loop (DLL). Section VI analyzed the monitoring indicators which are used in a new approach to achieve a robust tracking loop control. Section VII provides results and performance of the designed adaptive tracking loop and finally, section VIII summarizes some conclusions and future work. II. SIGNAL MODEL AND SYSTEM ARCHITECTURE A. Signal Model In the presence of MP, the received signal can be characterized as a function of the amplitude, the delay, the frequency and the phase of both LOS and MP signals. As this study considers pilot channel or Data wipe-off, the complex representation of the low pass signal is represented as follows; where: N 1 s(t) = A l. C(t τ l ) exp (jφ l (t)) + n(t) l= φ l (t) = φ l () + π f l t (u)du with: - l represents the l th path (index l = represents the DP). - A l = P l is the amplitude of the received l th path signal (P l is its power). - C(t) represents the PRN Code related to the considered satellite - τ l, φ l represent the code delay and the carrier phase of the l th path received signal. - f l (. ) represents the signal frequency of the l th path. - n(t) represents the additive white Gaussian noise. A tracking module consists of a matched filter which needs to correlate the received signal, sampled at the frequency F s = 1/T s, with a locally generated replica. A conventional integrate-and-dump block is used to provide the matched filter output. The coherent correlation, over the duration T k, leads to the following in-phase (I) and quadrature-phase (Q) representation, k which is obtained at the time t k = m= T m.

3 N 1 I k P l R δτ l,k sin πδf l,k T k sin πδf l,k T s cos δφ l,k + n i [k] l= N 1 Q k P l R δτ l,k sin πδf l,k T k sin πδf l,k T s sin δφ l,k + n q [k] l= The parameters δτ l,k, δf l,k and δφ l,k represent respectively, for each path, the mean errors (i.e. the difference between the received signal parameter and the parameter of the locally generated replica) of the code delay, the signal frequency and the carrier phase. R(. ) denotes the spreading code autocorrelation function. The noises n i and n q are assumed to be independent white Gaussian processes with zero mean. Afterwards we ll adopt the following expression to define the correlator output: u z (k) = I k + jq k = N 1 f A k,l δf l,k R δτ l,k exp jδφ l,k + n k l= (1) Figure 1: Vector tracking architecture In presence of MP a further consideration is the benefit that flows from the knowledge of the navigation solution achieved by the EKF algorithm for detecting an abnormal behaviour inside a tracking module and to switch this module in an appropriate mode. This proposed adaptive tracking loop architecture is presented in Figure. In this expression, the amplitude A k,l represents the amplitude of the l th path signal. This amplitude depends on the power of the l th path incoming signal, but also of its frequency error versus the coherent integration time (δf l,k T k ). A k,l = P l sin πδf l,k T k sin πδf l,k T s () At this point we would like to clearly emphasize that a signal with a frequency error which is not much lower than the inverse of the integration time is strongly attenuated. This property will be used to mitigate out of band MP signals. B. System Architecture Usually tracking loops are used to perform the joint time delay and frequency estimation which are used to generate the local replica. In the frame of this study, a vector-based architecture is considered as in Figure 1 in which each channel of the receiver tracks the incoming signal of one satellite by taking advantage of the global navigation solution [4]. The core of the architecture is the navigator which estimates the vehicle position and velocity. It is based on an extended Kalman filter (EKF) which uses as observations the PR (or the DR) provided at the outputs of the tracking channels. In a very constrained environment, or for high dynamic vehicle, complementary systems such as inertial sensors could also be used. The primary advantage of this approach is that it provides high-sensitivity loops for improving the GNSS receiver availability. Figure : Architecture of the proposed adaptive tracking module The advantages of this adaptive architecture are summarized below: 1. The use of an FFT-based discriminator block allows us to take advantage of the knowledge of the vehicle velocity, to detect the presence of the LOS signal and of non-coherent MP. Moreover, frequency characterization of MP signal makes easy the integration time and the tracking loop bandwidth selection.. Monitoring the IQ outputs allows the control stage to validate the selected value of the integration time. 3. The use of a multiple discriminator allows us to detect coherent MP. Tests are carried out to select the most appropriate discriminator output or to discard unreliable delay estimate.

4 III. DESCRIPTION OF THE MP CHANNEL MODEL Different models were proposed for modeling MP channel as in [5]. In the context of this project, assessment of the improvement afforded by the proposed techniques will be regarded in very simple scenarios. These scenarios which consider DP in presence of one MP are illustrated in Figure 3. In this context the expression of the coherent correlator output, which is deduced from equation (1), is: u z (k) = A k, δf,k R δτ,k exp jδφ,k + A k,1 δf 1,k R δτ 1,k exp jδφ 1,k + n k f (3) with: δφ,k δφ,k 1 π δf,k (T k T k 1 ) δφ 1,k δφ 1,k 1 π δf 1,k (T k T k 1 ) (4) (a) (b) Figure 3: Two path signals (a) at different frequencies and (b) at the same frequency. Assuming that slow fading channel are considered, MP can be classified in two categories depending on the value of the Doppler frequency and are further characterized as coherent or non-coherent MP. In the case (a), when the vehicle moves with an inclination to the reflecting surface, frequencies of DP and MP are assumed to be different. In the case (b), when the vehicle is stationary or moves parallel to the reflecting surface, frequencies of DP and MP are assumed to be equal. The following expression is used for describing the impulse response of the channel in presence of one MP. h c (t) = a (t) δ t τ (t) exp{jδφ (t)} + a 1 (t) δ t τ 1 (t) exp{jδφ 1 (t)} where: - a and a 1 represent respectively the DP and MP attenuation. - τ and τ 1 represent respectively the DP and MP propagation delay. - φ and φ 1 represent respectively the DP and MP carrier phase. t φ (t) = φ () + π f (u) t du φ 1 (t) = φ 1 () + π f 1 (u) du We define two time domains, D 1 and D, depending on the vehicle environment. Over the domain D 1 where the vehicle is stationary or moves (as shown Figure 3-b) the MP signal is called coherent. On the complementary domain D the MP signal is called non-coherent. D 1 t f 1 (t) = f (t) D t f 1 (t) f (t) In this expression, δf,k and δf 1,k denote respectively the frequency error related to the DP and to the MP. δf,k = f,k f k δf 1,k = f 1,k f k where f,k, f 1,k represent, over the k th integration, the mean value of the incoming DP and MP signal frequencies, and f k an estimation of the DP frequency provided inside the receiver by the considered the tracking module. In the framework on this study specific processing will be proposed depending on the vehicle environment. Over the domain D, while a noncoherent MP is considered (f,k f 1,k ), DP and MP decorrelation is possible in the frequency domain. On the contrary, over the domain D 1 (f,k = f 1,k ), MP decorrelation requires time domain representation. These two situations and combinations of these will be considered for performance evaluation. IV. ADAPTIVE FLL-ASSISTED PLL In the frame of this paper an FLL aid is combined with the navigator aid to provide a relevant estimate of the incoming signal frequency. Indeed the FLL aid requires the LOS signal to be available. Similarly the navigator can be contaminated in poor GNSS environment. The architecture of the proposed tracking loop is described in Figure 4. It is based on a first order FLL assisting a second order PLL as in [3]. Figure 4: The proposed adaptive FLL-assisted PLL tracking loop. The main originality of the proposed approach is the use of an FFT-based discriminator (replacing the

5 conventional discriminator of [3]) for the FLL discriminator. Precisely, the purposed discriminator is based on 18 samples FFT (N FFT = 18) computed from the output of the correlator whose correlation time is equal to T corr = 1ms. Note that the corresponding frequency resolution is: 4. A module is implemented for monitoring delay discriminator outputs. f = 1 1 =.7813 Hz. N FFT T corr This FFT-based discriminator (which ran at the FLL sampling frequency, i.e., at the inverse of the coherent integration time ( T k = λt corr where λ is a whole number, λ 1), is used to tackle non-coherent MP. In the presence of one MP, we can define the FFT input samples under the hypothesis that DP and MP frequency errors are constant in the spectrum analysis interval (in practice slow variations of signal frequencies and amplitudes are accepted). According to (3) and (4) the samples that are used to compute the k FFT at the instant t k = m= T m are defined as u z (k, l) = A k, R δτ,k 17+l exp jδφ,k 17 exp {jπδf lt corr } + A k,1 R δτ 1,k 17+l exp jδφ 1,k 17 exp {jπδf 1 lt corr } + n k f for l =,, 17. Note that δτ,k 17+l and δτ 1,k 17+l are the LOS and the MP delay errors at the instant t k (17 l)t corr. Similarly δφ,k 17 and δφ 1,k 17 denote respectively the phase of the LOS carrier and of the MP carrier at the time t k 17T corr. In the domain D, as the MP frequency is different from the DP frequency, DP and MP decorrelation can be performed in the frequency domain, each signal yielding a peak in the FFT modulus. This adaptive architecture allows us to monitor the incoming signal in the frequency domain, to control the integration time, and to switch the module in the relevant configuration. Mechanisms benefitting from this MP mitigation design are described in section VI. V. ADAPTIVE DLL The main objective of the adaptive DLL is to estimate accurately the LOS code delay τ in the presence of MP. A conventional PLL-assisted DLL is designed where a first order DLL with noise loop bandwidth reduction, is considered. The proposed adaptive DLL architecture is displayed in Figure 5. The major innovative features of this DLL are: 1. An adaptive coherent discriminator based on multiple correlators allows us to adjust its time resolution by adjusting the chip spacing (CS).. A non-coherent early minus late (EML) discriminator can also be selected. 3. The coherent integration time can be modified. Figure 5: The proposed adaptive DLL architecture. An important innovation is the use of an adaptive discriminator. It is obtained from the outputs of a bank of 9 coherent correlators which make possible the design of a conventional EML correlator and of two discriminators that differ from the value of the CS. The output of a correlator in presence of one coherent MP (non-coherent MP is mitigated through the coherent integration) is u z (k, p) A k, R δτ,k + p exp{jδφ } + A k,1 R δτ 1,k + f p exp{j(δφ + δφ 1 )} + n k (5) with p = for the prompt correlator, p { 5, 4,, 1} for the late correlators and p { +1, +, +4, + 5} for the early correlators. Here, the parameter is set to =.1T c, where T c is the code chip duration. The phase error δφ represents the difference between the DP phase and the estimated phase provided by the PLL (δφ = φ φ ), whereas the phase difference δφ 1 is the coherent MP phase with respect to the DP phase (δφ 1 = φ 1 φ ). In the domain D 1, as the MP frequency is equal to the DP frequency the phase difference δφ 1 is constant. The discriminators are designed from the I-branch of the correlators I(k, p) = A k, R δτ,k + p cos (δφ ) + A k,1 R δτ 1,k + p cos(δφ + δφ 1 ) + R n k f where R{z} denotes the real part of the complex number z. The discriminator outputs are finally obtained as follows Disc #1 = I(k, 1) I(k, 1) 1 I(k, ) I(k, ) Disc # = I(k, ) I(k, ) 1 I(k, 4) I(k, 4) Disc EML = I(k, 5) I(k, 5)

6 Moreover, in order to face a loss-lock of the tracking module in degraded environment, a classical tracking loop that uses a non-coherent EML discriminator is available. The error envelop of these discriminators, as well as that of the normalized EML discriminator are shown in Figure 6. accuracy of this aid. The PR and the DR provided by this module are discarded.. On the contrary, in the presence of LOS signal the FLL aid is validated and the PLL is closed. 3. The appearance of multiple spectral lines allows the monitoring module to detect non-coherent MP. To mitigate this MP, the integration time is set to the inverse of the lowest MP frequency (Equation () shows that a signal is strongly attenuated if its frequency is not much lower than the inverse of the integration time). The loop noise bandwidth (B n ) is adjusted depending on this integration time (B n T int 1). Figure 6 : MP error envelopes (MEE). VI. MONITORING & CONTROLLING TRACKING LOOPS The proposed adaptive architecture needs to define some monitoring indicators for selecting the relevant operating mode of the two tracking loops (and setting efficiently the different parameters). A. Control of the FLL-assisted PLL tracking loop. By monitoring the FFT output and the statistic of the DP frequency obtained from the LOS velocity, the control stage is able to configure the adaptive PLL in the most appropriate mode. The LOS velocity is estimated by the navigator by using an EKF. Therefore we assume that the probability density function (pdf) of the signal estimated frequency is a Gaussian pdf with a variance σ f. In nominal conditions, as the navigator is used for providing a frequency aid, the pdf of the remaining frequency error (measured by the FLL) is p f (f) = 1 f exp σ f π σ f An example of FFT output superimposed with the pdf of the remaining LOS frequency is shown in Figure 7. The peak with the lowest frequency is associated with the LOS signal (or with a coherent MP that can only be detected in the time domain). The presence of multiple peaks indicates a high probability of having non-coherent MP. Based on the results of Figure 7, we proposed the following monitoring strategy: 1. In the absence of spectral line with a frequency lower than 1.σ f, or higher than 1 1.σ T f, the corr monitoring module indicates that the LOS signal is not available. The tracking module is then set to a degraded configuration based on the navigator frequency aid. In this mode the error on the estimated phase will drift depending on the Figure 7: Magnitude of the FFT obtained from 18 samples of the correlator output. Moreover, in order to verify that the PLL is operating properly (i.e., the carrier frequency has been estimated correctly), a specific test is carried out. A conventional frequency discriminator is used as indicator. It measures the frequency error over the integration time, allowing the monitoring stage to verify that the PLL is tracking coherently the frequency of the LOS signal. The expression of the frequency discriminator is related to the IQ outputs of the prompt correlator [3] πε(δf)t int = ATAN(cross, dot) with dot = I k 1 I k + Q k 1 Q k and cross = I k 1 Q k + I k Q k 1. In these expressions I k and Q k denote the I and Q branches of the prompt correlator, at the current time t k. According to (5), I k = R{u z (k, ) } and Q k = I{u z (k, ) } (R{z} and I{z} denote the real part and the imaginary part of the complex number z), whereas I k 1 and Q k 1 are the outputs at the end of the previous integration (i.e., at t k 1 = t k T int ). The current integration time is validated under the hypothesis H 1, which corresponds to a locked PLL. The corresponding decision rule is given by ε θ = πε(δf)t int < H 1 α rad where α is a detection threshold which depends on the desired probability of false alarm (PFA). Under the

7 hypothesis H 1, the distribution of the coherent integrator output is p uz (I, Q) = 1 C) exp (I + Q πσ n σ n σ n where σ n denotes the noise power at both I and Q branches. This distribution is represented in Figure 9 by a histogram of the correlator output for the I and Q branches (here the C/N ratio of the incoming signal is set to 44dBHz and the integration time is set to 1ms). Figure 8: Histogram of the correlator outputs. By considering high values of the signal to noise ratio ( CT int 1), a linearization around zero of the N atan function is possible. The additive noise that is added to the signal ε θ is assumed to be Gaussian. Its standard deviation is approximated by Figure 9: Complex representation of the correlator output in presence of one coherent MP. B. DLL Control Separating the LOS signal from the MP signal requires an estimation of the amplitude, the phase and the propagation delay of each component of the resulting signal (LOS + MP) [6]. However, this method exhibits a high computational complexity. We propose here a relevant control of the adaptive DLL addressing the following issues: 1. Non-coherent MP is mitigated by a coherent integration, even if the phase estimated by the PLL is the phase of a combination between the LOS and the coherent MP signals.. An adaptive coherent discriminator based on the use of multiple correlators allows the control stage to adjust the value of the chip spacing (CS) in order to reduce the impact of MP and to improve the accuracy of the code delay estimator. It also facilitates the DLL re-lock when the MP disappears. 3. PR measurements are discarded if an unbiased discriminator output is not available. and the threshold is set to σ εθ = σ n S α = 3 σ n S = 3 N CT int We would like to outline that the so-designed PLL, while it achieves non coherent MP mitigation, is affected by a coherent MP. In that case the PLL is able to track the LOS signal frequency whereas the LOS phase is not correctly estimated. A complex representation of the IQ correlator output is shown in Figure 9. The left plot illustrates that the LOS phase is correctly estimated in the absence of coherent MP (The LOS signal is projected onto the I branch). When a coherent MP occurs (middle plot) the PLL will track the resulting signal (right plot) that combines coherently the LOS and MP signals, providing an estimate of the phase of the composite signal (LOS+MP signal). Figure 1: Linear model of DLL architecture The DLL is based on a scheme illustrated in Figure 1 where the adaptive correlator consists of 3 coherent discriminators and a non-coherent discriminator (see Figure 5). In nominal conditions, a coherent EML discriminator is used. A test statistic, which addresses the output of each discriminator, is defined. As a frequency-aided DLL is used the power of the error ε τ should remain lower than a threshold depending on the carrier to noise density ratio (C/N ). We assume that this error is distributed according to a Gaussian distribution with a variance σ ετ. The variance of the error ε τ can be computed as follows σ ετ = E{(τ τ ) } = B τ S τ + B φ S φ where S τ and S φ represent the power spectrum density of the code delay noise in cycle /Hz and of the carrier

8 phase noise in rad /Hz (these noises are assumed to be white noises). In this expression B τ and B φ are the noise bandwidth related to the transfer function ε τ /τ and ε τ /φ. The noise bandwidth B φ is deduced from the PLL PLL noise loop bandwidth B n as follows ε τ φ (z) = ε τ (z) f aid f f aid f φ (z) φ φ (z) and B φ = 4π 154 B n PLL. = T int 1 z 1 1 π 1 z 1 φ f L1 T c T int φ (z) = π 154 φ φ (z) In nominal condition, when the phase loop is tracking the LOS signal, the power of the error ε τ related to the carrier phase noise can be neglected. σ ετ = B τ S τ + B φ S φ B τ S τ According to [7], the variance of the error ε τ depends on the used correlator. We use the index i to refer to the discriminator (i = 1,, 3 denote respectively the #1, #, EML discriminators). For high C/N this variance is expressed as σ ετ (i) = d(i) C (6) N T int with d(1) =.1 for the 1 discriminator, d() =. for the discriminator, d(3) = 1 for the EML discriminator. We propose to detect coherent MP or DP fading by comparing the time delay error provided by each of the discriminator to an appropriate threshold. We consider the two following hypotheses H : Multipath absence H 1 : Multipath presence In nominal condition the coherent EML discriminator is used. When its output becomes sensitive to a multipath (i.e.,t k,3 > υ(3)) the narrowest 1 discriminator (or the if the 1 does not satisfies the test statistic) is selected as the other coherent discriminators are contaminated (i.e., T k, > υ(), T k,3 > υ(3)). Moreover the location provided by the navigator is used to verify the reliability of the estimated propagation delay. In case of corrupted estimation, the non-coherent EML discriminator is used instead. In such situation the PR estimate (that is computed from the estimated propagation delay) is discarded. The frequency estimate (which is that of the LOS signal) is used as DR measurement. Finally it is interesting to note that the DLL is switched back in its nominal operating mode as soon as MP effects are negligible. The decision is taken depending on the value of the estimated parameter τ, by using the knowledge of the vehicle location. VII. SIMULATION RESULTS AND ANALYSIS The signal simulator is operated by generating samples of the baseband signal. It is based on a predetermined path associated with the vehicle acceleration and velocity. In any point of the path, a MP can be introduced and removed by specifying the exact instant of occurrence and disappearance. Moreover its parameters can be tailored in term of amplitude, delay and Doppler frequency (all relative to the DP). Finally a white Gaussian noise is added to imitate the effect of propagation channel. The composite generated signal is inserted into the tracking loop for further evaluation. A classical tracking loop is operating in parallel with the one that is being investigated for performance comparison. Figure 11 below illustrates the simulation methodology of this project. and the following test statistic T k,i = 1 N s ε τ (i, j) k j=k N s where ε τ (i, j) is the i th discriminator output at the time t j and N s denotes the number of output samples that is chosen in order to ensure a bias-variance tradeoff. The corresponding decision rule is given by T k,i H < > H 1 υ(i) (7) where υ(i) is a detection threshold that is deduced from (6), i.e., d(i) υ(i) =.5 (8) N C s N T int Figure 11: Simulation methodology. The simulation is conducted for three different scenarios with different sets of MP parameters. Scenarios 1 and study respectively the impact of noncoherent and coherent MP on the estimated frequency and delay. The third scenario is devoted to the combination of both types of MP. The results are observed over a time frame which lasts 35s. At the beginning of this time frame all the

9 loops are operating in a tracking mode. Note that the simulation time instant is chosen when the vehicle is at a constant speed of 17.5 m/s (without IMU the navigator is not able to provide aid which satisfies requirements for high dynamic of the vehicle) while the C/N ratio is set to 44dBHz. The amplitude of each MP is adjusted to half the DP amplitude. Note that the values of MP parameters are displayed in Table 1 whereas the different simulation scenarios are summarized in Table. For each scenario, the frequency estimation error (Δf = f f ) and delay estimation errors (Δτ = τ τ ) are computed for both classical and adaptive approaches. The mean μ and variance σ of these errors are also determined to provide performance assessment. The first 5s duration for each scenario is necessary to ensure that the PLL and DLL is correctly locked. Type of MP Amplitude ratio relative to DP Doppler frequency, Δf d [Hz] Code delay, τ [chips] Code phase, φ [rad] Table 1: MP parameters. MP #1 MP # MP #3 Non- Non- Coherent Coherent Coherent π π 4 π 4 4 Table : Scenario Parameters. Time frame [s] Scenario #1 No MP MP#1+MP# No MP Scenario # No MP No MP MP#3 Scenario #3 No MP MP#1+MP# All MP In scenario #1, two non-coherent MP with different Doppler frequencies are introduced at the same time. Figure 1 shows that the error of the estimated frequency increases in presence of MP, while the DLL performance degrades. More precisely, the mean and variance of the estimation frequency error using the classical receiver increase to μ = Hz and σ = Hz. In the same conditions, the adaptive tracking loop leads to μ =.Hz and σ =.33Hz showing that MP can be mitigated significantly. It is clear that the proposed approach which is based on an increase of the integration time T int and a decrease of the PLL noise bandwidth B n PLL allows us to reduce the impact of the white noise and to mitigate out of band multipath. f [Hz] τ [chips] 1-1 Frequency Estimation Error x Delay Estimation Error Figure 1: Estimation errors for frequency (above) and delay (below) using a classical tracking loop (Scenario #1). f [Hz] τ [chips] 1 Frequency Estimation Error x Delay Estimation Error Figure 13: Estimation errors for frequency (above) and delay (below) using the proposed adaptive tracking loop (Scenario #1). For scenario #, the impact of coherent MP is being evaluated when only one MP is introduced during the time period sec of the simulation. The resulting errors for the estimated frequency and delay are displayed in Figure 14 when a non-coherent EML discriminator is used. While the frequency error remains centered around zero, the estimated delay is strongly affected (we observe an error that increases with time depending on the response time of the DLL). On the other hand, the carrier phase discriminator output shown in Figure 15 indicates a phase transient response of the PLL which then achieves to track the composite signal, i.e., the signal which combines the DP and MP components (see the red plot at t=175s). Once MP is detected, the 1 discriminator is selected and its output becomes therefore centered around zero (see Figure 16 which represents the test statistics for N s = 1,T Int = 1 ms and the threshold value υ). On the contrary, the other discriminators provide an output that is contaminated until the disappearance of the coherent

10 multipath as shown in the same Figure 16. Note that, for this particular simulation, the duration is extended for 5s to show that the disappearance of the coherent multipath can be detected by monitoring discriminator outputs. Indeed the test statistic related to the different discriminators goes back to zero at this instant. τ [chips] f [Hz] 1 Frequency Estimation Error Delay Estimation Error Figure 14: Estimation errors for frequency (above) and delay (below) using a classical approach (Scenario #). Carr Error, φ [rad] Carrier Discriminator Output Figure 15: Carrier discriminator outputs zoom from 174s to 176s. Test Statistic, T k,i In scenario #3, two non-coherent MP are introduced at the beginning of the simulation (at time t=16s) and an additional coherent MP appears at time instant t=175s. Both frequency and delay estimators obtained using the classical tracking loop suffer from this severe MP conditions as shown in Figure 17 and 18. It is interesting to observe that the variance of the frequency estimation error decreases in the presence of additional MP from Hz to 4.798Hz. Indeed, here the coherent MP is instructive, and thus induces an increased power for the composite signal. Note also that the delay estimation error is increasing in time due to the additional coherent MP. The effects of MP are clearly mitigated with the proposed adaptive tracking strategy as shown in Figure 19 and. At the instant t=16 sec, non-coherent multipath detection allows the control stage to adapt the integration time depending of the MP frequency which is determined from a FFTbased frequency analysis. At the time t=175 sec a coherent multipath is detected by performing a test statistic which addresses the used coherent EML discriminator and the 1 discriminator is selected. Moreover, Figure 1 shows that the frequency error resulted from the adaptive tracking loop are mostly inside the detection threshold. This indicates that the PLL is able to track correctly the DP during almost the whole simulation. Delay [Chips] Frequency [Hz] Signal Freq vs. Estimate Freq Signal Delay vs. Estimate Delay , d = Figure 17: Signal delay vs. estimation delay using classical approach (Scenario #3)., d =. coh EML, d = Figure 16: Test Statistic for DLL discriminator.

11 f [Hz] 1-1 Frequency Estimation Error.4.3. Frequency Discriminator Output α, detection threshold τ [chips] Delay Estimation Error πε(δf)t int [rad] Figure 18: Estimation errors for frequency (above) and delay (below) using a classical approach (Scenario #3). Delay [Chips] τ [chips] Frequency [Hz] Signal Freq vs. Estimate Freq Signal Delay vs. Estimate Delay Figure 19: Signal delay vs. estimation delay using adaptive approach (Scenario #3). f [Hz] Frequency Estimation Error Delay Estimation Error Figure : Estimation errors for frequency (above) and delay (below) using an adaptive approach (Scenario #3). Figure 1: Frequency discriminator output bounded by detection threshold. VIII. CONCLUSION AND FUTURE WORK This paper presented adaptive GNSS signal tracking techniques using a simple approach for tackling multipath in urban environment. These techniques were assessed through simulations by considering different scenarios based on a simplified MP channel model. These simulations showed that efficient processing can be performed by monitoring a set of indicators controlling the knowledge of the receiver antenna environment and the vehicle state. Thus this paper allows us, through an unpretentious approach, to exhibit some principles which can be used to design a robust and advanced receiver that will be able to tackle multipath in urban environment. An important conclusion resulting from this study is that non coherent MP mitigation can be achieved in the frequency domain by taking advantage of a FFT-based frequency discriminator. Conversely, coherent MP can be handled in the time domain by using multiple discriminators. The good results obtained with the proposed receiver are mainly due to the possibility of performing long coherent integration. In practice such integration needs to track the phase of the carrier signal. An important effort should be made to improve the robustness of the PLL. Interesting ideas are the use of a very stable receiver clock, the implementation of an estimator which uses efficiently the knowledge of the vehicle velocity (that can be improved by integrating an IMU to the navigator), and the development of an observation model associated with carrier phase measurements. Future investigations should include the application of our approach to a deeply integrated GNSS/INS navigation system based on a decentralized architecture. In particular, we will study a Bayesian estimator able to provide a reliable estimate of the signal parameters in presence of multipath. Particularly a major effort will be made to improve the estimation of the signal carrier phase.

12 This adaptive estimator will use the navigation solution as a command in order to reduce the covariance of the process noise. Investigating a model which fits the measurements of the propagation delay in presence of coherent multipath is also an interesting prospect. ACKNOWLEDGMENT The authors would like to thank the Ministry of Higher Education of Malaysia, National Defense University of Malaysia and DGA for providing the financial support in term of scholarship. REFERENCES [1] N. Sokhandan, A. Broumandan, J. T. Curran and G. Lachapelle, "High Resolution Delay Estimation for Urban GNSS Vehicular Navigation," in Proceedings of the 5th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 1), Nashville, TN, 1. [] K. Dragunas and K. Borre, "Multipath Mitigation Based on Deconvolution," Journal of Global Positioning System 11, vol. 1, no. 1, pp , 11. [3] P. W. Ward, J. W. Betz and C. J. Hegarty, "Chapter 5: Satellite Signal Acquisition, Tracking and Data Demodulation," in Understanding GPS: Principles and Applications, nd ed., E. D. Kaplan, Ed., Norwood, MA, Artech House, 6, pp [4] M. Petovello and G. Lachapelle, "Comparison of Vector-Based Software Receiver Implementations with Application to Ultra-Tight GPS/INS Integration," in Proceedings of the 19th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 6), Fort Worth, 6. [5] A. Lehner and A. Steingass, "A Novel Channel Model for Land Mobile Satellite Navigation," in 18th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 5), Long Beach, 5. [6] M. Spangenberg, V. Heiries, A. Giremus and V. Calmettes, "Multi-Channel Extended Kalman Filter for Tracking BOC modulated signals in the presence of multipath," in 18th International Technical Meeting of the Satellite Division of the Institute of Navigation, Long Beach, 5. [7] G. A. McGraw and M. S. Braasch, "Multipath Mitigation Using Gated and High Resolution Correlator Concepts," in Proceedings of the National Technical Meeting of the Satellite Division of the Institute of Navigation, San Diego, 1999.