Code Tracking Loop Research Articles

Simulation of range code tracking loop for multipath mitigation in NavIC receiver

Abstract The Operational Navigation with Indian Constellation (NavIC) comprises seven satellites in the orbit, including three in geostationary orbit (GEO) and four in geosynchronous orbit (GSO). NavIC provides both Standard Positioning Service and Restricted Service, using L5 (1176.45 MHz) and S1 (2492.028 MHz) frequencies, with coverage extending 1500 km around the mainland of India. In an urban canyon, multipath interference severely reduces the precision and reliability of NavIC positioning. Many current multipath mitigation techniques often exhibit high computational requirements or reliance on external assistance. In this paper, a ranging code tracking loop is proposed that can sustain either a late or early branch in contrast to the Narrow-Spacing (NS) correlation technique for mitigating multipath for NavIC receiver. The design of proposed code tracking loop is based on steepest descent algorithm. The findings demonstrate that, in terms of calculation time and code multipath mitigation, the suggested technique performs better than both Multipath Estimated Delay Locked Loop (MEDL) and NS correlation. The proposed method produces less than 0.016 chips for the tracking error Standard Deviation (STD). In addition, the recommended method takes 24 % less computation time.

Robust GNSS Positioning Using Unbiased Finite Impulse Response Filter

In a typical GNSS receiver, pseudorange and pseudorange rate measurements are generated through the code and carrier tracking loops, respectively. These measurements are then employed to calculate the user’s position and velocity (PV) solutions, which is typically achieved using a Kalman filter (KF) or the least squares (LS) algorithm. However, the LS method only uses the current observation without error analysis. The positioning result is greatly affected by the errors in the observed data. In KF, by using an iterative approach that combines predictions and measurements of PV information, more accurate estimates can be obtained because the PV information is time-correlated. Meanwhile, its optimal estimate requires that both the model and noise statistics are exactly known. Otherwise, achieving optimality cannot be guaranteed. To address this issue, this paper proposes and implements a novel GNSS solution method based on an unbiased finite impulse response (UFIR) filter. Two different field tests were conducted. The position results of UFIR are compared with those from the LS and KF methods, and the horizon positioning mean error is improved by 44% and 29%, respectively, which highlights its efficacy. The method offers two primary benefits: it is robust to noise uncertainty, and it leverages historical data within the UFIR framework to provide a more accurate estimate of the current state.

Overview of multipath mitigation technology in global navigation satellite system

The global navigation satellite system is a high-precision radio navigation system based on artificial satellites. Among the factors affecting the positioning accuracy of the navigation satellite system, the multipath signal is the most significant and challenging to eliminate. Furthermore, the multipath environment of the receiver is also becoming more complex, and it seriously threatens the measurement accuracy and stability of the receiver. The multipath mitigation technology is also continuously improved and developed in practical application. This paper firstly introduces the concept and characteristics of multipath signals, and summarizes the influence of multipath signals on navigation satellite systems from two aspects of code tracking loop and carrier tracking loop. Furthermore, the existing multipath mitigation technology is summarized in four stages: signal system design, antenna design, baseband signal processing, and navigation data processing. Finally, according to the summary of the existing technology and the new demand, the future development direction of multipath suppression technology is prospected.

A multipath mitigation algorithm for GNSS signals based on the steepest descent approach

Multipath interference seriously degrades the performance of Global Navigation Satellite System (GNSS) positioning in an urban canyon. Most current multipath mitigation algorithms suffer from heavy computational load or need external assistance. We propose a multipath mitigation algorithm based on the steepest descent approach, which has the merits of less computational load and no need for external aid. A new ranging code tracking loop is designed based on the steepest descent method, which can save an early branch or a late branch compared with the narrow-spacing correlation method. The power of the Non-Line-of-Sight (NLOS) signal is weaker than that of the Line-of-Sight (LOS) signal when the LOS signal is not obstructed and with a relatively high Carrier Noise Ratio (CNR). The peak position in the X-axis of the ranging code autocorrelation function does not move with the NLOS interference. Meanwhile, the cost function is designed according to this phenomenon. The results demonstrate that the proposed algorithm outperforms the narrow-spacing correlation and the Multipath Estimated Delay Locked Loop (MEDLL) in terms of the code multipath mitigation and computation time. The Standard Deviation (STD) of the tracking error with the proposed algorithm is less than 0.016 chips. Moreover, the computation time of the proposed algorithm in a software defined receiver is shortened by 24.21% compared with the narrow-spacing correlation.

GNSS induced spoofing simulation based on path planning

Global navigation satellite Systems (GNSS) are highly susceptible to various interferences because of their inherent vulnerability. In these interferences, induced spoofing is very difficult to be detected because it can gradually drag off the tracking points without unlocking the tracking loops of the attacked receiver and cause the victim to obtain a wrong position and/or time information. Furthermore, it is also very difficult to generate induced spoofing data, including simulation data and real data, to evaluate various induced spoofing detection and suppression algorithms. Existing generation algorithms need to precisely control and adjust many parameters of GNSS simulation software even for simulation data. To address this problem, this study proposes a GNSS-induced spoofing simulation algorithm based on path planning. First, through given planned paths, the proposed algorithm independently generates the authentic and spoofing signals without changing the parameters of GNSS simulation software. After that, the induced spoofing simulation data are synthesised by only adjusting the powers of authentic and spoofing signals. The effectiveness of the proposed algorithm is verified by the positioning solutions and the correlation function outputs of the code and carrier tracking loops.

A probabilistic model for on-line estimation of the GNSS carrier-to-noise ratio

This article is dedicated to the estimation of the GNSS signal carrier-to-noise ratio using the in-phase component of the signals as observations. In a GNSS receiver, it is the statistic of the correlation provided by the code tracking loop that is used to estimate the carrier-to-noise ratio. In fact, carrier-to-noise estimation is used to monitor the performance of GNSS receivers and the quality of the received signals. In this article, we aim at high rate carrier-to-noise estimation, namely the code repetition rate (e.g. 1ms for GPS C/A), in order to maximize the time resolution of carrier-to-noise observations. We show that in a 1-bit quantization receiver, the in-phase component of the signal can provide a direct observation of the signal amplitude, and therefore of the carrier-to-noise ratio. However, the model that links the 1ms rate observations of the in-phase component with the signal amplitude is non-linear. The non-linear expression that links the maximum value of the in-phase correlation component to the signal amplitude is derived. In order to estimate the time varying amplitudes of the signals, we propose an Extended Kalman Filter to reverse the non-linear expression with the noisy observations of correlation provided by the tracking loop. The proposed model and filter inversion method are assessed on synthetic and real data, while investigating the effect of the cross-correlation contribution of the visible satellites on the estimations. We show using real data that, for a 1-bit quantization receiver, the proposed estimator can achieve the same accuracy as a widely known commercial GNSS receiver with a much higher data rate. We also show that the proposed approach can cope with abrupt changes in the observations compared to a classical C/N0 estimate.

A subspace-based code tracking loop design for GPS multi-antenna receiver in multipath environment

Global Navigation Satellites Systems have been greatly developed in recent years, but receivers usually suffer the undesired measurement bias errors caused by multipath incidence in an urban area. We propose an effective subspace-based estimator cooperating with the conventional delay-locked loop (DLL) for Global Positioning System L1 C/A Signal. With the help of the multi-antenna, the incident rays could be distinguished in space. A forward and backward space spatial smooth technique is then taken to solve the coherent problem in signal subspace estimation. By using the structure of the receiving array, a subspace rotation invariance can be built, and the angles of arrival and relative delays of incident rays could be estimated jointly. After combining the estimates from DLL and subspace-based estimators, we can enhance the strength of the line-of-sight ray and achieve a modified delay tracking output without multipath bias effectively. Simulation results prove that compared with the existing methods, such as the narrow early-minus-late and the multipath estimating delay lock loop, the proposed method has the best multipath mitigation in the delay estimation.

Zero‐bias elimination with selective non‐commensurate sampling for PN code tracking

Zero bias is the main source of error in high-precision applications based on pseudo-noise (PN) ranging. This study proposes a selective non-commensurate sampling frequency design method applied to the digital code-tracking loop which can effectively suppress the code-phase zero bias caused by incomplete sampling of the spread spectrum signal. The maximum (MAX) and standard deviation (STD) of the zero bias independent of code and the initial phase are used to design the sampling frequency. The code correlation reference waveform is utilised to establish a statistical analysis model of the digital discriminator zero bias. Analytical expressions of the zero-bias MAX and STD are derived. The performance of the proposed method is assessed as per code Doppler, binary offset modulation, and thermal noise. Fibre optic time synchronisation equipment is used to determine the feasibility of eliminating PN code-tracking zero bias based on selective non-commensurate sampling.

Implementation and Analysis of Signal Tracking Loops for Software Defined GPS Receiver

Software defined GPS receiver has been developing because it can be processed advanced signal algorithms and also developed for precise navigation. Signal processing modules such as signal acquisition, signal tracking and navigation demodulation are implemented in software to estimate the receiver position, velocity and time (PVT). Signal tracking is important task in order to estimate the receiver’s and satellites position by demodulating navigation bits which are obtained from this. In this paper, implementation and analysis of signal tracking loop is mainly described and there are two main tracking loop as carrier and code tracking loop on GPS L1 signal. Delay Locked Loop (DLL) is to track code delay or code phase of GPS Coarse or Acquisition (C/A) code while Phase Locked Loop (PLL) is used to track GPS L1 carrier frequency as well as Doppler Frequency Shift. The implementation of DLL and PLL, and analyses of parameters which effects on navigation bits is also briefly discussed. The results confirm the analysis of signal tracking loops for software defined GPS receiver based on the experimental studies. The real time applications for software defined GPS receiver are very important to implement the navigation system in future because of the effective analyses on theoretical consideration.

A model for assessing the impact of linear and nonlinear distortions on a GNSS receiver

The tracking performance of a global navigation satellite system (GNSS) receiver is altered by signal distortions of different kinds, ranging from transmitter and receiver imperfections to various forms of channel impairments. Accurate modeling of the receiver performance in the presence of signal distortions allows to improve GNSS-based positioning, tighten error bounds, and thus enhance the integrity and the availability of the GNSS services. We present a model for the code-tracking loop performance of a GNSS receiver when the GNSS signal undergoes an arbitrary cascade of nonlinear and linear distortions. The impact of the distortions on the pseudorange estimation is analyzed by deriving closed-form expressions for the bias and variance of the tracking error. These analytical expressions are based on the well-known open-loop linearized delay-locked loop model. The validation is then performed using a GNSS software receiver that evaluates the tracking error numerically.

Optimal regenerative PN code tracking based on non‐commensurate sampling and double‐loop structure

Gold codes are widely used for pseudo-noise (PN) ranging, and non-commensurate sampling is an effective solution to improving the tracking performance of digital code tracking loops. However, the sequence transition density of gold codes is low, which limits the achievable ranging accuracy. Here, the authors present a non-commensurate sampling and double-loop-based regenerative PN code tracking approach. With this approach, the tracking of the original regenerative code is equivalent to that of its clock component, and the sequence transition density is maximised. Thus, the tracking error is apparently reduced and optimal tracking performance is achieved. In the double-loop structure, a unified tracking loop is employed to facilitate performance comparison. Simulation results demonstrate the performance improvement of the proposed approach over the traditional gold code tracking scheme, and the relationship between the non-commensurate sampling parameters and the achievable tracking accuracy. The approach is especially suitable for precision ranging applications, and can be extended to other applications involving accurate signal tracking in digital equipment.

Mathematical Analysis for the GPS Carrier Tracking Loop Phase Jitter in Presence of Different Types of Interference Signals

The performance of a Global Positioning System (GPS) receiver usually depends on the tracking loops, so they can be considered the heart of the GPS receivers. It has been proven that the carrier tracking loop is more sensitive to noise and interference than the code tracking loop. Therefore, the carrier tracking loop can be used as a means for investigating the GPS receiver performance in presence of interference. In this paper, closed form analytical expressions for the carrier tracking loop phase error are derived in presence of different types of interference signals such as continuous wave interference, narrowband interference, partial band interference, broadband interference, match spectrum interference, and pulse interference. Also the carrier-to-noise ratio threshold is analytically derived. The derived analytical expressions have been validated with the aid of simulation experiments.

Analysis of noncommensurate sampling effects on the performance of PN code tracking loops

Noncoherent early-late processing (NELP) code tracking loops are often implemented using digital hardware for digital global positioning system (GPS) receivers. Noncommensurate sampling technology is widely used because it is viewed as an effective solution to cope with the drawback of digital effects. However, the relationship between the sampling rate and auto-correlation function (ACF) is not adequately characterized by traditional analysis. The principles for selecting the sampling rate are still not apparent. In order to solve this problem, we first analyzed the effects of different sampling rates on ACF and obtained the analytical form of a discrete auto-correlation function (DACF) for a noncommensurate sampling rate. Based on the result, the relationship between the step variation in DACF and NELP parameters such as sampling rate, integration time, and correlator spacing was determined. The maximum step variation size of DACF was also determined. However, considering the actual situation, additional factors such as code Doppler shift, precorrelation filter, and thermal noise may degrade the step variation of DACF. The relationship between the step variation and these factors was analyzed separately. An appropriate sampling rate and appropriate correlator spacing were proposed to achieve the typical accuracy of measurement. The numerical simulation verified the validity of the above theoretical analyses, and finally, the conclusions and design constraints for the digital GPS receiver are summarized.

PN Ranging Based on Noncommensurate Sampling: Zero-Bias Mitigation Methods

This paper proposes two methods to mitigate the zero bias of noncommensurate sampling based code-tracking loops to significantly improve the pseudonoise ranging accuracy. For the compensation-based method, a set of algorithms is developed to directly calculate the zero bias which is then removed from the range measurement. For the compensation-free method, a special category of sampling ratios are selected such that the zero bias is self-cancelled. Simulations validate the effectiveness of the proposed methods.

Universal evaluation criteria for code delay estimation error of satellite navigation signals

With the system upgrading and construction demand for new generation global navigation satellite system (GNSS), the navigation signal modulation and multiplexing technology have made great progress. Up to now, many modulation modes for single signal component and many constant-envelope multiplexing methods for multiple signal components have been proposed, meanwhile the new signal structure continues to be presented. The satellite navigation signal code delay estimation error is the most critical factor that determines system service performance. Therefore, it is urgent to give an overall performance evaluation on code delay estimation error of GNSS signals with different modulation and multiplexing modes, and consequently provide a crucial selection basis for subsequent system application. The code delay estimation error is related to not only signal structure, but also receiver's receiving model and processing method of code tracking loop. The receiving models of new generation navigation receivers can be classified as two types. One is matched receiving model which means that the reference signal is the same as receiving signal, and the other is unmatched receiving model, where the reference signal is not the same as receiving signal. Recently, the unmatched receiving model has been extensively applied to the processing of binary offset carrier class signals. Therefore, in this paper we propose an integrated evaluation method for code delay estimation error of navigation signals. Firstly, the equivalent model for the code tracking loop of navigation receivers is generalized and the current navigation receivers are classified as four types based on whether matched receiving or coherent processing is used. Because the code delay estimation error is dependent on the type, it is necessary to provide an evaluation method for each type. Then, on the assumed condition that the code delay estimation error is very small, the expressions of code delay estimation error for coherent processing and non-coherent processing under matched receiving model are respectively presented and the relationships between each other are discussed under various noise environments and the code loop interval going to zero. The expression of code delay estimation error for non-coherent processing under unmatched receiving model is derived and the relationship with coherent processing is discussed under the same condition as matched receiving model. Finally, the Ziv-Zakai bound of code delay estimation error is derived, which provides a perfect evaluation method when the code delay estimation error is not very small. The proposed method is expressed by power spectrum density of navigation signals, which provides important theoretical guidance for signal design and receiver development, and simultaneously brings great convenience to the evaluation of the signal. Simulation experiment attests to effective evaluation on the code delay estimation error of new generation typical navigation signals.

Generalized unambiguous tracking method based on pseudo correlation function for multi-level coded symbol modulated signals

The global navigation satellite system (GNSS) signal modulation type plays a crucial role in determining the performances of positioning, navigation and timing (PNT) services. Currently, the binary offset carrier (BOC) modulation signal and binary coded symbol (BCS) modulation signal are both bipolar signals, which greatly restrict the room of improving the GNSS signal performance. Therefore, multi-level coded symbol (MCS) modulation has received great attention in the field of GNSS signal design. The MCS modulation is the most extensive step-coded symbol modulation mode, where BOC modulation and BCS modulation are its special cases. Since the waveform symbol of the MCS modulation signal can be arbitrarily valued, the optimal GNSS signal can be designed. However, like the BOC modulation signal, the MCS modulation signal also has the problem of ambiguous tracking, and then results in a large pseudo range measurement error, which is unacceptable for the new generation GNSS with high accuracy. In recent years, the unambiguous tracking of GNSS signals has become a hot research subject in the navigation signal processing domain and many methods are presented, and those methods can be divided into three categories:BPSK-like method, bump jump (BJ) method, and side-peak cancellation (SC) method. However, these methods are designed for BOC signal, and they are not suitable for MCS signal. Therefore, in this paper we propose a general unambiguous tracking algorithm based on the pseudo correlation function (PCF), which is suitable for MCS modulated signals. Firstly, the unitary expression of MCS modulated signal based on waveform value vector is given, then the unitary formula of cross-correlation function for MCS signal is derived and the definition of PCF is given. Then the constraint condition which should be satisfied to realize unambiguous tracking is analyzed in depth, and the universal constructing method of two reference signals and the relationship between each other are derived according to this constraint condition, which brings great convenience for solving the specific MCS signal. The code tracking loop model of GNSS receiver based on the proposed method is illustrated. It is observed that the proposed method can receive different MCS signals under the same receiver loop framework, and can simplify the design of the receiver while eliminating the tracking ambiguous problem. Finally, as a special case of MCS signal, the applications of the proposed method in four kinds of BOC signals are discussed respectively, and then the waveform value vector of the reference signal and the unitary expression of code discriminator are derived. Simulation results show that the proposed method can effectively solve the ambiguous tracking problem of MCS signal, which has good performance and broad application prospect.

The Ionospheric Scintillation Effects on the BeiDou Signal Receiver.

Irregularities in the Earth’s ionosphere can make the amplitude and phase of radio signals fluctuate rapidly, which is known as ionospheric scintillation. Severe ionospheric scintillation could affect the performance of the Global Navigation Satellite System (GNSS). Currently, the Multiple Phase Screen (MPS) technique is widely used in solving problems caused by weak and strong scintillations. Considering that Southern China is mainly located in the area where moderate and intense scintillation occur frequently, this paper built a model based on the MPS technique and discussed the scintillation impacts on China’s BeiDou navigation system. By using the BeiDou B1I signal, this paper analyzed the scintillation effects on the receiver, which includes the acquisition and tracking process. For acquisition process, this paper focused on the correlation peak and acquisition probability. For the tracking process, this paper focused on the carrier tracking loop and the code tracking loop. Simulation results show that under high scintillation intensity, the phase fluctuation could be −1.13 ± 0.087 rad to 1.40 ± 0.087 rad and the relative amplitude fluctuation could be −10 dB to 8 dB. As the scintillation intensity increased, the average correlation peak would decrease more than 8%, which could thus degrade acquisition performance. On the other hand, when the signal-to-noise ratio (SNR) is comparatively lower, the influence of strong scintillation on the phase locked loop (PLL) is much higher than that of weak scintillation. As the scintillation becomes more intense, PLL variance could consequently results in an error of more than 2.02 cm in carrier-phase based ranging. In addition, the delay locked loop (DLL) simulation results indicated that the pseudo-range error caused by strong scintillation could be more than 4 m and the consequent impact on positioning accuracy could be more than 6 m.

Performance Comparison of Code Discriminators in the Presence of CW Interference

This paper considers the effect of continuous wave interference (CWI) on code tracking loops for global navigation satellite system signal. Based on the integrate-dump model analysis, the overall correlation results in the presence of CWI are theoretically analyzed incorporating the sum frequency interference terms which were regarded as negligible quantities in previous studies. Using the obtained correlation results, the closed-form expressions of the code tracking errors caused by CWI for three types of code discriminators (coherent, noncoherent, and barycenter) are derived and formulated as the solutions of quadratic equations using reasonable assumptions of trigonometric functions. Simulations are performed to demonstrate the accuracy of the theoretical correlation results. Also, the simulated code tracking errors are also presented to corroborate the effectiveness of the closed-form code tracking errors in terms of interference parameters (frequency and phase). It is indicated that the barycenter discriminator has the superior performance and could be preferred for mitigating CWI in tracking stage. These results can be applied for performance comparison, signal design, receiver design, and interference mitigation techniques in the presence of CWI.

A novel satellite-equipped receiver for autonomous monitoring of GNSS navigation signal quality

Global navigation satellite system (GNSS) comes with potential unavoidable application risks such as the sudden distortion or failure of navigation signals because its satellites are generally operated until failure. In order to solve the problems associated with these risks, receiver autonomous integrity monitoring (RAIM) and ground-based signal quality monitoring stations are widely used. Although these technologies can protect the user from the risks, they are expensive and have limited region coverage. Autonomous monitoring of satellite signal quality is an effective method to eliminate these shortcomings of the RAIM and ground-based signal quality monitoring stations; thus, a new navigation signal quality monitoring receiver which can be equipped on the satellite platform of GNSS is proposed in this paper. Because this satellite-equipped receiver is tightly coupled with navigation payload, the system architecture and its preliminary design procedure are first introduced. In theory, code-tracking loop is able to provide accurate time delay estimation of received signals. However, because of the nonlinear characteristics of the navigation payload, the traditional code-tracking loop introduces errors. To eliminate these errors, the dummy massive parallel correlators (DMPC) technique is proposed. This technique can reconstruct the cross correlation function of a navigation signal with a high code phase resolution. Combining the DMPC and direct radio frequency (RF) sampling technology, the satellite-equipped receiver can calibrate the differential code bias (DCB) accurately. In the meantime, the abnormities and failures of navigation signal can also be monitored. Finally, the accuracy of DCB calibration and the performance of fault monitoring have been verified by practical test data and numerical simulation data, respectively. The results show that the accuracy of DCB calibration is less than 0.1 ns and the novel satellite-equipped receiver can monitor the signal quality effectively.

Double Strobe Technique for Unambiguous Tracking of TMBOC Modulated Signal in GPS

A time-multiplexed double strobe scheme for unambiguous tracking of time-multiplexed binary offset carrier (TMBOC) modulated signal in GPS is presented. In the code tracking loop, two kinds of time-multiplexed strobe pulses are generated to track the BOC(1,1) and BOC(6,1) components, respectively. The strobe based on BOC(1,1) subcarrier eliminates the false lock points in the code discriminator, and the bump-jumping algorithm is not required. The other strobe employs the BOC(6,1) component to prevent additional signal-to-noise ratio loss. Thus, the proposed method simplifies the hardware structure in comparison with conventional strobe techniques, and improves the tracking performance in the presence of thermal noise and multipath.