Performance analysis of a novel chip tracking loop used for regenerative pseudo-noise ranging clock recovery

To improve the performance of composite pseudo-noise （PN） code clock recovery in a regenerative PN ranging system at a low symbol signal-to-noise ratio （SNR）, a novel chip tracking loop （CTL） used for regenerative PN ranging clock recovery is adopted. The CTL is a modified data transition tracking loop （DTTL）. The difference between them is that the Q channel output of the CTL is directly multiplied by a clock component, while that of the DTTL is multiplied by the Ⅰ channel transition detector output. Under the condition of a quasi-squareware PN ranging code, the tracking （ mean square timing jitter） performance of the CTL is analyzed. The tracking performances of the CTL and the DTTL, are compared over a wide range of symbol SNRs. The result shows that the CTL and the DTTL have the same performance at a large symbol SNR, while at a low symbol SNR, the former offers a noticeable enhancement.

Optimization of the carrier tracking loop for GPS high dynamic receivers

A carrier tracking loop which can adjust the loop parameters adaptively is proposed for high dynamic application. Three modules, called the α-β-γT filter model, adaptive loop structure mod- el and adaptive loop bandwidth model respectively, are added in the presented tracking loop com- pared with the traditional carrier tracking loop based on the second-order frequency lock loop （FLL） assisting third-order phase lock loop （PLL） loop filter. And the optimization methods for the track- ing bandwidth and the carrier loop order are analyzed. The real-time estimation methods of the dy- namic parameters, the velocity, acceleration and jerk along the line of sight （LOS） between the sat- ellite and the receiver＇ s antenna, and the measurement parameters are discussed based on the pres- ented α-β-γ filter algorithm. A method is introduced to improve the filter＇ s dynamic response to meet high dynamic application by self-adjusted α-β-γ filter coefficient used in the tracking loop. The performance of three cases with different carrier tracking loop is compared by simulation.

GPS Vector Tracking Loop with Fault Detection and Exclusion

In this paper,both the integrity monitoring and fault detection and exclusion(FDE)mechanisms are incorporated into the vector tracking loop(VTL)architecture of the Global Positioning System(GPS)receiver for reliability enhancement.For the VTL,the tasks of signal tracking and navigation state estimation no longer process separately and a single extended Kalman filter(EKF)is employed to simultaneously track the received signals and estimate the receiver’s position,velocity,etc.In contrast to the scalar tracking loop(STL)which utilizes the independent parallel tracking loop approach,the VTL technique is beneficial from the correlation of each satellite signal and user dynamics.The VTL approach provides several important advantages.One of the merits is that the tracking loop can be assisted for overcoming the problem of signal blockage.Although the VTL architectures provide several important advantages,they suffer some fundamental drawbacks.For example,the errors in the navigation solutions may degrade the tracking accuracy.The most significant drawback is that failure of tracking in one channel may affect the entire tracking loop and possibly lead to loss of lock.For reliability enhancement,the EKF based integrity monitoring and FDE algorithms are developed to prevent the error from spreading into the entire tracking loop.The integrity monitoring is utilized to check the possible fault in the pseudorange and the pseudorange rate,followed by the FDE mechanism employed to exclude the abnormal satellite signals.Performance assessment and evaluation for the proposed approach will be presented.

Minimum Error Entropy Based EKF for GPS Code Tracking Loop

This paper investigates the minimum error entropy based extended Kalman filter(MEEKF)for multipath parameter estimation of the Global Positioning System(GPS).The extended Kalman filter(EKF)is designed to give a preliminary estimation of the state.The scheme is designed by introducing an additional term,which is tuned according to the higher order moment of the estimation error.The minimum error entropy criterion is introduced for updating the entropy of the innovation at each time step.According to the stochastic information gradient method,an optimal filer gain matrix is obtained.The mean square error criterion is limited to the assumption of linearity and Gaussianity.However,non-Gaussian noise is often encountered in many practical environments and their performances degrade dramatically in non-Gaussian cases.Most of the existing multipath estimation algorithms are usually designed for Gaussian noise.The I(in-phase)and Q(quadrature)accumulator outputs from the GPS correlators are used as the observational measurements of the EKF to estimate the multipath parameters such as amplitude,code delay,phase,and carrier Doppler.One reasonable way to obtain an optimal estimation is based on the minimum error entropy criterion.The MEEKF algorithm provides better estimation accuracy since the error entropy involved can characterize all the randomness of the residual.Performance assessment is presented to evaluate the effectivity of the system designs for GPS code tracking loop with multipath parameter estimation using the minimum error entropy based extended Kalman filter.

A robust vector tracking loop structure based on potential bias analysis

This paper proposes a robust vector tracking loop structure based on potential bias analysis. The influence of four kinds of biases on the existing two implementations of Vector Tracking Loops(VTLs) is illustrated by theoretical analysis and numerical simulations, and the following findings are obtained. Firstly, the initial user state bias leads to steady navigation solution bias in the relative VTL, while new measurements can eliminate it in the absolute VTL. Secondly, the initial code phase bias is transferred to the following navigation solutions in the relative VTL, while new measurements can eliminate it in the absolute VTL. Thirdly, the user state bias induced by erroneous navigation solution of VTLs can be eliminated by both of the two VTLs. Fourthly,the multipath/NLOS likely affects the two VTLs, and the induced tracking bias in the duration of the multipath/NLOS would decrease the performance of VTLs. Based on the above analysis,a robust VTL structure is proposed, where the absolute VTL is selected for its robustness to the two kinds of initialization biases;meanwhile, the instant bias detection and correction method is used to improve the performance of VTLs in the duration of the multipath/NLOS. Numerical simulations and experimental results verify the effectiveness of the proposed robust VTL structure.

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 DACE 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.

GPS Vector Tracking Receivers with Rate Detector for Integrity Monitoring

In this paper,the integrity monitoring algorithm based on a Kalman filter(KF)based rate detector is employed in the vector tracking loop(VTL)of the Global Positioning System(GPS)receiver.In the VTL approach,the extended Kalman filter(EKF)simultaneously tracks the received signals and estimates the receiver’s position,velocity,etc.In contrast to the scalar tracking loop(STL)that uses the independent parallel tracking loop approach,the VTL technique uses the correlation of each satellite signal and user dynamics and thus reduces the risk of loss lock of signals.Although the VTL scheme provides several important advantages,the failure of tracking in one channel may affect the entire system and lead to loss of lock on all satellites.The integrity monitoring algorithm can be adopted for robustness enhancement.In general,the standard integrity monitoring algorithm can timely detect the step type erroneous signals.However,in the presence of ramp type slowly growing erroneous signals,detection of such type of error takes much more time since the error cannot be detected until the cumulative exceeds the specified threshold.The integrity monitoring based on the rate detector possesses good potential for resolving such problem.The test statistic based on the pseudorange residual in association with the EKF is applied for determination of whether the test statistic exceeds the allowable threshold values.The fault detection and exclusion(FDE)mechanism can then be employed to exclude the hazardous erroneous signals for the abnormal satellites to assure normal operation of GPS receivers.Feasibility of the integrity monitoring algorithm based on the EKF based rate detector will be demonstrated.Performance assessment and evaluation will be presented.

Continuous Tracking of GPS Signals with Data Wipe-Off Method

The decentralized pre-filter based vector tracking loop(VTL)configuration with data wipe-off(DWO)method of the Global Positioning System(GPS)receiver is proposed for performance enhancement.It is a challenging task to continuously track the satellites’signals in weak signal environment for the GPS receiver.VTL is a very attractive technique as it can provide tracking capability in signal-challenged environments.In the VTL,each channel will not form a loop independently.On the contrary,the signals in the channels of VTL are shared with each other;the navigation processor in turn predicts the code phases.Thus,the receiver can successfully track signals even the signal strength from individual satellite is weak.The tracking loop based on the pre-filter provides more flexible adjustment to specific environments to reduce noise interference.Therefore,even if the signals from some satellites are very weak the receiver can track them from the navigation results based on the other satellites.The navigation data,which contains information necessary to perform navigation computations,are binary phase-shift keying(BPSK)modulated onto the GPS carrier phase with the bit duration of 20 ms(i.e.,50 bits per second)for the GPS L1 C/A signals.The coherent integration interval can be extended for improved tracking performance in signal-challenged environment.However,tracking accuracy is decreased by possible data bit sign reversal.The DWO algorithm can be employed to remove the data bit in I and Q correlation values so as to avoid energy loss due to bit transitions when the integration interval of the correlator is extended over 20 ms under the low carrier-to-noise ratio(C/No)environments.The proposed method has an advantage to provide continuous tracking of signals and obtain improved navigation performance.Performance evaluation of the tracking capability as well as positioning accuracy will be presented.

Quantitative analysis of the performance of vector tracking algorithms

Vector tracking changes the classical structure of receivers. Combining signal tracking and navigation solution,vector tracking can realize powerful processing capabilities by the fusion technique of receiving channel and feedback correction. In this paper,we try to break through the complicated details of numerical analysis,consider the overall influencing factors of the residual in observed data,and use the intrinsic link between a conventional receiver and a vector receiver. A simple method for performance analysis of the vector tracking algorithm is proposed. Kalman filter has the same steady performance with the classic digital lock loop through the analysis of the relation between gain and band width. The theoretical analysis by the least squares model shows that the reduction of range error is the basis for the superior performance realized by vector tracking. Thus,the bounds of its performance enhancement under weak signal and highly dynamic conditions can be deduced. Simulation results verify the effectiveness of the analysis presented here.

A novel high precision Doppler frequency estimation method based on the third-order phase-locked loop

In deep space exploration,many engineering and scientific requirements require the accuracy of the measured Doppler frequency to be as high as possible.In our paper,we analyze the possible frequency measurement points of the third-order phase-locked loop(PLL)and find a new Doppler measurement strategy.Based on this finding,a Doppler frequency measurement algorithm with significantly higher measurement accuracy is obtained.In the actual data processing,compared with the existing engineering software,the accuracy of frequency of 1 second integration is about 5.5 times higher when using the new algorithm.The improved algorithm is simple and easy to implement.This improvement can be easily combined with other improvement methods of PLL,so that the performance of PLL can be further improved.

A novel Doppler frequency measurement method based on the closed-loop signal correlation for deep space exploration

In deep space exploration,it is necessary to improve the accuracy of frequency measurement to meet the requirements of precise orbit determination and various scientific studies.A phase detector is one of the key modules that restricts the tracking performance of phase-locked loop(PLL).Based on the phase relationship between adjacent signals in the time domain,a novel phase detector is presented to replace the arctangent phase detector.The new PLL,which is a closed loop signal correlation algorithm,shows good performance in tracking signals with high precision and the tracking accuracy of frequency of1 second integration is close to Cramer-Rao lower bound(CRLB)when setting proper parameters.Actual data processing results further illustrate the excellent performance of the novel PLL.

Support Vector Machine Assisted GPS Navigation in Limited Satellite Visibility

This paper investigates performance improvement via the incorporation of the support vector machine(SVM)into the vector tracking loop(VTL)for the Global Positioning System(GPS)in limited satellite visibility.Unlike the traditional scalar tracking loop(STL),the tracking and navigation modules in the VTL are not independent anymore since the user’s position can be determined by using the information from other satellites and can be predicted on the basis of the states of the user.The method proposed in this paper makes use of the SVM to bridge the GPS signal and prevent the error growth due to signal outage.Similar to the neural network,the SVM is motivated by its ability to approximate an unknown nonlinear input-output mapping through supervised training.The SVM is employed for predicting adequate numerical control oscillator(NCO)inputs,i.e.,providing better prediction of residuals for the Doppler frequency and code phase in order to maintain regular operation of the navigation system.When the navigation processing is in good condition,the SVM is at the training stage,and the output information from the discriminator and navigation filter is adopted as the inputs.Other machine learning(ML)algorithms such as the radial basis function neural network(RBFNN)and the Adaptive Network-Based Fuzzy Inference System(ANFIS)are employed for comparison.Performance evaluation for the SVM assisted architecture as compared to the RBFNNand ANFIS-assisted methods and the un-assisted VTL will be carried out and the performance evaluation during GPS signal outage will be presented.The proposed design is very useful for navigation during the environment of limited satellite visibility to effectively overcome the problem in the environment of GPS outage.

ModiΡed pseudo-noise code regeneration method

A modiΡed pseudo-noise（PN） code regeneration method is proposed to improve the clock tracking accuracy without impairing the code acquisition time performance.Thus,the method can meet the requirement of high accuracy ranging measurements in short time periods demanded by radio-science missions.The tracking error variance is derived by linear analysis.For some existing PN codes,which can be acquired rapidly,the tracking error variance performance of the proposed method is about 2.6 dB better than that of the JPL scheme（originally proposed by Jet Propulsion Laboratory）,and about 1.5 dB better than that of the traditional double loop scheme.

A double sideband combined tracking method for Galileo E5 AltBOC signals

The Galileo navigation satellite system(Galileo)E5 Alternative Binary Offset Carrier(AltBOC)signal brings various challenges due to its complex modulation,wide bandwidth,and multi-peaked auto-correlation function.While wideband tracking needs to solve the ambiguity problem and design dedicated baseband channels,the single-sideband cannot have the outstanding performance of the AltBOC signal.We propose a new tracking method called“Double Sideband Combined Tracking”(DSCT),which can fully exploit the AltBOC signal’s code tracking accuracy without ambiguity and ensure compatibility with Binary Phase Shift Keying(BPSK)processing channels,easily implemented in hardware.The DSCT employs one phase locked loop and one delay locked loop to track the carrier and code,respectively.The double-sideband correlation results used by the two loops are recovered by coherently combining the singlesideband correlation results of the two BPSK channels.Meanwhile,the combined model,the loop discriminator,and the ambiguity detection of the DSCT are discussed.Furthermore,the code tracking error caused by thermal noise is modeled and analyzed.The test results based on real Galileo E5 signals show that the DSCT exhibits better or comparable code tracking accuracy to the AltBOC wideband tracking method.When the loop falsely locks onto a sidepeak,the DSCT can quickly detect and re-lock on the main peak.

A high dynamics algorithm based on steepest ascent method for GNSS receiver

High dynamic conditions impose critical challenges on Global Navigation Satellite System(GNSS)receivers,leading to large tracking errors or even loss of tracking.Current methods that intend to improve receivers’adaptability for high dynamics require either complicated structures or prior statistical information of noises.This paper proposes a high dynamics algorithm based on steepest ascent method that can circumvent the deficiencies of existing methods.First,the relationship between the error of carrier tracking and the maximum of Fast Fourier Transform(FFT)outputs is established,and a performance function based on the steepest ascent method is designed.It can keep stable in high dynamics.Second,a new carrier-tracking loop is constructed by deploying the performance function.When the variation of GPS receiver acceleration ranges from 10 g to 100 g,compared with the PLL that either loses lock or keeps tracking accuracy less than 33.89 Hz,the experimental results show that the proposed method can not only keep tracking,but also achieve tracking accuracy more than 2.77 Hz.

A novel joint navigation state error discriminator based on iterative maximum likelihood estimation

To break through the limitations of traditional discriminators used in vector tracking loops, this paper presents an iterative maximum likelihood estimation(IMLE) method for extracting navigation state errors from multi-satellite signals. The IMLE method takes into account both computational cost and estimation accuracy. The associated gradient vector and Hessian matrix of the MLE cost function are derived. The characteristics of the proposed joint discriminator are analyzed based on the properties of the MLE cost function,gradient vector, and Hessian matrix. The effectiveness of IMLE is verified by Monte Carlo simulation.