Tracking Loop Research Articles

A MCKF-based cascade vector tracking method designed for ship navigation

In ship navigation, the most widely used technology is global navigation satellite systems (GNSS), which provide the ship’s position and velocity continuously over a period of time. However, when ships are blocked by port buildings or bridges, the quality of signals received from shipborne GNSS receivers may be reduced, resulting in inaccurate ship positioning that poses a risk to navigational safety. In an occluded environment, the measurement process during the signal processing of shipborne GNSS receivers is nonstationary and prone to measurement anomalies, which can contaminate measurement noise with outliers. To address this problem, a cascaded non-coherent vector tracking loop is designed, with the maximum correntropy Kalman filter serving as a cascaded carrier/code pre-filter for shipborne GNSS receivers. The measurement noise covariance matrix of the pre-filter is adaptively calculated and corrected using the carrier-to-noise ratio and the maximum correntropy criterion, respectively. The algorithm proposed is more sensitive to outliers than the traditional tracking methods and can effectively solve the state estimation problem under the condition of measurement anomalies. Specifically, the algorithm offers ships with more precise position and velocity estimations and lower signal tracking errors than traditional tracking methods under both static and dynamic conditions, as demonstrated by shipboard experiments. The horizontal positioning is increased by 88.4% and the horizontal velocity error is reduced by 62.1% in the occluded environment under dynamic conditions.

KinKal: A Kinematic Kalman filter Track Fitting Package for the Mu2e Experiment

Many current physics experiments require precision reconstruction of low-energy particles. One example is the Mu2e experiment, which requires reconstructing an isolated 105 MeV electron with better than 500 KeV/c momentum resolution. Mu2e uses a low-mass straw tube tracker, and a CsI crystal calorimeter, to reconstruct tracks. In this paper, we present the design and performance of a track reconstruction algorithm optimized for Mu2e’s unusual requirements. The algorithm is based on the KinKal [1] kinematic Kalman filter track fit package. KinKal supports multiple track parameterizations, including one optimized for looping tracks, such as Mu2e signal tracks, and others optimized for straight or slightly-curved tracks, such as the high-momentum (>1 GeV/c) cosmic ray muons used to calibrate and align the Mu2e detectors. All KinKal track parameterizations include the track origin time, to correctly model correlations arising from measurements that couple time and space, such as the straw drift time or the calorimeter cluster time. KinKal employs magnetic field inhomogeneity and material effect correction algorithms with 10−4 fractional precision. The Mu2e fit uses Artificial Neural Net functions to discriminate background hits from signal hits, and to resolve the straw tube hit left-right ambiguity, while iterating the extended Kalman filter. The efficiency, accuracy, and precision of the Mu2e track reconstruction, as tested on detailed simulations of Mu2e data, are presented.

A robust GNSS sensors in presence of signal blockage for USV application

Unmanned surface vehicle (USV) can navigate autonomously via the global navigation satellite system (GNSS). However, the traditional GNSS scalar tracking loop easily loses lock in low carrier-to-noise ratio (CNR) situations, such as signal occlusion and weak signals. Meanwhile, an increase in the carrier/code phase error leads to an increase in the measurement error of the navigation filter, which decreases the accuracy of the position estimation. To solve this problem, this paper proposes a carrier and code tracking structure based on a forward and backward Kalman filter to dynamically adjust the gain of the vector tracking loop. The carrier and code phase errors calculated by the loop discriminators were linearly transformed into pseudo-range rate and pseudo-range errors after filtering and smoothing, which were used as the measurements of the navigation filter. The signal CNR was used to adaptively adjust the measurement noise covariance matrix of the loop filters. The field tests used a commercial receiver’s navigation solution as the reference. In the stationary test, the proposed structure reduced the localization error by 44.3% compared with the traditional methods. In kinematic experiments, the proposed structure reduced the carrier and code phase errors in a harsh signal environment and improved the positioning accuracy at the source. The test results demonstrate that the proposed GNSS tracking method can provide a possible solution for the development of navigation systems for USV.

Robust factor graph optimisation method for shipborne GNSS/INS integrated navigation system

AbstractRobust Global Navigation Satellite System (GNSS) factors are introduced into a factor graph optimisation based integrated navigation system to address the challenge of occluded GNSS signals during ship navigation, which leads to increased errors in positioning results. To enhance the robustness of the GNSS tracking loop, a vector tracking method is applied to receiver tracking loop. Then, the Mahalanobis distance was employed to assess the pseudorange residual and identify and reject signals that exhibit anomalies. Specifically, the pseudorange residual is computed as the difference between the predicted pseudorange of the GNSS receiver and the measured pseudorange. Using the historical information in the window, robust GNSS factors were constructed for use in the factor graph. The robust factor graph optimisation method for a shipborne GNSS/Inertial Navigation System integrated navigation system was implemented by constructing robust GNSS factors and Inertial Measurement Unit factors. The experimental results confirm that the positioning accuracy of the proposed method is superior to those of the factor graph optimization and extended Kalman filter.

“Did you fall asleep?” – Younger and older drivers’ recollection of prior sleepiness while driving

Determining causality and driver culpability in fall asleep crashes requires extensive forensic examination, with post-crash interviews forming a critical part of the process. To date, there is no evidence regarding whether drivers’ recollection of sleepiness and associated symptoms accurately reflects driving impairment during an earlier drive. To address this, our study examined whether established questionnaires assessing sleepiness (Karolinska Sleepiness Scale) and sleepiness symptoms (Sleepiness Symptoms Questionnaire) taken post-drive accurately reflected earlier driving impairment as characterised by near-crash events and lane deviations during a closed loop track drive. Sixteen younger (21–33 years) and seventeen older (50–65 years) drivers completed two 2 h afternoon track drives under supervision of a licensed driving instructor under two conditions: well rested (8 h sleep opportunity) and sleep deprived (0 h sleep). For younger drivers, all sleepiness symptoms (except mind wandering) significantly predicted prior severe (near-crashes AUC 0.78–1.00) and moderate (lane deviations AUC 0.78–0.94) driving impairment, with good to excellent accuracy. For older drivers, only severe impairment was accurately reflected in post-drive ratings (near crashes AUC 0.86–0.94), and for fewer symptoms (8/9 vs. 6/9). Optimal thresholds for the frequency of these symptoms, in addition to thresholds for minimum acceptable false positives are presented. Our data suggest that post-crash interviews should utilise questions around subjective sleepiness and associated symptoms, providing evidence regarding the presence and awareness of drowsiness while driving, taking into account the reliability of self-report evidence. This may aid in the investigation of fall-asleep crashes where drowsiness is suspected.

Relocated internal model control based cascade control strategy for stable and unstable systems with delay

To control unstable and stable plants a new series cascade control structure (SCCS) is proposed. The proposed SCCS incorporates two or three controllers (setpoint tracking controller, secondary disturbance rejection controller and stabilising controller for only unstable plants). Internal model control scheme (IMCS) augmented with integration of square error (ISE) minimisation along with robustness considerations are applied to design the secondary loop disturbance rejection controller. In contrast, relocated IMCS augmented with ISE minimisation is applied for the outer loop or setpoint tracking controller. Routh Hurwitz stability criteria and maximum sensitivity considerations are used to design the proportional-derivative (PD) controller, which stabilises the unstable plant. It is important to note that the suggested SCCS only needs four controller parameters to be tuned, which is less than the recently reported techniques. Robust stability analysis of the proposed SCCS is performed in the presence of uncertainty. The simulation results depict that the suggested approach imparts pre-eminent improvement in closed-loop performance such as faster setpoint tracking and better disturbance rejection for nominal and perturbed plants.

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 on the Effect of Phase Noise on the Performance of Satellite Communication and Measurement System

An oscillator is a key component of a satellite communication measurement and control system, performing symmetry precisely as a time frequency reference. At the same time, the phase noise index has a close coupling relationship with the overall performance of the entire system, while persistently breaking the symmetry property of the oscillator during work. It is very important to study and reasonably allocate the phase noise index. According to the theoretical formula of phase noise, this paper analyzes the power law spectral model in the frequency domain and the noise jitter characteristics in the time domain. Using the carrier tracking loop in the measurement system, the frequency domain transfer model of phase noise is established, and typical analysis results are given. A discrete fractional integration algorithm is proposed, which can generate the phase noise time domain sequence under the given power law spectral model coefficients. The proposed algorithm is more realistic compared with the previous numerical calculation method, and has sufficient accuracy compared with the results of the instrument. After frequency domain conversion, the RMS deviation between the simulated noise sequence in the frequency domain and the measured single sideband power spectral density is less than 2.5 dB, indicating that the phase noise sequence can reflect the frequency domain characteristics more completely. A communication measurement simulation system is built, and a discrete sequence simulation analysis method combining frequency domain and time domain is provided, and the coupling relationship of key indicators such as phase noise, thermal noise, communication data rate, modulation method and bit error rate is synthesized. The results show that the BER of the QPSK/BPSK communication system will not be significantly reduced if the phase jitter RMS caused by the phase noise is less than 5 degrees, so 5 degrees can be used as a reference for the decomposition of the carrier SSB phase noise index. The simulation results have been successfully applied to a satellite inter-satellite link system, which has universal practical application value.

Effects of the Relative Dynamics of Ionospheric Irregularities and GPS Satellites on Receiver Tracking Loop Performance

AbstractTransionospheric satellite signals are exposed to perturbation, caused by irregularities generated in the ionosphere. However, the characteristics of the satellite motion can have an additional impact on signal perturbation, in addition to the effects of irregularity structures, that drift from west to east during geomagnetic quiet conditions. This paper reports the effect of Global Positioning System satellite geometry, on tracking loop performance of ground‐based receivers, during occurrence of ionospheric scintillations. Observations are made from station Calcutta (22.58°N, 88.38°E geographic; magnetic dip 34.54°), located near the northern crest of Equatorial Ionization Anomaly, during three different solar activity periods (March 2014, March 2015, and March 2022). Efforts have been made to study the correlation of east‐west component of satellite velocity at Ionospheric Pierce Point (IPP) with duration of loss‐of‐lock and rate of signal fading (<−10 dB), from ground scintillation pattern observations. Results of this study show 75%–78% correlation between duration of loss‐of‐lock and eastward component of satellite velocity, for all three period of observation. Subsequently, shorter duration of loss‐of‐lock has been observed corresponding to satellite velocity being westward. Signal fading rate is found to decrease with increasing satellite velocity, having median value of the fading rate cumulative distribution percentage, corresponding to satellite velocity of 16.69, 31.76, and 19.14 m/s respectively during March 2014, March 2015, and March 2022. Results of this study also indicate direction and component of satellite velocity at IPP to be a dominant cause of signal outage, even during periods of weak to moderate scintillations.

Using the Orthogonal Conditional Nonlinear Optimal Perturbations Approach to Address the Uncertainties of Tropical Cyclone Track Forecasts Generated by the WRF Model

Abstract The orthogonal conditional nonlinear optimal perturbations (O-CNOPs) approach for measuring initial uncertainties is applied to the Weather Research and Forecasting (WRF) Model to provide skillful forecasts of tropical cyclone (TC) tracks. The hindcasts for 10 TCs selected from 2005 to 2020 show that the ensembles generated by the O-CNOPs have a greater probability of capturing the true TC tracks, and the corresponding ensemble forecasts significantly outperform the forecasts made by the singular vectors, bred vectors, and random perturbations in terms of both deterministic and probabilistic skills. In particular, for two unusual TCs, Megi (2010) and Tembin (2012), the ensembles generated by the O-CNOPs successfully reproduce the sharp northward-turning track in the former and the counterclockwise loop track in the latter, while the ensembles generated by the other methods fail to do so. Moreover, additional attempts are performed on the real-time forecasts of TCs In-Fa (2021) and Hinnamnor (2022), and it is shown that O-CNOPs are very useful for improving the accuracy of real-time TC track forecasts. Therefore, O-CNOPs, together with the WRF Model, could provide a new platform for the ensemble forecasting of TC tracks with much higher skill.

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.

Robust packet loss compensation in the cloud‐based TT&C receiver using a predictive tracking loop with RBF network identification

AbstractIn recent years, ground‐based aerospace tracking, telemetry and control (TT&C) systems have been shifting towards an IP‐based cloud TT&C network architecture to improve signal transmission efficiency and system flexibility. However, this new architecture presents new challenges for the performance of tracking loops in the cloud‐based TT&C receiver. The authors present a predictive compensation tracking loop that addresses the problem of packet loss. The loop utilises radial basis function (RBF) online network identification for robust carrier and code frequency offset tracking. To account for packet loss, the phenomenon is modelled as a Bernoulli random process, and the predictive compensation loop uses the trained RBF network to maintain the system's tracking state. When normal data are received again, the loop can track the received information well and align the frequency offset locking state. The authors compare the performance of the proposed predictive compensation tracking loop with traditional loop tracking performance using data hold strategies under different packet loss rates. The results demonstrate the effectiveness of the proposed approach in maintaining stable tracking and solving in the discontinuous reception of the loop under packet loss environments. The proposed predictive compensation tracking loop offers a practical solution for addressing packet loss, which is a common issue in real‐world applications.

Quadrotor Trajectory Tracking Using Model Reference Adaptive Control, Neural Network-Based Parameter Uncertainty Compensator, and Different Plant Parameterizations

A quadrotor trajectory tracking problem is addressed via the design of a model reference adaptive control (MRAC) system. As for real-world applications, the entire quadrotor dynamics is typically unknown. To take that into account, we consider a plant model, which contains uncertain nonlinear terms resulting from aerodynamic friction, blade flapping, and the fact that the mass and inertia moments of the quadrotor may change from their nominal values. Unlike many known studies, the explicit equations of the parameter uncertainty for the position control loop are derived in two different ways using the differential flatness approach: the control signals are (i) used and (ii) not used in the parametric uncertainty parameterization. After analysis, the neural network (NN) is chosen for both cases as a compensator of such uncertainty, and the set of NN input signals is justified for each of them. Unlike many known MRAC systems with NN for quadrotors, in this study, we use the kxx+krr baseline controller, which follows from the control system derivation, with both time-invariant (parameterization (i)) and adjustable (parameterization (ii)) parameters instead of an arbitrarily chosen non-tunable PI/PD/PID-like one. Adaptive laws are derived to adjust the parameters of NN uncertainty compensator for both parameterizations. As a result, the position controller ensures the asymptotic stability of the tracking error for both cases under the assumption of perfect attitude loop tracking, which is ensured in the system previously developed by the authors. The results of the numerical experiments support the theoretical conclusions and provide a comparison of the effectiveness of the derived parameterizations. They also allow us to make conclusions on the necessity of the baseline controller adjustment.

A Single-Stage AC–DC Converter Based on Semi Dual-Active-Bridge With Decoupled Inductor Current Modulation Strategy

In this article, a novel decoupled inductor current modulation strategy for a single-stage AC-DC converter based on semi-dual-active-bridge (semi-DAB) is proposed, which helps to minimize the total harmonics distortion (THD) and improve the conversion efficiency. The transformer turns ratio is designed in an optimized method for higher conversion efficiency. Only two control variables are used. And the converter could achieve wider output voltage range and high power factor without mandatory current tracking loop and look-up tables. In addition, losses, THD and backflow power comparisons between the decoupled inductor current and the optimal peak current modulation are presented. The power transfer capability, mode transition mechanism, soft switching range and mode operation region and parameter design are analyzed. Switches can achieve zero-voltage-switching (ZVS) within wide operating rang and rectifier diodes can achieve zero-current-switching (ZCS) off in all operation situations. Besides, a 1kW experimental prototype was built to verify the effectiveness of the proposed control strategy.

Enhancing GNSS receiver performance with software-defined vector carrier tracking for rocket launching

It is well-known that the use of Vector Tracking Loops (VTL) in GNSS receivers can result in improved tracking performance and sensitivity, faster acquisition, and improved interference robustness. However, despite the availability of software-defined radio (SDR) GNSS receivers in practical applications, there is currently no open-source implementation of Vector Tracking techniques able to operate in real-time. This work introduces a VTL algorithm applied to track the Doppler shift and its rate, using the open-source GNSS-SDR framework. This leads to a novel real-time SDR GNSS VTL receiver capable to work with different COTS front-ends. The proposed implementation was tested in a challenging non-conventional, high dynamics positioning scenario to obtain the position and velocity vectors of a rotation-stabilized guided rocket. The scenario was simulated with a GNSS RF signal generator, captured with a COTS front-end and processed by GNSS-SDR. Results show that the algorithm and its proposed implementation are able to provide full tracking, even under demanding accelerations. The positioning performance is measured using standard metrics, and we provide a fully automated reproducibility path. The source code is released under the General Public License v3.0, and will contribute to GNSS-SDR's open-source code base.

A Monolithic Polarization Controller and Tracking Loop for Optical Interconnect Demonstrated on a 90 nm Silicon CMOS-Photonic Platform

We report, to the best of our knowledge, the first monolithically-integrated silicon CMOS-photonic co-designed polarization tracking circuit implemented in a 90 nm CMOS SOI process. The Polarization Splitter and Rotator (PSR) decompose the optical input into TE and TM component and rotate the TM component to TE mode. The directional couplers combine the two TE components from PSR into single optical output. The thermal phase shifters on the optical path maximize the final optical output. A feedback loop implemented with monitoring photodetector, current mode ADC and Finite State Machine (FSM), control the current mode DACs to adjust the current input of thermal phase shifter. The circuit tracks randomized polarization rotation across the Poincaré sphere, maximizes TE-mode optical power, and experimentally achieves a BER of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$10^{-11}$</tex-math></inline-formula> with 10 Gb/s PAM-2 modulation.

A post-correlation graphical way for continuous GNSS spoofing detection

Global navigation satellite system (GNSS) receivers are under the threat of spoofing attacks. The signal quality monitoring (SQM) technique is effective in monitoring the distorted auto-correlation function (ACF). However, it has limited detection effectiveness in detecting spoofing signals that are greatly overpowered and with significant code phase shifts. This paper introduces a new metric called ACF similarity to characterize the ACF distortion and power abnormality in the tracking loop based on image feature extraction techniques. The spoofing detection algorithm and the optimal threshold utilizing the generalized likelihood ratio test (GLRT) are further developed. The performance of the proposed detector has been verified by utilizing the Texas Spoofing Test Battery (TEXBAT) dataset and Monte Carlo simulation tests. Results show that with 1% false alarm rate, the proposed detector achieves a detection probability of 87% in the TEXBAT datasets and provides better detection sensitivity than the conventional SQM metrics.

A Novel Approach for GNSS Signal Tracking Based on Sliding Mode Control

Designing a robust carrier tracking loop for GNSS receivers is a challenging task under strong scintillation, multipath, clock uncertainty, interference, and vehicle high dynamics. The conventional tracking methods such as proportional integral filter (PIF), Wiener filter (WF), and Kalman filter (KF) are known to perform well under given GNSS signal model parameters and noise characteristics. If it is not the case, then performance deteriorates and may result in loss of the carrier lock. To circumvent this problem, we propose a robust control and filtering method based on the well-known sliding mode approach. In this paper, a sliding mode control and state estimation framework is developed for GNSS carrier tracking. The efficacy of the proposed method is proved by simulation studies for GPS(L1) signal. From static to high dynamics operating cases are simulated for proving its usage on the high dynamics vehicles such as high speed trains, flighter jets, and missile systems. The achieved results are promising for use of the proposed method on these vehicles and the receiver operating in the adverse (weak GNSS signal) conditions.

Performance analysis of cross-frequency Doppler-assisted carrier phase tracking

Using the Doppler frequency obtained from tracking a GNSS pilot signal to aid in tracking another signal modulated with higher rate navigation messages in a different frequency band can improve tacking robustness and lower the message demodulation threshold. Based on an analysis of received signal frequency coherence, a linearized mathematical model of the cross-frequency Doppler-assisted carrier phase tracking loop is built, a thermal noise jitter calculation equation for the assisted tracking loop is derived, and its dynamic stress response characteristics are examined. The loop design requirements for eliminating the influence of inter-frequency frequency bias are clarified, as are the cross-frequency assist signal selection criteria. Monte Carlo simulations and preliminary field tests validate the theoretical results using the B1C pilot signal-aided tracking B2b signal of the MEO satellite in the BeiDou satellite navigation system (BDS). Experimental results show that the carrier phase tracking threshold of the B2b signal can be reduced by about 4 dB.

Control of Pneumatic Artificial Muscle Actuated Two Degrees-of-Freedom Robot Using PD-Based Pulse Width Modulation Strategy With Feed-Forward Outer Control Loop

AbstractThis work presents a novel approach for the design and control of a two degrees-of-freedom (DOF) robotic manipulator driven by one pneumatic artificial muscle (PAM) and one passive spring for each of its DOFs. The required air pressure is supplied to the PAMs using fast-switching on/off type pneumatic flow control valves. The proposed control architecture uses a proportional-derivative (PD) controller with a feed-forward term in the outer control loop to correct the position errors using an approximate model of the system dynamics and approximate PAM force-contraction characteristics. An inner pressure regulator loop tracks the reference pressure signals supplied by the outer loop using a pulse width modulation (PWM) scheme to control the pneumatic valves based on the approximated inflation–deflation characteristics for the given pneumatic flow circuit. The proposed controller is unique for PAM actuated robots that simultaneously consider three levels of complications, namely, coupled dynamics of multi-degrees-of-freedom system, non-linearities in the force-contraction characteristics of PAMs, and non-linearities involved in the use of on/off type pneumatic flow control valves. Experiments carried out using a laboratory prototype validate the effectiveness of the proposed control scheme.