Tracking Loop Research Articles

Research on High-Dynamic Tracking Algorithms for FH-BOC Signals

The rapid development of Low Earth Orbit (LEO) satellite navigation systems requires modulation schemes with strong anti-jamming capabilities, high spectral efficiency, and the ability to achieve precise tracking in high-dynamic environments. Traditional Binary Offset Carrier (BOC) modulation suffers from multi-peak ambiguity, leading to false lock issues. To address this, FH-BOC modulation, which integrates BOC modulationand frequency hopping, significantly improves both anti-jamming performance and spectral efficiency. Against this background, this paper proposes a comprehensive high-dynamic tracking algorithm for FH-BOC signals. (1) Based on the adaptive Kalman filter algorithm, high-precision carrier tracking was achieved in high-dynamic environments. (2) By leveraging the correlation between the ranging code and frequency-hopping offset carrier, a composite pseudo-code is generated through the XOR operation, and a corresponding composite code-tracking loop is introduced. (3) Based on code loop tracking results, the frequency-hopping moments of the subcarrier are detected, and a phase-locked loop for the frequency-hopping subcarrier is established. Simulation results indicate that the algorithm achieves centimeter-level pseudorange measurement accuracy for FH-BOC navigation signals under the JPL high-dynamic model.

FPGA-Based High-Frequency Voltage Injection Sensorless Control with Novel Rotor Position Estimation Extraction for Permanent Magnet Synchronous Motor

This study developed a realization of sensorless control for a permanent magnet synchronous motor (PMSM) using a field-programmable gate array (FPGA). Both position and speed were estimated using a high-frequency (HF) injection scheme. Accurate estimation is essential to ensure the proper functioning of sensorless motor control. To improve the estimation accuracy of the rotor position and reduce the motor speed ripple found in conventional methods, a new extraction strategy for estimating the rotor position and motor speed is proposed. First, signal modulation compensation was applied to expand the information of the error function in order to provide more accurate data to the tracking loop system for rotor position extraction. Second, to minimize the motor speed ripple caused by the HF injection, motor speed estimation was performed after obtaining the rotor position information using a differential equation with a low-pass filter (LPF) to avoid the direct effect of the injected signal. Verified experimentally, the results showed that the rotor position error did not exceed 10 el.deg, so these methods effectively reduce the rotor position estimation error by about 30%, along with the motor speed ripple. Therefore, better performance in sensorless PMSM control can be achieved in motor control applications.

Simulation study of spread spectrum communication on satellite

Abstract All the basic principles and simulation models of the PMF-FFT capture algorithm, overlap-transform interference suppression, digital matched filter capture algorithm, delayed phase-locked loop tracking algorithm and Costas ring carrier synchronization in the starborne spread spectrum communication system are elaborated in detail. The waveforms and spectral variations in each stage of spread spectrum communication are simulated and verified using the Simulink tool. The results show that the model can achieve interference suppression, fast capture tracking of pseudocodes, and accurate synchronization of carriers at -30 dB SNR.

Enhanced Multi-UAV Formation Control and Obstacle Avoidance Using IAAPF-SMC

In response to safety concerns pertaining to multi-UAV formation flights, a novel obstacle avoidance method based on an Improved Adaptive Artificial Potential field (IAAPF) is presented. This approach enhances UAV obstacle avoidance capabilities by utilizing segmented attraction potential fields refined with adaptive factors and augmented with virtual forces for inter-UAV collision avoidance. To further enhance the control and stability of multi-UAV formations, a Sliding Mode Control (SMC) method is integrated into the IAAPF-based obstacle avoidance framework. Renowned for its robustness and ability to handle system uncertainties and disturbances, the SMC method is combined with a feedback control system that utilizes inner and outer loops. The outer loop generates the desired path based on the leader’s state and control commands, while the inner loop tracks these trajectories and adjusts the follower UAVs’ motions. This design ensures that obstacle feedback is accounted for before the desired state information is received, enabling effective obstacle avoidance while maintaining formation integrity. Integrating leader-follower formation control techniques with SMC-based multi-UAV obstacle avoidance strategies ensures the effective convergence of the formation velocity and spacing to predetermined values, meeting the cooperative obstacle avoidance requirements of multi-UAV formations. Simulation results validate the efficacy of the proposed method in reaching otherwise unreachable destinations within obstacle-rich environments, while ensuring robust collision avoidance among UAVs.

Defeating angle tracking: A comprehensive analysis of scan rate modulation jamming against sequential lobing radars

AbstractThe authors analyse the sequential lobing radar (SLR) resistance against the scan rate modulation (SRM) jamming technique. Unlike previous studies, the authors analyse SLRs with sinc antenna patterns, enabling investigation of the sidelobe region's vulnerability. By incorporating second‐order angular tracking loops (SOATLs), the first analysis of break‐lock probability for SLRs under SRM jamming is introduced. The analysis reveals the influence of SOATL parameters (damping ratio and natural frequency) on both angular root‐mean‐square‐error at low jamming‐to‐signal‐ratio (JSR) region and break‐lock probability at high JSR region. Additionally, the impact of squint angle on SLR resistance to SRM jamming is examined. Furthermore, the optimal duty cycle as a function of JSR, which maximises break‐lock probability is presented. Significantly, the theoretical results support the 20 dB JSR requirement for SRM effectiveness, often cited experimentally in literature, and extend the theoretical analysis of the SRM technique carried out for the main lobe region of SLRs. This finding bridges the gap between theoretical analysis and practical observations.

A robust integrated navigation optimization method for USV in signal occlusion environment

Unmanned surface vehicles (USV) can use global navigation satellite systems (GNSS) and inertial navigation systems (INS) for combined positioning and navigation. However, buildings such as port facilities and bridges blocking GNSS signals will increase the error in the discriminator output in the GNSS vector tracking loop and reduce positioning accuracy. Meanwhile, due to the cumulative error in the inertial navigation system, the credibility of the navigation results when the signal is blocked is further reduced. In this regard, this study proposes a robust integrated navigation optimization method. Specifically, the RTS smoothing optimized Kalman filter is used to constrain the carrier phase error and code phase error output by the discriminator, which can dynamically adjust the gain of the vector tracking loop, thereby improving the signal tracking capability. Simultaneously, the prediction results of the gated recurrent unit (GRU) network optimized based on the attention mechanism are combined with the inertial navigation system to improve navigation accuracy. Furthermore, an adaptive Kalman filter is utilized as the integrated navigation filter. The actual path of the carrier refers to the navigation solution of the existing receiver. In the open environment, the proposed optimization method reduces horizontal positioning error and speed error by 44.7% and 37.1% respectively compared with existing methods. Simultaneously, it can effectively improve the robustness of positioning in signal obstruction environments. The proposed integrated navigation method provides new possibilities for optimizing USV navigation solutions.

Intelligent mitigation of GPS spoofing using the Kalman filter in the tracking loop based on multi-correlator

In the last decade, spoofing attack has been known as the most dangerous intentional interference in Global Positioning System (GPS). This work suggested an algorithm that performs spoofing mitigation by utilising the Kalman filter. In particular, first, in the tracking stage multi-correlator structure is established and correlators output are investigated by using a Multi-Layer Perceptron Neural Network (MLP NN) in other to detect the spoofing attack, after that, the Kalman filter estimates the DLL discriminator output. The proposed method was verified using three different spoofing in which, the mitigation rate was 84.25%, 93.20% and 97.24%, respectively.

Quadrotor Trajectory Tracking Via SMC-Embedded Wild Horse Optimization

This study provides an integrated control strategy with proportional derivative (PD) and sliding mode control (SMC) for a quadrotor. For inner loop control, the SMC, a robust nonlinear control method, is used to increase the system's resistance to uncertainty and shocks. By using high-speed switching in variable structure control, it reduces tracking mistakes. In the meantime, the PD control concentrates on tracking a helical path while controlling the outer loop for trajectory tracking. The PD and SMC parameters (k1, k2, and k3) could not be manually adjusted to produce acceptable results at first. As a result, this work presents an improvement by optimizing these control parameters using the Wild Horse Optimization (WHO) algorithm, a modern and cutting-edge optimization technique. This improvement shows good results in improving the quadrotor's tracking precision and stability, and it also greatly increases system performance.All simulations were performed in MATLAB, which facilitated detailed analysis and validation of the proposed control strategy.

Environment adaptive navigation (EAN): A data-driven approach for improved navigation accuracy

The quality of GNSS-based navigation services is highly influenced by the type of operating environment. The urban environments with buildings and structures pose substantial challenges for GNSS navigation accuracy. To address this challenge, we propose a data-driven approach Environment Adaptive Navigation (EAN) because complex mathematical models for GNSS environments are impractical for real-time use due to their processing load. This data-driven approach analyzes real-time GNSS data to understand how the environment affects performance and optimize receiver settings for each scenario. Keeping this in view, raw GNSS data was collected through field trials including the three environments: clear sky, partially degraded, and highly degraded. We then analyzed this data to pinpoint factors affecting accuracy, such as the number of available satellites and standard error measurements. The proposed solution, the EAN algorithm, tackles these limitations of the GNSS due to the urban environments and improves the navigation performance. This data-driven approach analyzes real-time GNSS data to identify the specific environment (clear, partially degraded, or highly degraded). Based on this assessment, EAN dynamically adjusts receiver settings, like tracking loop bandwidth, to achieve optimal performance under those conditions. Integrating the EAN model into GNSS receivers allows for real-time environment detection and adaptive configuration. This EAN-based GNSS receiver holds significant promise for safety-critical applications like Intelligent Transportation Systems (ITS). Precise navigation is crucial for functionalities within ITS, such as route optimization and autonomous vehicle operation. The effectiveness of the EAN-based receiver was validated through a field experiment demonstrating a notable increase in tracked satellites and a substantial reduction in outages within a highly degraded environment.

Tracking Loop Current Eddies in the Gulf of Mexico Using Satellite-Derived Chlorophyll-a

During the period of 2018–2022, there were six named Loop Current Eddy (LCE) shedding events in the central Gulf of Mexico (GoM). LCEs form when a large anticyclonic eddy (AE) separates from the main Loop Current (LC) and propagates westward. In doing so, each LCE traps and advects warmer, saltier waters with lower Chlorophyll-a (Chl-a) concentrations than the surrounding Gulf waters. This difference in water mass permits the study of the effectiveness of using Chl-a from satellite-derived ocean color to identify LCEs in the GoM. In this work, we apply an eddy-tracking algorithm to Chl-a to detect LCEs, which we have validated against the traditional sea surface height-(SSH) based eddy-tracking approach with three datasets. We apply a closed-contour eddy-tracking algorithm to the SSH of two model products (HYbrid Coordination Ocean Model; HYCOM and Nucleus for European Modelling of the Ocean; NEMO) and absolute dynamic topography (ADT) from altimetry, as well as satellite-derived Chl-a data to identify the six named LCEs from 2018 to 2022. We find that Chl-a best characterizes LCEs in the summertime due to a basin-wide increase in the horizontal gradient of Chl-a, which permits a more clearly defined eddy edge. This study demonstrates that Chl-a can be effectively used to identify and track LC and LCEs in the GoM, serving as a promising source of information for regional data assimilative models.

Analysis of Power-Maximizing Region 2 Controllers for Wind and Marine Turbines

Wind and marine energy are rapidly growing and complementary technologies that share some techniques for simplified modeling and control, particularly in below-rated flow speeds. A turbine operator has several choices of controller for maximizing power in Region 2. The simple and ubiquitous KΩ2 control law is often effective but limited in its flexibility. Alternative controllers use reference tracking to split the control objectives into a low-bandwidth optimal tip-speed ratio tracking loop to maximize steady-state power and a higher-bandwidth proportional-integral control loop to reject inflow turbulence. Several options exist for identifying the slowly varying optimal set point during operation, based on estimating the inflow velocity or filtering the power or torque signals. This study compares the trade-offs between performance and other design priorities for a few choices of reference-tracking controller in the literature for reference wind and marine turbines. Analysis is performed in the frequency domain using the linearization of each controller, and the impact of turbulent disturbances on the closed-loop system is described. The controllers are simulated in OpenFAST to analyze their performance with higher-order nonlinear turbine dynamics.

Performance Enhancement and Evaluation of a Vector Tracking Receiver Using Adaptive Tracking Loops

The traditional receiver employs scalar tracking loops, resulting in degraded navigation performance in weak signal and high dynamic scenarios. An innovative design of a vector tracking receiver based on nonlinear Kalman filter (KF) tracking loops is proposed in this paper, which combines the strengths of both vector tracking and KF-based tracking loops. First, a comprehensive description of the vector tracking receiver model is presented, and unscented Kalman filter (UKF) is applied to nonlinear tracking loop. Second, to enhance the stability and robustness of the KF tracking loop, we introduce square root filtering and an adaptive mechanism. The tracking loop based on square root UKF (SRUKF) can dynamically adjust its filtering parameters based on signal noise and feedback Doppler error. Finally, the proposed method is implemented on a software-defined receiver (SDR), and the field vehicle experiment demonstrates the superiority of this method over other tracking methods in complex dynamic environments.

A High Dynamic Velocity Locked Loop for the Carrier Tracking of a Wide-Band Hybrid Direct Sequence/Frequency Hopping Spread-Spectrum Signal

For hybrid direct sequence/frequency hopping (DS/FH) spread spectrum signals, even if the relative motion speed between the transmitter and receiver remains constant, the Doppler frequency will vary due to the continuous hopping of the carrier frequency. Under high dynamic conditions, the first-order and second-order change rates of the Doppler frequency attached to the received signal further increase the Doppler frequency agility, making it difficult for the carrier tracking loop to maintain steady-state tracking. To address these issues, a high dynamic velocity locked loop (HD-VLL) is proposed in this paper. Specifically, the accumulated phase tracking error caused by acceleration and jerk is first analyzed. Subsequently, to compensate for this phase tracking error with the system clock, the proposed loop adds an acceleration compensation module and a jerk compensation module. However, this results in the output of the high dynamic loop filter being updated with the system clock, which contradicts the multiplexing design of a traditional loop filter for parallel signal processing, making the hardware implementation of an HD-VLL impractical. Therefore, this contradiction leads us to design an HD-VLL-based multi-carrier NCO (HD-VLL-NCO). The HD-VLL and HD-VLL-NCO are simulated, revealing the HD-VLL’s superior dynamic adaptability and steady-state tracking, while the HD-VLL-NCO achieves comparable accuracy with the appropriate truncation bit width.

High-performance finite-time adaptive control strategy for three-level T-type converters

Three-level T-type converters are necessary interfaces for distributed energy resources to interact with the public grid. Naturally, designing a control strategy, featuring superior dynamics and strong robustness, is a promising solution to guarantee the efficient operation of converters. This article presents an improved finite-time control (IFTC) strategy for three-level T-type converters to enhance the dynamic performance and anti-disturbance capacity. The IFTC strategy integrates a dual-loop structure to regulate the dc-link voltage and grid currents. Specifically, the voltage regulation loop employs a finite-time adaptive controller that can counteract load disturbances without relying on current sensors. In the current tracking loop, finite-time controllers combined with a command filter are constructed to obtain fast and accurate current tracking. In this loop, the command filter is utilized to avoid calculating the derivative of current references. Theoretical analysis and experimental results demonstrate the IFTC strategy’s effectiveness.

Enhancing USVs navigation based on minimum error entropy of GPS vector tracking

In recent years, unmanned surface Vessels (USVs) have increasingly been used for river monitoring and hydrological surveys. USVs rely on global navigation satellite systems (GNSS) for navigation. However, signal blocking can cause the traditional GNSS vector tracking (VT) loop to increase the code phase and carrier frequency errors, leading to higher positioning errors that do not meet USVs’ requirements. To address this problem, we propose a VT method based on the minimum error entropy (MEE) in the signal tracking module. The MEE Kalman filter is adopted as the loop filter to mitigate code phase and carrier frequency errors, reduce non-Gaussian noise and random errors generated by signal blocking, and enhance the positioning accuracy and robustness of USV navigation. The measurement noise covariance of the loop filter was adjusted adaptively using the signal carrier-to-noise ratio. A field experiment was conducted using a commercial GNSS receiver as reference. The results demonstrate a 19.3% improvement in positioning accuracy compared with the traditional method in an open environment. Moreover, the proposed method maintains stable operation and achieves a 79.4% improvement in positioning accuracy during signal blocking. This novel algorithm offers a new concept for USV navigation systems to cope with signal blocking.

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.

A Loop-Gain-Adaptive-Adjustment Method Based on Fuzzy Logic for Timing Recovery in Space TT&C Systems

This work proposes an loop-gain-adaptive-adjustment (LGAA) algorithm for the timing recovery tracking loop in space tracking, telemetry and command (TT&C) systems. The proposed algorithm generates an adjustment coefficient by using a fuzzy logic (FL) controller, which is designed based on the tracking loop convergence characteristics. The proposed algorithm could enhance the performance of the timing recovery without changing other parameters of the tracking loop. Simulation results show that the proposed LGAA-based tracking loop achieves a better balance between locking time and tracking accuracy compared to the conventional tracking loop that uses a fixed loop gain.

Precision Landing of Unmanned Aerial Vehicle under Wind Disturbance Using Derivative Sliding Mode Nonlinear Disturbance Observer-Based Control Method

Unmanned aerial vehicles (UAVs) are extensively employed in civilian and military applications because of their excellent maneuverability. Achieving fully autonomous quadrotor flight and precision landing on a wireless charging station in the presence of wind disturbance has become a crucial research topic. This paper presents a composite control technique for UAV altitude and attitude tracking in harsh environments, i.e., wind disturbance. A composite controller was developed based on nonlinear disturbance observer (NDOB) control theory to allow the UAV to land in the presence of random external wind disturbances and ground effects. The NDOB estimated the unknown wind disturbance, and the estimation was fed into the derivative sliding mode nonlinear disturbance observer-based control (DSMNDOBC), allowing the UAV to perform autonomous precision landing. Two loop designs were applied: the inner loop for stabilization and the outer loop for altitude tracking. The quadrotor model dynamics and the proposed controller, DSMNDOBC, were simulated employing MATLAB/Simulink®, and the results were compared with the one obtained by the proportional derivative (PD) controller and the sliding mode controller (SMC). The simulation results indicated that the DSMNDOBC has superior altitude and attitude control compared to the PD and SMC controllers and better disturbance estimation and attenuation performance.

Anti-Multipath Underwater Acoustic Time-Delay Detection Algorithm Based on Dual-Delta Correlators

For the underwater acoustic (UAC) positioning system based on continuous waveform signal, the time-delay estimation of the Line-of-sight (Los) is not robust under the UAC strongly time-varying multipath channel. So an anti-multipath time-delay detection algorithm based on dual-delta (DD) correlators is proposed in this paper to address the issue. The algorithm uses a differential processing code-phase discriminator model to improve the traditional delay-locked-loop (DLL) time-delay detection algorithm, and combines it with the signal tracking loop adapted to the UAC channel condition to estimate time-delay. Theoretical analysis indicates that due to the reduction of local code interval and the differential processing operation, the proposed algorithm effectively mitigates the effect of time-varying multipath signals on time-delay estimation compared with conventional methods. Simulation analysis further demonstrates that the proposed algorithm can robustly detect the Los and achieve high-precision time-delay estimation under the time-varying multipath channel. The algorithm shows great potential for practical applications.

Perturbed Unicycle Mobile Robots: A Second-Order Sliding-Mode Trajectory Tracking Control

This paper contributes to the design of a second–order sliding–mode controller for the trajectory tracking problem in perturbed unicycle mobile robots. The proposed strategy takes into account the design of two particular sliding variables, which ensure the convergence of the tracking error to the origin in a finite time despite the effect of some external perturbations. The straightforward structure of the controller is simple to tune and implement. The global, uniform and finite–time stability of the closed–loop tracking error dynamics is demonstrated by means of Lyapunov functions. Furthermore, the performance of the proposed approach is validated through some experiments using a QBot2 unicycle mobile robot.