High-Speed Target Tracking Method for Compact HF Radar | IEEE Journals & Magazine | IEEE Xplore

High-Speed Target Tracking Method for Compact HF Radar | IEEE Journals & Magazine | IEEE Xplore

G. Liu, Y. Tian, J. Yang, S. Ma and B. Wen, "High-Speed Target Tracking Method for Compact HF Radar," in IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol. 17, pp. 13276-13291, 2024, doi: 10.1109/JSTARS.2024.3431535.

Abstract: Compact high-frequency (HF) surface wave radar can be used for remote sensing of sea surface dynamic parameters, such as winds, waves, and currents, as well as hard targets, such as ships and low-altitude aircrafts. Due to its small antenna aperture, compact HF radar usually has a large error in direction of arrival (DOA) estimation, which significantly reduces its accuracy of target tracking. For a high-speed target, the DOA estimation error is greater due to range migration and Doppler frequency migration as well as rapid change in the DOA of target echo. 

A high-speed target tracking method for compact HF radar is proposed in this article, which utilizes the zero-mean property of the DOA error. First, the generalized Radon Fourier transform is used to estimate the target's motion parameters, and the multiple signal classification algorithm is used to estimate the target's DOA. The original target track is obtained by combining the range and DOA estimates. Next, multiple positions on the original track are selected as the base points, and for each base point, a predicted track can be calculated based on the target motion parameter estimates, thus multiple predicted tracks are obtained. Then, these predicted tracks are screened according to their headings. The remaining predicted tracks after screening are fused to obtain the final track. Numerical simulations and field experiments demonstrate that this method reduces the impact of DOA error on tracking accuracy and expands the application of compact HF radar for high-speed target tracking.

keywords: {Target tracking;Radar tracking;Direction-of-arrival estimation;High frequency radar;Accuracy;Doppler effect;Sea surface;Compact high-frequency (HF) radar;direction of arrival (DOA);Doppler frequency migration (DFM);generalized Radon Fourier transform (GRFT);high-speed target tracking;range migration (RM)},

URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10605987&isnumber=10330207

Authors

Based on the information provided in the paper, here are details about the authors, their institutional associations, and some indications of their prior related works:

1. Gan Liu:
   - Affiliation: School of Electronic Information, Wuhan University, Wuhan, China
   - Education: Received B.Eng. from Hubei University of Arts and Sciences in 2017, M.S. from Kunming University of Science and Technology in 2020
   - Currently pursuing Ph.D. in electronic information at Wuhan University
   - Research interests: Target detection and tracking using high-frequency radar

2. Yingwei Tian (Member, IEEE):
   - Affiliation: School of Electronic Information, Wuhan University, Wuhan, China; also with Wuhan University Shenzhen Research Institute, Shenzhen, China
   - Education: Received B.Eng. and Ph.D. from Wuhan University in 2010 and 2015 respectively
   - Current position: Associate Professor at Wuhan University
   - Prior experience: Postdoctoral Fellow in geophysics at Wuhan University (2015-2018), Visiting Scholar at Memorial University, Canada (2018-2019)
   - Research interests: Hardware design and signal processing of HF and UHF radar systems, ocean surface remote sensing

3. Jing Yang (Member, IEEE):
   - Affiliation: School of Electronic Information, Wuhan University, Wuhan, China
   - Education: Received B.E. and Ph.D. from Wuhan University in 2005 and 2010 respectively
   - Current position: With the School of Electronic Information, Wuhan University since 2011
   - Research interests: Ocean surface remote sensing and signal processing

4. Shengbo Ma:
   - Affiliation: School of Electronic Information, Wuhan University, Wuhan, China
   - Education: Received bachelor's degree from South Central University for Nationalities in 2017, Master's degree from Wuhan University in 2024
   - Research focus: Detecting vessel targets and optimizing their tracks using high-frequency ground wave radar

5. Biyang Wen:
   - Affiliation: School of Electronic Information, Wuhan University, Wuhan, China
   - Education: Received B.Eng. from Shanghai Jiao Tong University in 1983, M.S. and Ph.D. from Wuhan University in 1990 and 1997 respectively
   - Current position: Professor at Wuhan University (since 1990)
   - Research interests: Radio wave propagation and remote sensing of ocean surface via high-frequency ground wave radar and UHF radar Research Gate

Prior related works:
While the paper doesn't provide a comprehensive list of the authors' prior works, it does reference several related papers by some of the authors, indicating their ongoing work in this field:

1. Tian et al. (2017) on pattern distortion and DOA estimation performance of crossed-loop/monopole antenna in HF radar
2. Tian et al. (2021) on wave-height map extraction from compact HF surface-wave radar network
3. Tian et al. (2023) on robust track association for ship localization with multiple compact HF radars

These works suggest an ongoing research program at Wuhan University focusing on various aspects of HF radar technology, particularly for maritime applications and ocean surface sensing.

Summary

Researchers at Wuhan University, Wuhan, China have developed a method to use bistatic HF radar with a compact antenna for ship and aircraft tracking. Here are the key points summarizing the high-speed target tracking method for compact HF radar:

1. The method addresses challenges in tracking high-speed targets that cause significant range migration (RM) and Doppler frequency migration (DFM) with compact HF radar.

2. It uses the generalized Radon Fourier transform (GRFT) algorithm to detect targets and estimate motion parameters, overcoming issues caused by RM and DFM.

3. The method leverages the zero-mean distribution property of direction of arrival (DOA) estimation errors to reduce their impact on tracking accuracy.

4. Key steps include:
   - Estimating original track using GRFT and MUSIC algorithms
   - Predicting multiple tracks based on the original track
   - Screening predicted tracks based on average headings  
   - Fusing screened tracks to generate the final track

5. Numerical simulations and field experiments demonstrated the method's effectiveness, especially for targets with large DOA estimation errors.

6. Compared to conventional CV-Kalman and CA-Kalman filters, the proposed method showed superior performance in reducing tracking errors.

7. The method works for both circular and rectilinear target motions.

8. Limitations include the requirement for constant DOA trend over a coherent processing interval (CPI) and potential impacts from sea clutter.

9. Future work may focus on reducing CPI length, joint processing of multiple CPIs, and testing in coastal environments with sea clutter.

In summary, this method improves high-speed target tracking for compact HF radar by addressing RM and DFM issues and mitigating DOA estimation errors through innovative signal processing techniques.

Figures and Tables

Here's a list of the figures and tables in the paper, along with explanations of what each shows:

1. Figure 1: Shows simulated Range-Time (RT) and Range-Doppler (RD) maps for low-speed and high-speed targets, illustrating the effects of range migration (RM) and Doppler frequency migration (DFM).
2. Figure 2: Presents the framework of the proposed method, showing the main steps of the algorithm.
3. Figure 3: Illustrates the geometric relationship between the target and radar, explaining the circular motion model used in the paper.
4. Figure 4: Demonstrates the schematic of track prediction within the Cartesian coordinate system.
5. Figure 5: Displays simulated echo spectra (RT and RD maps) of a target in circular motion within a Coherent Processing Interval (CPI).
6. Figure 6: Shows processing results of a simulated circular motion, including original track, predicted tracks, histogram of average headings, and comparison of different tracking methods.
7. Figure 7: Presents simulated echo spectra (RT and RD maps) of a target in rectilinear motion within a CPI.
8. Figure 8: Illustrates processing results of a simulated rectilinear motion, similar to Figure 6 but for straight-line movement.
9. Figure 9: Displays RMSEs of GRFT parameter estimation for different echo SNRs.
10. Figure 10: Shows target localization RMSEs under different GRFT searching intervals.
11. Figure 11: Presents target localization RMSEs under different DOA errors.
12. Figure 12: Illustrates fusion track RMSEs under different retention proportions.
13. Figure 13: Shows the transmitting and receiving antennas of the compact HF radar used in the field experiment.
14. Figure 14: Displays echo spectra (RT and RD maps) of a real target measured during the field experiment.
15. Figure 15: Presents tracking results of a real target (Target 2), including various tracks and histograms.
16. Figure 16: Shows tracking results and DOA estimation errors for six additional real targets.
17. Figure 17: Illustrates RMSEs of tracking results and DOA estimates for seven real targets.

Tables:

1. Table I: Lists the compact HF radar parameters used in the study.
2. Table II: Provides the target parameters used in the simulation.
3. Table III: Details the parameter searching scope of the GRFT algorithm.

These figures and tables provide visual and numerical support for the method's development, implementation, and performance evaluation through simulations and field experiments. 

Proposed Approach

Figure 2 presents the framework of the proposed high-speed target tracking method for compact HF radar. Let me break down the process and explain how the technique works:

1. Input:
The method starts with RT (Range-Time) spectra corresponding to three receiving antenna elements of the compact HF radar.

2. Estimation of Original Track:
   a. GRFT (Generalized Radon Fourier Transform):
      - Applied to the RT spectrum of the monopole antenna.
      - Detects the target and estimates motion parameters (initial range, speed, projection angle, curvature).
      - Calculates target range estimates for each pulse.

   b. MUSIC (Multiple Signal Classification):
      - Applied to the RT spectra of all three antenna elements.
      - Estimates the Direction of Arrival (DOA) for each pulse.

   c. Original Track Synthesis:
      - Combines range estimates from GRFT and DOA estimates from MUSIC.
      - Creates an initial track that may have significant errors due to DOA inaccuracies.

3. Track Prediction:
   - Selects multiple base points on the original track.
   - For each base point, calculates a predicted track using the estimated motion parameters.
   - Results in a set of multiple predicted tracks.

4. Screening of Predicted Tracks:
   - Calculates the average heading for each predicted track.
   - Creates a histogram of these average headings.
   - Sets upper and lower boundaries for acceptable headings.
   - Screens out tracks with average headings outside these boundaries.

5. Track Fusion:
   - Averages the remaining predicted tracks after screening.
   - Produces the final fusion track.

How the technique works:

1. Overcoming Range and Doppler Migration:
   - GRFT is used instead of conventional methods to handle the Range Migration (RM) and Doppler Frequency Migration (DFM) caused by high-speed targets.
   - This allows for coherent integration over longer times, improving detection and parameter estimation.

2. Mitigating DOA Errors:
   - The method leverages the fact that DOA errors typically follow a zero-mean distribution.
   - By predicting multiple tracks based on different points (with different DOA errors) and then averaging them, the method tends to cancel out these errors.

3. Improving Accuracy:
   - The screening process removes predicted tracks that deviate significantly from the majority, helping to eliminate outliers caused by large DOA errors.
   - The fusion of multiple screened tracks further reduces the impact of remaining errors.

4. Adaptability:
   - The method can handle both linear and curved target motions by estimating curvature as one of the motion parameters.

5. Robustness:
   - By relying more on the GRFT-estimated motion parameters and less on individual DOA estimates, the method is more robust to DOA errors than conventional tracking filters.

The key innovation of this technique is its ability to leverage multiple predicted tracks to overcome the large DOA errors typical in compact HF radar systems, while also handling the RM and DFM issues associated with high-speed targets. This results in more accurate tracking compared to conventional methods, especially in challenging scenarios with high-speed targets and significant DOA errors.

Demo Performance

The field experiment used a compact HF radar with the following key parameters:

1. Carrier frequency: 13 MHz
2. Bandwidth: 60 kHz
3. Pulse repetition frequency: 3.704 kHz
4. Coherent processing interval: 69.12 s
5. Range resolution: 2.5 km
6. Velocity resolution: 0.167 m/s

The radar used a monopole antenna for transmitting and a crossed-loop/monopole (CLM) antenna for receiving. It was located about 20 km from a civilian airport, primarily observing civil aircraft.

Target Parameters:

The paper doesn't provide specific velocity components for individual targets. However, it mentions that the observed civil aircraft were at altitudes between 6 and 12.6 km, with ranges comparable to their altitudes. This suggests they were likely in various phases of takeoff, landing, or cruising, with velocities typical for commercial aircraft (roughly 100-250 m/s, though exact figures aren't given).

An Automatic Dependent Surveillance-Broadcast (ADS-B) system was used during the field tests to provide ground truth data for the target tracking experiments. Specifically:

1. ADS-B System: The paper mentions that an ADS-B system was located adjacent to the radar site.

2. Purpose: This ADS-B system was used to provide real-time information about aircraft positions, serving as the ground truth for evaluating the performance of the proposed tracking method.

3. Data Provided: The ADS-B system provided accurate information on the aircraft's position, including altitude. This was crucial for:

• Calculating the true horizontal range of the aircraft (by combining ADS-B altitude data with the slant range measured by the radar).
•  Determining the actual track of the aircraft for comparison with the estimated tracks.
•  Calculating the errors in the radar's direction of arrival (DOA) estimates.

4. Performance Evaluation: The ADS-B data allowed the researchers to:

• Calculate the Root Mean Square Errors (RMSEs) of the various tracking methods (proposed method, CV-Kalman filter, CA-Kalman filter).
• Assess the accuracy of the DOA estimates.
• Validate the performance of the proposed method under real-world conditions.

5. Altitude Information: The ADS-B system provided crucial altitude information, which was used to convert the radar's slant range measurements to horizontal range estimates. This was particularly important because the compact HF radar itself cannot measure target altitude.

The use of the ADS-B system for ground truth data was a key component of the field experiments, allowing for a thorough and accurate assessment of the proposed high-speed target tracking method under real-world conditions with actual aircraft targets.

Performance Demonstrated:

1. Position Estimation Accuracy:

• For the best-case scenario (Target 6), the Root Mean Square Error (RMSE) of the fusion track was 0.64 km.
• For the worst-case scenario (Target 7), the RMSE was 2.08 km.
• The method consistently outperformed conventional CV-Kalman and CA-Kalman filters across all targets.

2. Velocity Estimation:
   The paper doesn't provide explicit velocity estimation errors. However, the accuracy of velocity estimation is implicit in the overall tracking performance, as the method uses estimated motion parameters (including velocity) to predict and refine tracks.

3. DOA Estimation:
   - DOA estimation errors varied across targets, with RMSEs ranging from about 5° to over 25°.
   - The proposed method showed robustness to these DOA errors, maintaining good tracking performance even with large DOA errors.

4. Comparison to Other Methods:
   - The proposed method consistently achieved lower RMSEs compared to CV-Kalman and CA-Kalman filters for all observed targets.
   - For example, for Target 2, the RMSEs were:
     * Proposed method (fusion track): 1.71 km
     * CV-Kalman filter: 3.68 km
     * CA-Kalman filter: 3.94 km

5. Robustness:
   The method demonstrated good performance across various target trajectories, including curved and straight paths, and maintained accuracy even with significant DOA estimation errors.

It's important to note that while the paper demonstrates good overall tracking performance, it doesn't provide separate accuracy metrics for radial and cross-range velocity components. The focus is more on the overall tracking accuracy in terms of position RMSE and the method's ability to handle large DOA errors effectively.

Extension to OTH Ionobounce HF Radar for Hypersonic Targets

The proposed technique could potentially be adapted for use in an over-the-horizon (OTH) HF radar using ionospheric bounce to track hypersonic targets, but several significant modifications and considerations would be necessary:

1. Ionospheric Effects:
   - The technique would need to account for ionospheric variations, which affect signal propagation and introduce additional uncertainties.
   - Models for ionospheric refraction and multipath effects would need to be incorporated.

2. Range and Doppler Migration:
   - For hypersonic targets, range migration (RM) and Doppler frequency migration (DFM) would be even more severe.
   - The GRFT algorithm might need to be extended to handle extremely high velocities and accelerations.

3. Parameter Modifications:
   a. Frequency: Likely need to use lower frequencies (5-30 MHz) for better ionospheric penetration.
   b. Bandwidth: Might need to be reduced to mitigate ionospheric dispersion effects.
   c. Coherent Processing Interval (CPI): Likely needs to be shorter due to faster target motion and ionospheric variability.
   d. Velocity Resolution: Must be adjusted for much higher target velocities (>5 Mach).
   e. Range Resolution: May be coarser due to ionospheric effects and potentially reduced bandwidth.

4. Motion Model:
   - The circular motion model might need to be replaced or extended to account for ballistic or more complex hypersonic trajectories.
   - Higher-order motion parameters (like jerk or snap) might need to be included.

5. DOA Estimation:
   - The MUSIC algorithm would need to be adapted for the complex, multi-path environment of ionospheric propagation.
   - Angle-of-arrival estimation would need to consider both azimuth and elevation due to the 3D nature of ionospheric propagation.

6. Track Prediction and Fusion:
   - The prediction step would need to account for the curved Earth geometry and ionospheric ray paths.
   - The screening and fusion processes might need to be more robust to handle larger uncertainties.

7. Coordinate System:
   - The tracking would likely need to be done in a 3D coordinate system rather than the 2D system used in the original method.

8. Clutter Handling:
   - Additional clutter suppression techniques might be necessary to handle ionospheric clutter, which can be more complex than sea clutter.

9. Update Rate:
   - The tracking update rate might need to be increased to handle the rapid changes in hypersonic target position.

10. Computational Requirements:
    - The computational load would likely increase significantly, potentially requiring more powerful hardware or optimized algorithms.

11. Multi-static Configuration:
    - OTH radars often use separate transmit and receive sites. The method would need to be adapted for this configuration.

12. Ambiguity Resolution:
    - Techniques for resolving range and Doppler ambiguities, which are more pronounced in OTH systems, would need to be incorporated.

While the core idea of using multiple predicted tracks to mitigate DOA errors could still be valuable, the implementation would require substantial modifications to handle the unique challenges of OTH radar and hypersonic targets. Extensive simulation and testing would be necessary to validate the adapted method's performance in this more complex scenario.

Hardware

Described in Z. Li, B. Wen, and Y. Tian, "Design and implementation of a dual-frequency compact antenna system for HF radar," IEEE Antennas Wireless Propag. Lett., vol. 16, pp. 1887–1890, 2017.

This document provides more details on the antenna system used in the HF radar described in the previous article. Here's a summary of the key design aspects:

1. Antenna System Overview:
   - Dual-frequency compact antenna system for HF radar
   - Operates at 7.8 MHz and 13 MHz
   - Composed of three sensing elements: one monopole and two crossed-loop antennas

2. Monopole Antenna:
   - Height: 2.5 meters
   - Electrically small antenna in vertical polarization
   - Efficient enough to receive both frequencies (45% efficiency at 7.8 MHz, 70% at 13 MHz)

3. Crossed-Loop Antennas:
   - Two orthogonal, vertically polarized loops
   - Each loop composed of two parallel halves for symmetry
   - Each half contains four ferrite rods with induction coils
   - 14 turns of wire, total length about 1.2 meters
   - Very low efficiency (about 8.8 × 10^-5 at 7.8 MHz and 9.4 × 10^-4 at 13 MHz)

4. Frequency Control Module (FCM):
   - Uses symmetric p-i-n diodes as an electronic switch
   - Allows time-shared dual-frequency operation
   - Switches between two resonant frequencies: f1 = 7.8 MHz, f2 = 13 MHz

5. Electrical Performance:
   - Bandwidth: 2.1 MHz at 7.8 MHz, 2.3 MHz at 13 MHz
   - Quality factor (Q): 3.7 at 7.8 MHz, 5.7 at 13 MHz
   - Low-Q/broadband antenna design

6. Field Performance:
   - Isolation between loops: 28 dB at 7.8 MHz, 28.5 dB at 13 MHz
   - Directivity: 25-32 dB difference between maximum and minimum for each loop
   - Sea echo spectra show SNRs of about 35 dB at 7.8 MHz and 40 dB at 13 MHz

The design allows for dual-frequency operation using a single compact antenna system, enabling multi-scale ocean observation and improved adaptability to various sea states and electromagnetic environments. The key innovation is the use of the FCM with p-i-n diodes to switch between frequencies, allowing the low-efficiency loop antennas to operate effectively at both frequencies.

Software

The article doesn't provide detailed descriptions of specific software packages used for simulation and radar processing. However, I can describe the key algorithms and processes that would need to be implemented in software, based on the information in the paper. I'll provide a high-level overview and some sample Python code to illustrate key concepts.

Key Software Components:

1. GRFT (Generalized Radon Fourier Transform) Algorithm
2. MUSIC (Multiple Signal Classification) Algorithm
3. Track Prediction and Fusion
4. Kalman Filters (for comparison)
5. Simulation of radar signals and target motion

Here's a simplified Python implementation of some key components:

```python
import numpy as np
from scipy.signal import chirp
from scipy.linalg import eig

def generate_radar_signal(t, f0, f1, t1, method='linear'):
    return chirp(t, f0=f0, f1=f1, t1=t1, method=method)

def simulate_target_echo(t, r0, v, a):
    # Simplified target echo simulation
    r = r0 + v*t + 0.5*a*t**2
    phase = 4*np.pi*r/0.23  # Assuming wavelength of 0.23m (13 MHz)
    return np.exp(1j * phase)

def grft(signal, t, r_range, v_range):
    # Simplified GRFT implementation
    result = np.zeros((len(r_range), len(v_range)))
    for i, r in enumerate(r_range):
        for j, v in enumerate(v_range):
            phase = 4*np.pi*(r + v*t)/0.23
            result[i,j] = np.abs(np.sum(signal * np.exp(-1j * phase)))
    return result

def music(data, n_signals):
    # Simplified MUSIC implementation
    R = np.cov(data)
    eigenvalues, eigenvectors = eig(R)
    idx = eigenvalues.argsort()[::-1]
    En = eigenvectors[:, idx[n_signals:]]
    
    theta = np.linspace(0, np.pi, 181)
    music_spectrum = np.zeros_like(theta)
    
    for i, angle in enumerate(theta):
        a = np.exp(-1j * np.pi * np.sin(angle) * np.arange(data.shape[0]))
        music_spectrum[i] = 1 / np.abs(a.conj().T @ En @ En.conj().T @ a)
    
    return music_spectrum, theta

def kalman_filter(z, x_init, P_init, F, H, Q, R):
    # Simplified Kalman filter implementation
    x = x_init
    P = P_init
    x_posterior = []
    
    for measurement in z:
        # Predict
        x = F @ x
        P = F @ P @ F.T + Q
        
        # Update
        y = measurement - H @ x
        S = H @ P @ H.T + R
        K = P @ H.T @ np.linalg.inv(S)
        x = x + K @ y
        P = (np.eye(len(x)) - K @ H) @ P
        
        x_posterior.append(x)
    
    return np.array(x_posterior)

# Simulation parameters
t = np.linspace(0, 69.12, 256)  # 69.12s CPI, 256 pulses
r0, v0, a = 30000, 200, 2  # Initial range (m), velocity (m/s), acceleration (m/s^2)

# Generate simulated radar signal
radar_signal = generate_radar_signal(t, f0=13e6, f1=13.06e6, t1=69.12)
target_echo = simulate_target_echo(t, r0, v0, a)
received_signal = radar_signal * target_echo

# Perform GRFT
r_range = np.linspace(25000, 35000, 100)
v_range = np.linspace(150, 250, 100)
grft_result = grft(received_signal, t, r_range, v_range)

# Perform MUSIC (assuming 3 antenna elements)
antenna_data = np.array([received_signal, received_signal*np.exp(1j*np.pi/4), received_signal*np.exp(1j*np.pi/2)])
music_spectrum, theta = music(antenna_data, n_signals=1)

# Kalman Filter setup (simplified)
F = np.array([[1, 1], [0, 1]])  # State transition matrix
H = np.array([[1, 0]])  # Measurement matrix
Q = np.eye(2) * 0.1  # Process noise covariance
R = np.array([[100]])  # Measurement noise covariance
x_init = np.array([r0, v0])  # Initial state
P_init = np.eye(2) * 1000  # Initial covariance

# Generate noisy measurements
measurements = r0 + v0*t + 0.5*a*t**2 + np.random.normal(0, 10, len(t))

# Apply Kalman filter
kalman_result = kalman_filter(measurements, x_init, P_init, F, H, Q, R)

# Results would be further processed for track prediction and fusion

This code provides a basic framework for simulating radar signals, implementing key algorithms (GRFT, MUSIC, Kalman filter), and processing the results. However, it's greatly simplified and doesn't include the full complexity of the method described in the paper, such as track prediction, screening, and fusion.

To fully replicate the research, you would need to expand this code significantly, implement more sophisticated versions of these algorithms, and add additional components for track prediction and fusion as described in the paper.