Radar High-speed Target Tracking via Quick Unscented Kalman Filter

SONG Jiazhen; SHI Zhuoyue; ZHANG Xiaoping; LIU Zhenyu

doi:10.11999/JEIT250010

Volume 47 Issue 8

Aug. 2025

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SONG Jiazhen, SHI Zhuoyue, ZHANG Xiaoping, LIU Zhenyu. Radar High-speed Target Tracking via Quick Unscented Kalman Filter[J]. Journal of Electronics & Information Technology, 2025, 47(8): 2703-2713. doi: 10.11999/JEIT250010

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SONG Jiazhen, SHI Zhuoyue, ZHANG Xiaoping, LIU Zhenyu. Radar High-speed Target Tracking via Quick Unscented Kalman Filter[J]. Journal of Electronics & Information Technology, 2025, 47(8): 2703-2713. doi: 10.11999/JEIT250010

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Radar High-speed Target Tracking via Quick Unscented Kalman Filter

doi: 10.11999/JEIT250010 cstr: 32379.14.JEIT250010

Tsinghua Shenzhen International Graduate School, Shenzhen 518055, China

Funds: The National Natural Science Foundation of China (62388102), Shenzhen Science and Technology Program (WDZC20231130080128001)

Received Date: 2025-01-07
Rev Recd Date: 2025-05-09

Available Online: 2025-05-24

Publish Date: 2025-08-27

Abstract

Abstract

Objective The increasing prevalence of high-speed targets due to advancements in space technology presents new challenges for radar tracking. The pronounced motion of such targets within a single frame induces large variations in range, causing dispersion of echo energy across the range-Doppler plane and invalidating the assumption of concentrated target energy. This results in “range cell migration” and “Doppler cell migration”, both of which degrade tracking accuracy. To address these challenges, this study proposes a Quick Unscented Kalman Filter (Q-UKF) algorithm tailored for high-speed radar target tracking. The Q-UKF performs recursive, pulse-by-pulse state estimation directly from radar echo signals, thereby improving tracking precision and eliminating the need for conventional energy correction and migration compensation. Furthermore, the algorithm employs the Woodbury matrix identity to reduce computational burden while preserving the estimation accuracy of the standard Unscented Kalman Filter (UKF). Methods The target state vector at each pulse time is modeled as a three-dimensional random vector representing position, velocity, and acceleration. Target motion is governed by a kinematic model that characterizes its temporal dynamics. A measurement model is formulated based on the radar echo signals received at each pulse, defining a nonlinear relationship between the target state and the observed measurements. This formulation supports recursive state estimation. In the classical UKF, the high dimensionality of radar echo data necessitates frequent inversion of large covariance matrices, imposing a substantial computational burden. To mitigate this issue, the Q-UKF is developed. By incorporating the Woodbury matrix identity, the Q-UKF reduces the computational complexity of matrix inversion without compromising estimation accuracy relative to the classical UKF. Within this framework, Q-UKF performs pulse-by-pulse recursive estimation, integrating all measurements up to the current pulse to improve prediction accuracy. In contrast to conventional radar tracking methods that process complete frame data and apply multiple signal correction steps, Q-UKF operates directly on raw measurements and avoids such corrections, thereby simplifying the processing pipeline. This efficiency makes Q-UKF well suited for real-time tracking of high-speed targets. Results and Discussions The performance of the proposed Q-UKF method is assessed using Monte Carlo simulations. Estimation errors of the Q-UKF and Extended Kalman Filter (EKF) are compared over time (Fig. 3). During the effective pulse periods within each frame cycle, both methods yield accurate target state estimates. Estimation errors increase during the delay intervals, but rapidly decrease and stabilize once effective pulse signals resume, forming a periodic error pattern. To evaluate robustness, the Root Mean Square Error (RMSE) of state estimation is examined under varied initial conditions, including different positions, velocities, and accelerations. In all scenarios, both Q-UKF and EKF perform reliably, with Q-UKF consistently demonstrating superior accuracy (Fig. 4). Under Signal-to-Noise Ratios (SNRs) from –15 dB to 0 dB, the RMSEs in both Gaussian and Rayleigh noise environments (Fig. 5a and Fig. 5b) decrease with increasing SNR. Q-UKF maintains high accuracy even under low SNR conditions. In the Gaussian noise setting, Q-UKF improves estimation accuracy by an average of 10.60% relative to EKF; in the Rayleigh environment, the average improvement is 9.55%. In terms of computational efficiency, Q-UKF demonstrates the lowest runtime among the evaluated methods (EKF, UKF, and Particle Filter (PF)). The average computation time per effective pulse is reduced by 8.91% compared to EKF, 72.55% compared to UKF, and over 90% compared to PF (Table 2). This efficiency gain results from applying the Woodbury matrix identity, which alleviates the computational load of matrix inversion in high-dimensional radar echo data processing. Conclusions This study presents the Q-UKF method for high-speed target tracking in radar systems. The algorithm performs pulse-by-pulse state estimation directly from radar echo signals, advancing estimation granularity from the frame level to the pulse level. By removing the need for energy accumulation and migration correction, Q-UKF simplifies the conventional signal processing pipeline. The method incorporates the Woodbury matrix identity to efficiently invert covariance matrices, substantially reducing computational load. Simulation results show that Q-UKF consistently outperforms the EKF in estimation accuracy under varied initial target states, achieving an average improvement of approximately 10.60% under Gaussian noise and 9.55% under Rayleigh noise. Additionally, Q-UKF improves computational efficiency by 8.91% compared to EKF. Compared to the classical UKF, Q-UKF delivers equivalent accuracy with significantly reduced runtime. Although the PF may yield slightly better accuracy under certain conditions, its computational demand limits its practicality in real-time applications. Overall, Q-UKF provides a favorable balance between accuracy and efficiency, making it a viable solution for real-time tracking of high-speed targets. Its ability to address high-dimensional, nonlinear measurement problems also highlights its potential for broader application.
- High-speed target tracking,
- Kalman filter,
- Range cell migration

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