Maneuvering weak target tracking using wavelet transform

This paper presents a novel single target particle filter with spawn model and particle labeling approach, abbreviated SL-PF. The purpose of this filter is to detect instantaneously occurring target maneuvers, e.g. course changes of maritime targets, and to provide accurate tracking performance before and after the maneuvers. The key idea is to borrow the spawn model from the probability hypothesis density (PHD) filter since this model is naturally suited for these kinds of maneuvers. Secondly, each particle in the filter carries a label which is updated in a systematic manner in the spawning step so that it is possible to recognize spawned particles representing a target maneuver. This provides an integrated maneuver detection procedure within the particle filter. Monte Carlo simulations verify the SL-PF approach and indicate a significant estimation accuracy improvement compared to a conventional particle filter.

HighlightsWhat are the main findings?This paper presents a high-order phase compensation and parameter estimation algorithm designed for maneuvering targets, which effectively balances detection performance and computational efficiency.The proposed method achieves precise compensation of high-order range migrations without the need for exhaustive parameter search, thereby circumventing the blind speed sidelobe effect. Futhermore, the incorporation of a time-delay variable significantly improves the anti-noise capability of the approach.What is the implication of the main finding?This algorithm introduces a novel motion compensation technique to address the challenges of range migration, Doppler frequency migration, and Doppler ambiguity in detecting weak maneuvering targets. It achieves precise range migration compensation with enhanced accuracy and robustness, forming a vital preprocessing step for high-quality SAR imaging.The algorithm supports simultaneous multi-target processing and holds promising application potential in fields such as airborne radar detection, maritime moving target indication, cooperative observation by UAV formations, and other fields.This study focuses on the key challenges in detecting and estimating motion parameters of ground maneuvering targets for airborne radar sensors. The complex unknown motion states of the ground maneuvering target, including velocity, acceleration, and jerk, result in range migrations (RMs) and Doppler frequency migrations (DFMs). These effects severely degrade the long-time coherent accumulation performance of the airborne radar, thereby limiting the reliable detection and precise parameter estimation of maneuvering targets. To address this issue, a new detection and motion parameter estimation method based on the range frequency reversal transform (RFRT) and searching Lv’s distribution (SLVD), i.e., RFRT-SLVD, is proposed. Specifically, the third-order RM (TRM) and quadratic DFM (QDFM) are considered. The proposed method operates as follows: First, RMs are eliminated simultaneously via the RFRT operation, which multiplies the echo by its reversed data in the range frequency and slow-time domains, leveraging the symmetric equal-interval sampling property of the range frequency. Subsequently, a phase compensation function (PCF) related to the jerk is constructed to compensate the QDFM. Finally, the LVD is performed to remove residual DFMs and achieve effective signal energy accumulation. Additionally, the case of a fast-moving target with Doppler ambiguity is analyzed, and a method for estimating three motion parameters is provided. A key advantage of the proposed technique is its ability to directly compensate the RMs without requiring prior knowledge of the maneuvering target, while also avoiding the blind speed sidelobe (BSSL) effect. In comparison with existing algorithms, RFRT-SLVD achieves a balanced trade-off between parameter estimation performance and computational efficiency. Numerical analyses and experiments are conducted to validate the method, assessing its detection capability for ground maneuvering targets, Doppler ambiguity resolution in parameter estimation, computational complexity, and method applicability in multi-target scenarios.

One of the primary techniques for target tracking is the Kalman filter or one of its many variants. While the Kalman filter has been the staple of the tracking community, it has been shown to have drawbacks. When a target performs a maneuver, the tracking solution of the filter can experience deleterious issues. The most common issue is a lag in the position of the target track compared to the true target position as the target performs its maneuver. A more problematic issue occurs when the filter covariance collapses which requires the filter to be reinitialized. While techniques exist that compensate for maneuvers, they rely on detecting the error in the estimated trajectory and the measured target position to generate their response. In this effort, a maneuver detection routine is developed that can be used in conjunction with the standard maneuver compensation approaches. This routine validates the existence of a maneuver more quickly than using inherent detection methods of the other methods. The maneuver detection is performed by an evidence accrual system that uses a fuzzy Kalman filter to incorporate new information and provide a level of evidence that maneuver is occurring. The input data uses behavior characteristics of the Kalman gain vector from the tracking algorithm.

Radar fast long-time coherent integration via TR-SKT and robust sparse FRFT

Radar maneuvering target detection in clutter background should not only consider the complex characteristics of the target to accumulate its energy as much as possible, but also suppress clutter to improve the signal-to-clutter ratio (SCR). The traditional fractional domain transform-based detection method requires parameters match searching, which costs heavy computational burden in case of a large amount of data. Sparse FT and sparse fractional FT can obtain high-resolution sparse representation of the target, but the signal sparsity needs to be known before, and the sparse representation performance is poor in clutter background. In this article, adaptive filtering method is introduced into the sparse fractional ambiguity function (SFRAF) method, and a SFRAF domain adaptive clutter suppression and highly maneuvering target detection algorithm is proposed, which is named as adaptive SFRAF (ASFRAF). The ASFRAF domain iterative filtering operation can suppress the clutter while retaining the signal energy as much as possible. Simulation results and measured radar data processing results show that the proposed algorithm can overcome the limitation of the SFRAF on the sparsity preset value and achieve high efficiency and robust detection of high-order phase maneuvering targets under a low SCR environment.

In order to solve the problem of detection and tracking of maneuvering weak targets by aerial sonobuoys, a track-before-detect method based on stochastic parabolic Hough transform was constructed. The azimuth measurement of the target was cross-located by the adaptive correlation detection buoy group, and the corresponding position information in the target measurement was obtained. The stochastic parabolic Hough transform method was used to convert the target expansion measurement to the parameter space, and the target's maneuvering track was accumulated in the parameter space. The traditional random parabolic Hough transform method was improved by means of azimuth transformation to reduce the computational complexity of the algorithm. The problem of passive detection of maneuvering weak targets was transformed into a track detection problem based on random parabolic Hough transform under the track-before-detect model, which reduces the missed track detection of weak targets with low signal-to-noise ratio. The simulation results show that the detection probability exceeds 70 % when the signal-to-noise ratio is greater than 5 dB.

This paper addresses the coherent integration problem for detecting a maneuvering target with complex motions, involving range migration (i.e., range walk and range curvature) and Doppler frequency migration (DFM) within the coherent processing interval. A new method based on adjacent cross correlation function (ACCF) and fractional Fourier transform (FRFT) is proposed, where the ACCF operation is firstly employed to remove the range migration (RM) and reduce the order of DFM. After that, the FRFT is applied to achieve the coherent accumulation. Several simulation experiments are provided to demonstrate the effectiveness.

For maneuvering target tracking, and based on the traditional “current” statistical model, the value of maneuvering frequency and maximum acceleration are set up in advance not in adaptive manner which is irrational for the reality. In the present work, a new adaptive filtering algorithm based on the “current” statistical model is proposed. In the proposed algorithm, the maneuvering frequency is adjusted based on fuzzy inference according to the value of the innovation and its change. At the same time, the maximum acceleration is adjusted according to the innovation and the estimated value. Compared to the traditional “current” statistical algorithm, the proposed algorithm improves not only the tracking accuracy and the robustness, but also the adaptation and the rapid response capabilities, for tracking non-maneuvering or weak maneuvering targets. The performance of the proposed algorithm is verified through the Monte Carlo simulations which validate the superiority of the proposed algorithm over the traditional “current” statistical algorithm from the point of view of rationality and validity.

High-speed, low-observable, and maneuvering target detection is always the difficult problem for the early warning and detection of space target, ballistic target, and passive radar signal processing. The high-order motion information of maneuvering target is employed in this paper, such as acceleration and jerk. Accordingly, several long-time coherent integration methods are demonstrated and illustrated, i.e., Radon-fractional Fourier transform (RFRFT), Radon fractional ambiguity function (RFRAF), Radon-linear canonical ambiguity function (RLCAF), and phase differentiation-Radon-Lv's distribution (PD-RLVD). These methods can compensate the across range unit (ARU) and Doppler frequency migration (DFM) effects simultaneously during the long-time integration. The background clutter and noise can be well suppressed with higher integration gain. Experimental results using real radar data show the superiority of the proposed methods.

The target motion parameter estimation is an important index to measure the performance of radar system. Accurate estimation of acceleration parameter has important influence on improving the detection and tracking performance of high maneuvering target. When radar transmits a signal with fixed frequency, the maneuvering target echo signal can be approximated as linear frequency modulation signal. Therefore, the acceleration parameter estimation of maneuvering target is transformed into the parameter estimation of linear frequency modulation signal. In this paper, a novel method for acceleration parameter estimation of maneuvering target is proposed based on the compressed sensing theory. The linear frequency modulation signal has sparse characteristic in fractional Fourier transform domain and compressed sensing theory asserts that we can employ nonadaptive linear projections to preserve the structure of the signal and reconstruct the signal with these projections using an optimization process. Theoretical analysis and experimental results verify that the method can effectively solve the precision problem of parameter estimation caused by the large sampling rate in the traditional signal processing method, and effectively reduce the data storage and transmission pressure in radar signal processing.

Using bearings only information, passive target tracking in under water scenario can be carried out for a target moving at a constant velocity. If the target changes its course or speed or both, the estimated parameters differ with those of actuals. Hence it is usual to find out target maneuver, before the solution diverges completely and appropriately the covariance matrix of target state vector is corrected. In general, the target maneuver is found out using chi-square test with normalized squared innovation process. J.L. Pirot and M.S. Smith used F-statistic to find out whether the target is stationary or not. In this paper, their work is extended to find out whether the target is maneuvering or not, as an alternate approach for chi-square test. The efficiency of the algorithm is demonstrated through Monte-Carlo simulation. The residuals generated from maximum likelihood estimator are used in sliding window format. The residuals are assumed to follow a second order polynomial. The mean squared errors of the innovations before and after maneuver is analyzed through F-statistic for deciding whether the target is maneuvering or not. Extensive simulation is carried out to evaluate the performance of the algorithm. For the purpose of evaluation, the results of two scenarios in Monte-Carlo simulation with and without target maneuver are presented.

In the multisensor passive location, the direction of arrival (DOA) and time differences of arrival (TDOA) are the most useful detection data. Applying multiple sensors to locate and track a maneuvering target is, in fact, a nonlinear uncertain problem. The extended Kalman filter (EKF) is usually used for maneuvering target tracking; however, this algorithm cannot achieve accurate estimation for uncertain or nonlinear systems. In order to increase the accuracy of locating and tracking of a maneuvering target, this paper proposes a novel EKF-cerebellar-model-articulation-controller (EKF-CMAC) multisensor data fusion algorithm for a 3-D maneuvering target. By combining the EKF with an adaptive CMAC, the tracking error of a maneuvering target can be much reduced. The Monte Carlo numerical simulation results illustrate that the proposed algorithm can achieve high accuracy for locating and tracking a maneuvering target.

Detect and tracking of maneuvering target is a complicated dynamic state estimation problem whose difficulty is increased in case of high noise environments or low signal-to-noise ratio (SNR). In this case, the track-before-detect filter (TBDF) that uses unthresholded measurements considers as an effective method for detecting and tracking a single target under low SNR conditions. Nevertheless, the performance of the algorithm will be affected with severe loss because of the mismatching of target model during maneuver. In this paper, to resolve the target maneuvers, we propose an application of particle filtering which depends on track before detect (PF - TBD) algorithm in order to track the maneuvering target. We employ the Constant Acceleration (CA) model and Coordinate Turn model (CT). Our simulation results show that the detection and tracking of maneuvering target performance of TBD-PF has been improved using the proposed algorithm.

The signal-to-noise ratio may be increased by the cross-range coherence integration so as to detect the moving target in low signal-to-noise ratio (SNR) condition. But, the radial velocity, acceleration and the change of acceleration due to the maneuvering motion of target may induce serious range migration and cross-range high-order phase terms leading to the unfocused cross-range image, the reduction of signal-noise ratio and the invalidation of target detection. Therefore, in order to solve these problems, this paper proposes a new method based on the adjacent correlation and scale transform methods for detection, parameters estimation and imaging of maneuvering targets in wide-band signal. This method can align the range and remove the cross-range high-order phase terms induced by the radial motion of target, enabling us to detect the target and estimate its moving parameters better. Finally, the simulated target is used to confirm that the method proposed by this paper can perfectly detect the maneuvering target in low signal-to-noise ratio condition, estimate its motion parameters and obtain an ISAR image of target.

Three-dimensional guidance law with precise control of attack time and constraints on attack angle.