Auxiliary Particle Flow Track-Before-Detect Algorithm for Marine Neighboring Weak Targets

Abstract

Detection and tracking of marine weak targets can be effectively solved by track-before-detect (TBD) algorithms based on particle filtering. However, these algorithms are susceptible to influence from neighboring targets, leading to potential issues like misassociation and tracking failure. In this paper, an auxiliary particle flow track-before-detect algorithm designed for marine neighboring weak targets is proposed which can effectively track marine neighboring weak targets under long-tail sea clutter. Firstly, marine neighboring targets are modeled by the generalized Pareto model, and an offline lookup table is utilized to obtain a non-closed solution, decreasing calculation cost. Subsequently, prediction is employed to classify targets, and measurement information is iteratively used to determine the sequence of target updates, effectively suppressing influence from neighboring targets. Finally, particles with higher measurement energy are chosen, and the Geodesic particle flow is employed to guide the particles toward better importance distribution, which enhances the accuracy of target trajectory estimation. Simulation experiments indicate that compared with track-before-detect algorithms based on parallel partition (PP) and auxiliary parallel partition (APP), the proposed algorithm shows an increase of 43.1% and 25.8% in detection probability at 6 dB, and a reduction of 76.6% and 66.2% in Root Mean Square Error (RMSE). Detection ability and trajectory estimation performance are effectively improved in the simulation, and excellent tracking performance is also confirmed in real clutter experiments.

1. Introduction

Due to the complex characteristics of ocean electromagnetic echoes, target tracking with maritime surveillance radars faces numerous challenges, particularly in scenarios involving neighboring weak targets. Neighboring weak targets refer to spatially proximate targets with a low signal-to-clutter ratio (SCR), caused by factors such as small radar cross-sections (RCSs), stealth technology, or complex sea state conditions [1]. For example, these include spatially proximate small boats, stealth vessels, and armed divers. These targets have low SCRs, leading to a high false alarm probability during detection. In addition, adjacent interference among neighboring targets often results in false tracking and missed detection. Current tracking technology has difficulties in handling these challenges.

Target tracking frameworks include two categories: detect-before-track (DBT) [2,3,4] and track-before-detect [5,6]. With pre-process measurements using single-frame detection thresholds, DBT offers advantages in terms of memory usage and computational efficiency. However, DBT discards potential target measurements during the compression of raw measurement data, which causes potential measurement information loss [7]. In contrast, utilizing all measurement data, TBD explores the temporal and spatial correlation of data to jointly detect and track targets, making it more effective for low-SCR targets. TBD methods are typically divided into multi-frame TBD and recursive TBD. Multi-frame TBD processes batches of consecutive frames based on dynamic programming [8,9,10] or the Hough transformation [11,12,13], obtaining outstanding performance under extremely low SCRs. Recursive TBD methods include particle filtering [14,15,16] and random finite set (RFS)-based [6,17] approaches, which recursively propagate the multi-target posterior probability density. Particle filter TBD methods are especially advantageous for nonlinear and non-Gaussian systems like radar [18], sonar [19], etc.

Particle filtering methods are commonly affected by the “particle degeneracy” problem [20], where particle weights concentrate on a few particles after several iterations, resulting in inaccurate representation of the posterior probability density. To address this issue, some improvement strategies are commonly employed. For example, the resampling method [21,22,23] generates new particles to increase particle diversity during resampling. This technique has limited effectiveness in high-noise environments. Additionally, auxiliary information from measurements is applied, which optimizes particle prediction distribution before Bayesian updates, such as auxiliary particle filtering [24] and intelligent particle optimization [25]. These approaches achieve notable improvements. Furthermore, particle flow filtering (PFF), a more recent method [26,27,28], is also effective in enhancing particle quality. Migrating the particles from prior distribution to posterior distribution, PFF offers significant performance compared with traditional sequence importance sampling particle filtering. In [29], PFF is applied to TBD for single-target tracking under Gaussian noise, designed for non-threshold radar measurements. In [30], particle flow importance sampling is proposed, which uses PFF outputs to approximate the optimal importance density for bootstrap filtering, leading to auxiliary particle flow filtering (APFF). In [31,32,33], APFF with EDH, LEDH, and Gromov methods are investigated, where PFF is embedded in the conduction of importance distribution by particle migration, leading to significant improvements in state estimation. In [34], LEDH particle flow is used to design reversible mappings, improving particle quality in Bernoulli TBD. However, these methods are designed for single-target scenarios, in which the targets overlap with each other. Multiple-target particle filtering methods in radar tracking suffer from adjacent interference between multiple targets [35,36]. This adjacent interference exacerbates missing tracking in the tracking process. To address this issue, the parallel partition (PP) technique [37] utilizes predicted information and designs multi-target importance distributions to suppress interference from neighboring target measurements. Furthermore, the auxiliary parallel partition (APP) technique [38] incorporates current measurement information but still suffers from tracking errors and missed detections when neighboring targets exist due to insufficient utilization of measurement data.

The modeling of sea clutter is essential for maritime surveillance radars [39]. When the radar operates at small grazing angles, the echo exhibits significant non-Gaussian characteristics. The K distribution model [40,41,42] is commonly used to describe clutter amplitude in such cases. Brekke [43] conducted amplitude-assisted tracking studies for fluctuating sea surface targets under this model, and Ristic [44,45] carried out a series of studies on TBD for marine targets. Various new sea clutter models for high-resolution and low-grazing-angle scenarios have been proposed in recent years. These models can be divided into two types: models that add extra sea spike components via linear superposition, such as KA [46,47] and KK [48,49] models, and models employing more robust probability density functions in composite Gaussian frameworks, such as the generalized Pareto (GP) distribution [50,51] and CG-IG distribution [52]. Compared to the K-distribution, the generalized Pareto distribution is better suited for handling long-tailed functions; a similar model has been applied to TBD methods based on dynamic programming [53] and the RFS framework [54]. However, none of the aforementioned TBD algorithms model the influence of neighboring targets, which can lead to performance degradation in complex scenarios.

In order to solve the problems of insufficient utilization of measurement information and lack of modeling of neighboring weak targets, an auxiliary particle flow filter track-before-detect (APFF-TBD) algorithm is proposed, which can effectively track marine neighboring weak targets. Firstly, for the neighboring target scenario, a neighboring target modeling method under generalized-Pareto-distributed clutter is proposed, and an offline lookup table is prepared to reduce the computational cost. Then, in order to reduce the energy cross-interference of the nearest neighbor targets, the prediction information is used to cluster the targets, and the particle covariance information is used to iteratively determine the order of the targets to be updated. Finally, Geodesic flow is used to guide the multi-target particles to flow to a better importance distribution. In the experimental part, the proposed algorithm is simulated in the scenario of neighboring weak targets plus the real sea clutter collected under the X-band radar to test the detection and tracking performance of the algorithm.

The rest of this paper is organized as follows. The motion model and the marine neighboring measurement model are proposed in Section 2. The principle of APFF-TBD and its implementation are developed in Section 3. Simulation results follow in Section 4. The discussion on the performance of APFF-TBD is presented in Section 5. Concluding remarks and future research are stated in Section 6.

2. System Model

2.1. Motion Model

Suppose at time k, multiple targets exist in the interest region detected by marine surveillance radar. In the 2D surveillance area, the evolution of the target state is described with the near-constant velocity (CV) motion model. The total number of targets at time k is M, considering the m-th target, whose motion state is fully characterized by $x_k^m$:

$$x_k^m=F_k{x}_{k-1}^m+w_k,\hspace{1em}m=1,2,\dots ,M$$

(1)

where the target motion vector is described with an ($n_x=5$) dimensional target state. $x_k^m={\left[x_k^m,{\dot{x}}_k^m,y_k^m,{\dot{y}}_k^m,{\eta }_k^m\right]}^T$, $\left(x_k^m,y_k^m\right)$ is the Cartesian coordinates of the m-th target position, $\left({\dot{x}}_k^m,{\dot{y}}_k^m\right)$ is the Cartesian coordinates of the m-th target velocity, and ${\eta }_k^m$ is the signal intensity. $F_k$ is the state-transition matrix given by

$$\begin{array}{c}{\mathit{F}}_k=\end{array}\left(\begin{array}{ccc}\mathit{F}& 0& 0\\ 0& \mathit{F}& 0\\ 0& 0& 1\end{array}\right)\hspace{1em}\mathit{F}=\left(\begin{array}{cc}1& T\\ 0& 1\end{array}\right),$$

(2)

where T is the measurement interval, and $w_k$ denotes the motion noise, described by zero-mean white Gaussian PDF with covariance matrix ${\mathit{Q}}_k$:

$$\begin{array}{c}{\mathit{Q}}_k=\end{array}\left(\begin{array}{ccc}\mathit{Q}& 0& 0\\ 0& \mathit{Q}& 0\\ 0& 0& q_{2}T\end{array}\right)\hspace{1em}\mathit{Q}=q_1\left(\begin{array}{cc}{\displaystyle \frac{1}{3}}{T}^3& {\displaystyle \frac{1}{2}}{T}^2\\ {\displaystyle \frac{1}{2}}{T}^2& T\end{array}\right)$$

(3)

where $q_1$ and $q_2$ are used to describe the power spectral density of the target motion noise and the intensity noise.

2.2. Marine Neighboring Measurement Model

Existing superposition target models in TBD methods generally ignore the adjacent interference, which results in potential performance loss for multi-target overlap echo. In this section, we propose a marine neighboring measurement model based on the generalized Pareto (GP) model [50]. Compared with the traditional K + noise model, the generalized Pareto (GP) model has a simple form as well as outstanding precision.

The marine radar scans the interest area to obtain the measurement of the range–azimuth map, and the single-frame scanning includes $N_r*N_b$ resolution units. We denote the intensity measurement $z_k$ at time k as $z_k=\left\{z_k^{\left(i,j\right)},i=1,2,\cdots ,N_r,j=1,2,\cdots ,N_b\right\}$, where $z_k^{(i,j)}$ represents the amplitude measurement of resolution unit $(i,j)$.

The GP model interprets sea clutter as a modulation of the texture variable toward the speckle variable. In the GP model, the speckle variable is expressed as

$$p\left(z_k^{(i,j)}\mid \eta \right)={\displaystyle \frac{1}{\eta }}\exp \left(-{\displaystyle \frac{{(z_k^{(i,j)})}^2}{\eta }}\right), z_k^{(i,j)}>0,$$

(4)

where $\eta$ is the local sea clutter power density, following an inverse gamma distribution:

$$p(\eta )={\displaystyle \frac{{\beta }^{\alpha }{\eta }^{-\alpha -1}}{\Gamma (\alpha )}}\exp \left(-{\displaystyle \frac{\beta }{\eta }}\right), \eta >0$$

(5)

where $\alpha$ and $\beta$ denote the shape and scale parameters, respectively. From [55], the amplitude distribution of resolution unit $(i,j)$ without targets is given as follows:

$$p_0\left(z_k^{(i,j)}\right)={\displaystyle {\int }_0^{\infty }p}\left(z_k^{(i,j)}\mid \eta \right)p(\eta )d\eta ={\displaystyle \frac{\alpha {\beta }^{\alpha }}{{\left({(z_k^{(i,j)})}^2+\beta \right)}^{\alpha +1}}}, z_k^{(i,j)}>0$$

(6)

In our research, a marine neighboring target model is proposed. In multi-target scenarios, the local sea clutter power density $\eta$ is time-varying, influenced by neighboring targets. Each target can contribute to the resolution unit $(i,j)$. The Gaussian point spread function is given as

$$h_{\eta }^{(i,j)}(x_k^m)={\displaystyle \frac{\sigma }{2\pi {\Sigma }_r{\Sigma }_b}}\exp \left(-{\displaystyle \frac{{\left(i{\Delta }_r-r(x_k^m)\right)}^2}{2{\Sigma }_r^2}}-{\displaystyle \frac{{\left(j{\Delta }_b-b(x_k^m)\right)}^2}{2{\Sigma }_b^2}}\right),$$

(7)

where ${\Delta }_r$ and ${\Delta }_b$ denote the radar resolution of the range and azimuth. ${\Sigma }_r$ and ${\Sigma }_b$ denote the energy diffusion factor of the range and azimuth. $\sigma$ is a constant. ${[r(x_k^m),b(x_k^m)]}^T$ is the 2D measurement.

$$\left[\begin{array}{l}r(x_k^m)\\ b(x_k^m)\end{array}\right]=\left[\begin{array}{l}\sqrt{{(x_k^m)}^2+{(y_k^m)}^2}\\ \arctan \left({\displaystyle \frac{y_k^m}{x_k^m}}\right)\end{array}\right]$$

(8)

The local multi-target diffused power ${\eta }_k^{(i,j)}$ is the superposition measurement generated by multiple targets, denoted as ${\eta }_k^{(i,j)}={{\displaystyle \Sigma }}_{m=1}^M{\eta }_k^m{h}_{\eta }^{(i,j)}(x_k^m)$, where ${\eta }_k^m$ is the power measurement of the m-th target. The amplitude condition distribution of the speckle component with multiple targets is given by

$$p\left(z_k^{(i,j)}\mid \eta ,{\eta }_k^{(i,j)}\right)={\displaystyle \frac{1}{\eta +{\eta }_k^{(i,j)}}}\exp \left(-{\displaystyle \frac{{(z_k^{(i,j)})}^2}{\eta +{\eta }_k^{(i,j)}}}\right), z_k^{(i,j)}>0,$$

(9)

which is similar to (4). Then, the amplitude $z_k^{(i,j)}$ with targets follows PDF:

$$p\left(z_k^{(i,j)}|{\eta }_k^{(i,j)}\right)={\displaystyle {\int }_0^{\infty }p}\left(z_k^{(i,j)}\mid \eta ,{\eta }_k^{(i,j)}\right)p(\eta )d\eta ={\displaystyle \frac{{\beta }^{\alpha }}{\Gamma \left(\alpha \right)}}{{\displaystyle \int }}_0^{\infty }f(\eta ,{\eta }_k^{(i,j)})d\eta$$

(10)

where:

$$f(\eta ,{\eta }_k^{(i,j)})={\displaystyle \frac{{\eta }^{-\alpha -1}}{\eta +{\eta }_k^{(i,j)}}}\exp \left(-{\displaystyle \frac{{\left(z_k^{(i,j)}\right)}^2}{\eta +{\eta }_k^{(i,j)}}}-{\displaystyle \frac{\beta }{\eta }}\right)$$

(11)

where $\Gamma (\cdot )$ is the Gamma function. We denote the likelihood function as follows:

$$p\left(z_k^{\left(i,j\right)}\mid {\eta }_k^{(i,j)},H_k\right)=\left\{\begin{array}{c}p\left(z_k^{(i,j)}|{\eta }_k^{(i,j),\{1:M\}}\right)\hspace{1em}\hspace{1em} H_k^1:\mathrm{target}\mathrm{m}\mathrm{detected}\\ p\left(z_k^{(i,j)}|{\eta }_k^{(i,j),\{1:M\}/m}\right)H_k^0:\mathrm{target}\mathrm{m}\mathrm{missed}\end{array}\right.$$

(12)

where ${\eta }_k^{(i,j),\{1:M\}}$ denotes the power diffused to cell $(i,j)$ under the influence of targets 1 to M, and ${\eta }_k^{(i,j),\{1:M\}/m}$ denotes the power diffused except to target m. Assuming the measurement noise $p_0(z_k^{(i,j)})$ is independent between different cells, the superposition measurement area IDs of target m on the range and azimuth are denoted as $C_r(x_k^m)$ and $C_a(x_k^m)$. Then, the likelihood ratio of target m with neighborhood targets is given as follows:

$$p(z_k|x_k^m,x_k^{\{1:M\}/m})={\displaystyle \prod }_{i\in C_r\left(x_k^m\right)}{\displaystyle \prod }_{j\in C_a\left(x_k^m\right)}{\displaystyle \frac{p\left(z_k^{(i,j)}|{\eta }_k^{(i,j),m}\right)}{p\left(z_k^{(i,j)}|{\eta }_k^{(i,j),\{1:M\}/m}\right)}}$$

(13)

This likelihood model is proposed to remit diffused power from neighborhood targets. The classical likelihood model in [42,54] can be regarded as a special case for M = 1 and m = 1, which means no neighboring targets influence this area. This model quantitatively describes the influence of neighboring targets, and is especially suitable for situations in high-resolution radar where target energy is easily leaked to neighboring cells. In this model, accurate estimation of the neighboring target state is necessary, so APFF technology is applied in the following section.

3. Auxiliary Particle Flow Track-Before-Detect Algorithm

3.1. Multiple-Target Tracking by Particle Filtering

From the perspective of Bayesian, multiple-target tracking (MTT) is used to recursively estimate multiple target states based on joint multiple probability density (JMPD) [37]. JMPD uses the joint multi-target conditional probability density $p(x_k|z_{1:k})$ as the probability density for M targets with states $x_k={[{(x_k^1)}^T,{(x_k^2)}^T,\dots ,{(x_k^m)}^T,\dots ,{(x_k^M)}^T]}^T$ at time k based on the observation $z_{1:k}$. The calculation of JMPD includes two steps: prediction and update.

Suppose the posterior density $p(x_{k-1}|z_{1:k-1})$ at time k − 1 is available. Then, the prediction steps at time k involve the motion model (1) using the Chapman–Kolmogorov equation:

$$p\left(x_k|z_{1:k-1}\right)={\displaystyle \int p\left(x_k|x_{k-1}\right)p\left(x_{k-1}|z_{1:k-1}\right)}d{x}_{k-1}$$

(14)

where $p(x_k|x_{k-1})$ is the evolution of the multiple-target state defined by the motion model. With the assumption of Markov property, and ignoring the correlation between clutter background, the update equation can be given by Bayes rules:

$$p\left(x_k|z_{1:k}\right)={\displaystyle \frac{p\left(z_k|x_k\right)p\left(x_k|z_{1:k-1}\right)}{p\left(z_k|z_{1:k-1}\right)}}$$

(15)

where $p(z_k|x_k)$ is the likelihood function, and $p(z_k|z_{1:k-1})$ is the normalized constant.

Most algorithms assume that the targets are sufficiently separated in space and time. This independence means $p(x_k|x_{k-1})={\Pi }_{m=1}^{M}p(x_k^m|x_{k-1}^m)$. In addition, for the non-Gaussian and nonlinear radar system, particle filtering is adopted to approximately estimate the JMPD. In this technology, particles with weights $\left\{w_k^n\right\},n=1,2,\cdot \cdot \cdot ,N$ are used to sample the posterior probability density function $p(x_k|z_{1:k})$ of the target. According to [56], the multi-target posterior probability and multi-target particle weight at time k are as follows:

$$p(x_k|z_{1:k})\propto p(z_k|x_k){\displaystyle \prod }_{m=1}^{M}p(x_k^m|x_{k-1}^m)$$

(16)

$$w_k^n\propto {\displaystyle \frac{p(x_k^n|z_{1:k})}{q(x_k^n|z_{1:k})}}=p(z_k|x_k^n){\displaystyle \prod _{m=1}^{M}p(x_k^{m,n}|x_{k-1}^{m,n})/q(x_k^n|z_{1:k})}$$

(17)

where $q(x_k^n|z_{1:k})$ is the importance distribution.

In real scenarios, targets can diffuse energy to adjacent sensor units, affecting multiple targets while being influenced by multiple targets, so Equations (16) and (17) can lead to a degradation in tracking performance. To address these issues, we propose the APFF technique in Section 3.2, which introduces auxiliary particle flow technology to the track-before-detect algorithm for weak targets.

3.2. Auxiliary Particle Flow Filtering Track-Before-Detect (APFF-TBD) Algorithm

This section introduces the principle of APFF and TBD implementation. Auxiliary particle flow filtering, compared with the multi-target particle filter described in the previous section, is a method for adjusting the importance distribution [31]. To the best of our knowledge, this filter has not yet been used in adjacent multi-target scenarios. In our work, APFF with the neighboring model is applied to the TBD algorithm.

3.2.1. APFF for Neighboring Weak Target

In Figure 1, the importance distribution formed by APFF is explained. In Figure 1a, the initial importance distribution of the neighboring weak targets is “overlap”, which means the update of JMPD will suffer interference from other targets.

To overcome this problem, measurement intensity is used to determine the sequential update order, and the auxiliary Geodesic flow filter is employed. In Figure 1b–d, particles are guided to high-likelihood regions while keeping proper diversity, and in Figure 1e, the three particle distributions are well separated.

In the sequential update process, the target number to be updated is given by the measurement sampling result as follows:

$$m^{\ast }=\underset{m}{\arg \min }{\displaystyle \sum }_{n=1}^N{w}_k^{m,n}{(x_{k|k-1}^{m,n}-{\overline{x}}_{k|k-1}^m)}^2,\hspace{1em}m=1,2,\dots ,M$$

(18)

where m* is the target number, m marks the targets remaining to be updated, ${\overline{x}}_{k|k-1}^m={{\displaystyle \Sigma }}_{n=1}^N{w}_k^{m,n}{x}_{k|k-1}^{m,n}$ is the mean of the predicted state after considering the current measurement, and $w_k^{m,n}$ is the normalized first-order weights sampled at time k.

After deciding on the sub-partition to be updated, particle flow is used to update the high-quality importance density. The particle flow of the m-th sub-partition is defined as the homotopic transformation of the Bayesian update equation [26]:

$$p\left(x_k^m,\lambda |z_{1:k}\right)\propto {\left(p\left(z_k|x_k^m\right)\right)}^{\lambda }p\left(x_k^m|z_{1:k-1}\right)$$

(19)

where the homotopy transformation for the Bayesian update process is defined. The process of $\lambda$ increasing from 0 to 1 represents the transformation from the prior probability density to the posterior probability density. This transformation process satisfies the following:

$$d{x}_k^m=f\left(x_k^m,\lambda \right)d\lambda +\sigma \left(x_k^m,\lambda \right)dw$$

(20)

where $f\left(x_k^m,\lambda \right)$ is the flow function, and $\sigma \left(x_k^m,\lambda \right)dw$ denotes the wiener diffusion term. The solution to Equation (20) is not unique [28]. The solution used here is called Geodesic flow, with the flow function and zero-diffusion term solutions being as follows:

$$f\left(x_k^m,\lambda \right)=-{\left[{\displaystyle \frac{{\partial }^2\ln p\left(x_k^m,\lambda |z_{1:k}\right)}{\partial {(x_k^m)}^2}}\right]}^{-1}{\left({\displaystyle \frac{\partial \ln p\left(z_k|x_k^m\right)}{\partial x_k^m}}\right)}^T$$

(21)

$$\sigma \left(x_k^m,\lambda \right)=0$$

(22)

From [57], $f\left(x_k^m,\lambda \right)$ is given as follows:

$$f\left(x_k^m,\lambda \right)=A(\lambda )x_k^m+b(\lambda )$$

(23)

$$A=-{\displaystyle \frac{1}{2}}P{H}^{\mathrm{T}}{(\lambda HP{H}^{\mathrm{T}}+R)}^{-1}H$$

(24)

$$b=(I+2\lambda A)[(I+\lambda A)P{H}^{\mathrm{T}}{R}^{-1}{z}_k+A{\overline{x}}_{k|k-1}^m]$$

(25)

where P is the covariance matrix of prediction error, H is the Jacobian matrix of measurement, and R is the covariance matrix of measurement noise. The convergence discussion of this solution is confirmed in [58]. By integrating the pseudo-time term $\lambda$ over the interval [0, 1] using (21)–(25), the particles are moved to posterior distribution $p\left(x_k^{m,n},1|z_{1:k}\right)$. This distribution is regarded as the importance distribution in (17) and is used in the following update implementation of the APFF-TBD algorithm.

3.2.2. Implementation of APFF-TBD

• Step 1: Particle initiation. Assuming the number of targets is M, and the number of particles is N, then the initial multi-target state is defined as the concatenation of the individual target states as $x_0^n={[{(x_0^{1,n})}^T,{(x_0^{2,n})}^T,\dots ,{(x_0^{M,n})}^T]}^T,n=1,2,\dots ,N$. The initial individual weight is $w_0^{m,n}=1/N,m=1,2,\dots ,M;n=1,2,\dots ,N$.
• Step 2: Prediction and target clustering. In this step, neighboring targets are divided into clusters. We perform particle prediction by using $x_{k|k-1}^{m,n}=F_k{x}_{k-1}^{m,n},m=1,2,\dots ,M,n=1,2,\dots ,N$. We calculate the position prediction ${\tilde{x}}_k^m={{\displaystyle \Sigma }}_{n=1}^N{w}_{k-1}^{m,n}{x}_{k|k-1}^{m,n},m=1,2,\dots ,M$ to obtain the multi-target state ${\left\{{\tilde{x}}_k^m\right\}}_{m=1}^M$. If the distance between target predictions is less than the cluster threshold R, that is $D({\tilde{x}}_k^m,{\tilde{x}}_k^{m^{\prime }})<R$, then we regard these targets are neighbor targets. All of the neighboring targets have labels of ${\tilde{x}}_k^m$ with the set $G_m$, so as to obtain the neighboring label set $G_m=\{1,2,\dots \}$ for $m=1,2,\dots ,M$.
• Step 3: We apply auxiliary particle flow filtering for iterative updates. First, we sample the measurement with prediction at time k. Using (17), the weight $w_k^n$ of multi-target state particle is accessible. After the weight matrix of multi-target state ${\left\{w_k^{m,n}\right\}}_{m=1:M,n=1:N}\in {ℝ}^{M\times N}$ is obtained, the target label remains updated and $m^{\ast }$ is given by (18).

Second, we determine the guiding particle. The particles with the highest weight in the sub-partition $m^{\ast }$ are marked as high-quality particles, denoted as $x_{k|k-1}^{m^{*},n^{*}}$. The weighted high-quality particles are used to obtain the guiding particle $x_k^{m^{*}}={\displaystyle \sum w_k^{m^{*},n^{*}}{x}_{k|k-1}^{m^{*},n^{*}}}$.

Third, Geodesic flow is employed to guide the particles $x_{k|k-1}^{m^{\ast },n},n=1,2,\dots ,N$ of sub-partition $m^{\ast }$ flow to the guiding particle $x_k^{m^{*}}$, obtaining the importance distribution of the sub-partition sampling particles $u_k^{m^{*},n},n=1,2,\dots ,N$. With this distribution, sub-partition particles with the target $m^{*}$ as the neighbor and whose importance distribution has not been updated are sampled again.

The above operation is repeated until all sub-partitions with adjacent targets are processed by particle flow filtering. At this time, the importance distribution at time k is

$$q(x_k^n|z_{1:k})\propto {\displaystyle \prod }_{m=1}^{M}p(z_k|u_k^{m,n},u_k^{\{1:M\}/m})p(x_k^m|x_{k-1}^m).$$

(26)

Substituting (26) into formula (17), we obtain the particle weight at time k as

$$w_k^n\propto p(z_k|x_k^n)/{\displaystyle \prod _{m=1}^{M}p(z_k|u_k^{m,n},u_k^{\{1:M\}/m})},$$

(27)

where $p(z_k|u_k^{m,n},u_k^{\{1:M\}/m})$ is the likelihood ratio function given in (13).

• Step 4: State estimation and output. The state estimation of target m is as follows:

  $${\widehat{x}}_k^m={\displaystyle \sum _{n=1}^N{w}_k^n{u}_k^{m,n}}$$

  (28)

3.3. Target Initiation and Trajectory Termination

In real maritime target tracking scenarios, the intensity of clutter always exhibits high dynamism, and using a strategy that accumulates over a long period can help improve the performance of target initialization. Similar methods have been widely adopted in multi-frame tracking methods, as in [59,60,61]. In our algorithm, we select measurements with high energy at each step and then delete possible clutter measurements in subsequent steps. We set a threshold under a specific detection probability through Monte Carlo simulation.

Step 1: We sample a certain number of multi-target particle clusters in the candidate region to sample newborn targets ${\left\{{\tilde{x}}_k^{m_b}\right\}}_{m_b=1}^{M_k}$, where $M_k$ is the real newborn target number at time k. The newborn joint distribution $p({\tilde{x}}_k^B)$ is uniformly distributed as follows:

$$p({\tilde{x}}_k^B)\propto {\displaystyle \prod _{m_b=1}^{M_k}{\mathrm{U}}^r({\tilde{x}}_k^{m_b}{)\mathrm{U}}^b({\tilde{x}}_k^{m_b})}$$

(29)

where ${\mathrm{U}}^r(\cdot )$ and ${\mathrm{U}}^b(\cdot )$ are the uniform distribution in the surveillance range and bear, respectively. After sampling the birth particles, the particles close to existing targets are discarded because these particles are more likely to come from the measurements of existing targets. We denote the gated target state as $\{{\widehat{x}}_k^{m_b}\in {\tilde{x}}_k^{m_b}:\left|{\widehat{x}}_k^{m_b}-x_k^{\{1:M\}}\right|>{\tau }_B\}$, where ${\tau }_B$ is the deletion threshold.

Step 2: Accumulating the energy with particles. Here, the log-likelihood ratio method is applied to accumulate the energy function of each potential target. The threshold method is used to select potential targets. Let ${\gamma }_k=\left\{{\gamma }_k^i\right\},i=1,2,\cdot \cdot \cdot ,M_k$ denote the sample particle cluster ID variable for the newborn targets at time k, and ${\gamma }_k^B$ denote the real ID variable for the newborn targets at time k; then,

$${\gamma }_k^B=\left\{{\gamma }_k^i\in {\gamma }_k:{\displaystyle \sum _{t_b=k-T_B}^k\log \left(p(z_{t_b}|{\widehat{x}}_{t_b}^{m_b,{\gamma }_k},x_{t_b}^{\{1:M\}})\right)}>{\gamma }_B\right\},$$

(30)

where ${\widehat{x}}_{t_b}^{m_b,{\gamma }_k}$ denote the gated targets sampled with ID variable ${\gamma }_k$. Here, ${\gamma }_B$ is a threshold determined through the Monte Carlo method under certain false alarm probability. $T_B$ is the target initialization duration.

Step 3: Adding the newborn target particles ${\left\{x_k^{{\gamma }_k^B,j}\right\}}_{j=1}^{N_p}$ to the additional particle partition of the multi-target particles.

Trajectory termination is similar to target initiation. We denote trajectory termination duration as $T_D$, so the determined threshold ${\psi }_D$ can be obtained under certain missed detection rates by using the Monte Carlo method.

Let ${\Psi }_k=\left\{{\psi }_k^i\right\},i=1,2,\cdot \cdot \cdot ,N_k$ denote the multi-target particle cluster ID variable for the existing targets at time k, and ${\psi }_k^D$ denote the real ID variable for the death targets at time k; then,

$${\psi }_k^D=\left\{{\psi }_k^i\in {\Psi }_k:{\displaystyle \sum _{t_d=k-T_D}^k\log \left(p(z_{t_d}|{\widehat{x}}_{t_d}^{m_d,{\psi }_k},x_{t_d}^{\{1:M\}})\right)}<{\psi }_D\right\},$$

(31)

where the duration $T_D$ required for track termination is set. The implementation flowchart is provided in Figure 2.

3.4. Computational Complexity

Table 1. Comparison of three algorithms.

Algorithm	Auxiliary Information Source	Sequential Updates	Auxiliary Measurement Method	Computational Complexity
PP-TBD	Prediction	No	No	$O(MN+c)$
APP-TBD	Measurement	No	Particle filter	$O(2MN+c)$
APFF-TBD	Measurement	Yes	Particle flow filter	$O(dMN+c)~O(d{M}^{2}N+c)$

compares PP-TBD, APP-TBD, and the APFF-TBD algorithm proposed above. All three algorithms consider neighboring targets; PP-TBD only uses neighboring target prediction, while APP-TBD and APFF-TBD also use neighboring target measurement. Additionally, PP-TBD and APP-TBD ignore the update order, while APFF-TBD uses measurement information to determine the update order. In terms of the auxiliary measurement method, PP-TBD does not use the current measurement. APP-TBD selects high-quality particles for auxiliary particle filtering, while APFF-TBD uses auxiliary particle flow to guide particles toward the high-likelihood region. In terms of computational complexity, the computational complexity of PP-TBD is $O(MN+c)$, where M is the number of targets, N is the number of particles, and c is a constant term associated with initiation and termination. The computational complexity of APP-TBD is $O(2MN+c)$, which is due to the need to sample auxiliary variables, introducing the double sample. The worst computational complexity of APFF-TBD is between $O(dMN+c)$ and $O(d{M}^{2}N+c)$. If all M targets are neighboring to each other, then the sampling process will repeat for M times, and the computation complexity of the particle flow operation is $O(dMN)$, where d is the flow iterative parameter and c is a constant term. And if all targets are adjacent, then $O(d{M}^{2}N)$ represents the amount of calculation required for iterative sampling in the process of iterative decoupling of neighboring targets.

4. Numerical Results

In this section, the APFF-TBD algorithm’s tracking performance in practical scenarios is examined using real sea clutter data combined with weak simulated targets. In these experiments, a lookup table method is applied within the neighboring target model to enhance computational efficiency. Two scenarios are tested: one with a fixed number of targets and another with varying targets. The proposed APFF-TBD algorithm is compared with PP-TBD, APP-TBD, and HT-CPHD-TBD under similar conditions.

4.1. Pre-Process: The Production of the Lookup Table

In sea surveillance radars, clutter rather than noise is the primary source of background interference. Therefore, the signal-to-clutter ratio (SCR) is more valuable than the signal-to-noise ratio (SNR). The sea clutter likelihood function in (13) is non-analytic and computationally complex. To enhance computational efficiency, we adopt a variational resolution grid sampling method [43] to generate a lookup table for offline computation. The grid in this method comprises two parts, a low-resolution region and a high-resolution region, corresponding to the integration near the peak value and for larger values, respectively. The integration process is divided into the following steps.

Step 1: To cover the effective support domain of $f(\eta ,{\eta }_k^{(i,j)})$, set the upper limit of the integral as $\mu ={\mu }_p(2+1/{\epsilon }^{\frac{1}{2\alpha }})$, where $\epsilon =0.001$ is a small value, and the maximum value ${\mu }_p=\underset{\eta }{\arg \max }f(\eta ,{\eta }_k^{(i,j)})$. The shape of $f(\eta ,{\eta }_k^{(i,j)})$ under different sea clutter parameters is shown in Figure 3.

Step 2: Use a low-resolution grid to calculate the integral in the vicinity $[0,2{\mu }_p]$, with the sampling points being ${\eta }_m=2{\mu }_{p}m/N_L,m=1,2,\dots ,N_L$, where the number of low-resolution sampling points is $N_L$.

Step 3: Use a variable-resolution high-resolution grid to estimate the integral ${\eta }_{n+N_L}=2{\mu }_p+A\exp (Bn),n=1,2,\dots ,N_U$ when $\eta \to \infty$, with the number of high-resolution sampling points being $N_U$. The definitions of A and B are as follows:

$$A={\displaystyle \frac{2{\mu }_p}{N_L}}\exp (-B)$$

(32)

$$B={\displaystyle \frac{1}{N_U}}\exp \left({\displaystyle \frac{1}{\alpha }}\ln \left({\displaystyle \frac{{\mu }_p^{\alpha }}{\sqrt{\epsilon }}}\right)-\ln \left({\displaystyle \frac{2{\mu }_p}{N_L}}\right)\right)$$

(33)

In this experiment, we set $N_L=20$ and $N_U=80$. Under this marine neighboring target model, the difference between the numerator and denominator in (13) is only in the intensity of the targets, so a two-dimensional likelihood ratio table related to the amplitude of the measurement $z_k^{(i,j)}$ and the intensity of the multiple targets ${\eta }_k^{(i,j)}$ is made, as shown in Figure 3. The general measurement model is a special case of the marine neighboring target model, and it is represented by retrieving the corresponding likelihood ratio in the general scenario, while in the neighboring scenario, we retrieve the ratio of two likelihood ratios.

4.2. Scene 1: MTT with Fixed Number

The clutter data are derived from X-band sea observation data collected in 2020 at the Yantai No. 1 Bathing Beach, with a sea state level of 3. The radar frequency range is 9.3 GHz to 9.5 GHz, and the bandwidth is 25 MHz, working under a circular scanning mode with a scanning period of 2.5 s/r. The range resolution is 6 m. We select the dataset named “20200722150408_798_scanning.mat”. During this segment, the grazing angle of the radar remains below 6°, and the radar echo exhibits a distinct long-tail effect. We extract clutter data from the clutter region to conduct subsequent modeling of background clutter.

In our experiments, real-world recorded data are used to estimate the performance of the proposed APFF-TBD algorithm in comparison with PP-TBD and the APP-TBD. Two experiments are conducted to test the algorithm’s detection and tracking performance. In the first experiment, the number of targets remains constant, and we study the algorithm’s tracking error and the ability to maintain tracks. In the second experiment, the number of targets is changed, and we compare the ability of various algorithms to detect and track multiple targets. All experiments are simulated 100 times using the Monte Carlo method. The experimental platform has an Inter(R)Core(TM)I7-10875H@2.3 GHz CPU with 16 GB RAM, running Windows 11 with Matlab 2023a 64-bit. To guarantee fairness, similar false detection is kept in all three algorithms, so the detection and track performance can be evaluated.

In this section, a relatively simple scenario with a fixed number of targets is considered. In this scenario, the radar sensor is located at the origin, with a scanning range of [0, 30 m] × [0, 30 m] and a scanning period set to T = 1 s. Four targets move in a two-dimensional plane, and the target states are modeled using the 5D constant velocity model ${\mathit{x}}_k^m={\left[x_k^m,{\dot{x}}_k^m,y_k^m,{\dot{y}}_k^m,{\eta }_k^m\right]}^T$. There are four targets in the scenario, and initial state parameters are set as follows: [5 m, 0.2 m/s, 5 m, 0.2 m/s] for target 1, [7 m, 0.2 m/s, 25 m, −0.2 m/s] for target 2, [9 m, 0.2 m/s, 5 m, 0.2 m/s] for target 3, and [11 m, 0.2 m/s, 25 m, 0.2 m/s] for target 4. The total frame is 35, in which the targets move in a straight line with constant speed from frames 1 to 15, converge from frames 15 to 25, and perform maneuvers from frames 25 to 35. During this process, the energy of each target at each frame will spread to the tracks of nearby targets, which may affect the robustness of the tracks. In maritime scenarios, the echoes of targets during scanning intervals often fluctuate, so we use the Swerling 1 model to model these fluctuations. In our experiments, clutter parameters are set as shape parameter $\alpha$ = 2 and scale parameter $\beta$ = 1, and the SCR of the targets is set to 6 dB, calculated by $\mathrm{SCR}=10\lg (P(\alpha -1)/\beta )$, where P is the signal intensity.

Figure 4 shows the tracking results of different TBD methods. Comparing Figure 4a with Figure 4b,c, it can be seen that the PP-TBD algorithm performs the worst among the three algorithms, with target 4 incorrectly tracking target 2. The tracking performance of the APFF-TBD algorithm is slightly better than that of APP-TBD, as evidenced by the more robust track endpoints. However, the robustness of the three algorithms faces many challenges under low SCRs. In Figure 4c, the track estimation of target 4 initially lags behind the true position and then moves ahead of it.

Figure 5 shows the tracking performance of the three algorithms under different SCRs. In Figure 5a, the detection success probability $P_D$ is the proportion of tracking success events (the distance between the estimated position of each point in a track and the true target position is less than threshold $D_T$ = 3 in the overall trajectory). It can be seen that the APFF-TBD algorithm has the best performance, followed by APP-TBD, with PP-TBD performing the worst. Specifically, at 6 dB, the tracking success probability of APFF-TBD relative to APP-TBD and PP-TBD is improved by 43.1% and 25.8%, respectively. In Figure 5b, APFF-TBD also exhibits the best performance. Specifically, at 6 dB, the average RMSE of APFF-TBD is reduced by 76.6% and 66.2% relative to APP-TBD and PP-TBD, respectively. In particular, it is noteworthy that in Figure 5a, when the SCR is higher than 8 dB, the detection success probability does not significantly change. This may be because the interference from sea clutter is smaller with the increase in the SCR, and the adjacent interference between targets becomes the main factor affecting the stability of the tracks. This indicates that the APFF-TBD method has the best effect in overcoming adjacent interference out of the three algorithms. In Figure 5c,d, the three algorithms are evaluated under different clutter shape and scale parameters with the same SCR of 6 dB. When $\alpha$ becomes smaller, the clutter has more spikes and a longer tail, and when $\alpha$ is close to 50, clutter distribution degenerates to Rayleigh. APFF-TBD shows robustness under different clutter parameters, having the best performance compared with the PP-TBD and APP-TBD algorithms.

Next, we further analyze how the three algorithms handle adjacent interference between targets. Figure 6a shows the movement of the targets in one experiment, where triangles represent the true positions of the targets at frame 21, and the corresponding energy of the target echoes is shown in Figure 6b, where the tracks converge and the energies of the target group interfere with each other. Figure 6c shows the RMSE of tracking at this time, and it can be seen that after frame 21, there is a significant difference in the tracking performance of the three algorithms. Figure 6d–f show the particle importance distributions given by the APFF-TBD and APP-TBD algorithms at frame 21, where the asterisks represent the true positions of the targets and the points represent particle distribution. When particles can effectively sample the true measurement position, asterisks and points with the same color should be adjacent.

In Figure 6d,e, the importance particles of target 2 in PP-TBD and APP-TBD are dispersed into four clusters over a wider range, and this distribution cannot effectively sample the true measurement. In contrast, as shown in Figure 6f, the particle group in APFF-TBD is closer to the true measurement position. The quality of particle distribution may be the reason for the differences in the subsequent filtering results of the three algorithms: by comparing Figure 6c, it can be noted that after frame 21, the RMSE of PP-TBD and APP-TBD diverges, while the RMSE of APFF-TBD is more robust.

The average running times of the three algorithms are shown in

Table 2. Comparison of average runtime for three TBD algorithms.

Particle Number	PP-TBD (s)	APP-TBD (s)	APFF-TBD (s)
500	1.05	2.16	4.27
750	1.55	3.19	6.08
1000	2.08	4.36	8.29

. It can be seen that the running time of each algorithm roughly increases linearly with particle number. When the number of particles is fixed, APFF-TBD takes the longest time, which is because APFF-TBD provides the importance distribution of each sub-partition in an iterative form, and its computational cost is related to the square of the number of adjacent targets at the current frame. In the real-world experiment with 35 frames of scanning data, the running time of APFF-TBD is between 4.27 and 8.29 s.

4.3. Scene 2: MTT with Variable Target Number

In this section, we consider a complex scenario with a varying number of targets. In this scenario, up to six targets move simultaneously, and the simulation lasts for 70 radar frames. The times and initial positions of these targets being born and dying are shown in

Table 3. Target initial state parameters.

Target	Initial State	Appearing Frame	Disappearing Frame
1	[9.5 m, 0.2 m/s, 9.5 m, 0.2 m/s]	21	70
2	[11 m, 0.25 m/s, 21 m, −0.2 m/s]	21	70
3	[9 m, 0.25 m/s, 5 m, 0.25 m/s]	1	50
4	[11 m, 0.25 m/s, 25 m, −0.25 m/s]	1	70
5	[14 m, 0.25 m/s, 5 m, 0.25 m/s]	1	50
6	[16 m, 0.25 m/s, 25 m, −0.25 m/s]	21	70

. In order to evaluate the target detection capability of the APFF-TBD algorithm, the CPHD-TBD algorithm developed for long-tail clutter (HT-CPHD-TBD) [54] is added as the baseline algorithm. This algorithm uses a framework based on random finite sets to solve the multi-target birth and death problem.

In the experiment, to ensure fairness, all comparison algorithms share the same scenario parameters. We found that false alarm rates are significantly affected by sea clutter peaks, while missed detection probabilities are related to interference from adjacent targets. The target initial state parameters are shown in Table 3. In addition, initialization duration $T_B$ = 3 and termination duration $T_D$ = 1. The number of particles is 500, the cluster threshold R = 4, and the false detection probability $P_F$ = 10⁻³. The particle iteration time and particle flow parameters in APFF-TBD are set as follows: 20 iterations. The exponential method was used to select $\lambda$, $\lambda ={10}^{-4+4n/N_I},n=0,1,\dots ,N_I-1$. HT-CPHD-TBD has some unique parameters, which are set as follows: a survival probability $P_{s,cphd}=0.99$, a newborn target density $D_{b,cphd}=0.01$, and a detection probability $P_{d,cphd}=1$.

Figure 7 shows the tracking trajectory of different TBD methods. Comparing Figure 7a–d, it can be seen that compared to APFF-TBD, the track maintenance performance of PP-TBD, APP-TBD, and HT-CPHD-TBD is relatively poor, as their track estimates are quite incomplete or easily divergent. For example, in Figure 7a, targets 1, 2, 3, and 4 experience significant tracking losses at the point where their tracks intersect, and a similar situation can be seen in Figure 7b. In Figure 7c, HT-CPHD-TBD performs well initially but loses tracking during the neighboring target process. HT-CPHD-TBD requires the initial states of newborn targets without initial processing. In Figure 7d, APFF-TBD performs relatively well, though there is still a loss of tracking when targets 2 and 4 intersect, and it is not until the targets are relatively far away that the tracks are re-established. This may be because, in the initialization process, the program only samples new targets at a certain distance away from known targets, which is not conducive to initializing new targets that are close to existing targets.

The performance of the four algorithms at 3 dB and 6 dB is shown in Figure 8. Figure 8a shows the mean of the estimated cardinality versus time. For the cardinality estimation, APFF-TBD shows superiority over the other algorithms. Specifically, the cardinality estimation performance of APFF-TBD at 3 dB is comparable to that of APP-TBD at 6 dB. For the first three frames in PP-TBD, APP-TBD, and APFF-TBD, the estimation is 0, as the targets have not yet been detected. There is a delay of about three frames between the estimation and the actual number of targets. Similar effects can be observed around frames 20 and 50. On the contrary, no detection and termination procession is used in HT-CPHD-TBD, so the OSPA changes faster.

The standard deviation of the target number, location, and distance of the optimal sub-pattern assignment (OSPA) with a cut-off parameter c = 2 and a metric parameter p = 1 is adopted to measure the estimation precision of the algorithm in Figure 8b–d. Figure 8b presents the OSPA error performance comparisons over time between the PP, APP, HT-CPHD, and APFF implementations under different SCRs. Overall, it is clear that the state estimate performance of APFF-TBD is much better than that of PP-TBD. Additionally, the estimated accuracy of the methods with 6 dB is significantly better than that with 3 dB. Specifically, in Figure 8b, PP-TBD at 3 dB shows a significant tracking divergence problem after frame 40, while APFF-TBD maintains the stability of the state estimates. Additionally, in Figure 8b, APFF-TBD at 3 dB shows comparable track estimation performance to APP-TBD at 6 dB. Finally, in Figure 8c, APFF-TBD shows comparable performance with HT-CPHD-TBD before frame 20, and much better performance after that.

These phenomena may result from APFF-TBD’s efficient use of measurement information. The multi-frame detection behaves well in PP, APP, and APFF implementations, while in HT-CPHD-TBD, detection is based on a single frame, which could have targets lost after frame 20. Specifically, around frame 50 in both Figure 8b–d, there is a dip in the error metrics, but this does not reflect the algorithm’s performance. This is because, as shown in Figure 8a, real targets are dying at this time, and due to the significant underestimation of the number of targets by most TBD methods, the cardinality error decreases incorrectly over three frames, during which the target tracks are ending.

In conclusion, the simulation experiment is set under quite low SCR values. The proposed algorithm behaves better than the baseline methods in the tracking of multiple weak targets in challenging marine scenarios with low SCRs.

5. Discussion

This paper proposes a track-before-detect algorithm based on auxiliary particle flow for tracking multiple marine neighboring weak targets. Our work primarily includes two aspects: First, a neighboring weak target model is established, accounting for adjacent interference between closely spaced targets under generalized Pareto distribution clutter. Second, a particle covariance feature-based auxiliary filtering strategy is proposed, along with a track-before-detect technique that uses Geodesic particle flow to iteratively optimize the importance distribution.

Compared with PP-TBD technology, which is a commonly used technique, the APFF-TBD algorithm offers significant advantages in both track estimation accuracy and robustness by using the current measurement as auxiliary information. Compared with APP-TBD, the APFF-TBD algorithm slightly improves tracking performance, particularly when tracking targets with low signal-to-noise ratios and dense target distributions. Roughly speaking, the performance improvement in terms of detection and tracking is equivalent to an approximately 3 dB increase. Compared with HT-CPHD-TBD, APFF-TBD behaves much better in neighboring weak target experiments after the trajectories intersect.

Experiments show that the commonly used target birth/death logic is still relatively simple. The proposed neighboring target model could help quickly initiate new tracks under conditions of highly proximate targets, but this needs further investigation relying on more detailed sea clutter and sea surface target datasets. Additionally, the iterative updating strategy and auxiliary particle flow technique we propose can be easily extended to detection-before-tracking techniques based on the RFS framework, which is a promising direction for future work.

6. Conclusions

A track-before-detect algorithm based on auxiliary particle flow is proposed for tracking marine neighboring weak targets. Our work consists of the following three parts: First, the generalized Pareto distribution model for marine neighboring targets is introduced, and an offline lookup table is created to obtain the likelihood ratio function with no closed-form solution, reducing computational costs. Next, a particle flow-assisted sampling strategy is proposed, where false track associations are eliminated iteratively using particle covariance features. Finally, measurement information is used to guide the Geodesic particle flow to obtain the importance distribution, enhancing tracking performance. Simulation results show that the proposed algorithm can track marine neighboring weak targets under strong sea clutter. In scenarios with fixed numbers of targets, compared with PP-TBD and APP-TBD, the detection probability at 6 dB increases by 43.1% and 25.8%, respectively, while the average RMSE is reduced by 76.6% and 66.2%. In scenarios with varying numbers of targets, the proposed algorithm also demonstrates good detection and tracking performance compared with the most advanced multi-target tracking algorithm under long-tail clutter. Future work should include research on track initialization and termination strategies for neighboring targets, as well as extending the target model and auxiliary particle flow theory to the framework based on random finite sets (RFSs).