# Passive Tracking of Multiple Underwater Targets in Incomplete Detection and Clutter Environment

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Signal Model and Problem Formulation

#### 2.1. System Model

#### 2.2. Measurement Model

## 3. CPHD Recursion Based on Bayesian Theory

#### 3.1. RFS Formulation of Multiple Target Filtering

#### 3.2. CPHD Recursion

- Each expected target produces bearing and Doppler measurements independently from one another;
- The targets’ birth RFS is independent of the surviving target RFS;
- The clutter’s RFS is independent from the true targets’ measurement RFS;
- The prior and predicted multiple targets’ RFSs are both independent and identically distributed processes.

#### 3.3. EKF-Based CPHD Recursion

## 4. Simulations

^{2}. The standard deviation values of the measurement noise for bearing and frequency were ${0.5}^{\circ}$ and 3 Hz, respectively. The clutter followed a Poisson distribution with clutter intensity ${\lambda}_{c}=0.3$ over the region $\left[-\pi /2,\pi /2\right]\mathrm{rad}\times \left[\mathrm{750,795}\right]\mathrm{Hz}$—that is, the average clutter each time was 42. For simplicity, the detection probability of all targets was assumed to be the same, and was set to ${p}_{D,t}=0.98$. We assumed that all targets’ survival probabilities were the same and they were set to ${p}_{S,t}=0.99$. To inspect the tracking performance of the EKF-based CPHD recursion, the 1000 Monte Carlo process was calculated.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Scans of the target trajectory estimates and true target positions in x- and y-coordinates for CPHD recursion versus time. (

**a**) x coordinate, (

**b**) y coordinate.

**Figure 5.**Scans of the target trajectory estimates and true target positions in x- and y-coordinates for the PHD recursion versus time. (

**a**) x coordinate, (

**b**) y coordinate.

**Figure 6.**Scans of the average OSPA distance for four targets versus time for both EKF-based CPHD recursion and PHD recursion.

**Figure 7.**Scans of the average OSPA localization for four targets versus time for the EKF-based CPHD and PHD recursion.

**Figure 8.**The Monte Carlo average mean of estimated cardinality for the EKF-based CPHD recursion and the true target cardinality.

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**MDPI and ACS Style**

Li, X.; Lu, B.; Ali, W.; Jin, H.
Passive Tracking of Multiple Underwater Targets in Incomplete Detection and Clutter Environment. *Entropy* **2021**, *23*, 1082.
https://doi.org/10.3390/e23081082

**AMA Style**

Li X, Lu B, Ali W, Jin H.
Passive Tracking of Multiple Underwater Targets in Incomplete Detection and Clutter Environment. *Entropy*. 2021; 23(8):1082.
https://doi.org/10.3390/e23081082

**Chicago/Turabian Style**

Li, Xiaohua, Bo Lu, Wasiq Ali, and Haiyan Jin.
2021. "Passive Tracking of Multiple Underwater Targets in Incomplete Detection and Clutter Environment" *Entropy* 23, no. 8: 1082.
https://doi.org/10.3390/e23081082