# Underwater Target Tracking Using Forward-Looking Sonar for Autonomous Underwater Vehicles

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. FLS Overview

- (1)
- The number of transducers that can be packed in an array is physically restricted because of the limitations of transducer size. Thus, the resolution of an FLS image is lower, and the gray level of the target area is generally smaller, so it is more difficult to find some details of targets inside it.
- (2)
- The scattering capability of different parts of the target surface is different, which is affected by the shape, material, and relative position between target and sonar. The incident angle of an acoustic wave is also changed with target movement, so different regions may be generated for the same target in the acoustic image, and they often appear to be unconnected regions in acoustic vision.
- (3)
- The phenomenon of multipath propagation is a distinctive feature in acoustic images, and reflected acoustic waves may have greater energy than that of ones reflected from obstacles, leading to false or lack of target detection, increasing the difficulty of acoustic-image processing.

## 3. Feature Selection Based on GRNN

#### 3.1. Feature Description

#### 3.2. Search Procedure

#### 3.3. GRNN for Classification

#### 3.4. Experiments and Analysis

## 4. Gaussian Particle Filtering

#### 4.1. Basic Principle

#### 4.2. Gaussian Particle-Filter Improvement

#### 4.2.1. Likelihood-Function Representation

#### 4.2.2. Feature-Set Fusion Strategy

#### 4.2.3. Target-Tracking steps

- Initialization: to select interesting targets in first image frame. After the image is processed, target features in Table 7 are calculated, and the number of sample particles $K$ is determined. It is assumed that the initial importance function is normal distribution function. Then, the mean value is the center coordinate $\left({x}_{target},{y}_{target}\right)$ of the target, and covariance $\mathsf{\sigma}$ is determined by the tracking environment, that is, particles collected by the initial importance function in the x- and y-axes can be written as $N\left(x;{x}_{target},45\right),\text{}N\left(y;{y}_{target},40\right)$, and each particle is calculated according to the kinematics model.
- To capture the image in the next frame, calculate features of particles ${\left\{{x}_{t,n}\right\}}_{n=1}^{K}$. According to Equation (17), feature clues are analyzed to check whether they are degenerated, and the fused weighted value of particles is calculated. The weighted particle value is normalized as ${w}_{t,n}={w}_{t,n}/{{\displaystyle \sum}}_{n=1}^{K}{w}_{t,n}$; then, ${\mu}_{t}$ and ${\sigma}_{t}$ are calculated.
- To sample according to posterior probability distribution $N\left({x}_{t};{\mu}_{t},{\sigma}_{t}\right)$, and ${\left\{{x}_{t,n}\right\}}_{n=1}^{K}$ is gained. Then, ${x}_{t+1,n}$ can be calculated by the kinematics model. According to Equation (18), the predicted mean and covariance values are calculated. If targets are lost, covariance value is expanded, otherwise, it is turned into Step 2.

## 5. Example Test and Discussion

#### 5.1. Tank Experiment

#### 5.1.1. Comparative Experiments of Tracking Methods

#### 5.1.2. Fusion-Strategy Experiments

#### 5.2. Sea Trial

#### 5.2.1. Acoustic-Vision-Based Processing Framework

#### 5.2.2. Target-Tracking Test under Noncrossing-Movement Condition

#### 5.2.3. Target-Tracking Test under Crossing-Movement Condition

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Diagram showing scanning procedure and idealization of expected return of used sonar [28].

**Figure 2.**Image of target under different conditions: optical image gained in: (

**a**) air and (

**b**) water. (

**c**) Acoustic image gained in water.

**Figure 5.**Selected experiment targets: (

**a**) first target, pontoon; (

**b**) second target, cube; (

**c**) third target, triangular prism; (

**d**) fourth target, reflector; and (

**e**) fifth target, sphere.

**Figure 12.**Tracking results obtained by presented method in (

**a**) (p + 1)th image and (

**b**) (p + 2)th image.

**Figure 13.**Comparison results obtained by different methods: (

**a**) tracking trajectory gained by each method and (

**b**) center-position-error (CLE) curve gained by each method.

**Figure 14.**Tracking results based on different fusion strategies gained by: (

**a**) multiplicative fusion (MF); (

**b**) weighted fusion (WF), and (

**c**) proposed method.

**Figure 16.**CLE gained by different fusion methods: results of (

**a**) first target and (

**b**) second target.

**Figure 17.**Tracking results based on different fusion strategies gained by (

**a**) MF; (

**b**) WF; and (

**c**) proposed method.

**Figure 18.**Tracking trajectory gained by different fusion methods of (

**a**) first target and (

**b**) second target.

**Figure 19.**CLE gained by different fusion methods: results of (

**a**) first target and (

**b**) second target.

**Figure 21.**Acoustic-vision-based framework: (

**a**) hardware architecture and (

**b**) software architecture.

**Figure 22.**Target-tracking results in: (

**a**) first and (

**b**) second sequence of forward-looking-sonar (FLS) images.

**Figure 24.**CLE gained by proposed method: results in (

**a**) first and (

**b**) second sequence of FLS images.

**Figure 27.**CLE gained by proposed method: results in (

**a**) first and (

**b**) second sequence of FLS images.

Parameter | Operating Frequency | Horizontal Beam Width | Vertical Beam Width | Maximum Range | Range Resolution | Scan Size | Weight |
---|---|---|---|---|---|---|---|

Low-frequency model | 325 KHz | 3.0° | 20° | 300 m | about 15 m | 0°–360° | 3 kg in air, 1.4 kg in water |

High-frequency model | 675 KHz | 1.5° | 40° | 100 m |

**Table 2.**(

**a**) Basic features of regions. (

**b**) Contrast features of regions. (

**c**) Shape moment features of regions. (

**d**) Moment-invariant features of regions. (

**e**) Statistical-texture features of regions.

No. | Function |
---|---|

(a) | |

1 | Area ${A}_{0}={N}^{o}$ |

2 | Perimeter length ${P}_{0}={N}^{eo}$ |

3 | Mean intensity ${\overline{I}}_{0}=\left[{{\displaystyle \sum}}_{i=1}^{m}{{\displaystyle \sum}}_{j=1}^{n}f\left(i,j\right)\right]/{N}^{o}$ $\text{}\mathrm{and}\text{}p\left(\mathrm{i},\mathrm{j}\right)\in {R}_{k}$ |

4 | Intensity standard deviation ${\sigma}_{0}=\left[{{\displaystyle \sum}}_{i=1}^{m}{{\displaystyle \sum}}_{j=1}^{n}{\left[f\left(i,j\right)-{\overline{I}}_{0}\right]}^{2}\right]/{N}^{o}$ $\mathrm{and}\text{}p\left(\mathrm{i},\mathrm{j}\right)\in {R}_{k}$ |

5 | Compactness ${O}_{0}=4\pi {A}_{0}/{\left({P}_{0}\right)}^{2}$ |

6 | Background mean ${\overline{B}}_{0}=\left[{{\displaystyle \sum}}_{i=1}^{m}{{\displaystyle \sum}}_{j=1}^{n}f\left(i,j\right)\right]/{N}^{b}\text{}\mathrm{and}\text{}p\left(\mathrm{i},\mathrm{j}\right)\notin {R}_{k}$ |

(b) | |

7 | ${C}_{0}^{1}={\overline{I}}_{0}-{\overline{B}}_{0}$ |

8 | ${C}_{0}^{2}={\overline{I}}_{0}/{\overline{B}}_{0}$ |

9 | ${C}_{0}^{3}=\left({\overline{I}}_{0}-{\overline{B}}_{0}\right)/\left({\overline{I}}_{0}+{\overline{B}}_{0}\right)$ |

(c) | |

10 | $S{M}_{1}={\left[\left({{\displaystyle \sum}}_{t=1}^{{P}_{0}}{\left[{D}_{e}^{o}\left(i\right)-{{\displaystyle \sum}}_{t=1}^{{P}_{0}}{D}_{e}^{o}\left(i\right)/\text{}{P}_{0}\right]}^{2}\right)/{P}_{0}\right]}^{1/2}/{{\displaystyle \sum}}_{t=1}^{{P}_{0}}{D}_{e}^{o}\left(i\right)/\text{}{P}_{0}$ |

11 | $S{M}_{2}={\left[\left({{\displaystyle \sum}}_{t=1}^{{P}_{0}}{\left[{D}_{e}^{o}\left(i\right)-{{\displaystyle \sum}}_{t=1}^{{P}_{0}}{D}_{e}^{o}\left(i\right)/\text{}{P}_{0}\right]}^{3}\right)/{P}_{0}\right]}^{1/3}/{{\displaystyle \sum}}_{t=1}^{{P}_{0}}{D}_{e}^{o}\left(i\right)/\text{}{P}_{0}$ |

12 | $S{M}_{3}={\left[\left({{\displaystyle \sum}}_{t=1}^{{P}_{0}}{\left[{D}_{e}^{o}\left(i\right)-{{\displaystyle \sum}}_{t=1}^{{P}_{0}}{D}_{e}^{o}\left(i\right)/\text{}{P}_{0}\right]}^{4}\right)/{P}_{0}\right]}^{1/4}/{{\displaystyle \sum}}_{t=1}^{{P}_{0}}{D}_{e}^{o}\left(i\right)/\text{}{P}_{0}$ |

13 | $S{M}_{4}=S{M}_{3}-S{M}_{1}$ |

(d) | |

14 | ${M}_{1}={\eta}_{20}+{\eta}_{02}$ |

15 | ${M}_{2}={\left({\eta}_{20}-{\eta}_{02}\right)}^{2}+4{\eta}_{11}^{2}$ |

16 | ${M}_{3}={\left({\eta}_{30}-3{\eta}_{12}\right)}^{2}+{\left(3{\eta}_{21}-{\eta}_{03}\right)}^{2}$ |

17 | ${M}_{4}={\left({\eta}_{30}+{\eta}_{12}\right)}^{2}+{\left({\eta}_{21}+{\eta}_{03}\right)}^{2}$ |

18 | ${M}_{5}=\left({\eta}_{30}-3{\eta}_{12}\right)\left({\eta}_{30}+{\eta}_{12}\right)\left[{\left({\eta}_{30}+{\eta}_{12}\right)}^{2}-3{\left({\eta}_{21}+{\eta}_{03}\right)}^{2}\right]+\left(3{\eta}_{21}-{\eta}_{03}\right)\left({\eta}_{21}+{\eta}_{03}\right)$$\left[3{\left({\eta}_{30}+{\eta}_{12}\right)}^{2}-{\left({\eta}_{21}+{\eta}_{03}\right)}^{2}\right]$ |

19 | ${M}_{6}=\left({\eta}_{20}-{\eta}_{02}\right)\left[{\left({\eta}_{30}+{\eta}_{12}\right)}^{2}-{\left({\eta}_{21}+{\eta}_{03}\right)}^{2}\right]+4{\eta}_{11}\left({\eta}_{30}+{\eta}_{12}\right)\left({\eta}_{21}+{\eta}_{03}\right)$ |

20 | ${M}_{7}=\left(3{\eta}_{21}-{\eta}_{03}\right)\left({\eta}_{30}+{\eta}_{12}\right)\left[{\left({\eta}_{30}+{\eta}_{12}\right)}^{2}-3{\left({\eta}_{12}+{\eta}_{03}\right)}^{2}\right]+\left({\eta}_{30}-3{\eta}_{12}\right)\left({\eta}_{21}+{\eta}_{03}\right)$$\left[3{\left({\eta}_{30}+{\eta}_{12}\right)}^{2}-{\left({\eta}_{21}+{\eta}_{03}\right)}^{2}\right]$ |

(e) | |

21 | Inertia ${M}_{1}^{co}={{\displaystyle \sum}}_{i=0}^{s-1}{{\displaystyle \sum}}_{j=0}^{s-1}{(i-j)}^{2}h\left(i,j\right)$ |

22 | Entropy ${M}_{2}^{co}=-{{\displaystyle \sum}}_{i=0}^{s-1}{{\displaystyle \sum}}_{j=0}^{s-1}h\left(i,j\right)\mathit{ln}h\left(i,j\right)$ |

23 | Angular second moment ${M}_{3}^{co}={{\displaystyle \sum}}_{i=0}^{s-1}{{\displaystyle \sum}}_{j=0}^{s-1}h{\left(i,j\right)}^{2}$ |

24 | Inverse difference moment ${M}_{4}^{co}={{\displaystyle \sum}}_{i=0}^{s-1}{{\displaystyle \sum}}_{j=0}^{s-1}\{h\left(i,j\right)/[1+\left(i-j{)}^{2}\right]\}$ |

25 | Correlation |

26 | Variance ${M}_{6}^{co}={{\displaystyle \sum}}_{i=0}^{s-1}{{\displaystyle \sum}}_{j=0}^{s-1}{(i-{\mu}_{x})}^{2}h\left(i,j\right)$ |

27 | Sum average ${M}_{7}^{co}={{\displaystyle \sum}}_{k=2}^{2s}k\left[{{\displaystyle \sum}}_{i=0}^{s-1}{{\displaystyle \sum}}_{j=0}^{s-1}h\left(i,j\right)\right]$,$i+j=k$ |

28 | Sum entropy ${M}_{8}^{co}=-{{\displaystyle \sum}}_{k=2}^{2s-2}\left[{{\displaystyle \sum}}_{i=0}^{s-1}{{\displaystyle \sum}}_{j=0}^{s-1}h\left(i,j\right)\right]\mathit{ln}[{{\displaystyle \sum}}_{i=0}^{s-1}{{\displaystyle \sum}}_{j=0}^{s-1}h\left(i,j\right)],\text{}i+j=k$ |

29 | Sum variance ${M}_{9}^{co}={{\displaystyle \sum}}_{k=2}^{2s-2}{(k-{M}_{7}^{co})}^{2}\left[{{\displaystyle \sum}}_{i=0}^{s-1}{{\displaystyle \sum}}_{j=0}^{s-1}h\left(i,j\right)\right],i+j=k$ |

30 | Difference entropy ${M}_{10}^{co}=-{{\displaystyle \sum}}_{k=0}^{s-1}\left[{{\displaystyle \sum}}_{i=0}^{s-1}{{\displaystyle \sum}}_{j=0}^{s-1}h\left(i,j\right)\right]\mathit{ln}[{{\displaystyle \sum}}_{i=0}^{s-1}{{\displaystyle \sum}}_{j=0}^{s-1}h\left(i,j\right)],\left|i-j\right|=k$ |

Algorithm of SBS | |
---|---|

1 | Start with the full set ${Y}_{0}=X$ |

2 | Remove the worst feature ${x}^{-}=\mathrm{arg}\mathrm{max}J\left({Y}_{k}-x\right)$, $x\in {Y}_{k}$ |

3 | Update ${Y}_{k+1}={Y}_{k}-{x}^{-}$;$\text{}k=k+1$ |

4 | Go to 2 |

Algorithm of SFS | |
---|---|

1 | Start with the empty set ${Y}_{0}=\{\varnothing \}$ |

2 | Select the next best feature ${x}^{+}=\mathrm{arg}\mathrm{max}J\left({Y}_{k}+x\right)$, $x\in {Y}_{k}$ |

3 | Update ${Y}_{k+1}={Y}_{k}+{x}^{+}$;$\text{}k=k+1$ |

4 | Go to 2 |

No. | Description |
---|---|

1 | Only first target moves. |

2 | Only second target moves. |

3 | Only third target moves. |

4 | Only fourth target moves. |

5 | First and fourth targets move together in the same direction. |

6 | Second and fourth targets move together in the same direction. |

7 | Fourth and fifth targets move together in the same direction. |

8 | Third and fourth targets move together in the opposite direction, and their trajectory is crossed. |

9 | Third and fifth targets move together in the opposite direction, and their trajectory is crossed. |

10 | First and second targets move together in the opposite direction, and their trajectory is crossed. |

11 | Second and third targets move together in the opposite direction, and their trajectory is crossed. |

12 | Second, third, and fourth target moves together in the same direction. |

13 | Second, third, and fourth targets move together in the opposite direction. |

14 | Second target does not move. |

Interval No | B | C | D | E | F | G |
---|---|---|---|---|---|---|

Feature No | 1–5 | 6–10 | 11–15 | 16–20 | 21–25 | 26–30 |

Feature Order Gained by SFS | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

Feature No. | 20 | 17 | 3 | 6 | 24 |

$\mathbf{Algorithm}\text{}\mathbf{of}\text{}{\mathit{a}}_{\mathit{i}}\mathbf{Calculation}$ | |
---|---|

1 | Calculate value ${\overline{f}}_{else,i}$, which is written as: ${\overline{f}}_{else,i}=\left({{\displaystyle \sum}}_{j=0}^{n}1/{\mathsf{\Delta}}_{j}\right)/m,j\ne i$ |

2 | Design fuzzy controller to translate $1/{\mathsf{\Delta}}_{j}$ and ${\overline{f}}_{else,i}$ to fuzzy domain; fuzzy-rule table is shown in Table 9. |

3 | Input $1/{\mathsf{\Delta}}_{j}$ and ${\overline{f}}_{else,i}$ into the fuzzy controller, and obtain fuzzy output ${b}_{i}$ of i^{th} feature. |

4 | Calculate weighting coefficients of each feature ${a}_{i}$, which is written as: ${a}_{i}={b}_{i}/{\mathsf{\Sigma}}_{i=1}^{m}{b}_{i}$ |

${\overline{\mathit{f}}}_{\mathit{e}\mathit{l}\mathit{s}\mathit{e},\mathit{i}}$ | $1/{\Delta}_{\mathit{j}}$ | ||||
---|---|---|---|---|---|

$\mathbf{N}\mathbf{B}$ | $\mathbf{N}\mathbf{S}$ | $\mathbf{Z}\mathbf{E}$ | $\mathbf{P}\mathbf{S}$ | $\mathbf{P}\mathbf{B}$ | |

$\mathrm{NB}$ | 3 | 4 | 4 | 5 | 5 |

$\mathrm{NS}$ | 2 | 3 | 4 | 4 | 5 |

$\mathrm{ZE}$ | 2 | 2 | 3 | 4 | 4 |

$\mathrm{PS}$ | 1 | 2 | 2 | 3 | 4 |

$\mathrm{PB}$ | 1 | 1 | 2 | 2 | 3 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, T.; Liu, S.; He, X.; Huang, H.; Hao, K.
Underwater Target Tracking Using Forward-Looking Sonar for Autonomous Underwater Vehicles. *Sensors* **2020**, *20*, 102.
https://doi.org/10.3390/s20010102

**AMA Style**

Zhang T, Liu S, He X, Huang H, Hao K.
Underwater Target Tracking Using Forward-Looking Sonar for Autonomous Underwater Vehicles. *Sensors*. 2020; 20(1):102.
https://doi.org/10.3390/s20010102

**Chicago/Turabian Style**

Zhang, Tiedong, Shuwei Liu, Xiao He, Hai Huang, and Kangda Hao.
2020. "Underwater Target Tracking Using Forward-Looking Sonar for Autonomous Underwater Vehicles" *Sensors* 20, no. 1: 102.
https://doi.org/10.3390/s20010102