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Abstract

To solve the false terrain problem caused by the tunnel effect in the conventional multibeam seafloor terrain detection, a detection method of multibeam seafloor terrain based on the ADOS-CFAR (Amplitude Dichotomy Order-Statistics Constant False Alarm Rate) is developed. This paper first discusses the principles and existing problems of the OS-CFAR and K-FINDER algorithms and then suggests the ADOS-CFAR algorithm and its fast calculation method for those problems. By adopting this algorithm into the detection method of multibeam seafloor terrain and carrying out the simulation study on the computational load of the ADOS-CFAR, it is shown that this method has a lower computational load on the premise of ensuring the detection performance. Finally, the proposed algorithm is analyzed and verified through the test data in Songhua Lake. The result indicates that this method can effectively avoid the false terrain caused by tunnel effect with higher terrain detection accuracy.

1. Introduction

The multibeam echo sonar is one of the widely used marine surveying and mapping instruments at present. Its principle is, by estimating the TOA (time of arrival) and DOA (direction of arrival) of the scattered echo signal in each cross beam, to calculate the seafloor depth on the condition that the sound speed is known. The multibeam seafloor terrain detection technology plays an important role in the multibeam detection technologies; its robustness is directly related to the reliability of the detection results. The research focus of the multibeam echo sonar technology has been updated from the conventional technology to pursuing a wide swath width [1] and better robustness [2–5]; more attention has been paid to the effectiveness and authenticity of the detection results. For example, the bathymetric algorithm has been developed from the single “energy center” algorithm to a new algorithm which incorporates the WMT (weight mean time) and the phase difference detection, namely, adopting the WMT in the mirrored area while adopting the phase difference detection in the nonmirrored area. But due to the unknown and invisibility of the real depth of the sea, no matter which bathymetric algorithm is used, we can only obtain the estimation of the so-called genuine seafloor depth under a certain condition (or criterion). Some studies found that the main factors affecting the robustness are the bathymetric artifacts and abnormal values in the multibeam bathymetric technology, where the most typical bathymetric artifact is “tunnel effect” and “refraction effect.” In order to improve the SNR (Signal-to-Noise Ratio) of the received echo from seafloor, the multibeam echo sonar uses various beam forming methods (spatial filters) to enhance the signal and suppress the noise in the received echo. And the FT beam former is the most common used one among those filters. It has been widely applied in the multibeam echo sonar technologies due to its simple principle and good real-time operation. However, the defect of energy leakage is prone to cause the side lobe interference; the echo energy of the vertical-incidence beam leaks into the main lobe directions of all other beams, which impacts the subsequent WMT. The influence on the bathymetric results is that the genuine flat seafloor terrain will be wrongly measured into the false cambered terrain with upturned shapes on the both ends, which is called the “tunnel effect.” Because of the existence of the tunnel effect, a multibeam echo sonar often outputs erroneous terrain information in detection, and Wei et al. [6, 7] did some research from two aspects of side lobe reduction and adaption. The lower side lobe increases the width of main lobe and reduces the terrain detection resolution to a certain extent. The adaptive method, for best results, must be used under the condition in which accurate interference source is confirmed. More importantly, the above methods cost large computation with less efficiency, which leads to many restrictions in practical applications. Chen et al. proposed a tunnel effect elimination method which is based on the apFFT beam forming algorithm [8], further reducing the computational load under the premise of decreasing the leakage of mirrored beam energy, but without the high efficiency also.

On the other hand, the CFAR (Constant False Alarm Rate) has made a great progress in the field of radar; the resultant methods such as CA-CFAR (Cell Averaging Constant False Alarm Rate) and OS-CFAR (Order-Statistics Constant False Alarm Rate) [9] can realize the automatic target detection under the condition of ensuring constant false alarm. Although the OS-CFAR has been applied into multibeam underwater target and seafloor terrain detections with a good capability of detecting marine multitarget [10], it is difficult to be applied in practical applications due to its complex calculation and low terrain detection accuracy while effectually removing tunnel effect. For the real-time implementation of the OS-CFAR algorithm, some details have been studied by many scholars [11–17]. Magaz and Bencheikh improved the calculation efficiency by repeated iterations and maximum value removal [11]. Considering the characteristic of synthetic aperture radar image, Sun et al. [12] raised the computational efficiency by 5 times (target image, 480 × 340, background window, 61 × 61, and protection window, 41 × 41) compared with the conventional methods by fully using the information of the previous 2D sliding window. Hyun and Lee sorted all the data before sliding window detection to increase detection accuracy [13]. More significantly, Ali et al. [14] proposed the K-FINDER algorithm based on OS-CFAR, which avoids large computational load in sorting method and quickly determines order statistics by the iterative-comparative method; Shin et al. [15] proposed the ABIS method based on the principles of insertion sort and sliding window to decrease the computational load to between 44% and 90% of the quick sort algorithm. In the multibeam bathymetry, the efficient and real-time computation is still a challenge. In order to realize better constant false alarm detection, the unified threshold has to be extracted from hundreds of beams in every sampling, and the redundant information of the sliding window cannot be used. Aiming at these problems, we propose the ADOS-CFAR method and apply it to multibeam seafloor terrain detection in order to improve the accuracy of terrain detection in the premise of eliminating tunnel effect.

This paper discusses the principles of the OS-CFAR and K-FINDER algorithms and then proposes ADOS-CFAR and its application in the multibeam seafloor terrain detection method. The computational load of ADOS-CFAR is simulated and researched, and the experimental data is validated and analyzed in Songhua Lake.

2. Fundamental Principles

2.1. OS-CFAR Principle

In order to improve the detection performance of conventional mean methods in multitarget environment, the order statistics (OS) method [9] was proposed by Rohling; the specific progress of the algorithm is shown in Figure 1.

Figure 1

OS-CFAR progress.

Here the CUT (Cell Under Test) is a detection unit; firstly we sort the data near CUT (sampling point from $X_{1}$ to $X_{N}$ ; N is the total number in sorting) and extract the kth order statistics $x (k)$ and multiply it by a factor $α_{O S}$ to get decision threshold. In the OS-CFAR, the traditional sorting method requires at least $N (N - 1) / 2 d$ times calculation; the sorting time can be shortened to $N l o g 2 (N)$ by quick sorting method. However, the computational load is still large when N is a large number; some difficulties still exist in efficient and real-time processing, so a further reduction of the computational load is necessary.

2.2. K-FINDER Algorithm

To settle the problem of OS-CFAR in calculation, Ali et al. [14] suggested K-FINDER algorithm; the processing progress of the algorithm is shown in Figure 2 and the specific progress is as follows: (1)

Calculate the mean from $X_{1}$ to $X_{N}$ except CUT, and then count $C_{u}$ , and set $T_{u}$ to be $C_{u}$ (where $C_{u}$ represents the number of the remaining data greater than the mean, while $T_{u}$ represents the number of all the data greater than the mean).

(2)

Determine whether $C_{u}$ is equal to zero; if not, keep iterating and enter step (3); if it is equal to zero, stop iteration and directly assign the mean to $x (k)$ as the result, and then the calculation is completed.

(3)

If $T_{u}$ is greater than $N - k$ , reserve the data greater than the mean and set $T_{u} = T_{u} - C_{u}$ , and discard the rest; otherwise reserve the data less than the mean; enter step (4).

(4)

Calculate the mean of the remaining data, and compare the mean with the remaining data; enter step (5).

(5)

Count $C_{u}$ of the remaining data greater than the mean, set $T_{u} = T_{u} + C_{u}$ , and return to step (2) to repeat iterations.

Figure 2

K-FINDER algorithm progress.

Through this method, the time-consuming sorting process is avoided, and $x (k)$ can be found directly by the comparative determination. Compared with other conventional methods, it greatly improves the calculation speed.

3. ADOS-CFAR Algorithm for Seafloor Terrain Detection

3.1. ADOS-CFAR Algorithm Principle

Although the K-FINDER algorithm has a fast speed, the mean calculation costs too much time, and too many of the iterations need to be finished because the iteration target is $C_{u} = 0$ . In this paper, firstly, the mean of the decision condition is replaced by the mean of the iterative data in the front part before the CUT, which avoids computing the mean over the whole, potentially large data volume. And, secondly, the condition of stopping iterations in advance is set; $x (k)$ can be obtained by finding the maximum or minimum value of the remaining data after stopping iterations, which decreases the number of iterations. Therefore, this method can further improve the computation speed, and the algorithm progress is shown in Figure 3; the specific steps are as follows: (1)

Calculate the mean M of the data in the front part before the CUT; select the data greater than M and put them into array B and put the remaining data into array S, count $C_{u}$ in B, and set $T_{u} = C_{u}$ .

(2)

Determine whether $T_{u}$ is equal to $N - k + 1$ ; if yes, find out the minimum value in B and take it as the result $x (k)$ and stop iterations; otherwise enter step (3).

(3)

Determine whether $T_{u}$ is equal to $N - k$ ; if yes, find out the maximum value in S as the result $x (k)$ and stop iterations; otherwise enter step (4).

(4)

Determine whether $T_{u}$ is greater than $N - k$ ; if yes, take B as an array to be compared, and set $T_{u} = T_{u} - C_{u}$ ; otherwise take S as an array to be compared; enter step (5).

(5)

Calculate the mean M of the data in the front part of the array to be compared, put the data greater than M into B, and put the remaining data into S; count $C_{u}$ in B, and set $T_{u} = T_{u} + C_{u}$ ; then enter step (2) for further iterations.

Figure 3

ADOS-CFAR algorithm progress.

3.2. ADOS-CFAR under Loose k Condition

Although the ADOS-CFAR has improved the computational speed, the condition of stopping iterations is still relatively harsh with the complex iterations, causing a large computational load. The basic goal of the OS-CFAR is to set the estimated value $\hat{T} = α_{O S} x (k)$ of interference level to ensure average false alarm probability, and the average false alarm probability ${\bar{P}}_{F A}$ in the case of Gauss distribution is

\begin{matrix} {\bar{P}}_{F A} = k (\begin{pmatrix} N \\ k \end{pmatrix}) \frac{Γ (α_{O S} + N - k + 1) Γ (k)}{Γ (α_{O S} + N + 1)} . \end{matrix}

(1)

Here

Γ (*)

is the Gamma function. Equation (1) shows that when

{\bar{P}}_{F A}

is given a fixed value,

α_{O S}

can be determined by the length of the array N and the serial number k. N is often a fixed value, and a corresponding relationship exists between k and

α_{O S}

. But k is not an arbitrary value. It is known that the optimal value of k is about 0.75N [18]. Moreover, even for small deviations, from this optimal value the Constant False Alarm Rate can still be guaranteed. Therefore, in this paper, step (2) and step (3) of the ADOS-CFAR are simplified as follows: determine whether

(N - k - N_{L}) < T_{u} < (N - k + N_{L})

(

N_{L}

is a loose range); if yes, take the minimum value in the array B as the result

x (k)

, and recalculate

k = N - T_{u} + 1

; otherwise enter step (4). Obviously the greater

N_{L}

, the less number of iterations and the less the computational load. After obtaining

x (k)

, plug k into (1) to calculate out

α_{O S}

(the look-up table method), obtaining

\hat{T}

and completing the threshold estimation.

3.3. Fast Calculation under Sliding Condition

In the conventional OS-CFAR, because the detection window slides forward, abundant redundant information can be utilized. Shin et al. [15] introduced insertion sort idea and proposed the ABIS (Anchor-based Insertion Sorting) method to utilize the redundant information, greatly enhancing the processing speed with only computational load N of a single sliding. Nevertheless, this still scarcely solved the computational load problem. Based on the idea of amplitude dichotomy, this paper completely abandons the sorting process; the principle diagram and algorithm progress are shown in Figures 4 and 5, respectively (in the diagram, $U_{h}$ is the first unit of the sliding window, $U_{t}$ is the tail unit to enter the sliding window, $U_{k}$ is the kth order statistics unit in previous search, $I_{u h}$ is $U_{h}$ 's serial number, $I_{u t}$ is $U_{t}$ 's serial number, $I_{u k}$ is $U_{k}$ 's serial number, the array S stores the data less than $U_{k}$ , and the array B stores the data greater than $U_{k}$ ).

Figure 4

The principle of ADOS-CFAR under sliding condition.

Figure 5

ADOS-CFAR algorithm progress under sliding condition.

The progress (1)–(8) in Figure 5 is as follows: (1)

Remove the first serial number of the array S, and add $I_{u t}$ to the back of the array S (when the serial number $I_{u k}$ is removed, search the maximum value in array S and update $U_{k}$ and $I_{u k}$ ).

(2)

Add $I_{u t}$ to the back of B, remove the first serial number of S, and then search the minimum value in B and update $U_{k}$ and $I_{u k}$ .

(3)

Search $I_{u k}$ in array S and delete it, and add $I_{u t}$ to the back of array S, insert $I_{u k}$ into B, and delete the first serial number in array B, and then search the maximum value in array S and update $U_{k}$ and $I_{u k}$ .

(4)

Delete the first serial number in B, and add $I_{u t}$ to its back.

(5)

Delete the first serial number in S, and add $I_{u t}$ to its back.

(6)

Search $I_{u k}$ in B and delete it, and add $I_{u t}$ to the back of array B, insert $I_{u k}$ into array S, and delete the first serial number in B, and then search the minimum value in B and update $U_{k}$ and $I_{u k}$ .

(7)

Add $I_{u t}$ to the back of S, and delete the first serial number in B, and then search the maximum value in S and update $U_{k}$ and $I_{u k}$ .

(8)

Remove the first serial number in B, and add $I_{u t}$ to the back of B (when the serial number $I_{u k}$ is removed, search the maximum value in B and update $U_{k}$ and $I_{u k}$ ).

Assume that the background noise of data is the Gauss white noise, the length of processing window is N, and k is set to $3 N / 4$ ; the computational load of the processes 1, 4, 5, and 8 can be neglected when N is large; the computational load of the processes 2 and 7 is $N / 4$ and $3 N / 4$ , respectively, while that of processes 3 and 6 is $N / 2 + 3 N / 4$ and $N / 2 + N / 4$ , respectively. According to the determination condition in Figure 5, the probabilities of processes (1)–(8) are, respectively, 9/32, 3/32, 3/32, 1/32, 9/32, 3/32, 3/32, and 1/32. So that when the number of slides is large, the computational load of each slide is $9 N / 32$ , which is only 0.28125 times ABIS and improves the computational speed.

3.4. Seafloor Terrain Detection Based on ADOS-CFAR

In order to eliminate the tunnel effect with less computational load, the fast processing method in Section 3.2 is adopted in the beam forming result of each time slice to obtain the estimated value $\hat{T}$ of the interference level [10]. To standardize data, divide the beam data of each time slice by $\hat{T}$ , so that the data of each time slice has the same reference of the signal-to-clutter ratio. Afterwards, each beam is extracted via the fast processing method described in Section 3.3 to determine whether the echo signal is the target.

The essence of the tunnel effect is that the reflection intensity in the mirror beam irradiation area is strong, and the energy leaks into the side lobe, which affects the demodulation of weak echo in the same direction. Through the first step, the strong and weak reflection side lobe energy can be unified on the same interference level; through the second step, the target can be detected automatically in the condition of the constant false alarm, so that the tunnel effect interference can be availably eliminated under the premise of the high computational speed, therefore detecting seafloor terrain effectively and accurately.

4. Simulation and Analysis

4.1. The Rationality Analysis of Loose k Condition

Equation (1) shows that when the average Constant False Alarm Rate is fixed, k has a corresponding relationship with $α_{O S}$ . But considering the formula's complexity, the squeeze iteration method is employed to obtain the relationship between k and $α_{O S}$ , which is shown in Figure 6 ( ${\bar{P}}_{F A} = 0.001$ ), to ensure that the constant false alarm can be maintained even if k floats in a certain range.

Figure 6

The relationship between $α_{O S}$ and k.

The flexible value range of k, however, inevitably leads to some loss. In order to quantitatively analyze the loss, the Gauss white noise with 20 dB amplitude and $N = 1024$ are taken as the parameters of a signal; the average power $P_{w}$ of the sample is estimated as the reference object, and then some target signals with 40 dB amplitude are added in a random location; the relative amplitude of the signal is shown in Figure 7. Finally, the methods in Section 3.1 ( $k = 768$ ) and Section 3.2 ( $716 < k < 820$ ) are adopted for calculating $\hat{T}$ .

Figure 7

The signal under Gauss white noise background.

The two methods are counted independently for one hundred thousand times, and the relative deviation of the scale factor $β = \hat{T} / P_{w}$ is shown in Figure 8, where the standard deviations are 0.1234 ( $k = 768$ ) and 0.1946 ( $716 < k < 820$ ), respectively. From the statistical results, it can be seen that the introduction of the loose k condition leads to bigger estimation deviation, which causes a partial loss. By observing the deviation value, it is acceptable when the test requirement is not too stringent; the loss also can be decreased by narrowing the range of k. Hence, in this paper, we suggest a compromised solution between the detection loss and computational load.

Figure 8

The comparison of relative deviation between the two methods.

4.2. Computational Load Analysis

For quantitative analysis, the statistics of the average number of iterations and computational load of searching $x (k)$ are needed (single comparison calculation and single accumulation calculation are counted as one computational load, resp.). Since all the previous algorithms need the comparisons and determinations to the data, the randomness of the data will lead to different computation load, so the number of independent statistics was set as one hundred thousand to ensure a full verification in the paper. The simulation condition of the signal to be detected is the same as Section 4.1; the three methods K-FINDER, ADOS-CFAR, and ADOS-CFAR (under loose k condition) are used, respectively, to search $x (k)$ of the signal; the corresponding number of iterations and computational load are shown in Figures 9 and 10. It can be seen that the K-FINDER method needs a large number of iterations, average 11.4411 after statistics, and the computational load also has a large average number of 6351. Compared with the K-FINDER, the iteration process of ADOS-CFAR is based on the average value obtained through simply using the partial data, so the average number of iterations is not very stable and merely 9.0993. However, due to the less data used in the mean calculation and terminating iteration in advance, the average computational load is relatively small, only 3333. Under the loose k condition, the number of iterations of ADOS-CFAR is greatly reduced to only 2.6656, and the computational load is also relatively small, down to 2722. Therefore, this method has the great advantages in both the number of iterations and computational load, and it is conducive to efficient seafloor terrain detection.

Figure 9

The number of iterations of the three methods.

Figure 10

The computational load of the three methods.

In order to further analyze the generality of this method, the number of iterations and computational load of data with different lengths are analyzed according to the above conditions. The average number of iterations is shown in Figure 11, and the average computational load is shown in Figure 12. The figures illustrate that both the number of iterations and computational load of ADOS-CFAR method are less than those of K-FINDER method in the 20~2000 range of N and are even less under loose k condition, which confirms the strong generality of this novel method.

Figure 11

The average number of iterations of the three methods.

Figure 12

The average computational load of the three methods.

4.3. Algorithm Comparison under Sliding Condition

Due to the introduction of sliding condition, more redundant information can be utilized; the setting of the simulation condition is the same as that in Section 4.1. The sliding window length N is set to be 1024, the signal length is set to be 1001024, and the sliding search of the signal is carried out by the novel method and ABIS. The statistics demonstrate that the average computational load of a single sliding search in ABIS method is 0.9992 N, while the load in the novel method is 0.2808N, which are consistent with the theoretical analysis. It is shown that, under sliding condition, the proposed novel method has a faster processing speed than the ABIS method.

5. The Method Validation by Data Acquired in Tank and Lake

5.1. The Tank Experiment and Data Processing

In order to evaluate the detection accuracy of the proposed method, an experiment was carried out with self-developed HT-300PA multibeam echo sounder in the water tank located in College of Underwater Acoustic Engineering, Harbin Engineering University. The main technical parameters are as follows: operation frequency: 300 kHz, beam width: ${2.5}^{°} \times {1.5}^{°}$ , beam number: 256, bathymetric range: 2–200 m, max swath width: 127°, and transmitted signal mode: single frequency rectangular pulse. The composition of HT-300PA multibeam echo sounder is shown in Figure 13.

Figure 13

HT-300PA multibeam echo sonar.

The structure of the HT-300PA multibeam echo sonar is shown in Figure 14. The HT-300PA multibeam echo sounder (MBES) is based on Mill's cross array Sonar Architecture that networks all of the modules and embeds the processor and controller in the sonar head to make for a very simple installation. The HTCS-3.4 Control Graphical User Interface (GUI) is a simple program that can be installed on any Windows based computer and allows the surveyor to control the operating parameters of the HT-300PA. HTCS-3.4 communicates with the Sonar interface module (SIM) via Ethernet. The SIM supplies power to the sonar head, synchronizes sonar heads, time tags sensor data, relays commands to the sonar head, and routes the raw multibeam data to the customer's data collection computer.

Figure 14

The structure of HT-300PA multibeam echo sonar.

The schematic diagram of the experimental site and the photos of the installed sonar head are shown in Figures 15 and 16, respectively. The length $\times$ width $\times$ depth of the water tank is 45 m $\times$ 6 m $\times$ 5 m, the bottom is flat, and the quality is cement. The sonar head was installed 0.4 m under the water surface, and the beam footprints are shown in Figure 16.

Figure 15

The schematic diagram of the experimental site.

Figure 16

The photos of the installed sonar head.

The length of transmitted signal in the experiment is 0.1 ms; ping rate is 1 Hz. The raw echo was collected during the experiment, and the raw echo signals of partial channels are shown in Figure 17.

Figure 17

The raw echo signals of partial channels.

In the conventional method, the raw echo signal is processed by filtering, IQ demodulation, FFT transformation, and sector transformation, and the result is shown in Figure 18(a), and the novel method in this paper is normalized by ADOS-CFAR after the FFT transformation, followed by sector transformation. The result is shown in Figure 18(b).

Figure 18

The echo intensity comparison between the conventional method and novel method.

The comparison in Figure 18 illustrates that the proposed method can effectively remove the side lobe interference of the mirror reflection echo. Every beam of results obtained through the two methods is demodulated by the fast processing method in Section 3.3; the results of that are shown in Figure 19. In the conventional method, tunnel effect causes a semicylinder surface terrain (tunnel effect) in the demodulation result, and the novel method completely avoids the interference of tunnel effect, truthfully reflecting the seafloor terrain, which shows that this method is capable of efficiently eliminating the tunnel effect.

Figure 19

The comparison of demodulation results between the conventional method and novel method.

In the terrain detection by a multibeam echo sonar, considering the echo signal, tunnel effect caused by the side lobe interference level is the interference level of the terrain detection, which can cause the false terrain. From the above results, it can be seen that the proposed method can effectively detect the underwater terrain when avoiding the interference of the tunnel effect with high detection accuracy.

5.2. The Lake Experiment and Data Processing

The limitations of the tank experiment are as follows: the depth of water is shallow; the bottom of tank and experimental environment are very ideal. In order to fully verify the effectiveness of the method, an experiment is carried out in a typical water area located in Songhua Lake in Jilin City, Jilin Province, China. The experiment site is shown in Figure 20, the depth of water was about 60 m, and the sonar head was installed on the port of the surveying vessel.

Figure 20

Sonar mounting and placement at the experiment site.

The length of transmitted signal in the experiment is 0.1 ms; ping rate is 2 Hz. The raw echo was collected during the experiment, and the raw echo signals of partial channels are shown in Figure 21.

Figure 21

The raw echo signals of partial channels.

The data from Songhua Lake were processed through the same processing method as the data acquired in the water tank; the comparisons of echo intensity and demodulation result between the conventional method and novel method are shown in Figures 22 and 23, respectively. It can be seen that the proposed method can effectively detect the underwater terrain when eliminating the tunneling effect.

Figure 22

The echo intensity comparison between the conventional method and novel method.

Figure 23

The comparison of demodulation results between the conventional method and novel method.

Three methods of K-FINDER, ADOS-CFAR, and ADOS-CFAR under loose k condition are applied to the standardization of the experimental data of Songhua Lake, and the average number of iterations and computational load are shown in Table 1, in which ADOS-CFAR under loose k condition needs less number of iterations and computational load.

Table 1

The average number of iterations and computational load of the three methods.

Algorithm	Iteration times	Computational load
K-FINDER	11.2297	5504
ADOS-CFAR	9.7738	4897
ADOS-CFAR (loose k)	3.6956	4339

The computational load in the demodulation between ABIS and ADOS-CFAR is compared (sliding window length, 1024; sliding times, 6176). The statistics show that the average single sliding computational load of ABIS is 1.0001 N, while that of the novel method is 0.3553 N. The actual signal is not a Gauss distribution, which causes the calculation speed to fail to reach the theoretical value. However, the result demonstrates that the method we proposed has an obvious function for calculation speed improvement.

6. Conclusion

In this paper, the ADOS-CFAR algorithm for multibeam seafloor terrain detection is proposed, and the following conclusions are proven: (1)

For the OS-CFAR detection without sliding window under Gauss white noise background, the computational speed of the proposed method is higher than that of K-FINDER. In the condition with a sliding window, the speed is higher than that of ABIS.

(2)

The application of this method in multibeam seafloor terrain detection could eliminate tunnel effect efficiently with a decent computational speed.

(3)

The fast calculation method proposed in this paper is not limited to OS-CFAR; it also has some reference value for the high-speed calculation of other sorting algorithms.

Footnotes

Competing Interests

The authors declare that they have no competing interests.

Authors' Contributions

Weidong Du, Tian Zhou, Baowei Chen, and Bo Wei contributed equally to this work.

Acknowledgments

This work was financially supported by the National Natural Science Foundation of China (Grant nos. 41327004, 41376103, and 41306038) and the Fundamental Research Funds for the Central Universities of China (Grant no. HEUCF160510).

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Design and implementation of an OS-CFAR processor based on a new rank order filtering algorithm

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September 2010

Tampere, Finland

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10.1109/ISSOC.2010.5625543

15.

Shin

Kim

Bang

Kwon

K. K.

Anchor based insertion sorting algorithm for OS-CFAR

Proceedings of the IEEE Radar Conference (RadarCon '14)

May 2014

Cincinnati, Ohio, USA

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10.1109/radar.2014.6875621

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Bales

M. R.

Benson

Dickerson

Real-time implementations of ordered-statistic CFAR

Proceedings of the IEEE Radar Conference

May 2012

Atlanta, Ga, USA

896 901

10.1109/RADAR.2012.6212264

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Shafiq

M. A.

Real time implementation and profiling of different CFAR algorithms over DSP kit

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January 2014

Islamabad, Pakistan

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Nathanson

F. E.

Radar Design Principles 1991 2nd

New York, NY, USA

McGraw-Hill

ADOS-CFAR Algorithm for Multibeam Seafloor Terrain Detection

Abstract

1. Introduction

2. Fundamental Principles

2.1. OS-CFAR Principle

2.2. K-FINDER Algorithm

3. ADOS-CFAR Algorithm for Seafloor Terrain Detection

3.1. ADOS-CFAR Algorithm Principle

3.2. ADOS-CFAR under Loose k Condition

3.3. Fast Calculation under Sliding Condition

3.4. Seafloor Terrain Detection Based on ADOS-CFAR

4. Simulation and Analysis

4.1. The Rationality Analysis of Loose k Condition

4.2. Computational Load Analysis

4.3. Algorithm Comparison under Sliding Condition

5. The Method Validation by Data Acquired in Tank and Lake

5.1. The Tank Experiment and Data Processing

5.2. The Lake Experiment and Data Processing

6. Conclusion

Footnotes

Competing Interests

Authors' Contributions

Acknowledgments

References