Parameters used in Matlab simulation.
In the past, cross-correlation-based fisheries stock assessment technique utilized the mean and the ratio of standard deviation to the mean of cross-correlation function (CCF) as estimation parameter. However, in this paper, we have utilized only standard deviation of CCF as estimation parameter to estimate the population size. We utilized four acoustic sensors and considered chirp sound which is commonly generated by damselfish (Dascyllus aruanus), humpback whales (Megaptera novaeangliae), dugongs (Dugong dugon), etc., species to accomplish the simulations. We found that a robust estimation can be obtained using standard deviation of CCF as estimation parameter even when the distances between acoustic sensors are small.
- acoustic sensor
- fisheries stock assessment
- standard deviation
Passive acoustic monitoring of fish abundance is an emerging field of research among the conservation researchers and marine ecologists. It has upgraded understanding of the temporal distribution and repertoire of soniferous fish and mammals [1, 2]. Generally, passive acoustic monitoring is used to have an insight about the population size of soniferous fish and mammals, which are problematic to locate using visual sampling techniques [3, 4, 5, 6] in a certain marine area. These types of fishery surveys utilize the advantage of sound production nature of many species of fish and mammals which possess natural acoustic tags. It has the merit of being a non-destructive and non-invasive monitoring technique, unlike the conventional fisheries stock assessment methods, that is, mark recapture techniques, environmental DNA, visual census, echo, minnow traps, etc. [7, 8]. Generally, mechanical instrument-based conventional fishery surveys suffer from poor accuracy, time consuming nature, overly human interaction, costly instruments, etc., which can be overcome by passive acoustic monitoring techniques. Passive monitoring can provide unbiased data on the location and movement of sound producing source in underwater situations . Low-frequency (<10 kHz) acoustic sensors, that is, hydrophones, are used to detect natural sound production by fish and mammals . Usually, fish sound is associated with courtship, feeding or aggressive encounters . Researchers categorized the sound types of fish and mammals by different names, that is, chirps, pops, grunts, whistles, growls, hoots, etc., which are associated with their frequency and temporal characteristics .
However, cross-correlation-based fisheries stock assessment technique, a passive acoustic survey technique, was proposed in [12, 13, 14, 15, 16]. In this technique, the sound signals of vocalizing fish and mammals are processed to estimate their population size . This statistics-based technique has the potential to resolve some main drawbacks of conventional techniques like complexity, reliance on human interaction, time consuming nature of estimation, sensitivity, high cost, etc. A simplified block diagram representation of this technique is illustrated in Figure 1.
In the past, the researchers associated with this technique utilized the mean of CCF  ratio of standard deviation to the mean of CCF [13, 14, 15, 16, 17, 18, 19, 20] to estimate population size. In this paper, we have introduced standard deviation of CCF as estimation parameter to perform our desired estimation. We considered four acoustic sensors case , that is, hydrophones, in this research. For four acoustic sensors case, different types of topologies, that is, acoustic sensors in line, acoustic sensors in a rectangular shape, acoustic sensors in a triangular shape, are possible. Similarly, Acoustic sensors in a triangular shape can be a square shape, a rhombus shape or a trapezoidal shape. In this paper, we considered acoustic sensors in line case (ASL case). The main reason of considering four acoustic sensors is increasing number of cross-correlation function ensures better accuracy in this technique . Likewise, from diverse sound types of fish and mammals, we considered chirp sound which is commonly generated by damselfish (
2. Utilization of the CCF
The formulation of cross-correlation of sound signals of fish and mammals is analogous to the formulation of cross-correlation of Gaussian signal , which are the starting materials to estimate the population size. Chirp sound of fish and mammals are received by the acoustic sensor and recorded in the associated computer in which cross-correlation is executed. Transmission and reception of sound signals are performed for a time frame, called “signal length.” Sound (chirp) generating fish and mammals are considered as the sources of sound signals and
In the water medium, a constant propagation speed
Let us consider, a sound signal coming from
Therefore, the CCFs are:
To find out the CCFs for
Thus, the composite signals received by
Therefore, the total CCFs are:
This is the form of series of delta functions because in cross-correlation procedure one sound signal is the delayed copy of another .
3. Theoretical estimation from standard deviation of CCF
As we considered chirp generating fish and mammals to estimate their population size, an introduction to chirp signal is an important task in this perspective. Chirps belong to a swept-frequency sound signal, which possess a time varying frequency. From a sound analysis of
However, the mean of CCF can be expressed by ensemble average of the chirp-signal cross-correlation as .
Now, the variance of the CCF can be defined as :
Therefore, we can get the standard deviation,
However, to analyze the random signal cross-correlation problem to find the standard deviation in the above way is very hard. Therefore, the problem can be reframed as a binomial probability problem which can make the analysis simpler. Since, cross-correlation function follows the binomial probability distribution in which the parameters are the number of balls, that is, fish and mammals,
From Eq. (25), we can write the following formula:
Now, for four acoustic sensors ASL case, the final standard deviation will be found from the average of
Thus, from Eq. (26), we can obtain that
4. Simulation and discussion
Simulations were executed considering that four acoustic sensors lay on the center of a sphere. We also considered a uniform random distribution of fish and mammals. Thousand iterations were averaged to accomplish the simulated results. To ease the simulation, the power difference among the acoustic pulses transmitted by each fish and mammal was considered negligible. Here, we considered
|Dimension of the sphere||2000 m|
|0.25, 0.5, 0.75, 1 m|
|Absorption coefficient, ||1 dBm−1|
|dispersion factor, ||0|
|19, 39, 59, 79|
Figure 4 shows the theoretical and corresponding simulated results for the population estimation of fish and mammals in terms of the estimation parameter
Figure 5 shows the difference between theoretical and simulated population size of fish and mammals for
However, our work has some limitations, for example, assuming the delays to be integer, negligence of multipath interference, consideration of negligible amount of power difference among the fish sound pulses during transmitting time.
Passive acoustic monitoring is a potential tool to survey the population size of fish and mammals in a certain marine area. It can overcome the major drawbacks of conventional techniques. Cross-correlation-based stock assessment technique is also a passive acoustic survey technique dedicated to fish and mammals. An investigation on this technique with different estimation parameters was the cardinal goal of this research. To do that, we performed our desired estimation with standard deviation of CCF as estimation parameter. The small difference between theoretical and simulated results proved that it is highly possible to pursue this passive monitoring technique utilizing standard deviation of CCF as estimation parameter. Here, we considered four acoustic sensors because from the previous research, we found that an increasing number of CCF ensures better accuracy using this technique. In this paper, we considered four different numbers of bins to show its impact on estimation also. It is shown that a robust estimation is possible using standard deviation of CCF as estimation parameter even when the distances between acoustic sensors are small. Therefore, during practical implementation of this technique, these findings will contribute significantly.