Using the sea clutter image from X-Band radar for current retrieval is an effective way of obtaining information on ocean currents. Traditional methods used for current retrieval have been based on the least squares algorithm, which is not only simple and efficient but also generally speaking accurate. In order to improve the precision of current retrieval, this paper has, as its goal, the study of the used radar connected with sea clutter imaging for current retrieval, with the particle swarm optimization (PSO) algorithm being proposed. This method is achieved by obtaining a three-dimensional image spectrum, taking the high-order dispersion relation model as the theoretical distribution model of the wave energy points of three-dimensional image spectra, using a forward model within the PSO framework, and considering the requirements of the order of the model, weights and optimal distribution of the energy points, and so on in fitness function. Simulation results show that, compared with the traditional ILSM methods, the method provided in this paper is more flexible, with a capacity for a high dispersion relationship order, higher precision, and an increased stability in terms of current inversion.
Ocean currents are the result of a variety of physical effects arising from a relatively stable large-scale flow. Ocean currents have a very close relationship for marine exploration, marine development, and marine navigation safety. Existing methods for obtaining the sea surface current include moored wave buoys, an analysis of stereo images, and analyses of satellite altimetry data and marine radar images. Although buoys provide reliable measurements, they are easily subject to damage and loss. The method for collecting stereo images from synthetic aperture radar is costly and time-consuming. Furthermore, orbiting satellites cannot obtain continuous data around a specified zone [
Current retrieval based on marine radar related to sea clutter images is essentially an optimization problem, with the least squares method (LSM) being used to implement the current strategy for solving the problem. In 1985, Young et al. were the first to suggest the use of marine radar sea clutter imaging for current retrieval [
The least squares strategy, when adopted as the method for current retrieval, has the advantage of a simple, fast solution and certainty, but, in the terms of constraint handling, processing complex optimization problems, nonlinear optimization, and so on, it has obvious shortcomings. In addition, its objective function is inflexible. In order to rectify this problem, the PSO algorithm is proposed here as a model for current retrieval. Using this algorithm, with the flexible design of this objective function, constraint condition positive expression, self-organization solving, and other characteristics for current retrieval, this model for current retrieval is discussed with a view to assess the observational data selection, the initial selection, fitness function design, process of algorithm design, and other related issues in detail. The numerical simulation results verify the correctness of the proposed method. It improves the precision and stability of the current retrieval effectively and provides a new solution for the modeling method of the current retrieval based on marine radar.
The method used for current retrieval based on the marine X-Band radar related to sea clutter images was proposed by Young et al. [
Schematic diagram illustrating current retrieval.
In order to obtain a radar three-dimensional image spectrum, three-dimensional fast Fourier transformation (3-D FFT) for sea clutter images sequence continuously measured by marine radar is required, to enable us to transform the time and space domain of radar sea clutter image sequencing into the frequency domain of a radar image spectrum.
As shown in Figure
Sea clutter image data for current retrieval.
Schematic diagram of sea clutter sequences
Schematic illustrating rectangular analysis area of the Cartesian coordinate system
With the grid image sequence
Considering the symmetry of the Fourier transforms and in order to eliminate the 180° ambiguity problems,
Assuming that the waves satisfy the linear wave theory, homogeneous space, and stable time of the sea surface current filed in the analysis area, then when the water depth is greater than or equal to half the wavelength, a first-order approximation gravity wave will satisfy the following dispersion relation equation [
Considering that the presence of the currents
The surface schematics of dispersion relation in various cases are shown in Figure
Surface schematics of dispersion relation.
Surface for velocity of 0 m/s
Surface for velocity of 1 m/s
The detection process carried out by the marine radar found that nonlinear effects are caused by the influence of sea surface imaging and the relative weakness of the sea surface waves themselves. The wave energy of the three-dimensional image spectrum
After
Current retrieval was first proposed by Young et al. in 1985 in the literature [
The principle of LSM is used. The minimum of SSE is needed to find out the optimal value of
In 2001, in their consideration of the impact of the higher-order dispersion relation based on the LSM method, Senet et al. proposed a current estimation method based on the Iterative Least Squares Method (ILSM) [
In 2002, Gangeskar put forward the weighted least squares method [
The LSM used to obtain the current estimation value is
In 2010, Tang considered the use of the overall attributes belonging to the dispersion relation set and,by improving the objective function in the framework of the ILSM algorithm, they proposed a current retrieval method of minimum variance based on error sequence [
Current retrieval using observational data is the point set of energy in the power spectral density
As far as the PSO algorithm is concerned, the location of the information of particles is the optimization object of the algorithm. In this paper, for the current retrieval, the particle’s position is the current component of
The selection of the initial value of the position and speed has a bearing on the PSO. As far as the initial value of the position is concerned, if it is relatively close between the initial position and the distance of the optimal point, the initial position of the fitness value of the particle is high, which is easy to find the optimal solution for particles quickly, and if it is far between the initial position and the distance of the optimal point, the algorithm will increase the optimization time. For the initial value of the speed, if the initial value of the speed is much big, the particle can jump over a wide range in the search space and it is easy for these particles to exceed the permissible range. As far as the initial value of the speed is small, a particle that only moves within a small area is not conducive to global optimization. Generally, the initial value of position and speed of the actual solution are randomly selected within the permissible range.
In order to speed up the current retrieval and shorten the time of optimization as much as possible, the calculation of the value of the algorithm using the formula specified in (
Due to the fact that the selection of the initial position has a particular directional meaning, the initial speed value can also be appropriately small selected.
In the process of current retrieval, a PSO algorithm with an adaptive value function evaluates the advantages and disadvantages of the position (current component) of each particle. The design of the fitness function is, therefore, particularly important. In this paper, the algorithm fitness function design is defined as follows:
Let us assume that the weight
As far as the method of current retrieval is concerned, in the framework based on the LSM, the deviation coefficient of the objective function SSE is 2, which is equivalent to weakening the role of the weights.
The process based on the current retrieval of PSO used in this paper is shown in Figure
The algorithmic process.
Set the learning factors
The fitness function is used to assess the current position of each particle to obtain the fitness value of the current position of each particle.
The current position fitness value of each particle and the individual extreme
The individual extreme value
If the termination condition is deemed to have been satisfied, then the global extremum
Current retrieval essentially uses the energy points of a three-dimensional image spectrum as observed data, according to the dispersion relation for optimal estimation. The method used for the dispersion relation used to simulate a three-dimensional image spectrum is outlined as follows.
Based on the previous analysis, we already know that the energy points of the three-dimensional image spectrum can be divided into two categories in line with the wave energy points of a dispersion relation and do not meet the noise energy points of the dispersion relation. These two types of energy points are therefore sufficient when the three-dimensional image spectrum is generated in the simulation. This simulation takes place for a three-dimensional image spectrum according to the following principles.
The simulation process of the three-dimensional image spectrum is shown in Figure
Simulation chart representing three-dimensional image spectrum.
The formula of each energy value during the simulation of energy points of three-dimensional image spectrum is as follows:
Both the ILSM method and the method proposed here (using the PSO representation) are used for current retrieval. Among the three cases of the highest order 0, 1, and 2 of dispersion relations are, respectively, taken into consideration using the ILSM method, and, in this paper, 2-order is only considered as being the highest order. The solutions of wave power point distribution on the different orders of dispersion in three-dimensional image spectrum are counted in different simulation experiments.
150 maximum energy points from the three-dimensional image spectrum are selected as the observed data on which to carry out the simulation experiments. If the difference of current speed is continuous less than 0.1 two times, the ILSM method will be stopped. When the current speed of optimal particles remains unchanged for consecutive 10 times, the PSO method will be stopped. In the PSO algorithm,
Operating parameters of PSO algorithm.
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10 | 2.05 | 2.05 | 0.9 | 0.4 | 100 |
Different simulation results are given in Table
Distributive point statistics on curve of different orders of dispersion relation.
Method for estimated current | Order of dispersion relation | Total number of distribution points |
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ILSM | ||
0-order only considered | 0-order | 5473 |
1-order the highest consideration | 0-order | 5201 |
1-order | 272 | |
2-order the highest consideration | 0-order | 5201 |
1-order | 233 | |
2-order | 39 | |
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PSO (2-order the highest consideration) | 0-order | 5139 |
1-order | 334 | |
2-order | 0 |
Table
It is apparent that, when ILSM is used for current retrieval, the requested dispersion relation order should correspond to the actual dispersion relation order contained in three-dimensional image spectrum, while the order is not necessary correspondent in the PSO for the current retrieval, so that only the highest dispersion relation order needs to be set.
The simulation of the three-dimensional image spectrum is taken into 2-order, with the ILSM and PSO methods also being taken into a 2-order situation. The PSO method is random. In order to evaluate the method as accurately as possible, it is necessary to count it 10 times. The mean of the 10 results and the results of 10 times for the optimum value of the standard of current speed are used to calculate the variance.
The simulation curve representing the simulation and variance of current retrieval are given in Figure
The variance of current retrieval based on a simulated three-dimensional image.
Method | Current speed variance | Current direction variance |
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ILSM | 2.3651 | 2.2066 |
PSO (mean) | 0.0470 | 1.3481 |
PSO (optimal value) | 0.0025 | 1.4861 |
Simulation experiment results of current retrieval precision based on simulated three-dimensional image spectrum.
Means of the results using PSO method for 10 times
Optimal value of results using the PSO method for 10 times, based on the standard of current speed
The results of the simulation show that, compared with the current retrieval results obtained by the ILSM method, the PSO method obtains better results, especially at current speed parameters. When the current speed is greater than 4 m per second, the current retrieval precision using PSO is obviously superior to the ILSM.
The imitative radar sea clutter image sequence derived from literature [
Due to the fact that the dispersion relationship in the three-dimensional image spectra is unknown, corresponding to simulation-generated radar sea clutter images, 0-order, 1-order, and 2-order are taken into account in the ILSM method, with only 2-order being taken into account in the PSO method. Simulation parameter selection and methods are consistent with Section
Inversion variance based on simulation sea clutter images.
Method | Current speed variance | Current direction variance |
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ILSM (0-order) | 1.2745 | 2.0465 |
ILSM (1-order) | 1.0989 | 2.0656 |
ILSM (2-order) | 1.0648 | 2.0656 |
PSO (average) | 0.9972 | 1.8284 |
PSO (optimal value) | 0.8553 | 1.9255 |
Results of simulation experimental of current retrieval precision based on imitation sea clutter images.
Means of the results using PSO method for 10 times
Optimal value of results using the PSO method for 10 times based on the standard of current speed
The simulation results show that PSO method obtains a higher degree of precision than the ILSM method for curve retrieval of simulative radar sea clutter images.
In the simulation experiment, real data from a radar sea clutter image sequence measured in Pingtan, Fujian, Haitan Island, China, on October 23, 2010, were used.
Consider that, for certain area current filed, its speed and directional values within the space range are uniform with small changes occurring over time. That is to say, the current changes occurring at adjacent times were small. In view of this, the mean of the differences in the continuous current retrieval results was taken as the performance evaluation indicator of the current retrieval. The calculations were made according to
The simulated parameter selection is consistent with Section
ILSM method evaluation indicators of different orders.
Method | Current speed indicators | Current direction indicators |
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ILSM (0-order) | 0.0937 | 0.8708 |
ILSM (1-order) | 0.1139 | 0.6960 |
ILSM (2-order) | 0.1165 | 0.6918 |
The ILSM method can obtain the best current estimation results which are shown in current speed indicators in Table
Evaluation indicators of different observational data selection methods.
Method | Current speed indicators | Current director indicators | |
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LSM | 150 points of maximum energy are selected | 0.0937 | 0.8708 |
PSO | 0.2002 | 0.5269 | |
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LSM | 1000 points of maximum energy are selected | 0.0887 | 0.6025 |
PSO | 0.0875 | 0.3556 | |
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LSM | Points higher than 1% of the maximum energy are selected | 0.0947 | 0.2957 |
PSO | 0.0840 | 0.1908 | |
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LSM | All points | 0.0284 | 0.2289 |
PSO | 0.0662 | 0.2466 |
Simulation results of different data selection method.
150 points of maximum energy selected
1000 points of maximum energy selected
Points higher than 1% of the maximum energy selected
All energy points selected
Simulation results show that, as the selected data points increase, the current retrieval results using the PSO method are improved in terms of the polymerization and stability of the data in question. When all the data points are selected, the current retrieval is not affected by noise points, but better results are obtained. As far as the LSM method is concerned, the stability of the current retrieval results is best when 1000 points are selected. When 150 data points and higher 1% of maximum energy value are selected, current retrieval results deteriorate slightly and when all energy points are selected, current retrieval results deviate markedly from the true value, although an increased stability can be obtained. If we compare the PSO and LSM methods, the PSO method is slightly less stable than the LSM method when 150 points are selected, while the performance of the PSO method is better in the other cases.
Evaluation indicators of different initial data selection methods.
Method | Current speed indicators | Current direction indicators |
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PSO (initialization at random) | 0.0842 | 0.1564 | 11 | 100 | 33.4 |
PSO (initial results reference LSM) | 0.0840 | 0.1908 | 11 | 100 | 27.5 |
Evaluation indicators show that the stability of current retrieval is consistent in the two strategies with speed optimization showing that the strategy for the initial value of the LSM results is faster and the number of algorithm iterations is less.
Evaluation indicators of different deviation order values.
Method | Current speed indicators | Current director indicators |
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PSO ( |
0.1864 | 0.2521 |
PSO ( |
0.0840 | 0.1908 |
PSO ( |
0.0750 | 0.1614 |
Simulation results of different deviation order value.
The simulation results show that, when deviation order value is small, the current order is more stable. That is to say, it can be beneficial to the stability of the current retrieval when there is a focus on the three-dimensional image spectrum related to large energy points.
This paper had, as its goal, an improvement in the accuracy of current retrieval methods, with a study concerning radar related to sea clutter images used for current retrieval. The principle of current retrieval and methods used for current retrieval based on the least squares algorithm were introduced in this paper with the PSO algorithm being proposed as a viable method for current retrieval. Observational data and the selection strategy of the position of initial particles constituted its main focus, with the fitness function of the design, taking into account the impact of a higher dispersion relationship order and providing the framework for execution of the algorithms. Simulation experiments were based on three cases related to the three-dimensional image spectrum, sea clutter images analog, and real sea clutter in order to verify several aspects of the algorithms under investigation, namely, the adaptive capacity of the order of higher-order dispersion relations, the observational data selection method, the particle initialization selection method, the order bias selection method, and the current retrieval accuracy performance. Simulation results show that, compared with the traditional ILSM methods, the method provided in this paper is more flexible, with a capacity for high dispersion relationship order, higher precision, and an increased stability in terms of current inversion.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by the National Natural Science Foundation of China under Grant nos. 51009036, 51109041, 51109045, and 51379049, Postdoctoral Foundation of Heilongjiang under Grant no. LBH-Z10217, and Foundation of Central University nos. HEUCF041216 and HEUCFX41302.