CN112765557B - Ship high-resolution range profile power conversion method and system - Google Patents

Ship high-resolution range profile power conversion method and system Download PDF

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CN112765557B
CN112765557B CN202011634424.5A CN202011634424A CN112765557B CN 112765557 B CN112765557 B CN 112765557B CN 202011634424 A CN202011634424 A CN 202011634424A CN 112765557 B CN112765557 B CN 112765557B
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但波
孙铭浩
刘瑜
高山
韩建立
王旭坤
张军涛
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Naval Aeronautical University
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Abstract

The invention relates to a ship high-resolution range profile power transformation method and a system, wherein the power transformation pretreatment is carried out on the actually measured range profile by a power transformation parameter obtained by improving a parameter estimation method of Jarque-Bera normality test through a normal probability map and the verification of the actually measured ship high-resolution range profile, and the result is closer to and normally distributed; meanwhile, the measured ship distance image data after power transformation is utilized to carry out a target classification and identification experiment, and the identification accuracy is improved to a certain extent.

Description

Ship high-resolution range profile power conversion method and system
Technical Field
The invention relates to the field of power transformation preprocessing, in particular to a ship high-resolution range profile power transformation method and system.
Background
In the identification of an actually measured High Resolution Range Profile (HRRP) target, especially in a battlefield environment, the measured target is mostly a non-cooperative target, and it is difficult to implement data recording and measurement in a full angular domain of the target, so that the traditional processing method for the attitude sensitivity of the target HRRP, such as a method of performing target identification by optimally matching an average Range image in a certain angular domain with a sample to be tested, is limited in use. The power transformation improves the flicker phenomenon of the HRRP by weakening the shielding of the strong scattering points on the weak scattering points, and relieves the posture sensitivity of the HRRP to a certain extent.
When performing power transformation processing on HRRP, selection of power transformation parameters is one of the key points of research. According to the HRRP statistical characteristics, the distance image data can tend to be normally distributed by performing power transformation processing under appropriate parameters on the data, so that the identification effects of common classifiers such as a linear discriminant function and K Nearest Neighbor (KNN) are improved, power transformation parameters need to be estimated and selected, and the HRRP identification rate after power transformation is improved. The power transformation parameter learning based on the normality test is to test power transformation results under different parameters by a method of the normality test and search for the power parameters which enable the results to be most approximate to normal distribution, thereby realizing the improvement of the target identification effect.
At present, a plurality of mature normality test methods including a person test, a partial kurtosis test, a high-order moment test, a Jarqe-Bera test and the like exist, in the prior art, the person test is applied to documents, but the error rate is high under the condition that a sample is small, the documents apply the high-order moment normality test to learn power parameters, but the statistical accuracy is inversely proportional to the statistical speed, so that the efficiency is not high, the partial kurtosis test is applied to the documents, the Jarqe-Bera normality test is applied to the documents, but the two methods discard effective information to a certain extent, and the test effect is poor. Based on the problems existing in the method, the invention provides a power parameter learning method based on self-adaptive Jarqe-Bera normality test, and the validity of the power parameter learning method is tested by using actually measured data.
Disclosure of Invention
The invention aims to provide a ship high-resolution range profile power conversion method and a ship high-resolution range profile power conversion system, so that the result is closer to normal distribution, the identification effects of common classifiers such as a linear discriminant function and K nearest neighbors are improved, the effect of weak scattering points in identification can be increased, the shielding effect of the strong scattering points on the weak scattering points in the presence of the strong scattering points is weakened, and the problem of attitude sensitivity of a range profile is solved.
In order to achieve the purpose, the invention provides the following scheme:
a ship high-resolution range profile power transformation method, comprising:
s1: obtaining an original sample set { xi,i＝1,2,…,N}；
S2: determining an initial value λ ═ λ of a power transformation parameter0,λ0∈(0,1]And a step size;
s3: performing power transformation on an original sample set based on the initial value of the power transformation parameter;
s4: calculating skewness and kurtosis of the original sample after power transformation;
s5: calculating the estimators of skewness and kurtosis of the original samples after power transformation;
s6: judging whether the estimated skewness quantity and the estimated kurtosis quantity meet a first set condition;
s7: if yes, then the lambda at the moment is counted into a lambda' set;
s8: if not, executing the next step;
s9: and increasing the lambda by one step, repeating the steps S3-S8 until all values of the lambda are traversed, and obtaining lambda' ═ lambda { lambda1,λ2,…,λsH or λ' ═ Φ;
s10: when λ' is Φ, an estimate of skewness is calculated, traversing all λ, λoutput＝argmin|g1|；
S11: when λ' ═ λ1,λ2,…,λsCalculating the estimation quantity of skewness and the estimation quantity of kurtosis;
s12: judging whether the estimated amount of the skewness and the estimated amount of the kurtosis meet a second set condition or not;
s13: if so, then λoutput＝λ；
S14: if not, then λoutput＝argmin|g|；
Figure BDA0002875884280000021
Optionally, performing power transformation on the original sample set based on the initial value of the power transformation parameter specifically adopts the following formula:
Figure BDA0002875884280000022
wherein, yiRepresenting samples after power transformation, λ representing power transformation parameters, xiRepresenting the original samples and N the number of samples.
Optionally, the calculating the skewness of the original sample after the power transformation specifically adopts the following formula:
Figure BDA0002875884280000031
where skewness denotes skewness, E denotes expectation, and Y denotes a sample set after power transformation.
Optionally, the kurtosis of the original sample after the power transformation is calculated specifically adopts the following formula:
Figure BDA0002875884280000032
wherein Kurtosis represents Kurtosis, E represents expectation, and Y represents a sample set after power transformation.
Optionally, the estimator for calculating skewness specifically uses the following formula:
Figure BDA0002875884280000033
wherein, g1Representing the estimated amount of skewness, N representing the total number of samples, yiA sample after the power transformation is represented,
Figure BDA0002875884280000034
optionally, the estimator for calculating the kurtosis specifically adopts the following formula:
Figure BDA0002875884280000035
wherein, g2Representing the estimated amount of skewness, N representing the total number of samples, yiA sample after the power transformation is represented,
Figure BDA0002875884280000036
optionally, the first setting condition is:
Figure BDA0002875884280000037
Figure BDA0002875884280000038
wherein, g1An estimate representing skewness, g2Representing an estimate of kurtosis and N representing the total number of samples.
Optionally, the second setting condition is:
g1＝0,g2＝3，g1an estimate representing skewness, g2An estimate of kurtosis is indicated.
Optionally, the step size is 0.01.
The invention further provides a ship high-resolution range image power transformation system, which comprises:
an original sample set acquisition module for acquiring an original sample set { x }i,i＝1,2,…,N}；
An initial value and step size determination module for determining an initial value λ ═ λ of the power transformation parameter0,λ0∈(0,1]And a step size;
a power transformation module for performing power transformation on the original sample set based on the initial values of the power transformation parameters;
the skewness and kurtosis calculation module is used for calculating skewness and kurtosis of the original sample after power transformation;
the skewness estimator and kurtosis estimator calculation module is used for calculating the skewness estimator and the kurtosis estimator of the original sample after power transformation;
the first judgment module is used for judging whether the estimators of the skewness and the kurtosis meet a first set condition or not;
the first output module is used for counting the lambda at the moment into a lambda' set when a first set condition is met;
the skip module is used for executing a next module when the first set condition is not met;
a circulation module for increasing the lambda by a step length and repeating the step of the power transformation module-the jump module until all the values of the lambda are traversed to obtain the lambda' ═ { lambda1,λ2,…,λsH or λ' ═ Φ;
a second output module for calculating an estimate of skewness, traversing all λ, λ when λ ═ Φoutput＝argmin|g1|；
A third output module for outputting the signal when λ' ═ λ1,λ2,…,λsCalculating the estimation quantity of skewness and the estimation quantity of kurtosis;
the second judgment module is used for judging whether the estimated value of the skewness and the estimated value of the kurtosis meet a second set condition or not;
a fourth output module for outputting lambda when the second setting condition is satisfiedoutput＝λ；
A fifth output module for outputting λ when the second setting condition is not satisfiedoutput＝argmin|g|；
Figure BDA0002875884280000041
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the method provided by the invention researches the problem of power transformation preprocessing of a High Resolution one-dimensional Range Profile (HRRP), enables Range Profile data to tend to be normally distributed through power transformation, improves the identification effects of common classifiers such as a linear discriminant function and K neighbor, can increase the effect of weak scattering points in identification, weakens the shielding effect on the weak scattering points when strong scattering points exist, and accordingly relieves the attitude sensitivity problem of the Range Profile. Aiming at the defects of the parameter estimation method based on the biased kurtosis normality test and the Jarqe-Bera normality test, the parameter estimation method of the self-adaptive Jarqe-Bera normality test is provided. The method still follows the principle that the skewness has more important influence on the result of the normality test, and meanwhile, the weight of the kurtosis on parameter selection is increased. The method comprehensively utilizes the information of skewness and kurtosis, and does not only depend on the skewness or the kurtosis for parameter selection, thereby solving the problem that the sample is in non-normal distribution when the skewness is 0 or the kurtosis is 3, and ensuring that the data after power transformation is close to normal distribution; meanwhile, the method optimizes the selection of skewness and kurtosis, ensures the optimization of the utilization of kurtosis information under the condition that the skewness has more important influence on the result of the normality test, and has a better conversion effect than the Jarqe-Bera test.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flow chart of a ship high-resolution range image power conversion method according to an embodiment of the present invention;
FIG. 2(a) is a diagram showing the result of the kurtosis normality test according to the embodiment of the present invention;
FIG. 2(b) is a Jarqe-Bera normality test normal probability chart according to an embodiment of the present invention;
FIG. 2(c) is a diagram illustrating the normality test normality probability of an adaptive Jarqe-Bera embodiment of the present invention;
FIG. 2(d) is a HRRP normal probability chart of a certain vessel according to an embodiment of the present invention;
FIG. 3(a) is a graph of original range profile features in accordance with an embodiment of the present invention;
FIG. 3(b) is a graph of the original single-pass recognition results of the embodiment of the present invention;
FIG. 4(a) is a diagram of an off-peak normality test range profile according to an embodiment of the present invention;
FIG. 4(b) is a graph of a single-pass identification rate result of a skewness normality test according to an embodiment of the present invention;
FIG. 5(a) is a Jarqe-Bera normality detection range profile of embodiments of the present invention;
FIG. 5(b) is a graph showing the result of single-pass discrimination in Jarqe-Bera normality test according to the embodiment of the present invention;
FIG. 6(a) is a graph of adaptive Jarqe-Bera normality check distance image features according to an embodiment of the present invention;
FIG. 6(b) is a graph showing the result of single-pass recognition rate of the adaptive Jarqe-Bera normality test according to the embodiment of the present invention;
fig. 7 is a schematic structural diagram of a ship high-resolution range image power conversion system according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
The invention aims to provide a ship high-resolution range profile power transformation method and a ship high-resolution range profile power transformation system, so that the result is closer to normal distribution, the identification effect of common classifiers such as a linear discriminant function and K nearest neighbor is improved, the function of weak scattering points in identification can be increased, the shielding effect of the strong scattering points on the weak scattering points is weakened, and the problem of attitude sensitivity of a range profile is solved.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
The power transform is a non-linear preprocessing method. The theoretical basis is as shown in formula 1:
Y(t)＝Xλ(t)，0＜λ≤1 (1)
wherein λ is a power factor, x (t) is a range profile vector, and y (t) represents the HRRP after power transformation.
The attitude sensitivity of HRRP is mainly shown in two points: (1) the scattering point moves away from the unit due to the posture change; (2) the change of the posture causes the phase difference of the scattered point sub-echoes to change, so that the HRRP wave shape fluctuates, namely the so-called angular flicker phenomenon.
The attitude sensitivity of HRRP causes its amplitude to vary too much, so position information plays a more important role in target recognition. Because the power transformation parameter lambda belongs to (0, 1), the function of the weak scattering point in identification after power transformation is increased, the shielding function of the weak scattering point in the presence of the strong scattering point is weakened, the angular flicker phenomenon in the HRRP is improved, and the attitude sensitivity of the HRRP is relieved to a certain extent.
On the statistical characteristic, the power transformation can enable the HRRP to tend to be normally distributed, so that the identification accuracy of classifiers such as a linear discriminant function and a K Nearest Neighbor (KNN) is improved.
The normal distribution performance of the HRRP after conversion is determined by the parameter lambda of the power conversion, and the better parameter lambda ensures that the HRRP after conversion is more similar to the normal distribution. Therefore, the estimation of the parameter λ is the focus of the power transformation study. The power parameter lambda is estimated by experience at present, but for HRRP under different conditions, the parameter setting is often different, and a better effect cannot be obtained by depending on experience alone, so that the estimation method of the parameter lambda needs to be researched, the normal distribution performance of the HRRP after power transformation is better, and the ship target identification effect is improved.
Off-peak normality test
Normally, a normality test is used to determine whether a sample follows a normal distribution. Karl Pearson first realized that deviations from the normal distribution can be characterized by normalized 3 th and 4 th moments, which are considered as originators of the normality test, and have a significant impact on the development of the relevant theory.
For the purpose of detailed description, the definition of moments is first given:
let total Y-N (mu, sigma)2) Where μ, σ2Respectively representing the mean and variance of normal distribution, the k-th order center distance of Y is defined as
Figure BDA0002875884280000071
Wherein (k-1)! ! 3 × 1, (k-1) × (k-3).. 3.
The standard moment of order k of Y is defined as
Figure BDA0002875884280000072
Skewness reflects the symmetry of the sample probability density function. For the population Y, skewness is defined as follows:
Figure BDA0002875884280000073
skewness ═ 0 indicates that the distribution of overall Y is symmetrical; skewness > 0 is referred to as a positive bias, and Skewness < 0 is a negative bias.
The kurtosis represents the sharpness of the probability density function, and is defined as shown in formula (5):
Figure BDA0002875884280000074
the formula (2) is substituted for the formulae (4) and (5), and the arbitrary normal distribution has a skewness of 0 and a kurtosis of 3. Thus, the sample { y } may be judged by the estimates of skewness and kurtosis1,y2,...,yNWhether it conforms to a normal distribution, the formula is as follows:
Figure BDA0002875884280000081
Figure BDA0002875884280000082
wherein the content of the first and second substances,
Figure BDA0002875884280000083
if sample { y1,y2,...,yNFrom a normal distribution ensemble, g1，g2Should be approximately normally distributed, and E (g)1)≈0，
Figure BDA0002875884280000084
E(g2)≈3，
Figure BDA0002875884280000085
Therefore, if one of the inequalities in the following equations does not hold, the sample is considered not to follow a normal distribution.
Figure BDA0002875884280000086
Figure BDA0002875884280000087
In practical applications, the number of samples, N, is typically large, so the test statistic can be approximated as:
g1＝0 (10)
g2＝3 (11)
Jarqe-Bera normality test
By the theorem of the central limit,
Figure BDA0002875884280000088
and with
Figure BDA0002875884280000089
Asymptotically follows a normal distribution, so at g1 g2Under the assumption that the two are independent of each other,
Figure BDA00028758842800000810
and when n → ∞ is reached, E (g)1)＝0，
Figure BDA00028758842800000811
E(g2)＝3，
Figure BDA00028758842800000812
Then the Jarque-Bera test statistic is constructed, i.e.:
Figure BDA0002875884280000091
the corresponding assay is called the Jarqe-Bera assay or the J-B assay. If the variables are normally distributed, then g is known from the above1＝0，g 23, and thus JB 0.
As shown in the formulas (12) and (13), the skewness test is performed by using the skewness g1The distance from 0 is minimized, and the kurtosis test is to make kurtosis g2Distance from 3 is minimal, and J-B test is to make g1To 0 and g2The sum of distances to 3 is minimal. The J-B test enables the skewness and the kurtosis to participate in the process of the normality test, solves the problem that the result is in non-normal distribution caused by single use of the skewness test or the kurtosis test, and has better test effect than the skewness test in theory. However, in principle, the J-B test is such that g1、g2The sum of the distances to 0 and 3 is the shortest, however, the sum of the distances to the two is not necessarily the shortest, that is, one of the skewness and the kurtosis can better satisfy the normality test condition, while the other has a larger deviation, in this case, the normal distribution conditions of the following formulas (8) and (9) cannot be satisfied at the same time, and the effect of the normality test is still not ideal.
Based on the defects, the invention provides a self-adaptive Jarqe-Bera normality test method. The construction test statistics were:
Figure BDA0002875884280000092
if the data generally tends to be normally distributed, the statistic g1→0，
Figure BDA0002875884280000093
Thus g → 0.
Adaptation to a mobile stationThe Jarqe-Bera normality test method still follows the principle that skewness is more important to the result of the normality test, and meanwhile, the weight of kurtosis on parameter selection is increased. When λ '═ φ, i.e. λ' is the empty set, then E (g)1)＝0，
Figure BDA0002875884280000094
And E (g)2)＝3，
Figure BDA0002875884280000095
And the skewness can not be met simultaneously, and the skewness is preferentially enabled to meet the normal distribution range according to the principle that the skewness has more importance on the result of the normality test. In this case, the power transformation parameters are preferably selected so that the transformed range image is more symmetrical. When λ' ≠ φ, then E (g)1)＝0，
Figure BDA0002875884280000101
And E (g)2)＝3，
Figure BDA0002875884280000102
Can be satisfied at the same time. At the moment, a J-B normality test method is selected for parameter estimation under the condition that the skewness and the kurtosis meet the normal distribution range. The method comprehensively utilizes the information of skewness and kurtosis, and does not only depend on the skewness or the kurtosis for parameter selection, so that the problem that the sample is in non-normal distribution when the skewness is 0 or the kurtosis is 3 is solved, and the fact that the data after power transformation is close to normal distribution is ensured; meanwhile, the method optimizes the selection of skewness and kurtosis, ensures the optimization of the utilization of the kurtosis information under the condition that the skewness has more important influence on the result of the normality test, and has a better conversion effect than the Jarqe-Bera test.
Assume that the original sample population is X, and its N samples are { X }i1, 2. The power parameter learning process based on the adaptive Jarqe-Bera normality test comprises the following specific steps of:
fig. 1 is a flowchart of a ship high-resolution range profile power conversion method according to an embodiment of the present invention, as shown in fig. 1, the method includes:
s1: obtaining an original sample set { xi,i＝1,2,…,N}。
S2: determining an initial value λ ═ λ of a power transformation parameter0,λ0∈(0,1]And a step size.
The initial value λ is 0.01 and the step size is 0.01.
S3: performing power transformation on the original sample set based on the initial values of the power transformation parameters.
The following formula is specifically adopted:
Figure BDA0002875884280000104
wherein, yiRepresenting samples after power transformation, lambda represents power transformation parameter, xiRepresenting the original samples and N the number of samples.
S4: and calculating skewness and kurtosis of the original sample after power transformation.
The skewness of the original sample after the power transformation specifically adopts the following formula:
Figure BDA0002875884280000103
where skewness denotes skewness, E denotes expectation, and Y denotes a sample set after power transformation.
The kurtosis of the original sample after the power transformation specifically adopts the following formula:
Figure BDA0002875884280000111
kurtosis represents Kurtosis, E represents expectation, and Y represents a sample set after power transformation.
S5: and calculating the estimators of skewness and kurtosis of the original samples after the power transformation.
The estimation of skewness specifically uses the following formula:
Figure BDA0002875884280000112
wherein, g1Indicating an estimate of skewnessMeasurement, N denotes total number of samples, yiA sample after the power transformation is represented,
Figure BDA0002875884280000113
the kurtosis estimation is specifically based on the following formula:
Figure BDA0002875884280000114
wherein, g2Representing the estimated amount of skewness, N representing the total number of samples, yiA sample after the power transformation is represented,
Figure BDA0002875884280000115
s6: and judging whether the estimators of the skewness and the kurtosis meet a first set condition or not.
The first setting condition is as follows:
Figure BDA0002875884280000116
Figure BDA0002875884280000117
wherein, g1An estimate representing skewness, g2Representing an estimate of kurtosis and N representing the total number of samples.
S7: if so, then the λ at that time is taken into the λ' set.
S8: if not, executing the next step.
S9: and increasing the lambda by one step length, and repeating the steps S3-S8 until all values of the lambda are traversed to obtain the lambda' ═ lambda { lambda1,λ2,…,λsEither j or λ' ═ Φ.
S10: when λ' is Φ, an estimate of skewness is calculated, traversing all λ, λoutput＝argmin|g1|。
S11: when λ' ═ λ1,λ2,…,λsAn estimate of skewness and an estimate of kurtosis are computed.
S12: and judging whether the estimators of the skewness and the kurtosis meet a second set condition or not.
The second setting condition is as follows:
g1＝0,g2＝3，g1an estimate representing skewness, g2An estimate of kurtosis is indicated.
S13: if so, then λoutput＝λ。
S14: if not, then λoutput＝argmin|g|；
Figure BDA0002875884280000121
The normal probability map (norm plot) can embody the Gaussian performance of the sample. Normal probability maps of HRRP of a certain ship obtained by three normal testing methods are shown in fig. 2(a) -2 (d). The better the Gaussian performance of the sample, the closer the curve coincides with the straight line in the graph.
The power transformation parameter estimation method and the adaptive Jarqe-Bera parameter learning method are respectively utilized to carry out power transformation parameter selection on a certain actually-measured HRRP, and the obtained parameters are respectively as follows: the skewness test power parameter lambda is 0.38, the Jarqe-Bera test power parameter lambda is 0.33, the self-adaptive Jarqe-Bera test power parameter lambda is 0.20, the distance image is subjected to power transformation by using three groups of parameters, and an image under the improved relaxation skewness test can be found to be closer to a straight line through an obtained normal probability diagram, namely the HRRP after the power transformation is closer to normal distribution. Next, the influence of the power transformation on the recognition rate is examined.
And (3) carrying out experimental verification on the proposed power parameter learning method based on the self-adaptive Jarqe-Bera normality test by utilizing the actually measured ship data. The experiment is divided into four groups, the original distance image, the partial kurtosis test power transformation distance image, the J-B test power transformation distance image and the self-adaptive Jarqe-Bera normality test distance image are respectively used as four groups of identification features, KNN is used as a classifier, target classification identification is carried out, and the identification rates of the four groups of data are calculated. The identified test set is from random 10 groups of data in 50 groups of data of four classes of ship targets, and 40 groups of data are left as an identification training set. The experiment was performed ten times in total. Fig. 3-6 show four sets of images after range profile characteristic power transformation and the identification rate of the set in a certain experiment. Table 1 shows the recognition rate and the average recognition rate for each experiment.
TABLE 1 four-group feature Classification recognition Rate
Figure BDA0002875884280000122
Figure BDA0002875884280000131
By comparison, it can be seen that the HRRP envelope gradually approaches a normal distribution. And as can be seen by comparing table data, the target identification rate can be improved by power transformation preprocessing, and the HRRP data subjected to power transformation by the adaptive Jarqe-Bera normality test has the highest target identification rate. Therefore, the distance image flicker problem can be relieved to a certain extent through the adaptive Jarqe-Bera normality test power transformation, the classification and identification capacity of the KNN classifier is improved, and the target identification effect is improved.
Fig. 7 is a schematic structural diagram of a ship high-resolution range image power transformation system according to an embodiment of the present invention, and as shown in fig. 7, the system includes:
an original sample set obtaining module 201 for obtaining an original sample set { x }i,i＝1,2,…,N}；
An initial value and step size determining module 202 for determining an initial value λ ═ λ of the power transformation parameter0,λ0∈(0,1]And a step size;
a power transformation module 203, configured to perform power transformation on the original sample set based on the initial value of the power transformation parameter;
a skewness and kurtosis calculation module 204, configured to calculate skewness and kurtosis of the original sample after power transformation;
a skewness estimator and kurtosis estimator calculation module 205, configured to calculate an estimator of skewness and an estimator of kurtosis of the original sample after power transformation;
a first determining module 206, configured to determine whether the estimated skewness and the estimated kurtosis satisfy a first setting condition;
a first output module 207, configured to, when a first set condition is satisfied, count λ at this time into a λ' set;
a skip module 208 for executing a next module when the first setting condition is not satisfied;
a loop module 209, configured to add a step size to λ, repeat the step of the power transformation module-the skip module, until all values of λ are traversed, and obtain λ' ═ { λ ═ λ1,λ2,…,λsPhi or lambda';
a second output module 210, configured to compute an estimate of skewness when λ' ═ Φ, traversing all λ, λoutput＝argmin|g1|；
A third output module 211 for outputting λ' ═ λ1,λ2,…,λsCalculating the estimation quantity of skewness and the estimation quantity of kurtosis;
a second judging module 212, configured to judge whether the estimated skewness and the estimated kurtosis satisfy a second set condition;
a fourth output module 213 for outputting λ when the second setting condition is satisfiedoutput＝λ；
A fifth output module 214 for outputting λ when the second setting condition is not satisfiedoutput＝argmin|g|；
Figure BDA0002875884280000141
The scheme of the invention mainly researches the power transformation preprocessing problem of the High Resolution one-dimensional distance image (HRRP). The power transformation can enable the range image data to tend to be normally distributed, the recognition effect of a linear discriminant function, K Nearest Neighbor (KNN) and other common classifiers is improved, meanwhile, the effect of weak scattering points in recognition can be increased, the shielding effect of strong scattering points on the weak scattering points is weakened, and therefore the problem of attitude sensitivity of the range image is solved. The description first introduces the statistical properties of HRRP, and then introduces the properties of power transformation and parameter estimation methods, including parameter estimation based on the skewness normality test and the Jarqe-Bera normality test. Through analysis and summary of the defects of the two, a parameter estimation method of self-adaptive Jarqe-Bera normality test is provided, through verification of a normal probability map and an actually measured ship high-resolution range profile, a power transformation parameter obtained by improving the parameter estimation method of the Jarqe-Bera normality test is utilized, power transformation preprocessing is carried out on the actually measured range profile, and the result is closer to normal distribution; meanwhile, the power-transformed actually-measured ship distance image data is used for carrying out a target classification identification experiment, and the identification accuracy is improved to a certain extent.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the description of the method part.
The principle and the embodiment of the present invention are explained by applying specific examples, and the above description of the embodiments is only used to help understanding the method and the core idea of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the foregoing, the description is not to be taken in a limiting sense.

Claims (8)

1. A ship high-resolution range profile power transformation method is characterized by comprising the following steps:
s1: obtaining an original sample set { xi,i＝1,2,…,N}；
S2: determining an initial value λ ═ λ of a power transformation parameter0,λ0∈(0,1]And a step size;
s3: performing power transformation on an original sample set based on the initial value of the power transformation parameter;
s4: calculating skewness and kurtosis of the original sample after power transformation;
s5: calculating the estimators of skewness and kurtosis of the original samples after power transformation;
s6: judging whether the estimators of the skewness and the kurtosis meet a first set condition or not; the first setting condition is as follows:
Figure FDA0003670700820000011
Figure FDA0003670700820000012
wherein, g1An estimate representing skewness, g2Represents an estimate of kurtosis, N represents the total number of samples;
s7: if yes, counting the lambda at the moment into a lambda' set;
s8: if not, executing the next step;
s9: and increasing the lambda by one step length, and repeating the steps S3-S8 until all values of the lambda are traversed to obtain the lambda' ═ lambda { lambda1,λ2,…,λsPhi, phi is an empty set;
s10: when λ' is phi and phi is null set, calculate the estimator of skewness, traverse all λ, λoutput＝arg min|g1|；
S11: when λ' ═ λ1,λ2,…,λsCalculating an estimator of skewness and an estimator of kurtosis;
s12: judging whether the estimated amount of the skewness and the estimated amount of the kurtosis meet a second set condition or not; the second setting condition is as follows:
g1＝0,g2＝3，g1an estimate representing skewness, g2An estimate of kurtosis is indicated.
S13: if so, then λoutput＝λ；
S14: if notSatisfy, then λoutput＝arg min|g|；
Figure FDA0003670700820000013
Wherein phi is an empty set;
2. the ship high-resolution range profile power transformation method according to claim 1, wherein performing power transformation on the original sample set based on the initial value of the power transformation parameter specifically adopts the following formula:
Figure FDA0003670700820000021
wherein, yiRepresenting samples after power transformation, lambda represents power transformation parameter, xiRepresenting the original samples and N the number of samples.
3. The ship high-resolution range profile power transformation method according to claim 1, wherein the skewness of the original sample after the power transformation is calculated specifically adopts the following formula:
Figure FDA0003670700820000022
where skewness denotes skewness, E denotes expectation, and Y denotes a sample set after power transformation.
4. The ship high-resolution range profile power transformation method according to claim 1, wherein the kurtosis of the original sample after power transformation is calculated by using the following formula:
Figure FDA0003670700820000023
wherein Kurtosis represents Kurtosis, E represents expectation, and Y represents a sample set after power transformation.
5. The ship high-resolution range profile power transformation method according to claim 1, wherein the estimator for the calculated skewness specifically uses the following formula:
Figure FDA0003670700820000024
wherein, g1Representing the estimated amount of skewness, N representing the total number of samples, yiA sample after the power transformation is represented,
Figure FDA0003670700820000025
6. the ship high-resolution range profile power transformation method according to claim 1, wherein the kurtosis estimator is specifically configured as follows:
Figure FDA0003670700820000026
wherein, g2Denotes the estimate of kurtosis, N denotes the total number of samples, yiA sample after the power transformation is represented,
Figure FDA0003670700820000031
7. the vessel high-resolution range profile power transformation method of claim 1, wherein the step size is 0.01.
8. A vessel high resolution range image power transformation system, the system comprising:
an original sample set acquisition module for acquiring an original sample set { x }i,i＝1,2,…,N}；
An initial value and step size determination module for determining an initial value λ ═ λ of the power transformation parameter0,λ0∈(0,1]And a step size;
the power transformation module is used for performing power transformation on the original sample set based on the initial value of the power transformation parameter;
the skewness and kurtosis calculation module is used for calculating the skewness and the kurtosis of the original sample after the power transformation;
the skewness estimator and kurtosis estimator calculation module is used for calculating an estimator of skewness and an estimator of kurtosis of the original sample after power transformation;
the first judgment module is used for judging whether the estimated deviation and the estimated kurtosis meet a first set condition or not; the first setting condition is as follows:
Figure FDA0003670700820000032
Figure FDA0003670700820000033
wherein, g1An estimate representing skewness, g2Represents an estimate of kurtosis, N represents the total number of samples;
the first output module is used for counting the lambda at the moment into a lambda' set when a first set condition is met;
the skip module is used for executing a next module when the first set condition is not met;
a circulation module for increasing λ by one step length and repeating the step of the power transformation module-the jump module until all values of λ are traversed to obtain λ' ═ λ1,λ2,…,λsPhi, phi is an empty set;
a second output module for calculating the estimation amount of the skewness when λ' ═ Φ and Φ are null set, traversing all λ, λoutput＝arg min|g1|；
A third output module for outputting the signal when λ' ═ λ1,λ2,…,λsCalculating the estimation quantity of skewness and the estimation quantity of kurtosis;
the second judgment module is used for judging whether the estimators of the skewness and the kurtosis meet a second set condition or not; the second setting condition is as follows:
g1＝0,g2＝3，g1an estimate representing skewness, g2An estimate representing kurtosis;
a fourth output module for outputting lambda when the second setting condition is satisfiedoutput＝λ；
A fifth output module for outputting λ when the second setting condition is not satisfiedoutput＝arg min|g|；
Figure FDA0003670700820000041
Wherein Φ is the null set.
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