CN112986996A - Multi-source SAR satellite combined three-dimensional positioning method based on geometric entropy - Google Patents
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Abstract
The invention provides a multisource SAR satellite combined three-dimensional positioning method based on geometric entropy, which comprises the following steps: acquiring SAR data of a target point of a multi-source SAR satellite imaging system; establishing an SAR satellite geometric positioning error source probability distribution model according to a position error, a speed error and a slope distance error of a multi-source SAR satellite imaging system; establishing an error probability distribution model of an SAR satellite imaging position observation value according to SAR data and an SAR satellite geometric positioning error source probability distribution model; establishing a multisource SAR satellite positioning geometric information entropy calculation model according to an error probability distribution model of an SAR satellite to an imaging position observation value of a target point, and deducing to obtain optimized parameters of multisource SAR satellite positioning by taking the minimized geometric information entropy as a target function; carrying out normalization processing on the traditional RD model, and constructing a normalized RD optimal positioning model according to the normalized RD model; and calculating a final result of the multi-source SAR satellite combined three-dimensional positioning according to the normalized RD optimized positioning model and the optimized parameters.
Description
Technical Field
The disclosure relates to the field of synthetic aperture radar three-dimensional positioning, in particular to a multisource SAR satellite combined three-dimensional positioning method based on geometric entropy.
Background
With the increasing number of Synthetic Aperture Radar (SAR) satellites in China, the space-time resolution of the SAR satellite data is continuously improved, and the current SAR satellite data has the characteristics of big data in the aspects of data volume, data type, data value, data growth rate and the like. The method has important significance in the face of massive and abundant SAR remote sensing big data and the development of a multi-source SAR three-dimensional positioning technology. Different from three-dimensional positioning of a single-scene image, in the three-dimensional positioning method of the multi-source satellite-borne SAR image, the geographic space coordinates of a target point are determined by selecting images of a plurality of SAR sensors in the same scene and utilizing a geometric conformation model and a front intersection method.
The three-dimensional positioning problem is essentially to extract three-dimensional information of the ground features from a large amount of SAR data. Currently, the mainstream three-dimensional positioning method for the multisource SAR satellite is mostly based on the least square theory, namely, a position solution is searched, and the sum of squares of distances from the position solution to all observed positions is minimum. Although the existing three-dimensional positioning method has been deeply researched in a plurality of layers such as a positioning model, a calculation method, an error correction method and the like, the research does not explore the information essence of SAR data, especially under the condition of multi-source SAR remote sensing data, the observed values of different satellites obey different probability distribution models, and even the observed values of the same satellite at different angles also obey different probability distribution models. At this time, it is not clear whether the least square theory can most effectively utilize the information amount of the large data and can reach the accuracy limit of the three-dimensional positioning. Therefore, how to furthest mine the three-dimensional information of the hidden ground objects in the multi-source SAR remote sensing data and establish a set of three-dimensional positioning method based on the remote sensing big data information theory still remains a topic worth researching.
Disclosure of Invention
Technical problem to be solved
In view of the above, the present disclosure provides a multi-source SAR satellite combined three-dimensional positioning method based on geometric entropy, so as to overcome the problem that the solution is inaccurate and unstable when the multi-source SAR satellite is combined for positioning in the existing method.
(II) technical scheme
The utility model provides a multisource SAR satellite combined three-dimensional positioning method based on geometric entropy, which comprises the following steps:
acquiring SAR data of a target point of a multi-source SAR satellite imaging system;
establishing a probability distribution model of a geometric positioning error source of each SAR satellite according to a position error, a speed error and a slope distance error of a multi-source SAR satellite imaging system;
establishing an error probability distribution model of each SAR satellite for an imaging position observation value of a target point according to the SAR data and the probability distribution model of the geometric positioning error source of each SAR satellite;
based on a classical information theory, taking an objective real position of a target point as an information source, taking a multi-source SAR satellite imaging system as a channel, establishing a multi-source SAR satellite positioning geometric information entropy calculation model according to an error probability distribution model of an imaging position observation value of each SAR satellite to the target point, and deducing to obtain an optimized parameter of multi-source SAR satellite positioning by taking a minimized geometric information entropy as a target function;
carrying out normalization processing on the traditional RD model, and constructing a normalized RD optimal positioning model according to the normalized RD model;
and calculating a final result of the multi-source SAR satellite combined three-dimensional positioning according to the normalized RD optimized positioning model and the optimized parameters of the multi-source SAR satellite positioning.
Optionally, the probability distribution model of the geometric positioning error source of each SAR satellite satisfies:
wherein ,ΔXs，ΔYS，ΔZSPosition errors of the SAR satellite in three directions of a geocentric earth-fixed coordinate system, namely delta VX，ΔVY，ΔVZRespectively are the speed errors of the SAR satellite in three directions of a geocentric coordinate system, delta R is the slant range error,
respectively, the variance of the position error, the velocity error and the slant range error of the SAR satellite.
Optionally, establishing an error probability distribution model of the imaging position observed value of each SAR satellite to the target point according to the SAR data and the probability distribution model of the geometric positioning error source of each SAR satellite, including:
and simulating to obtain an imaging real position according to the objective real position of the target point, wherein the imaging real position satisfies the following relation:
wherein ,
is the objective real position of the target point,
and
the SAR satellite position and speed at the time t respectively; f. ofDIs Doppler center frequency, λ, PRF, fsThe wavelength, pulse repetition frequency and sampling frequency of the radar are respectively; r, c are the slope distance and speed of light, respectively, of the target point; rnearThe slope distance of the near place; t, tsRespectively corresponding azimuth time and SAR satellite imaging starting time of the target point; (x)0，y0) The real position of the target point is imaged for the SAR satellite, wherein,
fD、λ、PRF、fs、R、t、tsobtaining from the SAR data;
simulating to obtain an imaging position observation value according to the objective real position of the target point and the position error, the speed error and the slope distance error of the SAR satellite, wherein the imaging position observation value satisfies the following relations:
the SAR target point observation method comprises the following steps that (x, y) is an imaging position observation value of an SAR satellite to a target point, wherein x and y are an imaging distance coordinate observation value and an azimuth coordinate observation value of the SAR satellite to the target point respectively;
the delta R is a position error, a speed error and an inclined distance error of the SAR satellite respectively;
obtaining an error of the observed value of the imaging position according to the real imaging position and the observed value of the imaging position, wherein the error (x) of the observed value of the imaging positione，ye) Satisfies the following conditions: (x)e，ye)＝(x，y)-(x0，y0)；
For each SAR satellite, sampling a position error, a speed error and a slope distance error under a probability distribution model of a geometric positioning error source of the SAR satellite at corresponding azimuth time, and repeating the steps to obtain an error probability distribution model of an imaging position observation value of the SAR satellite to a target point, wherein the error probability distribution model satisfies the following conditions:
wherein ,xe and yeRespectively the error of the SAR satellite imaging distance to the coordinate observation value and the error of the azimuth coordinate observation value,
the variances of the observed value errors of the imaging positions in the distance direction and the azimuth direction of the imaging image are respectively.
Optionally, establishing a multi-source SAR satellite positioning geometric information entropy calculation model according to an error probability distribution model of an observation value of an imaging position of each SAR satellite to a target point, and deriving to obtain an optimized parameter of multi-source SAR satellite positioning by taking the minimized geometric information entropy as a target function, including:
deducing the probability distribution of the imaging position observation value of the multi-source SAR satellite imaging system to the target point according to the error probability distribution of the imaging position observation value of each SAR satellite to the target point;
establishing a multisource SAR satellite positioning geometric information entropy calculation model according to probability distribution of an imaging position observation value of a target point by a multisource SAR satellite imaging system;
and (4) taking the minimized geometric information entropy as a target function, and deducing to obtain optimized parameters of multisource SAR satellite positioning based on a multisource SAR satellite positioning geometric information entropy calculation model.
Optionally, the probability distribution of the imaging position observed value of the target point by the multi-source SAR satellite imaging system satisfies the following relationship:
the method includes the steps that a multisource SAR satellite imaging system is assumed to obey probability distribution of M different imaging position observation values for all observation samples of a target point, and the sample capacity of the probability distribution obeying the M (M is 1, 2, M) th imaging position observation value is Nkm(kM ═ k 1.., kM), then:
the distances obeying the probability distribution of the M imaging position observations satisfy to the coordinate observations:
the azimuthal coordinate observations obeying the probability distribution of the M imaging location observations satisfy:
wherein ,x1，x2...，xMRespectively, a range-to-coordinate observation, y, obeying a probability distribution of the M imaging position observations1，y2...，yMRespectively are the azimuth coordinate observed values of the probability distribution of the M imaging position observed values, mu is the distance coordinate observed value or the mean value of the azimuth coordinate observed values of the M types of observation samples,
respectively in M classThe variance of the distance of the sample to the coordinate observation is measured,
and the variances of the azimuth coordinate observed values of the M types of observation samples are respectively.
Optionally, the multi-source SAR satellite positioning geometric information entropy calculation model includes a geometric information entropy function of the distance direction coordinate observation value and a geometric information entropy function of the orientation direction coordinate observation value, where:
the geometric information entropy function of the distance direction coordinate observed value satisfies the following conditions:
wherein ,
a geometric entropy function of distance to coordinate observations,
imaging distance of multi-source SAR satellite to real position x0M is the number of probability distributions of imaging position observations obeyed by the multisource SAR satellite imaging system on all observation samples of the target point, Nkm(kM ═ k 1.., kM) is the distance to observation sample x in the probability distribution of the M (M ═ 1, 2.., M) imaging position observationsmThe capacity of (a); sigmaxmThe standard deviation of the distance to coordinate observed values of the mth type observed sample; p is a radical ofxmA weighting factor corresponding to the distance-direction coordinate observation value of the mth type observation sample;
the geometric information entropy function of the azimuth coordinate observed value satisfies the following conditions:
wherein ,
a geometric entropy function of the orientation coordinate observations,
is to the true position y of the imaging azimuth of the multi-source SAR satellite0M is the number of probability distributions of imaging position observations obeyed by the multisource SAR satellite imaging system on all observation samples of the target point, Nkm(kM ═ k 1.., kM) is the azimuth observation sample y in the probability distribution of the M (M ═ 1, 2.., M) imaging position observationsmThe capacity of (a); sigmaymThe standard deviation of the azimuth coordinate observed value of the mth type observed sample is obtained; p is a radical ofymAnd the weighting factors are corresponding to the azimuth coordinate observed values of the m-th type observed samples.
Optionally, the optimized parameters for multi-source SAR satellite positioning include optimized parameters for a distance-oriented coordinate observation value and optimized parameters for a position-oriented coordinate observation value, where:
the optimized parameter of the range-direction coordinate observed value is a weight factor p corresponding to the range-direction coordinate observed value of the mth type observation samplexmWhich satisfies:
wherein ,pxmThe weight factor corresponding to the observation value of the distance coordinate of the mth type observation sample, M is the number of probability distribution of the observation value of the imaging position obeyed by the multisource SAR satellite imaging system to all observation samples of the target point, Nkm(kM ═ k 1.., kM) is the distance to observation sample x in the probability distribution of the M (M ═ 1, 2.., M) imaging position observationsmThe capacity of (a) is set to be,
the variance of the distance-to-coordinate observation value of the mth type observation sample;
the optimized parameter of the azimuth coordinate observed value is a weight factor p corresponding to the azimuth coordinate observed value of the mth type observation sampleymWhich satisfies:
wherein ,pymThe weight factor corresponding to the azimuth coordinate observation value of the mth type observation sample, M is the number of probability distribution of imaging position observation values obeyed by the multisource SAR satellite imaging system to all observation samples of the target point, and N is the number of the probability distribution of the imaging position observation values obeyed by the multisource SAR satellite imaging system to all observation samples of the target pointkm(kM ═ k 1.., kM) is the azimuth observation sample y in the probability distribution of the M (M ═ 1, 2.., M) imaging position observationsmThe capacity of (a) is set to be,
the variance of the azimuth coordinate observation value of the m-th type observation sample.
Optionally, the normalizing process is performed on the conventional RD model, and a normalized RD optimized positioning model is constructed according to the normalized RD model, including:
carrying out normalization processing on the traditional RD model to obtain a normalized RD model of each SAR satellite;
and converting the normalized RD equation solving problem of each SAR satellite into an optimization problem with equation residual error minimum as an objective function, and constructing a normalized RD optimization positioning model.
Optionally, the normalized RD model for each SAR satellite satisfies the following relationship:
wherein, (X, Y, Z) is the objective real position of the target point; (X)S，YS，ZS) For each SAR satellite's location; v ═ V (V)X，VY，VZ) For each SAR satellite velocity; the | V | is the modular length of the velocity vector of each SAR satellite; r, fDλ is the slant range of the target point, the radar doppler center frequency and the radar wavelength, respectively;
is SAR sensor squint angle;
the normalized RD optimized positioning model satisfies the following relationship:
wherein, (X, Y, Z) is the objective real position of the target point; (X)Sm，YSm，ZSm) The position of the M (M ═ 1, 2, …, M) th SAR satellite; vm＝(VXm，VYm，VZm) The speed of the mth SAR satellite; i Vm| | is the module length of the velocity vector of the mth SAR satellite; rm，fDmThe target point corresponding to the mth SAR satellite is the slant range and the radar Doppler center frequency, and lambda is the radar wavelength.
Optionally, the final result of the multi-source SAR satellite joint three-dimensional positioning satisfies the following relationship:
wherein ,pxm，pym(M is 1, 2, …, M) is the weighting factor corresponding to the distance coordinate observation value and the azimuth coordinate observation value of the mth type observation sample, respectively, (X, Y, Z) is the objective real position of the target point; (X)Sm，YSm，ZSm) Is the position of the mth SAR satellite; vm＝(VXm，VYm，VZm) The speed of the mth SAR satellite; i VmThe | | is the velocity vector modular length of the mth SAR satellite; rm，fDmThe target point corresponding to the mth SAR satellite is the slant range and the radar Doppler center frequency, and lambda is the radar wavelength.
(III) advantageous effects
Compared with the prior art, the method has the following advantages:
(1) the method is based on the classical information theory, introduces the concept of geometric entropy, converts the problem of improving the positioning precision in the three-dimensional positioning of the multi-source SAR satellite into the problem of minimizing the geometric entropy, provides a new approach for the combined three-dimensional positioning problem of the multi-source SAR satellite, and provides a new idea for a remote sensing big data processing mode.
(2) Compared with the traditional method, the method provided by the disclosure can establish a reasonable error source probability distribution model in the multi-source SAR data-oriented three-dimensional positioning, considers different probability distributions of different source data, and achieves the optimal positioning precision from the angle of obtaining the maximum information quantity and the minimum information entropy, wherein the method can achieve the Clarame-Luo lower bound of the three-dimensional positioning precision.
(3) The method introduces a normalized RD model and a solution method of an optimization theory, and performs equation weight distribution solution under the criterion of minimum entropy, so that the precision and the stability of the multisource SAR satellite combined three-dimensional positioning are effectively improved. The method disclosed by the invention overcomes the problems of inaccuracy and instability in solving when the multi-source SAR satellite is combined with three-dimensional positioning in the conventional method.
Drawings
Fig. 1 schematically shows a flowchart of a multi-source SAR satellite joint three-dimensional positioning method based on geometric entropy according to an embodiment of the present disclosure;
fig. 2 schematically shows a natural feature point photo and a position thereof on an SAR image in a second embodiment of the disclosure, where a is the natural feature point photo, and b to e respectively correspond to image points of the natural feature points on the SAR image 1 to 4.
Detailed Description
For the purpose of promoting a better understanding of the objects, aspects and advantages of the present disclosure, reference is made to the following detailed description taken in conjunction with the accompanying drawings.
Fig. 1 schematically shows a flowchart of a multisource SAR satellite joint three-dimensional positioning method based on geometric entropy according to an embodiment of the present disclosure.
As shown in FIG. 1, the method includes steps S1-S6.
In step S1, SAR data of the multi-source SAR satellite imaging system for the target point is obtained.
Specifically, a multi-source SAR satellite imaging system is used for observing the objective real position of a target point to obtain a plurality of groups of SAR data. The SAR data includes an imaging image of each SAR satellite and SAR satellite positioning related parameter information, such as a position, a velocity, a slant range to a target point, and the like of the SAR satellite. It should be noted that, for the result of the multi-source SAR satellite combined three-dimensional positioning to be solved, that is, the objective real position of the target point, various probability distribution models, geometric information entropy calculation models, normalized RD optimized positioning models, and the like are subsequently established, and the values of the relevant parameters involved in these models can be obtained from the SAR data, so that the result of the multi-source SAR satellite combined three-dimensional positioning, that is, an estimation of the objective real position of the target point, can be obtained. Therefore, the source of these data will not be described below for the sake of brevity.
In step S2, a probability distribution model of the geometric positioning error source of each SAR satellite is established according to the position error, the velocity error, and the slant range error existing in the multi-source SAR satellite imaging system.
Specifically, for each SAR satellite, because the SAR satellite itself has errors of orbit measurement and velocity measurement, and transmission errors of electromagnetic waves in the atmosphere, etc., the parameters of the geometric positioning model generally have errors, which are mainly expressed as satellite position errors
Error in satellite velocity
And a pitch error Δ R. The three types of errors of each SAR satellite can be set with empirical values according to SAR satellite design indexes or historical data, a probability distribution model of a geometric positioning error source of the SAR satellite is established according to the three types of errors of the SAR satellite, the three types of errors have randomness without loss of generality, and the three types of errors are assumed to obey the following Gaussian distribution:
wherein ,ΔXS，ΔYS，ΔZSPosition errors of the SAR satellite in three directions of a geocentric earth-fixed coordinate system, namely delta VX，ΔVY，ΔVZRespectively are the speed errors of the SAR satellite in three directions of a geocentric coordinate system, delta R is the slant range error,
the error of the SAR satellite is the variance of the position error, the speed error and the slant range error.
Because the multi-source SAR satellite imaging system comprises a plurality of SAR satellites with different sources, and the probability distribution models of the geometric positioning error sources of different SAR satellites are different, the reasonable probability distribution model parameters of the geometric positioning error sources are designed for each SAR satellite in the multi-source SAR satellite system according to the three types of errors (namely satellite position error, satellite speed error and slant range error) existing in each SAR satellite of the multi-source SAR satellite imaging system
Compared with the traditional method, in the three-dimensional positioning oriented to the multi-source SAR data, the SAR data from different sources are considered, a reasonable geometric positioning error source probability distribution model is established based on the SAR data of the different sources, and the probability distribution of observed values of different imaging positions of the SAR data of the different sources is aimed at, so that the optimal positioning precision is achieved from the angle of obtaining the maximum information quantity and the minimum information entropy.
In step S3, an error probability distribution model of the observed value of the imaging position of each SAR satellite to the target point is established based on the SAR data and the probability distribution model of the geometric positioning error source of each SAR satellite.
According to an embodiment of the present disclosure, the step S3 further includes steps S31 to S34.
In step S31, the imaging true position is obtained according to the objective true position simulation of the target point, which satisfies the following relationship:
wherein ,
is the objective real position of the target point,
and
the SAR satellite position and speed at the time t respectively; f. ofDIs Doppler center frequency, λ, PRF, fsThe wavelength, pulse repetition frequency and sampling frequency of the radar are respectively; r, c are the slope distance and speed of light, respectively, of the target point; rnearThe slope distance of the near place; t, tsRespectively corresponding azimuth time and SAR satellite imaging starting time of the target point; (x)0，y0) And imaging the real position of the target point for the SAR satellite.
In particular, the objective true position of the target point by the SAR satellites
Simulating to obtain the real imaging position (x)0，y0). If the Doppler center frequency f is setDIf 0 is set, the imaging true position (x) can be obtained according to the normalized RD equation of the formula (2)0，y0)。
In step S32, an imaging position observation value is obtained according to the objective real position of the target point and the position error, velocity error and slope error simulation of the SAR satellite.
Concretely, three types of errors under a probability distribution model of geometric positioning error sources of SAR satellites in the formula (1) are introduced
Δ R, simulating to obtain an observed value of the imaging position by adopting the mode of the step S31
Wherein the observed value of the imaging position
The following relationship is satisfied:
the SAR target point observation method comprises the following steps that (x, y) is an imaging position observation value of an SAR satellite to a target point, wherein x and y are an imaging distance coordinate observation value and an azimuth coordinate observation value of the SAR satellite to the target point respectively;
and the delta R is respectively a position error, a speed error and a slope distance error of the SAR satellite.
In step S33, an error of the imaging position observed value is obtained from the imaging true position and the imaging position observed value, wherein the error of the imaging position observed value (x)e，ye) Satisfies the following conditions:
(xe，ye)＝(x，y)-(x0，y0)。 (4)
in step S34, for each SAR satellite, the position error, the velocity error, and the slant range error under the probability distribution model of the geometric positioning error source of the SAR satellite are sampled at the corresponding azimuth time, and the above steps S31 to S33 are repeated, so that the error probability distribution model of the observed value of the imaging position of the SAR satellite on the target point can be obtained. According to the previous experimental results, the error probability distribution of the SAR satellite on the observation value of the imaging position of the target point is approximately subjected to zero mean Gaussian distribution, and the generality is not lost, wherein the error probability distribution model of the SAR satellite on the observation value of the imaging position of the target point is assumed to meet the following conditions:
wherein ,xe and yeRespectively the error of the SAR satellite imaging distance to the coordinate observation value and the error of the azimuth coordinate observation value,
the variances of the observed value errors of the imaging positions in the distance direction and the azimuth direction of the imaging image are respectively.
In step S4, based on the classical information theory, the objective real position of the target point is used as a signal source, the multi-source SAR satellite imaging system is used as a channel, a multi-source SAR satellite positioning geometric information entropy calculation model is established according to an error probability distribution model of the imaging position observation value of each SAR satellite to the target point, and the minimum geometric information entropy is used as a target function to derive the optimized parameters of the multi-source SAR satellite positioning.
Specifically, according to the classical information theory, the objective real position of the target point
And as an information source, the multisource SAR satellite imaging system is used as a channel. Taking into account the objective true position of a target point
Observation result of (2)
This is
Is a continuous random variable which appears in a certain support domain S according to probabilityx，Sy]At a certain position within, a support field [ S ]x，Sy]The error may be set according to a maximum error range that may occur in engineering, and is not limited herein. Is provided with
Is f (x, y), the following geometric information entropy can be defined:
the discretized geometric information entropy of the formula (6) is as follows:
wherein ,p(xi，yj) Is an imaging position observation
Appears at SAR image pixel (x)i，yj) The probability of (c) above.
Probability density function f (x, y) and support field [ S ] in the above entropy of geometric informationx，Sy]All implies an objective true position with respect to the observed target point
Observing different positions to obtain an observation result (i.e. imaging position observation value)
Are different in probability density. Although in practice f (x, y) is not a shift-invariant function, in local regions it can be approximated as a shift-invariant function.
The geometric information entropy is a measure of geometric position uncertainty. The larger the entropy of the geometric information is, the higher the uncertainty of the geometric position is; the smaller the entropy of the geometric information, the lower the uncertainty of the position, and thus the higher the accuracy of the three-dimensional coordinates that can be obtained. Therefore, the method is based on the classical information theory, introduces the concept of the geometric information entropy, and considers the problem of improving the positioning precision in the multi-source SAR satellite combined three-dimensional positioning as the problem of how to reduce the geometric information entropy.
According to the embodiment of the present disclosure, the step S4 further includes steps S41 to S43.
In step S41, a probability distribution of the imaging position observation value of the multi-source SAR satellite imaging system for the target point is derived according to the error probability distribution of the imaging position observation value of each SAR satellite for the target point.
In particular, the output imaging position observations will follow a certain probability distribution due to the presence of errors in the channel. However, the observations of the imaging position of the target point from different SAR satellites, and even from different angles of the same SAR satellite, generally follow different distributions. The imaging position observed value can be derived based on the assumption that the error probability distribution model of the imaging position observed value is gaussian distribution in step S2
Should also be gaussian distributed. Therefore, in the multi-source SAR satellite joint three-dimensional positioning problem, taking the range-direction coordinate observation value x as an example, it is assumed that the multi-source SAR satellite imaging system obeys probability distributions of M different imaging position observation values for all observation samples of the target point, respectively, and a sample capacity obeying the probability distribution of the M (M is 1, 2km(kM ═ k 1.., kM), then:
the distances obeying the probability distribution of the M imaging position observations satisfy to the coordinate observations:
wherein ,x1，x2...，xMRespectively, distance-to-coordinate observed values obeying the probability distribution of the M imaging position observed values, mu is the mean value of the distance-to-coordinate observed values of the M types of observed samples,
respectively, the variance of the distance to coordinate observed values of the M types of observed samples.
Likewise, the azimuthal coordinate observations obeying the probability distribution of the M imaging position observations satisfy:
wherein ,y1，y2...，yMRespectively the azimuth coordinate observed values of the probability distribution of the M imaging position observed values, mu is the mean value of the azimuth coordinate observed values of the M types of observation samples,
and the variances of the azimuth coordinate observed values of the M types of observation samples are respectively.
In step S42, a multisource SAR satellite positioning geometric information entropy calculation model is established according to probability distribution of the imaging position observation value of the target point by the multisource SAR satellite imaging system.
According to the embodiment of the present disclosure, in step S42, the multi-source SAR satellite positioning geometric information entropy calculation model includes a geometric information entropy function of the distance direction coordinate observation value and a geometric information entropy function of the orientation direction coordinate observation value. The establishment of the geometric information entropy calculation model will be described below by taking the establishment of the geometric information entropy function of the distance coordinate observation value as an example.
Order:
wherein ,
imaging distance of multi-source SAR satellite to real position x0An estimate of (a); x is the number ofm，km(M1, 2.. said, M) is a kM (kM k1, k 2.. said, kM) range coordinate observation obeying a probability distribution of M (M1, 2.. said, M) imaging location observations, M being the number of probability distributions of imaging location observations obeyed by the multi-source SAR satellite imaging system for all observation samples of the target point, Nkm(kM ═ k 1.., kM) is the distance to observation sample x in the probability distribution of the M (M ═ 1, 2.., M) imaging position observationsmThe capacity of (a); p is a radical ofxmIs observed for the M (M ═ 1, 2.., M) th classAnd the distance of the sample corresponds to the weight factor of the coordinate observation value.
The properties according to the gaussian distribution are then:
then, according to the formula of the entropy of the normal distribution, it can be obtained:
wherein ,
a geometric entropy function of distance to coordinate observations,
imaging distance of multi-source SAR satellite to real position x0M is the number of probability distributions of imaging position observations obeyed by the multisource SAR satellite imaging system on all observation samples of the target point, Nkm(kM ═ k 1.., kM) is the distance to observation sample x in the probability distribution of the M (M ═ 1, 2.., M) imaging position observationsmThe capacity of (a); sigmaxmThe standard deviation of the distance to coordinate observed values of the mth type observed sample; p is a radical ofxmAnd the weighting factors are corresponding to the distance direction coordinate observation values of the m-th class observation samples.
Likewise, the geometric information entropy function of the azimuth coordinate observed value can be derived in the above manner, and satisfies the following conditions:
wherein ,
entropy function of geometric information for azimuthal coordinate observationsThe number of the first and second groups is,
is to the true position y of the imaging azimuth of the multi-source SAR satellite0M is the number of probability distributions of imaging position observations obeyed by the multisource SAR satellite imaging system on all observation samples of the target point, Nkm(kM ═ k 1.., kM) is the azimuth observation sample y in the probability distribution of the M (M ═ 1, 2.., M) imaging position observationsmThe capacity of (a); sigmaymThe standard deviation of the azimuth coordinate observed value of the mth type observed sample is obtained; p is a radical ofymAnd the weighting factors are corresponding to the azimuth coordinate observed values of the m-th type observed samples.
In step S43, the minimum geometric information entropy is used as a target function, and an optimized parameter for multisource SAR satellite positioning is derived based on a multisource SAR satellite positioning geometric information entropy calculation model.
The optimized parameters of the multisource SAR satellite positioning comprise optimized parameters of a distance coordinate observation value and optimized parameters of an azimuth coordinate observation value, and the optimized parameters of the distance coordinate observation value and the optimized parameters of the azimuth coordinate observation value respectively correspond to weight factors p to be solved in the formula (12) and the formula (13)xm and pym. Therefore, the corresponding weight factors are obtained by solving the minimum geometric information entropy criterion and the geometric information entropy calculation model, and the optimization parameters of the distance-direction coordinate observation value and the optimization parameters of the orientation-direction coordinate observation value can be obtained.
Taking the distance coordinate x as an example, the multi-source SAR satellite imaging distance upward geometrical information entropy shown in formula (12)
In order to minimize the geometric entropy, there are:
wherein ,pxmDistance of observation sample for class M (M1, 2.., M)And M is the number of probability distributions of imaging position observation values obeyed by the multisource SAR satellite imaging system to all observation samples of the target point.
Further, an optimization parameter of the observation value of the range direction coordinate, namely a weight factor p corresponding to the observation value of the range direction coordinate of the mth type observation sample can be deducedxmWhich satisfies:
wherein ,pxmThe weight factor corresponding to the observation value of the distance coordinate of the mth type observation sample, M is the number of probability distribution of the observation value of the imaging position obeyed by the multisource SAR satellite imaging system to all observation samples of the target point, Nkm(kM ═ k 1.., kM) is the distance to observation sample x in the probability distribution of the M (M ═ 1, 2.., M) imaging position observationsmThe capacity of (c). It is to be noted that in the formula (15)
And σxm 2Representing the same physical quantity, σxm 2And
the variance of the distance to coordinate observation values of the class M (M, i ═ 1, 2.., M) observation samples is defined. The reason why the same physical quantity is expressed by two parameters in the formula (15) is to facilitate the description of NkmThe value of (kM ≠ k 1., kM) is not the same as the value of parameter M (i.e., i ≠ M in equation (15)). Similarly, the optimized parameters of the azimuth coordinate observed value, namely the weight factor p corresponding to the azimuth coordinate observed value of the mth type observation sample, can be derived by adopting the methodymWhich satisfies:
wherein ,pymThe weight factor corresponding to the azimuth coordinate observation value of the mth type observation sample, M is the number of probability distribution of imaging position observation values obeyed by the multisource SAR satellite imaging system to all observation samples of the target point, and N is the number of the probability distribution of the imaging position observation values obeyed by the multisource SAR satellite imaging system to all observation samples of the target pointkm(kM ═ k 1.., kM) is the azimuth observation sample y in the probability distribution of the M (M ═ 1, 2.., M) imaging position observationsmThe capacity of (a) is set to be,
the variance of the azimuth coordinate observation value of the m-th type observation sample.
Further, the imaging distance of the multi-source SAR satellite to the real position x can be obtained0An estimate of
Which satisfies the following conditions:
the lower bound of caramet-ro, where the method of the present disclosure achieves positioning accuracy, is also illustrated below by taking the distance-wise coordinate x as an example.
Further, considering the lower bound of krame-ro for positioning accuracy, there are:
wherein ,
is the desired cramer-lo lower bound; j (. mu.) is Fisher information, as given by the following formula:
wherein ,xm，kmIs the first to follow the probability distribution of the M (M1, 2.. multidot.M) th imaging position observationkM (kM ═ k1, k 2.., kM) range-to-coordinate observations, and μ is the mean of the range-to-coordinate observations for the M types of observation samples.
Thus, it is possible to obtain:
wherein mu is the mean value of the observation values of the distance direction coordinates of the M types of observation samples, M is the number of probability distributions of the observation values of the imaging positions obeyed by the multisource SAR satellite imaging system to all the observation samples of the target point, and N is the number of the probability distributions of the observation values of the imaging positions obeyed by the multisource SAR satellite imaging system to all the observation samples of the targetkm(kM ═ k 1.., kM) is the distance to observation sample x in the probability distribution of the M (M ═ 1, 2.., M) imaging position observationsmCapacity of (a), xm，kmIs a kM (k 1, k 2.., kM) distance to coordinate observation values that obey a probability distribution of the M (M1, 2.., M) imaging position observation values,
is the variance of the range-to-coordinate observations for the mth class of observation samples.
The cramer-lo lower bound is then:
comparing the formula (21) and the formula (17), it can be known that the Cramer-Rou lower bound of the positioning accuracy is achieved by adopting the multisource SAR satellite combined three-dimensional positioning method based on the geometric entropy.
Similarly, the observation result of the multisource SAR satellite combined three-dimensional positioning method based on the geometric entropy in the azimuth direction also reaches the lower Cramer-Rao boundary of the positioning precision. Therefore, the Cramer-Rou lower bound of the three-dimensional positioning precision can be achieved by adopting the multisource SAR satellite combined three-dimensional positioning method based on the geometric entropy.
In step S5, the conventional RD model is normalized, and a normalized RD optimized positioning model is constructed according to the normalized RD model. Specifically, according to the embodiment of the present disclosure, the step S5 further includes steps S51 to S52.
In step S51, the conventional RD model is normalized to obtain a normalized RD model for each SAR satellite.
Specifically, in order to overcome the problems of unstable positioning and low precision of the conventional RD model, the normalized RD model is provided, and according to an embodiment of the present disclosure, the normalized RD model of each SAR satellite satisfies the following relationship:
wherein, (X, Y, Z) is the objective real position of the target point; (X)S，YS，ZS) For each SAR satellite's location; v ═ V (V)X，VY，VZ) For each SAR satellite velocity; the | V | is the modular length of the velocity vector of each SAR satellite; r, fDλ is the slant range of the target point, the radar doppler center frequency and the radar wavelength, respectively;
is the SAR sensor squint angle.
Equation (22) normalizes the conventional RD model, specifically the doppler equation. By normalizing the doppler equation, the gradients of both the distance equation and the doppler equation are converted into unit vectors. Meanwhile, the dimensions of both equations are unified into a dimension in meters. It is worth noting that this normalization still has a physical significance: the right end of the doppler equation is the product of the skew distance and the sine of the skew angle, i.e. the projection of the distance vector in the flight direction. This projection is exactly equal to the dot product of the distance vector and the velocity vector, i.e. the left end of the equation.
In step S52, the normalized RD equation solution problem for each SAR satellite is converted into an optimization problem with the minimum equation residual as an objective function, and a normalized RD optimized positioning model is constructed.
Specifically, in order to better apply the weight distribution method to the multi-source SAR satellite combined three-dimensional positioning problem, the method utilizes an optimization theory to convert the solution problem of the normalized RD equation into an optimization problem with the equation residual error minimum as an objective function, and constructs the following normalized RD optimized positioning model:
wherein, (X, Y, Z) is the objective real position of the target point; (X)Sm，YSm，ZSm) The position of the M (M ═ 1, 2, …, M) th SAR satellite; vm＝(VXm，VYm，VZm) The speed of the mth SAR satellite; i Vm| | is the module length of the velocity vector of the mth SAR satellite; rm，fDmThe target point corresponding to the mth SAR satellite is the slant range and the radar Doppler center frequency, and lambda is the radar wavelength.
The equation (23) establishes an objective function based on the minimized residual error, and expresses the objective function in a display manner, so that the optimized weight distribution solution of the normalized RD optimized positioning equation is facilitated. There are many methods for solving the unconstrained optimization problem of equation (23), for example, the unconstrained optimization problem can be solved by using a DFP algorithm, which is not limited herein.
And S6, calculating the objective real position of the target point according to the normalized RD optimized positioning model and the optimized parameters of the multi-source SAR satellite positioning.
Specifically, with the weighting factor p in the formula (15) and the formula (16)xm and pymAnd (3) as a distance equation weight factor and a Doppler equation weight factor corresponding to the formula (23), and further obtaining a calculation model for solving a final result of the multi-source SAR satellite combined three-dimensional positioning:
wherein ,pxm，pym(M is 1, 2, …, M) is the distance to coordinate observed value and square of the M-th observation sampleThe weight factors corresponding to the observation values of the position coordinates, wherein (X, Y and Z) are objective real positions of the target points; (X)Sm，YSm，ZSm) Is the position of the mth SAR satellite; vm＝(VXm，VYm，VZm) The speed of the mth SAR satellite; i VmThe | | is the velocity vector modular length of the mth SAR satellite; rm，fDmThe target point corresponding to the mth SAR satellite is the slant range and the radar Doppler center frequency, and lambda is the radar wavelength.
The obtained SAR data is substituted into the formula (24), and the final result of the multi-source SAR satellite combined three-dimensional positioning can be obtained through solving, namely, the estimation of the objective real position of the target point is realized. Similarly, the unconstrained optimization problem shown in equation (24) can be solved by using an iterative method such as DFP, which is not limited herein.
In order to make those skilled in the art more clearly understand the technical solution of the present disclosure, the following will describe the advantages of the geometric entropy-based multi-source SAR satellite joint three-dimensional positioning method of the present disclosure in three-dimensional positioning with reference to specific embodiments. For convenience of description, the geometric entropy-based multi-source SAR satellite joint three-dimensional positioning method in the present disclosure is referred to as "geometric entropy-based method" below.
Example one
In a simulation experiment, in the first embodiment, six high-resolution three-number (GF-3) satellite images are selected to perform three-dimensional positioning on a virtual target point on an SAR image. The six pieces of GF-3 SAR image information are shown in the following table 1. In order to simulate SAR satellite data of different sources, different geometric positioning error source probability distribution models are introduced into different SAR images, and introduced geometric positioning error source information is shown in the following table 2.
TABLE 1 SAR image information in simulation experiments
| Image ID | Sensor with a sensor element | Mode(s) | Incident angle (degree) | Lifting rail/antenna pointing |
| 1 | GF-3 | SL | 42.71-43.39 | ASC/Right |
| 2 | GF-3 | SL | 38.92-39.64 | ASC/Right |
| 3 | GF-3 | SL | 25.43-26.45 | ASC/Right |
| 4 | GF-3 | SL | 20.25-21.45 | ASC/ |
| 5 | GF-3 | SL | 35.73-36.50 | DEC/ |
| 6 | GF-3 | SL | 21.42-22.81 | DEC/Right |
TABLE 2 probability distribution model of geometric positioning error source in simulation experiment
According to the method disclosed by the disclosure, the weight factor p corresponding to each image can be obtainedxm，pym(m ═ 1, 2,.., 6), the results of the calculations are shown in table 3 below. 1000 virtual target points are randomly selected from the SAR images shown in table 1, wherein the real positions of the 1000 virtual target points are known, the 1000 virtual target points are positioned by a geometric entropy-based method, and then positioning accuracy based on the geometric entropy method is obtained (the positioning accuracy is a positioning error of a positioning result based on the geometric entropy method relative to the real position of the virtual target point, and the description is omitted hereinafter).
TABLE 3 weight factor calculation results
| Image ID | pxm | pym |
| 1 | 0.7039 | 0.7077 |
| 2 | 0.7076 | 0.7053 |
| 3 | 0.0441 | 0.0283 |
| 4 | 0.0441 | 0.0284 |
| 5 | 0.0018 | 0.0011 |
| 6 | 0.0004 | 0.0003 |
Comparative example 1
Comparative example one: and positioning the 1000 virtual target points by adopting a traditional least square method, and obtaining the positioning precision based on the traditional least square method.
Table 4 shows the positioning accuracy comparison results based on the geometric entropy method and the least square method. As can be seen from table 4, compared with the conventional least square method, when the geometric positioning error source distribution of the SAR satellite follows different probability distributions, the positioning accuracy of the least square method is significantly lower than that of the geometric entropy-based method, that is, the geometric entropy-based method in the present disclosure can overcome the problem that the solution is inaccurate and unstable when the multi-source SAR satellite is jointly positioned by using the existing method. In addition, it is clear from the disclosure that the lower cramer-lo bound of geometric positioning accuracy is actually achieved based on the geometric entropy method.
TABLE 4 comparison of positioning accuracy based on geometric entropy method and least squares method
| Method | RMS(m) | Mean value (m) | Standard deviation (m) |
| Traditional least squares method | 3.57 | 3.04 | 1.89 |
| Method based on geometric entropy | 1.13 | 0.93 | 0.64 |
Example two
To further validate the effectiveness of the geometric entropy-based approach of the present disclosure, in example two, we performed three-dimensional localization experiments on natural feature points in the suzhou region. Three GF-3 images and one TerrraSAR-X (TSX) image were selected for the experiment. The SAR image information is shown in table 5, the established geometric positioning error source probability distribution model is shown in table 6, and the natural ground object target point in the experiment and the position thereof on the SAR image are shown in fig. 2. In the experiment, the position of the target point of the natural ground object is obtained through field measurement and is used as the real position of the target point.
TABLE 5 SAR image information for natural surface feature localization experiments
| Image ID | Sensor with a sensor element | Mode(s) | Incident angle (degree) | Lifting rail/antenna pointing |
| 1 | GF-3 | UFS | 49.32-50.69 | ASC/Left |
| 2 | GF-3 | UFS | 46.59-48.08 | ASC/Right |
| 3 | GF-3 | SL | 38.93-39.60 | ASC/Right |
| 4 | TSX | ST | 34.91-35.45 | ASC/Right |
Table 6 probability distribution model of geometric positioning error source in simulation experiment
| Image ID | Orbit error (m) | Speed error (m/s) | Skew error (m) |
| 1 | N(0，52) | N(0，0.0052) | N(0，3.52) |
| 2 | N(0，52) | N(0，0.0052) | N(0，3.52) |
| 3 | N(0，52) | N(0，0.0052) | N(0，1.52) |
| 4 | N(0，0.22) | N(0，0.00022) | N(0，0.52) |
Similarly, according to the method disclosed by the disclosure, the weight factors p corresponding to the four SAR images are obtained through calculationxm，pym(m ═ 1, 2.., 4), the calculation results are shown in table 7. And then, calculating to obtain a three-dimensional positioning result based on a geometric entropy method according to the obtained weight factor, and then calculating to obtain the positioning precision based on the geometric entropy method.
TABLE 7 weight factor calculation results
| Image ID | pxm | pym |
| 1 | 0.0128 | 0.0016 |
| 2 | 0.0128 | 0.0016 |
| 3 | 0.0249 | 0.0016 |
| 4 | 0.9995 | 0.9998 |
Comparative example No. two
Comparative example two: and positioning the target point of the natural ground object by adopting a traditional least square method, and obtaining the positioning precision based on the traditional least square method.
Table 8 shows the positioning accuracy comparison results of the natural ground object target point based on the geometric entropy method and the least square method. As can be seen from the results in table 8, when the images are combined into 1, 2, and 3, in this case, the case of single-source SAR satellite three-dimensional positioning is assumed, but since the imaging modes and the incident angles of the three GF-3 images are different, the probability distribution models of the geometric positioning error sources are also different, and the method of the present disclosure is superior to the least square method. In addition, other combination conditions are multi-source SAR satellite three-dimensional positioning, and due to the fact that the probability distribution models of the geometric positioning error sources are greatly different, the probability distribution models of the imaging position observation values are also greatly different, and if the least square method is used for solving, the positioning result with the optimal precision cannot be obtained. At this time, the positioning accuracy based on the geometric entropy method can be obviously superior to that of the least square method, and the effectiveness of the method disclosed by the invention is proved.
TABLE 8 comparison of positioning accuracy based on geometric entropy method and least squares method
| Image combination | Least square method | Method based on geometric entropy |
| 1，2，3 | 18.28 | 18.22 |
| 1，3，4 | 19.99 | 5.87 |
| 1，2，4 | 18.37 | 7.07 |
| 1，2，3，4 | 16.14 | 4.46 |
In conclusion, the method for the multisource SAR satellite combined three-dimensional positioning based on the geometric entropy effectively improves the precision and the stability of the multisource SAR satellite combined three-dimensional positioning, and solves the problems of inaccuracy and instability in solution in the multisource SAR satellite combined three-dimensional positioning in the conventional method.
The above-mentioned embodiments are intended to illustrate the objects, aspects and advantages of the present disclosure in further detail, and it should be understood that the above-mentioned embodiments are only illustrative of the present disclosure and are not intended to limit the present disclosure, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present disclosure should be included in the scope of the present disclosure.
Claims (10)
1. A multisource SAR satellite combined three-dimensional positioning method based on geometric entropy is characterized by comprising the following steps:
acquiring SAR data of a target point of a multi-source SAR satellite imaging system;
establishing a probability distribution model of a geometric positioning error source of each SAR satellite according to a position error, a speed error and a slope distance error of the multi-source SAR satellite imaging system;
establishing an error probability distribution model of an imaging position observation value of each SAR satellite to a target point according to the SAR data and the probability distribution model of the geometric positioning error source of each SAR satellite;
based on a classical information theory, taking the objective real position of the target point as an information source, taking the multi-source SAR satellite imaging system as a channel, establishing a multi-source SAR satellite positioning geometric information entropy calculation model according to an error probability distribution model of the imaging position observation value of each SAR satellite to the target point, and deriving to obtain optimized parameters of multi-source SAR satellite positioning by taking the minimized geometric information entropy as a target function;
carrying out normalization processing on the traditional RD model, and constructing a normalized RD optimal positioning model according to the normalized RD model;
and calculating a final result of the multi-source SAR satellite combined three-dimensional positioning according to the normalized RD optimized positioning model and the optimized parameters of the multi-source SAR satellite positioning.
2. The multisource SAR satellite combined three-dimensional positioning method based on geometric entropy of claim 1, wherein the probability distribution model of the geometric positioning error source of each SAR satellite satisfies:
wherein ,ΔXS，ΔYS，ΔZSPosition errors of the SAR satellite in three directions of a geocentric earth-fixed coordinate system, namely delta VX，ΔVY，ΔVZRespectively are the speed errors of the SAR satellite in three directions of a geocentric coordinate system, wherein Delta R is the slant range error,
respectively the variance of the position error, the speed error and the slant range error of the SAR satellite.
3. The multisource SAR satellite combined three-dimensional positioning method based on geometric entropy of claim 1, wherein the establishing an error probability distribution model of an imaging position observation value of each SAR satellite to a target point according to the SAR data and the probability distribution model of the geometric positioning error source of each SAR satellite comprises:
and simulating to obtain an imaging real position according to the objective real position of the target point, wherein the imaging real position satisfies the following relation:
wherein ,
is the objective real position of the target point,
and
the SAR satellite position and speed at the time t respectively; f. ofDIs the doppler center frequency, λ, PRF, the radar-only wavelength, pulse repetition frequency and sampling frequency, respectively; r, c are the slope distance and speed of light, respectively, of the target point; rnearThe slope distance of the near place; t, tsRespectively corresponding azimuth time and SAR satellite imaging starting time of the target point; (x)0，y0) The real position of the target point is imaged for the SAR satellite, wherein,
fD、λ、PRF、fs、R、t、tsobtaining from the SAR data;
simulating to obtain an imaging position observation value according to the objective real position of the target point and the position error, the speed error and the slope distance error of the SAR satellite, wherein the imaging position observation value satisfies the following relations:
the SAR target point observation method comprises the following steps that (x, y) is an imaging position observation value of an SAR satellite to a target point, wherein x and y are an imaging distance coordinate observation value and an azimuth coordinate observation value of the SAR satellite to the target point respectively;
the delta R is a position error, a speed error and an inclined distance error of the SAR satellite respectively;
obtaining an error of an imaging position observation value according to the imaging real position and the imaging position observation value, wherein the error (x) of the imaging position observation valuee，ye) Satisfies the following conditions: (x)e，ye)＝(x，y)-(x0，y0)；
For each SAR satellite, sampling a position error, a speed error and a slant range error under a probability distribution model of a geometric positioning error source of the SAR satellite at corresponding azimuth time, and repeating the steps to obtain an error probability distribution model of an imaging position observation value of the SAR satellite to a target point, wherein the error probability distribution model satisfies the following conditions:
wherein ,xe and yeRespectively the error of the SAR satellite imaging distance to the coordinate observation value and the error of the azimuth coordinate observation value,
the variances of the observed value errors of the imaging positions in the distance direction and the azimuth direction of the imaging image are respectively.
4. The multisource SAR satellite combined three-dimensional positioning method based on geometric entropy of claim 1, wherein the establishing of a multisource SAR satellite positioning geometric information entropy calculation model according to an error probability distribution model of an observation value of an imaging position of each SAR satellite to a target point, and deriving to obtain optimized parameters of multisource SAR satellite positioning by taking a minimized geometric information entropy as a target function, comprises:
deducing to obtain the probability distribution of the imaging position observation value of the multisource SAR satellite imaging system to the target point according to the error probability distribution of the imaging position observation value of each SAR satellite to the target point;
establishing a multisource SAR satellite positioning geometric information entropy calculation model according to probability distribution of an imaging position observation value of a target point by the multisource SAR satellite imaging system;
and deducing to obtain the optimized parameters of the multisource SAR satellite positioning based on the multisource SAR satellite positioning geometric information entropy calculation model by taking the minimized geometric information entropy as a target function.
5. The multisource SAR satellite combined three-dimensional positioning method based on geometric entropy of claim 4, wherein the probability distribution of the multisource SAR satellite imaging system to the imaging position observation value of the target point satisfies the following relationship:
the multi-source SAR satellite imaging system is assumed to obey probability distribution of M different imaging position observation values for all observation samples of a target point respectively, and the sample capacity of the probability distribution obeying the M (M is 1, 2km(kM ═ k 1.., kM), then:
the distances obeying the probability distribution of the M imaging position observations satisfy to the coordinate observations:
the azimuthal coordinate observations obeying the probability distribution of the M imaging location observations satisfy:
wherein ,x1，x2，...，xMRespectively, a range-to-coordinate observation, y, obeying a probability distribution of the M imaging position observations1，y2...，yMRespectively are the azimuth coordinate observed values of the probability distribution of the M imaging position observed values, mu is the distance coordinate observed value or the mean value of the azimuth coordinate observed values of the M types of observation samples,
respectively the variance of the distance to coordinate observations of the class M observation samples,
and the variances of the azimuth coordinate observed values of the M types of observation samples are respectively.
6. The multi-source SAR satellite combined three-dimensional positioning method based on geometric entropy of claim 4, wherein the multi-source SAR satellite positioning geometric information entropy calculation model comprises a geometric information entropy function of a distance direction coordinate observation value and a geometric information entropy function of an orientation direction coordinate observation value, wherein:
the geometric information entropy function of the distance-direction coordinate observation value satisfies the following conditions:
wherein ,
a geometric entropy function of the distance to coordinate observations,
is to image a multi-source SAR satelliteDistance to true position x0M is the number of probability distributions of imaging position observations obeyed by the multi-source SAR satellite imaging system on all observation samples of a target point, Nkm(kM ═ k 1.., kM) is the distance to observation sample x in the probability distribution of the M (M ═ 1, 2.., M) imaging position observationsmThe capacity of (a); sigmaxmThe standard deviation of the distance to coordinate observed values of the mth type observed sample; p is a radical ofxmA weighting factor corresponding to the distance-direction coordinate observation value of the mth type observation sample;
the geometric information entropy function of the azimuth coordinate observation value satisfies the following conditions:
wherein ,
a geometric entropy function of the orientation coordinate observations,
is to the true position y of the imaging azimuth of the multi-source SAR satellite0M is the number of probability distributions of imaging position observations obeyed by the multi-source SAR satellite imaging system on all observation samples of a target point, Nkm(kM ═ k 1.., kM) is the azimuth observation sample y in the probability distribution of the M (M ═ 1, 2.., M) imaging position observationsmThe capacity of (a); sigmaymThe standard deviation of the azimuth coordinate observed value of the mth type observed sample is obtained; p is a radical ofymAnd the weighting factors are corresponding to the azimuth coordinate observed values of the m-th type observed samples.
7. The method for jointly three-dimensionally positioning multisource SAR satellites based on geometric entropy of claim 6, wherein the optimized parameters for multisource SAR satellite positioning comprise optimized parameters for range-wise coordinate observations and optimized parameters for azimuth-wise coordinate observations, wherein:
the optimized parameter of the range-wise coordinate observation value is a weight factor p corresponding to the range-wise coordinate observation value of the mth type observation samplexmWhich satisfies:
wherein ,pxmThe weight factor corresponding to the observation value of the range coordinate of the mth observation sample, M is the number of probability distribution of the observation value of the imaging position obeyed by the multisource SAR satellite imaging system to all observation samples of the target point, and N is the number of probability distribution of the observation value of the imaging position obeyed by the multisource SAR satellite imaging system to all observation samples of the target pointkm(kM ═ k 1.., kM) is the distance to observation sample x in the probability distribution of the M (M ═ 1, 2.., M) imaging position observationsmThe capacity of (a) is set to be,
the variance of the distance-to-coordinate observation value of the mth type observation sample;
the optimized parameter of the azimuth coordinate observation value is a weight factor p corresponding to the azimuth coordinate observation value of the mth type observation sampleymWhich satisfies:
wherein ,pymThe weight factor corresponding to the azimuth coordinate observation value of the mth type observation sample, M is the number of probability distribution of imaging position observation values obeyed by the multisource SAR satellite imaging system to all observation samples of a target point, and N is the number of probability distribution of imaging position observation values obeyed by the multisource SAR satellite imaging system to all observation samples of the target pointkm(kM ═ k 1.., kM) is the azimuth observation sample y in the probability distribution of the M (M ═ 1, 2.., M) imaging position observationsmThe capacity of (a) is set to be,
for azimuthal coordinate observations of class m observation samplesThe variance.
8. The multi-source SAR satellite combined three-dimensional positioning method based on geometric entropy as claimed in claim 1, wherein the normalizing process is performed on the traditional RD model, and a normalized RD optimized positioning model is constructed according to the normalized RD model, which includes:
carrying out normalization processing on the traditional RD model to obtain a normalized RD model of each SAR satellite;
and converting the normalized RD equation solution problem of each SAR satellite into an optimization problem with equation residual error minimum as an objective function, and constructing the normalized RD optimized positioning model.
9. The multisource SAR satellite combined three-dimensional positioning method based on geometric entropy of claim 8, wherein the normalized RD model of each SAR satellite satisfies the following relationship:
wherein (X, Y, Z) is the objective true position of the target point; (X)S，YS，ZS) For each SAR satellite's location; v ═ V (V)X，VY，VZ) The speed of each SAR satellite; the | V | is a modular length of the velocity vector of each SAR satellite; r, fDλ is the slant range of the target point, the radar doppler center frequency and the radar wavelength, respectively;
is SAR sensor squint angle;
the normalized RD optimized positioning model satisfies the following relationship:
wherein the amount of the (X,y, Z) is the objective real position of the target point; (X)Sm，YSm，ZSm) The position of the M (M ═ 1, 2, …, M) th SAR satellite; vm＝(VXm，VYm，VZm) Is the speed of the mth SAR satellite; i Vm| | is a modular length of the velocity vector of the mth SAR satellite; rm，fDmThe target point corresponding to the mth SAR satellite is the slant range and the radar Doppler center frequency respectively, and lambda is the radar wavelength.
10. The multi-source SAR satellite combined three-dimensional positioning method based on geometric entropy as claimed in claim 1, characterized in that the final result of the multi-source SAR satellite combined three-dimensional positioning satisfies the following relationship:
wherein ,pxm，pym(M is 1, 2, …, M) is a weighting factor corresponding to the distance coordinate observation value and the azimuth coordinate observation value of the mth type observation sample, respectively, (X, Y, Z) is an objective real position of the target point; (X)Sm，YSm，ZSm) Is the position of the mth SAR satellite; vm＝(VXm，VYm，VZm) Is the speed of the mth SAR satellite; i Vm| | is the velocity vector modulo length of the mth SAR satellite; rm，fDmThe target point corresponding to the mth SAR satellite is the slant range and the radar Doppler center frequency respectively, and lambda is the radar wavelength.
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