Space-based Radar Real-time Measurement Method and Device for High-dynamic Weak Space Targets

Abstract

The present invention provides a real-time measurement method and device for high-dynamic weak space targets by a space-based radar, belonging to the technical field of radar measurement. This method uses search parameters for maximum likelihood estimation to obtain target parameters. For the selection of search values of radial relative acceleration and jerk in the search parameters, according to the circular cross-section where the radar search sphere and the target position error sphere intersect, the upper and lower limits of the radial relative velocity value are determined; according to the constraint relationship between the radial relative velocity and the radial relative acceleration, the upper and lower limits of the radial relative velocity value are converted into a range of radial relative acceleration, and a search value of radial relative acceleration is selected from it; using the search values of relative distance, radial relative velocity, and radial relative acceleration, through calculation, the search value of radial relative jerk is uniquely determined. Compared with traditional methods, the present invention reduces the parameter search dimension, can significantly reduce the amount of computation, and can be realized in real time on a space-based platform.

Description

Technical Field

[0001] The present invention relates to the technical field of radar measurement, and particularly relates to a real-time precise measurement method and device for high-dynamic weak space targets by a space-based radar. Background Art

[0002] With the rapid development of space activities, radar measurement of space targets, as a data source for space situation awareness, has gradually received wide attention. Traditional ground-based radars are limited by viewing angles, weather, and the earth's curvature, and it is difficult to simultaneously meet the requirements for all-weather, large-scale, and high-precision monitoring of space targets. In this context, space-based space target measurement radars rely on space-based platforms and can break through the limitations of ground-based radar observations to provide real-time measurement data of space targets with all-time and high-precision.

[0003] However, under strong constraints on resources such as layout space, weight, power consumption, and computing power in space-based platforms, there are many challenges in achieving high-precision measurement of large field-of-view and high-dynamic targets: Challenge 1, under the condition of limited power aperture of space-based radars, the power of radar echo signals of distant targets is weak and the signal-to-noise ratio is low, and long-time coherent integration is required to achieve target detection; Challenge 2, although prior information on the position of the target star can be obtained through the SDP / SGP (Simplified Deep-space Perturbations / Simplified Deep-space Perturbations) orbital model based on TLE (Two Line Element), this method simplifies the earth's gravitational field and atmospheric model, and there is a large error between the predicted position of the target star and the actual position, and this error will gradually accumulate during a large amount of calculations and long-time simulations.

[0004] Therefore, after the orbital parameter prediction by the ground observation station, the traditional space target measurement method based on maximum likelihood estimation still needs to perform multi-dimensional parameter searches such as distance, speed, and acceleration, with high computational complexity. Typical methods include Radon-FrFT, Radon-LVD, Radon-Fourier Transform, Radon linear canonical transform, etc. For example, the GRFT algorithm proposed in the paper "Radon-Fourier transform for radar target detection (I): Generalized Doppler Filter Bank" published by Xu Jia in IEEE Transactions on Aerospace and Electronic Systems in 2011 projects the received echo signal into the parameter space composed of the three to form a "multi-dimensional focused image" of the target when dealing with uniformly accelerating moving targets, and then jointly compensates for the range migration and Doppler spread of the target envelope to obtain accurate target parameter values. At the same time, for high-dynamic moving targets approaching from different orbital planes, the GRFT algorithm can also expand the jerk dimension on the basis of the traditional three-dimensional parameter search of distance, speed, and acceleration to perform a four-dimensional parameter search to match the more complex application scenarios of target motion.

[0005] In summary, in order to perform real-time precise measurement of the range and speed parameters of high-dynamic space targets, the traditional maximum likelihood estimation algorithm needs to perform parameter searches from multiple dimensions such as distance, speed, acceleration, and jerk. However, while improving the parameter estimation performance, the computational complexity of this algorithm has increased significantly. Considering the computing power constraints of the space-based radar system, it is difficult to implement this algorithm in real time on the space-based platform.

[0006] Therefore, on the basis of comprehensively considering factors such as the computational complexity and computational overhead of the algorithm, it is of great significance to study a low-complexity and high-precision parameter estimation algorithm adapted to the computing power of the space-based radar. Summary of the Invention

[0007] In view of this, the present invention provides a space-based radar real-time precise measurement method and device for high-dynamic weak space targets, which can achieve real-time precise measurement with low computing power.

[0008] In order to solve the above technical problems, the present invention is implemented as follows.

[0009] A space-based radar real-time measurement method for high-dynamic weak space targets, comprising:

[0010] According to the orbital parameters of our star and the target star, determine the prior information including the relative distance between the two stars and the position of the target star;

[0011] Select search parameters; among them, when selecting the search value of the radial relative acceleration and the search value of the radial relative jerk , according to the relative distance , the selected relative distance search value , and the positions of our star and the target star, determine the radar search sphere and the target position error sphere; determine the upper and lower limits of the radial relative velocity within the circular cross-section formed by the intersection of the radar search sphere and the target position error sphere; according to the constraint relationship between the radial relative velocity and the radial relative acceleration, convert the upper and lower limits of the radial relative velocity into the corresponding radial relative acceleration range, and select the radial relative acceleration search value from the radial relative acceleration range ; use the calculation relationship between the relative distance, the radial relative velocity, the radial relative acceleration and the radial relative jerk to calculate the radial relative jerk search value in the current search parameters ;

[0012] Use the search parameters to perform maximum likelihood estimation to obtain the target parameters.

[0013] Preferably, in the step of selecting search parameters, when selecting the relative distance search value , according to the relative distance between the two stars and the distance error , determine the relative distance search range; select the relative distance search value from the relative distance search range.

[0014] Preferably, in the step of selecting search parameters, when selecting the relative radial velocity search value , select the relative radial velocity search value from the set relative radial velocity search range.

[0015] Preferably, the determination of the upper and lower limits of the radial relative velocity within the circular cross-section formed by the intersection of the radar search sphere and the target position error sphere is as follows:

[0016] The center coordinates of the circular cross-section formed by the intersection of the radar search sphere and the target position error sphere are ;

[0017] Determine two orthogonal unit vectors and in the circular cross-section;

[0018] Calculate the variable ; where is the radius of the circular cross-section, is the position coordinate of our star in the geocentric coordinate system, is the prior value of the relative velocity determined by the orbital parameters;

[0019] The lower limit of the radial relative velocity value is calculated as follows: Determine whether is satisfied. If so, the lower limit value of the radial relative velocity is ; otherwise, ;

[0020] The upper limit of the radial relative velocity value is calculated as follows: Determine whether is satisfied. If so, the upper limit value of the radial relative velocity is ; otherwise is .

[0021] Preferably, according to the constraint relationship between the radial relative velocity and the radial relative acceleration, the upper and lower limits of the radial relative velocity are converted into the corresponding radial relative acceleration range as follows:

[0022] Based on the prior value of the relative velocity determined by the orbital parameters and the upper and lower limits of the radial relative velocity, calculate the upper limit and the lower limit of the tangential relative velocity:

[0023]

[0024] In the formula and are the upper limit of the radial relative velocity value and the lower limit of the radial relative velocity value determined within the circular cross-section formed by the intersection of the radar search sphere and the target position error sphere, respectively;

[0025] According to the relationship between the radial relative acceleration and the tangential relative velocity, determine the radial relative acceleration range as follows:

[0026]

[0027] In the formula is the relative distance search value in this set of search parameters;

[0028] Sample multiple acceleration search values from the radial relative acceleration range , corresponding to the same relative distance search value .

[0029] Preferably, the radial relative jerk search value in the current search parameters is calculated by using the calculation relationships among the relative distance, the radial relative velocity, the radial relative acceleration, and the radial relative jerk. It is:

[0030] The radial relative jerk search value is calculated by using the following formula :

[0031]

[0032] In the formula, is the prior value of the relative velocity determined from the orbital parameters, is the relative acceleration of our satellite and the target satellite obtained by differentiating the modulus value of the prior value of the relative velocity .

[0033] The present invention also discloses a space-based radar real-time measurement device for high-dynamic weak space targets, and the device includes:

[0034] An orbital parameter acquisition and calculation module, configured to determine the prior information including the relative distance between the two satellites and the position of the target satellite according to the orbital parameters of our satellite and the target satellite;

[0035] A distance search value determination module, configured to determine the relative distance search value ;

[0036] A velocity search value determination module, configured to determine the radial relative velocity search value ;

[0037] An acceleration search value determination module, configured to determine the radar search sphere and the target position error sphere according to the relative distance , the selected relative distance search value , the positions of our satellite and the target satellite; determine the upper and lower limits of the radial relative velocity value within the circular cross-section formed by the intersection of the radar search sphere and the target position error sphere; convert the upper and lower limits of the radial relative velocity value into the corresponding radial relative acceleration range according to the constraint relationship between the radial relative velocity and the radial relative acceleration, and select the radial relative acceleration search value from the radial relative acceleration range;

[0038] A jerk search value determination module, configured to calculate the radial relative jerk search value in the current search parameters by using the calculation relationships among the relative distance, the radial relative velocity, the radial relative acceleration, and the radial relative jerk ;

[0039] A maximum likelihood estimation module, which performs maximum likelihood estimation by using the determined search parameters to obtain the target parameters.

[0040] Preferably, the relative distance search value determining module determines a relative distance search value in the following manner: Based on the relative distance between two stars and the distance error , a relative distance search range is determined; a relative distance search value is selected from the relative distance search range;

[0041] The radial relative velocity search value determining module determines a radial relative velocity search value in the following manner: A relative radial velocity search value is selected from a set relative radial velocity search range.

[0042] Preferably, the acceleration search value determining module includes a radial relative velocity upper and lower limit calculation unit and a radial relative acceleration range calculation unit;

[0043] The radial relative velocity upper and lower limit conversion unit, based on the relative distance , the selected relative distance search value , the positions of our satellite and the target satellite, determines a radar search sphere and a target position error sphere; the center coordinates of the circular cross-section formed by the intersection of the radar search sphere and the target position error sphere are ; determines two orthogonal unit vectors and in the circular cross-section; calculates a variable ; where is the radius of the circular cross-section, is the position coordinate of our satellite in the geocentric coordinate system, is the prior value of the relative velocity determined from the orbital parameters;

[0044] Judges whether is satisfied. If so, the radial relative velocity lower limit value is ; otherwise, ; judges whether is satisfied. If so, the radial relative velocity upper limit value is ; otherwise is ;

[0045] The radial relative acceleration range calculation unit is used to calculate the upper limit and the lower limit of the tangential relative velocity value based on the prior value of the relative velocity and the upper and lower limits of the radial relative velocity value:

[0046]

[0047] In the formula and are respectively the upper limit and the lower limit of the radial relative velocity determined within the circular cross-section formed by the intersection of the radar search sphere and the target position error sphere;

[0048] Determine the radial relative acceleration range according to the relationship between the radial relative acceleration and the tangential relative velocity as:

[0049]

[0050] In the formula is the relative distance search value in this group of search parameters;

[0051] From the radial relative acceleration range Sample multiple acceleration search values corresponding to the same relative distance search value .

[0052] Preferably, the jerk search value determination module calculates the radial relative jerk search value using the following formula :

[0053]

[0054] In the formula, is the prior value of the relative velocity determined by the orbital parameters, is the relative acceleration of our satellite and the target satellite obtained by differentiating the modulus value of the prior value of the relative velocity .

[0055] Beneficial effects:

[0056] Compared with the traditional maximum likelihood estimation algorithm, a precise ranging and velocity measurement method based on the search of four-dimensional parameters of distance, velocity, acceleration, and jerk, the present invention considers various constraint conditions of the space-based platform and designs a high-dynamic weak space target low-computing power real-time precise measurement method under strong computing power constraints.

[0057] This scheme first proves that in the measurement coordinate system, there is a quantitative mapping relationship between the target relative acceleration and the relative distance and relative velocity, and the jerk can be approximately determined by the relative distance and acceleration.

[0058] Based on the above proof results, in the process of parameter search of the present invention, for the acceleration dimension, the acceleration distribution at different search distances is calculated in real time through the derived relationship, thereby reducing the search range, rather than directly adopting the given acceleration search range; for the jerk dimension, the present invention directly obtains it according to the calculation formula without parameter search. It can be seen that the present invention reduces the parameter search dimension by reducing the search range of the acceleration dimension and replacing the search with the calculation of the jerk dimension, significantly reducing the amount of computation and being able to be realized in real time on the space-based platform. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a schematic diagram of the relative measurement coordinate system.

[0060] Figure 2 It is a schematic diagram of radar search and error sphere in space.

[0061] Figure 3 It is a flowchart of the space-based radar real-time measurement method for high-dynamic weak space targets in the embodiment of the present invention.

[0062] Figure 4 It is a schematic diagram of the space-based radar real-time measurement device for high-dynamic weak space targets in the embodiment of the present invention.

[0063] Figure 5 It is a schematic diagram of the acceleration search range before and after dimension reduction.

[0064] Figure 6 It is a schematic diagram of the derived jerk range. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0065] The present invention will be described in detail below with reference to the accompanying drawings and by way of examples.

[0066] First, in the embodiment of the present invention, the relative motion model of the target is derived first to prove that there is a quantitative mapping relationship between the relative acceleration of the target, the relative distance, and the relative velocity; then the relationship that the jerk can be approximately determined by the relative distance and the acceleration is determined. The dimension reduction of parameter search is carried out according to the above relationship, which can effectively reduce the amount of computation.

[0067] The derivation process of the present invention includes the following aspects:

[0068] (1) First, according to the orbital parameters of our satellite and the target satellite, the radial acceleration constraint relationship is determined.

[0069] A relative measurement coordinate system of the target satellite is established. As Figure 1 shown, considering the motion state of two satellites approaching each other in space, an observation system is established with our satellite as the center. Let the relative distance between our satellite and the target satellite be , and the relative velocity be . Projecting respectively in the radial and tangential directions gives the radial relative velocity (hereinafter simply referred to as the radial velocity ), and the tangential relative velocity (hereinafter simply referred to as the tangential velocity ), where the radial direction is from our star to the target star. Similarly, the relative acceleration can be decomposed to obtain the radial relative acceleration (hereinafter simply referred to as the radial acceleration ) and the tangential relative acceleration (referred to as the tangential acceleration ), where the relationship between the radial acceleration and the tangential velocity can be expressed as:

[0070] (1)

[0071] As can be seen from equation (1), the radial acceleration can be uniquely determined by the tangential velocity and the relative distance , and the tangential velocity and the radial velocity satisfy relationship. Therefore, the search range of the radial acceleration at a certain search distance can be determined by solving the value range of the radial velocity.

[0072] (2) Determine the constraint relationship of the radial jerk

[0073] Based on equation (1), differentiating the radial acceleration gives the expression of the radial jerk as follows:

[0074] (2)

[0075] Expanding the above equation gives

[0076] (3)

[0077] And there is

[0078] (4)

[0079] Substituting equation (4) into equation (3), we get:

[0080] (5)

[0081] Also, because

[0082] (6)

[0083] Then substituting equations (5) and (6) into equation (2), we obtain the radial jerk The expression is:

[0084] (7)

[0085] where represents the differential of the relative velocity between the target star and our star, i.e., the relative acceleration. Here, the prior value of the relative velocity obtained by calculating based on the orbital parameters is adopted.

[0086] (3) Analyze the acceleration and the jerk correspondence.

[0087] Assume there is an acceleration at a certain determined point. According to Equation (1), it can be known that at this point is also determined. According to the following velocity vector relationship:

[0088] (8)

[0089] It can also be known that is also determined. Substituting Equations (1) and (8) into Equation (7) gives the expression of the radial jerk :

[0090] (9)

[0091] Considering the first term in the above formula , it is not difficult to find that for the known velocity determined by the orbital parameters and the determined unknown relative acceleration <000033z>, both are independent of the relative distance . Then, on the surface intercepted by the target prior position error sphere on the sphere with a radius of , Figure 2 is the set relative distance error. As shown in , the corresponding to each point is equal. Therefore, according to Equation (9), at each search value of the acceleration, only one search value of the jerk needs to be searched, thereby realizing search dimensionality reduction.

[0092] In practical applications, the orbital parameters of the target star can be obtained through ground measurements and other means, and then the prior information of the relative distance and relative velocity between the two stars can be obtained. However, due to the existence of orbital parameter errors, the prior information can only determine the approximate position of the target star. And the possible positions of the target star form a sphere in space with the possible position of the target star as the center and the distance error An error sphere with a radius is called the target position error sphere. During the process of measuring the distance and speed parameters of the target star by the space-based radar on our star, with the position of our star as the center and the relative distance search value as the radius, a search radar search sphere can be obtained. And because the distance search value is selected equidistantly within the relative distance search range, multiple radar search spheres are obtained, which are also called radar equidistant stepped projection spherical surfaces. The cross-section determined by the intersection of the radar search sphere and the target position error sphere is a circle. To reduce the computational complexity, it is necessary to calculate the dynamic range of the radial velocity changing with distance in real time.

[0093] As Figure 2 shown, the position coordinates of our star in the geocentric coordinate system, the relative velocity , for the intersecting circle: the center position coordinates , the radius is , and the normal vector of the plane where it is located , then the target position may be any point on the circle . The problem of the value range of the radial velocity can be transformed into solving the maximum and minimum values of the modulus of the inner product (the radial projection of the relative velocity ).

[0094] Using two orthogonal unit vectors and within the circular cross-section, any point Q on the circle can be parameterized in polar coordinates as:

[0095] (10)

[0096] In the formula, represents the center coordinates, are the polar radius and azimuth angle parameters in polar coordinates.

[0097] The radial velocity (the projection of the relative velocity in the direction ) can be expressed as:

[0098] (11)

[0099] In the formula , , . To ensure that the radial velocity takes the maximum and minimum values, when calculating the values of A and B, the maximum value, that is, the radius R of the circular cross-section, needs to be substituted.

[0100] Since , analyzing the above formula shows that:

[0101] For the minimum radial velocity, if , then the lower limit of the radial velocity is ; if , then the lower limit of the radial velocity is 0.

[0102] For the maximum radial velocity, if , then the upper limit of the radial velocity is ; if , then the upper limit of the radial velocity is .

[0103] It should be noted that the selected upper and lower limits of the radial velocity here are only intermediate quantities for calculating the range of the radial acceleration and do not serve as the range for selecting the search value of the radial velocity.

[0104] Based on the above analysis in (1)-(4), the implementation process of the space-based radar real-time measurement method for high-dynamic weak space targets of the present invention will be described in detail below in combination with Figure 3 . As shown in Figure 3 , the method includes the following steps:

[0105] Step 1: Obtain the orbital parameters of our satellite and the target satellite, and use the orbital parameters to determine the relative distance , the prior value of the relative velocity and the prior information of the position of the target satellite.

[0106] Step 2: Select the relative distance search value .

[0107] In this embodiment, according to the relative distance between the two satellites and the distance error , determine the relative distance search range ; select the relative distance search value from this relative distance search range.

[0108] Step 3: Select the relative radial velocity search value .

[0109] In this embodiment, set the relative radial velocity search range . The search methods for the relative distance and radial velocity in Step 2 and Step 3 are the same as those in the prior art. Therefore, the number of searches for the relative distance and radial velocity in Table 2 of the following examples is the same as that of the traditional maximum likelihood algorithm.

[0110] Step 4: Select the relative radial acceleration search value .

[0111] In this step, based on the relative distance , the selected relative distance search value and the positions of our satellite and the target satellite, determine the radar search sphere and the target position error sphere; determine the upper and lower limits of the radial velocity within the circular cross-section formed by the intersection of the radar search sphere and the target position error sphere; according to the constraint relationship between the radial velocity and the radial acceleration, convert the upper and lower limits of the radial velocity into the corresponding radial acceleration range, and select the radial acceleration search value from the radial acceleration range .

[0112] The specific implementation process of this step 4 includes the following sub-steps:

[0113] Step 41: Determine the radar equidistant stepped projection spherical surface with the coordinates of our satellite as the center and the relative distance search value as the radius; determine the radar search sphere with the coordinates of the target satellite determined based on the orbital parameters as the center and the distance error as the radius; the radar equidistant stepped projection spherical surface and the radar search sphere intersect to form a circular cross-section. The center coordinates of the circular cross-section are .

[0114] Step 42: Determine two orthogonal unit vectors and in the circular cross-section.

[0115] One way to obtain the orthogonal unit vectors and is as follows: The orthogonal unit vector is obtained by cross-multiplying the normal vector with the unit vector, and then cross-multiplying with to obtain .

[0116] Step 43: Calculate the variable ; in the formula, to ensure that the radial velocity reaches the maximum and minimum values, substitute the maximum value, that is, the radius of the circular cross-section, and substitute the prior value of the relative velocity determined from the orbital parameters.

[0117] Step 44: Calculate the upper and lower limits of the radial velocity.

[0118] For the lower limit of the radial velocity: Determine whether it satisfies , if so, the lower limit value of the radial velocity is ; otherwise, the lower limit value of the radial velocity .

[0119] For the upper limit of the radial velocity: Determine whether it satisfies , if so, the upper limit value of the radial velocity is ; otherwise, the upper limit value of the radial velocity is .

[0120] The upper and lower limits obtained in this step and are only used for calculating the radial acceleration range in Step 45 and are not used as the relative radial velocity search range adopted in Step 3.

[0121] Step 45: Using the constraint relationship between the radial velocity and the radial acceleration, convert the upper and lower limit values of the radial velocity into the corresponding radial acceleration range .

[0122] In this step, due to the constraint relationship between the tangential velocity and the radial velocity, when the radial velocity reaches the maximum, the tangential velocity reaches the minimum, and when the radial velocity reaches the minimum, the tangential velocity reaches the maximum, that is:

[0123] (12)

[0124] In the above formula, the prior value of the relative velocity determined by the orbital parameters is adopted. and the upper and lower limit values of the radial velocity calculated in Step 44 are adopted.

[0125] According to the constraint relationship of Equation (1), and at the same time, in the formula r take the relative distance search value , the maximum value and the minimum value of the radial acceleration search range can be obtained:

[0126] (13)

[0127] It can be seen from this that when searching for an object with a relative distance of , the radial acceleration search range is .

[0128] Sample multiple radial acceleration search values from the radial acceleration range , corresponding to the same relative distance search value . When the sampling step size is the same, the longer , the more radial acceleration search values are selected. If There is only one. Therefore, in Table 2 of the following examples, the number of acceleration searches is 1 - 336, which is a variable quantity.

[0129] Step 5: Select the search value of radial jerk .

[0130] In this step, using the calculation relationships among the relative distance, radial velocity, radial acceleration, and radial jerk, calculate the search value of radial jerk in the current search parameters. .

[0131] Specifically, as can be seen from Equation (9) above, the radial jerk can be uniquely determined by the relative distance , radial velocity , and radial acceleration . Therefore, when the relative distance search value , radial velocity search value , and radial acceleration search value have been determined in Steps 2 - 4, the radial jerk search value can be directly calculated from Equation (9) without searching within the range given by the jerk, thereby reducing the parameter search dimension.

[0132] Specifically, use the following formula to calculate the search value of radial jerk :

[0133]

[0134] In the formula, adopts the prior value of relative velocity determined by the orbital parameters, and is obtained by differentiating the modulus value of the velocity prior value , which is the relative acceleration between our satellite and the target satellite.

[0135] Step 6: Use the search parameters to perform maximum likelihood estimation to obtain the target parameters that maximize the coherent accumulation of the echo signal.

[0136] After the selection in Steps 2 - 5, a series of search parameters are determined. In this step, maximum likelihood estimation is performed based on the search parameters. The principle of the maximum likelihood estimation algorithm is as follows:

[0137] Assume that the transmitted signal in the n th period is , where is the slow time, is the pulse period, is the fast time, and the target echo signal can be modeled as:

[0138] (14)

[0139] In the formula represents the echo signal amplitude (including target reflection characteristics), τ represents the time delay (related to the target distance R), represents noise (usually assumed to be additive white Gaussian noise).

[0140] Performing coherent integration on the echo signal, the result of coherent integration is used as the likelihood function, which can be expressed as:

[0141] (15)

[0142] In the formula , is the speed of light, N is the number of coherent integrations, is the phase compensation function for realizing pulse coherent integration. respectively represent the relative distance, radial velocity, radial acceleration, and radial jerk. This formula (15) is a general formula. For simplicity, the parameter has no subscript.

[0143] The parameter estimates that maximize can be found according to the likelihood function, and are expressed as follows:

[0144] (16)

[0145] In the formula are the estimated results of the relative distance, radial velocity, radial acceleration, and radial jerk.

[0146] The maximum likelihood estimation only provides a theoretical framework for parameter estimation through model matching. Taking the GRFT (Generalized Radon-Fourier Transform) algorithm as an example, the distance and velocity measurement method for high-dynamic space targets is introduced. According to the GRFT algorithm, the third-order GRFT expression can be obtained as:

[0147] (17)

[0148] where is the result after coherent integration of the echo signal by GRFT, , are the search parameters determined in the above steps, . is the wavelength.

[0149] The discrete expression of formula (17) is:

[0150] (18)

[0151] Wherein is the discrete search serial number, is the echo signal after pulse compression, , is the sampling frequency, is the rounding function.

[0152] It can be seen from Equation (18) that when the search distance in the discrete domain, radial velocity radial acceleration and radial jerk are respectively equal to the true relative distance of the target, radial velocity radial acceleration and radial jerk of the target, the energy of each echo pulse within the coherent integration time can be aggregated, thereby achieving coherent integration and finally obtaining the target parameters, and the target parameters are mainly range and velocity.

[0153] In the parameter search process of the present invention, for the acceleration dimension, the acceleration distribution at different search distances can be calculated in real time according to the conclusions deduced from Formulas (11) to (13), thereby reducing the search range; for the jerk, it can be directly obtained according to Formula (9) without parameter search. It can be seen that the present invention reduces the parameter search dimension compared with the traditional method, can significantly reduce the computational amount, and can be realized in real time on the space-based platform.

[0154] Based on the above method, the present invention further provides a space-based radar real-time measurement device for high-dynamic weak space targets, as Figure 4 shown, the device includes: an orbital parameter acquisition and calculation module, a range search value determination module, a velocity search value determination module, an acceleration search value determination module, a jerk search value determination module, and a maximum likelihood estimation module. Wherein,

[0155] The orbital parameter acquisition and calculation module is used to determine the relative distance between the two satellites, relative velocity and the prior information of the target satellite position according to the orbital parameters of our satellite and the target satellite.

[0156] The range search value determination module is used to determine the relative range search value .

[0157] The velocity search value determination module is used to determine the radial velocity search value .

[0158] The acceleration search value determination module is used to determine according to the relative distance , the selected relative distance search value , the positions of our satellite and the target satellite, determine the radar search sphere and the target position error sphere; determine the upper and lower limits of the radial velocity within the circular cross-section formed by the intersection of the radar search sphere and the target position error sphere; according to the constraint relationship between the radial velocity and the radial acceleration, convert the upper and lower limits of the radial velocity into the corresponding radial acceleration range, and select the radial acceleration search value from the radial acceleration range .

[0159] The jerk search value determination module is used to calculate the radial jerk search value in the current search parameters by using the calculation relationship between the relative distance, radial velocity, radial acceleration and radial jerk .

[0160] The maximum likelihood estimation module uses the determined search parameters to perform maximum likelihood estimation to obtain the target parameters that maximize the coherent accumulation of the echo signal

[0161] Among them, the distance search value determination module determines the relative distance search value in the following way: according to the relative distance between the two satellites and the distance error , determine the relative distance search range; select the relative distance search value from the relative distance search range .

[0162] The velocity search value determination module determines the radial velocity search value in the following way: select the relative radial velocity search value from the set relative radial velocity search range .

[0163] In a preferred embodiment, the acceleration search value determination module includes a radial velocity upper and lower limit calculation unit and a radial acceleration range calculation unit

[0164] The radial velocity upper and lower limit conversion unit, according to the relative distance , the selected relative distance search value , the positions of our satellite and the target satellite, determine the radar search sphere and the target position error sphere. The center coordinates of the circular cross-section formed by the intersection of the radar search sphere and the target position error sphere are ; determine two orthogonal unit vectors and in the circular cross-section; calculate the variable ; where is the radius of the circular cross-section, is the position coordinate of our satellite in the geocentric coordinate system, is the prior value of the relative velocity determined from the orbital parameters

[0165] Determine whether it meets , if so, the lower limit value of the radial velocity is ; otherwise ; Determine whether it meets , if so, the upper limit value of the radial velocity is ; otherwise is ;

[0166] The radial acceleration range calculation unit is used to calculate the upper limit and the lower limit of the tangential relative velocity based on the prior value of the relative velocity determined by the orbital parameters :

[0167]

[0168] In the formula and are respectively the upper limit and the lower limit of the radial velocity value determined within the circular cross-section formed by the intersection of the radar search sphere and the target position error sphere;

[0169] Determine the radial acceleration range according to the relationship between the radial acceleration and the tangential relative velocity as:

[0170]

[0171] In the formula is the relative distance search value in this set of search parameters;

[0172] Sample multiple acceleration search values from the radial acceleration range , corresponding to the same relative distance search value .

[0173] In a preferred embodiment, the jerk search value determination module calculates the radial jerk search value using the following formula :

[0174]

[0175] In the formula, is the prior value of the relative velocity determined by the orbital parameters, is the relative acceleration of the satellite and the target star obtained by differentiating the modulus value of the prior value of the relative velocity .

[0176] The following gives a specific example to describe the solution and effect of the present invention in detail.

[0177] In this embodiment, our satellite approaches the target satellite with an orbital inclination, and measures the relative distance and velocity parameters between the two satellites. The specific simulation parameters are shown in Table 1 below:

[0178] Table 1

[0179]

[0180] First, through the guidance of orbital parameters, the prior information of the relative distance between the two satellites is obtained as 50 km, and the distance error is 5 km. Then the possible positions of the target satellite form a target position error sphere in space with a center distance of 50 km from our satellite and a radius of 5 km.

[0181] Using the present invention, by calculating in real time the cross-sectional geometric parameters of the radar equidistant stepped projection sphere and the target position error sphere, the dynamic error range of the acceleration varying with the distance is obtained, and through the derived jerk constraint relationship, the jerk can be obtained without searching. The comparison of the search ranges of the acceleration parameters before and after dimensionality reduction is as Figure 5 shown. The search range of the traditional GRFT algorithm is the area enclosed by the dashed line; the search range after dimensionality reduction by the present invention is the area enclosed by the solid line in the figure. The value ranges of the jerk parameters obtained before and after dimensionality reduction are as Figure 6 shown.

[0182] Using the parameters shown in Table 1 above, the operation amounts of the traditional maximum likelihood estimation algorithm and the dimensionality reduction search algorithm are calculated respectively (the operation amount is measured by the number of real number multiplications), and the results shown in Table 2 below are obtained.

[0183] Table 2

[0184]

[0185] From the comparison chart of the simulated acceleration and jerk search ranges and the fact that the total operation amount in Table 2 above is reduced by 92 times, it is concluded that the dimensionality reduction GRFT parameter search method proposed by the present invention can significantly reduce the operation amount and can realize high-precision distance and velocity parameter measurement in real time on a space-based platform with limited computing power.

[0186] The above specific embodiments only describe the design principle of the present invention. The shapes and names of the components in this description can be different and are not limited. Therefore, those skilled in the art of the present invention can modify or equivalently replace the technical solutions recorded in the foregoing embodiments; and these modifications and replacements do not depart from the gist and technical solutions of the present invention, and shall all fall within the protection scope of the present invention.

Claims

1. A real-time measurement method for high-dynamic weak space targets by space-based radar, characterized in that, Including: Determine the prior information including the relative distance between the two stars and the position of the target star according to the orbital parameters of our star and the target star ; Select search parameters; among them, select the search value of the radial relative acceleration and the search value of the radial relative jerk When, according to the relative distance , the selected relative distance search value and the positions of our satellite and the target satellite, determine the radar search sphere and the target position error sphere; determine the upper and lower limits of the radial relative velocity value within the circular cross-section formed by the intersection of the radar search sphere and the target position error sphere; according to the constraint relationship between the radial relative velocity and the radial relative acceleration, convert the upper and lower limits of the radial relative velocity value into the corresponding radial relative acceleration range, and select the radial relative acceleration search value from the radial relative acceleration range ; use the calculation relationships among the relative distance, the radial relative velocity, the radial relative acceleration, and the radial relative jerk to calculate the radial relative jerk search value in the current search parameters ; Performing maximum likelihood estimation using search parameters to obtain target parameters.

2. The real-time measurement method of the space-based radar for high-dynamic weak space targets according to claim 1, characterized in that In the step of selecting search parameters, when selecting the relative distance search value in the search parameters , according to the relative distance between two stars and the distance error , determine the relative distance search range; select the relative distance search value from the relative distance search range .

3. The space-based radar real-time measurement method for high-dynamic weak space targets as described in claim 1, characterized in that In the step of selecting search parameters, when selecting the relative radial velocity search value in the search parameters , select the relative radial velocity search value from the set relative radial velocity search range .

4. The real-time measurement method of the space-based radar for high-dynamic weak space targets according to claim 1, characterized in that, Determining the upper and lower limits of the radial relative velocity value within the circular cross-section formed by the intersection of the radar search sphere and the target position error sphere as: The center coordinates of the circular cross-section formed by the intersection of the radar search sphere and the target position error sphere are ; Determine two orthogonal unit vectors in the circular cross-section and ; Calculation variable ; where is the radius of the circular cross-section, is the position coordinate of our star in the geocentric coordinate system, is the prior value of the relative velocity determined from the orbital parameters; The lower limit of the calculated radial relative velocity value is: Determine whether it satisfies , if so, the lower limit value of the radial relative velocity is ; Otherwise, ; The upper limit of the calculated radial relative velocity value is: Determine whether it satisfies , if so, the upper limit value of the radial relative velocity is ; otherwise is .

5. The real-time measurement method of the high-dynamic weak space target space-based radar according to claim 1, characterized in that, According to the constraint relationship between the radial relative velocity and the radial relative acceleration, converting the upper and lower limits of the radial relative velocity value into the corresponding radial relative acceleration range as: Based on the prior value of the relative velocity determined from the orbital parameters and the upper and lower limits of the radial relative velocity value, calculate the upper limit of the tangential relative velocity value and the lower limit : In the formula and are respectively the upper limit and the lower limit of the radial relative velocity determined within the circular cross-section formed by the intersection of the radar search sphere and the target position error sphere; Determine the range of the radial relative acceleration according to the relationship between the radial relative acceleration and the tangential relative velocity as follows: In the formula is the relative distance search value in this group of search parameters; Sample multiple acceleration search values from the radial relative acceleration range and corresponding to the same relative distance search value . .

6. The space-based radar real-time measurement method for high-dynamic weak space targets as claimed in claim 1, wherein Calculating the search value of the relative radial jerk in the current search parameters by using the calculation relationships among the relative distance, the relative radial velocity, the relative radial acceleration, and the relative radial jerk is as follows: The radial relative jerk search value is calculated using the following formula :[[]]END]] In the formula, is the prior value of the relative velocity determined by the orbital parameters, is the relative acceleration of our satellite and the target satellite obtained by differentiating the modulus value of the prior value of the relative velocity.

7. A space-based radar real-time measurement device for high-dynamic weak space targets, characterized in that The device includes: An orbital parameter acquisition and calculation module, which is used to determine the prior information including the relative distance between two satellites and the position of the target satellite according to the orbital parameters of our satellite and the target satellite. and the position of the target satellite; A distance search value determination module for determining a relative distance search value ; A radial relative velocity search value determination module for determining a radial relative velocity search value ; An acceleration search value determination module, configured to determine a radar search sphere and a target position error sphere according to the relative distance , the selected relative distance search value and the positions of our satellite and the target star; determine the upper and lower limits of the radial relative velocity value within the circular cross-section formed by the intersection of the radar search sphere and the target position error sphere; convert the upper and lower limits of the radial relative velocity value into the corresponding radial relative acceleration range according to the constraint relationship between the radial relative velocity and the radial relative acceleration, and select a radial relative acceleration search value from the radial relative acceleration range ; The jerk search value determination module is used to calculate the radial relative jerk search value in the current search parameters by using the calculation relationships among the relative distance, the radial relative velocity, the radial relative acceleration, and the radial relative jerk ; The maximum likelihood estimation module uses the determined search parameters to perform maximum likelihood estimation and obtain the target parameters.

8. The space-based radar real-time measurement device for high-dynamic weak space targets according to claim 7, characterized in that The relative distance search value is determined by the distance search value determination module in the following manner: based on the relative distance between two stars and the distance error ; a relative distance search value is selected from the relative distance search range The speed search value determination module determines the radial relative speed search value in the following manner: selecting the relative radial speed search value from the set relative radial speed search range .

9. The space-based radar real-time measurement device for high-dynamic weak space targets according to claim 7, characterized in that, The acceleration search value determination module includes a radial relative velocity upper and lower limit calculation unit and a radial relative acceleration range calculation unit; The upper and lower limit conversion unit of the radial relative velocity determines a radar search sphere and a target position error sphere according to the relative distance , the selected relative distance search value and the positions of our satellite and the target satellite The center coordinates of the circular cross-section formed by the intersection of the radar search sphere and the target position error sphere are ; Determine two orthogonal unit vectors in the circular cross-section and ; Calculation variable ; where is the radius of the circular cross-section, is the position coordinate of our star in the geocentric coordinate system, is the prior value of the relative velocity determined from the orbital parameters; Determine whether it meets , if so, the lower limit value of the radial relative velocity is ; Otherwise, ; Determine whether it meets , if so, the upper limit value of the radial relative velocity is ; Otherwise For ; The radial relative acceleration range calculation unit is configured to calculate the upper limit and the lower limit of the tangential relative velocity based on the prior value of the relative velocity and the upper and lower limits of the radial relative velocity value as follows : where and are respectively the upper limit and the lower limit of the radial relative velocity determined within the circular cross-section formed by the intersection of the radar search sphere and the target position error sphere; Determine the radial relative acceleration range according to the relationship between the radial relative acceleration and the tangential relative velocity It is as follows: wherein is the relative distance search value in this group of search parameters; Sample multiple acceleration search values from the radial relative acceleration range and correspond to the same relative distance search value .​ 10. The space-based radar real-time measurement device for high-dynamic weak space targets according to claim 7, characterized in that, The jerk search value determination module calculates the radial relative jerk search value using the following formula :[[]]END]] In the formula, is the prior value of the relative velocity determined by the orbital parameters, is the relative acceleration of our satellite and the target satellite obtained by differentiating the modulus value of the prior value of the relative velocity.

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