CN112965041B - Differential array dividing method for wave control self-tracking of spherical phased array antenna - Google Patents
Differential array dividing method for wave control self-tracking of spherical phased array antenna Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
- G01S7/415—Identification of targets based on measurements of movement associated with the target
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/66—Radar-tracking systems; Analogous systems
- G01S13/72—Radar-tracking systems; Analogous systems for two-dimensional tracking, e.g. combination of angle and range tracking, track-while-scan radar
- G01S13/723—Radar-tracking systems; Analogous systems for two-dimensional tracking, e.g. combination of angle and range tracking, track-while-scan radar by using numerical data
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
- G01S2013/0236—Special technical features
- G01S2013/0245—Radar with phased array antenna
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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Abstract
The differential array dividing method for wave control self-tracking of the spherical phased array antenna is simple and reliable and consumes less hardware resources. The invention is realized by the following technical scheme: dividing the array into a plurality of subarrays by adopting a polar coordinate mode under a spherical phased array antenna coordinate system, taking polarity according to a clockwise or counter-clockwise direction, rotating an azimuth angle to zero degrees by taking a z-axis as a center, and rotating a pitch angle to an x-axis pointing target by taking a y-axis as a center to point the x-axis to the target; based on a difference array dividing algorithm, under a new rotated coordinate system, calculating a rotation vector of a target pointing coordinate system under an original coordinate system to obtain a maximum pitch angle threshold value of spherical array difference array division, and keeping the pitch angle of difference array maximization; and (3) utilizing the rotation characteristic of the spherical array antenna tracking over-top target time difference array to establish an equivalent antenna rotation model, and realizing the beam coverage of sensitive areas by multi-feed-source shaping to complete the tracking of an antenna wave control angle tracking loop at the target over-top point.
Description
The invention relates to a differential array division design method of wave control self-tracking of a spherical phased array antenna, which is applied to the field of aerospace measurement and control.
Background
With the increase of the number of satellites such as marine/meteorological satellites, communication/navigation satellites and other low-orbit aircrafts, the ground measurement and control system is rapidly increased to simultaneously measure and control a plurality of space targets at the same time and cooperatively manage tasks, and the load of the multi-target operation management and multi-target simultaneous measurement and control supporting capability of the measurement and control system is increased, which is a problem which is difficult to solve in the traditional measurement and control. Array signal processing is a signal processing technology developed in recent decades, and compared with a traditional single directional sensor, the array signal processing has the advantages of flexible beam control, high signal gain, strong anti-interference capability, high spatial resolution capability and the like. In satellite communication, beam synthesis in the space domain by using a shaped antenna is an indispensable key technology for ensuring normal satellite communication to inhibit strong interference. One important solution is to estimate multiple interference directions in as short a time as possible, and then zero-sinking can solve this problem well under conditions of high signal-to-noise ratio (SNR), a sufficiently large snapshot number, and incoherent sources. However, when these conditions are not satisfied, the performance of these methods drastically decreases. The Maximum Likelihood (ML) method can theoretically solve the above-encountered problems, but requires a global search of the maximum of the multivariate non-linearity, which would be unacceptably computationally intensive if an exhaustive approach were used, especially when multi-dimensional and multimodal searches were used. This problem is the bottleneck problem of the ML method for interference direction estimation. Many methods of maximizing likelihood functions have been proposed, including alternating projections, expectation maximization, newton's iterative algorithm, and so on. However, the convergence speed of these methods depends on the choice of the initial value. Most globally converging iterative algorithms have very fast converging performance in the region where the initial value is near the global optimum. However, if the initial value is not properly selected, the convergence speed decreases and easily falls into a local extremum point, resulting in a decrease in convergence accuracy. Large phased arrays have the advantage of large aperture but also add to the complexity of the multi-receiver system. In this case, it is particularly important to sub-divide the phased array in order to reduce the number of receivers on the engineering side.
The difference in the number of phased array antenna sub-arrays and the number of array elements within each sub-array can have a significant impact on the performance of the phased array system, such as a shift in the main lobe or an increase in the side lobe level, which can cause the lobe shape of the array antenna pattern to become asymmetric, resulting in an increase in the side lobe level. Phased array antennas can be divided into linear arrays, planar arrays, spherical arrays, conformal arrays and the like according to unit arrangement, and generally, the phased array antennas can scan in one direction of azimuth angle or pitch angle, and the planar arrays and the like can scan in two directions of azimuth angle and pitch angle at the same time because of one more degree of freedom. The most commonly used linear array is a linear array in which the centers of the units are sequentially arranged on a straight line at equal intervals. The units of the linear array are not equidistantly arranged, and the centers of the units are not necessarily arranged on a straight line, for example, on the circumference. The linear arrays are arranged at certain intervals on a certain plane to form a plane array, and if the centers of the units are arranged on the sphere, a spherical array is formed. The self-tracking technology of the phased array antenna on the aerospace measurement and control target is a key technology applied to the aerospace measurement and control field. The self-tracking characteristic of the spherical phased array antenna to the measurement and control target is closely related to the differential array division of the spherical phased array antenna, and when the spherical phased array antenna tracks a high-elevation over-top target, the over-top tracking problem same as that of the conventional measurement and control field using a parabolic antenna can also occur. Because the higher the orbit height of the aircraft is, the larger the dynamic state of the aircraft relative to the ground station is, and the ultra-low orbit with the orbit height below 300 km is subjected to great atmospheric resistance, so that the orbit height attenuation speed is high, more satellite fuel is required to be consumed for frequent orbit maintenance control, the service life of the satellite is limited, and therefore, the spherical array differential array division and the dynamic characteristics of the high-elevation overhead target must be carefully designed and analyzed in the design of the spherical phased array antenna aerospace measurement and control system so as to avoid the problem of high-elevation overhead tracking. In order to effectively utilize information energy and ensure information transmission quality, a transmitting antenna is required to radiate electromagnetic waves to a required direction as far as possible, and a receiving antenna also receives incoming waves in a specified direction, so that interference and noise in other directions are reduced as much as possible. Multi-beam spherical phased arrays typically divide thousands of array elements into groups according to a specific rule, with a portion of the array elements in each group, and such groups of array elements are called subarrays. Typically, the number of subarrays must be balanced in terms of hardware complexity, software computation, and system desired performance. After the array is divided into subarrays, the number of subarrays is obviously less than the number of array elements, each subarray serves as a receiving channel, and then adaptive array processing is performed on the subarray level. Although subarray-level adaptive beamforming reduces the dimensionality of the adaptive weight vector (i.e., the degree of freedom of the system), the number of large phased array elements is very large, much greater than the number of interference and noise to be suppressed, and thus the subarray division type is diverse. However, the larger the subarray is, the larger the phase center distance is, so that the period distance of grating lobes is shortened, and when the main lobe beam is scanned, the grating lobes can move into the subarray main beam or fall into high subarray side lobes, so that the antenna performance of the array is seriously damaged. And the scanning range of the antenna beam is limited, and the scanning range is smaller as the number of units included in the subarray is larger. The number of subarrays requires a tradeoff between hardware complexity, computational cost, and desired performance. The subarray division type subarray level self-adaptive wave beam forming base, namely the subarray division method. There are mainly 3 sub-array division rules: uniformly contiguous subarrays (regular non-overlapping subarrays), regularly overlapping subarrays, non-uniformly contiguous subarrays (irregular non-overlapping subarrays). The rule means that the array elements in each subarray are the same in number and the array elements in the subarray are equally distributed; "overlapping" means that the same array element is shared by different sub-arrays. The non-overlapping subarrays are easy to control in a microwave stage because no array elements are shared, and the engineering is easier to realize; but the regular subarrays have grating lobes and grating zero point effects, which affect the self-adaptive beam forming effect. The irregular non-overlapping subarrays destroy the periodicity of array beams, so that grating lobes and grating zero point effects can be effectively overcome. Phased array radars generally employ a large aperture antenna, which comprises multiple units, and if all the array elements are used as DBFs, the receiver needs multiple channels, and for signal processing, data acquisition and joint digital signal processing of the multiple channels are also needed, so that the operation is very complex and the cost is too high, and therefore, it is not practical to perform adaptive beam forming at the antenna unit level. The array is now divided into several sub-arrays, typically with digital beam steering at the sub-array level, and phase shifting inside the sub-array. In large arrays, the subarray approach can greatly reduce the hardware requirements and computational complexity, but the contiguous, equally sized subarray designs can result in high sidelobes, grating lobes, reduced gain, and offset in pointing angle. The interference from grating lobe direction can affect the detection and identification of the target signal, and the following methods are generally adopted to eliminate the influence of grating lobe: first, the subarrays are randomly divided so that the pitch is not uniform. This approach does not increase the complexity of the system, but is more complex than uniformly dividing the random partitions, and does not have a fixed principle to be found. Secondly, the subarray overlapping division method has a certain criterion, and can also reduce the influence of grating lobes, but the complexity of the system is increased. In order to reduce the number of active cells and reduce the cost, there is also a method of putting active and passive array elements together and using density weighting. The density weighted antenna array is an unequal spacing weighted antenna array, which approximates an ideal antenna port surface current distribution function through the change of the spacing between the active units, and the excitation current amplitude of each antenna unit is the same. Because the active array elements are randomly placed, the grating lobe problem is not serious under the weighting conditions of subarray level and the like.
Most radars now use azimuth-elevation antenna mounts. In principle, secant compensation is added to the azimuth branch during radar self-tracking, and the compensation coefficient gradually increases along with the elevation angle. Since the compensation coefficient will tend to infinity, the square azimuth error is always greater than both the lateral error angular velocity and the angular acceleration detected by the antenna feed, receiving system, which tend to infinity, resulting in a heel slip. Under the condition that the transverse error between the radar axis and the target is unchanged, the higher the elevation angle is, the larger the error angle is, and when the elevation angle tends to track the target in the azimuth branch, the target cannot be tracked, so that the target is unlocked. The azimuth error angle tends to infinity. Similarly, when the radar axis is to track a target, the transverse angular velocity and acceleration of the ship which is continuously operated under the influence of wind and waves at sea are not changed, the higher the elevation angle is, the more azimuth movement is required, the greater the angular velocity and angular acceleration of the ship-borne radar which is continuously and reversely operated along with the movement of the carrier are, and the radar is frequently reversed, continuously accelerated and decelerated, so that the angular velocity deteriorates the running stability of the radar. The random error of tracking is increased by noise amplification to form ideal feed source of angular acceleration and error demodulation, so that in the self-tracking loop of radar, azimuth branch, pitch branch difference voltage and transverse error angle are in strict linear relation, and compared with no noise path, the link has no secant compensation link, and the link changes the transverse error into sound. However, in practice, due to various interferences and noises, the ideal linearity is converted into a direction error, and then the direction error is sent to a servo driving system, a noise signal is superimposed upwards by a driving radar, and through a secant compensation link, the noise moves along the direction of error reduction and is amplified as well, so that the noise entering an azimuth servo control loop is larger for the same transverse error and the higher the elevation angle. The tracking system can influence the tracking performance of the high elevation angle arc radar after secant compensation is added. The factor of the high elevation angle arc section affecting the stable tracking of the radar, namely the servo system is more sensitive to the noise of an error demodulation and acquisition channel, so that the random tracking error is increased. When the measuring ship is in marine measurement and control, due to the influence of factors such as bad sea conditions, the tracking measurement and control task is sometimes required to be carried out in a high elevation angle arc section, and the high elevation angle arc section tracking is carried out in the Shenzhou and Chang tasks. With the continuous increase of the elevation angle, the jitter is larger and larger, and when the elevation angle reaches the highest, the jitter is the largest. Since the azimuth-elevation type radar apparatus tracks an antenna with azimuth jitter when tracking a target with high elevation angle and low speed. When the radar with the azimuth-elevation type antenna pedestal is used for general tracking at a high elevation angle, the tracking performance of the radar is affected by some factors, and a target cannot be tracked stably. When the elevation angle of the target is below the m9n beamwidth) the antenna main lobe is grounded) when the received signal is the vector sum of the direct signal and the ground reflected signal) corresponds to the occurrence of angular flicker between the target and its image) making low elevation tracking difficult. The data of radar tracking show that not only can dynamic lag influence the tracking performance of the radar at high elevation angles, but also the target is lost when heavy. When the radar works at a high elevation angle, the motor, the drive and the antenna structure are in a full-load working state, the targets are lost, and the ship is rocked, the insensitive area of the circuit is enlarged, and the service life is greatly damaged, so that a random error tracking strategy caused by more sensitivity of reasonable high elevation angle and error demodulation and acquisition channel noise is necessary. When tracking a high elevation target, the radar enters a tracking measurement and control task of an arc section with a severe elevation speed. After a changing area, a tracking "dead zone" may be formed due to the severe dynamic lag of the radar. The tracking performance of the radar at high elevation angle can be influenced, and the tracking strategy can be used for tracking the target at high relative station measuring speed. When the radar is tracked at a high elevation angle, the azimuth maximum tracking angular speed of the needle ship radar is required, and the needle ship radar can be completed at least in the time when the target is overtopped, so that the safety of equipment is ensured, effective data is obtained, and the high rotation of the radar is completed satisfactorily. At present, research on digital multi-beam formation at home and abroad is generally based on subarray division structures of non-uniform, overlapped subarrays and crossed subarrays, but research on digital multi-beam formation based on uniform subarray division of multi-beam spherical phased array antennas is quite available. The multi-beam spherical phased array aerospace measurement and control system is a multi-target measurement and control system which is suitable for the development of the requirement.
Disclosure of Invention
The invention aims to provide a differential array dividing method for wave control self-tracking of a spherical phased array antenna, which has the advantages of low hardware resource consumption, low cost and high reliability according to the characteristics of differential array division in the application of the multi-beam spherical phased array antenna in the range measurement and control field.
The technical scheme adopted for solving the technical problems is as follows: a differential array dividing method for wave control self-tracking of a spherical phased array antenna is characterized by comprising the following steps of: dividing an array into a plurality of subarrays in a polar coordinate mode under a spherical phased array antenna coordinate system, dividing array elements with the same quantization value into one subarray, dividing the spherical array antenna difference array into a plurality of subarrays according to azimuth and pitching directions, dividing the array plane azimuth difference array into a plurality of subarrays according to the azimuth and pitching directions, dividing the array plane pitching difference array into a plurality of subarrays according to the azimuth and pitching directions, taking the polarity in a clockwise or counter-clockwise direction, expressing the position information of a space target by using an azimuth angle, a pitching angle and a target distance, rotating the coordinate system by using a Z-axis as a center, rotating the azimuth angle psi to zero degrees, and rotating the pitching angle phi to an x-axis pointing target by using a y-axis as a center, so that the x-axis points at the target; based on a spherical phased array antenna differential array dividing algorithm, under a new coordinate system after rotation, calculating a rotation vector A of a target pointing coordinate system under an original coordinate system to obtain a maximum pitch angle threshold value of the spherical phased array antenna differential array division, dividing the pitch angle of the differential array when the target exceeds a certain elevation angle according to the obtained pitch angle threshold value, and keeping the pitch angle of the differential array to be maximum on the threshold angle; and according to the antenna caliber, obtaining the maximum pitch angle threshold of the target which is not lost when the antenna is tracked and is over-jacked according to the analysis and simulation of the given target tracking and over-jacked characteristics. By utilizing the rotation characteristic of a spherical array antenna tracking over-top target time difference array, an equivalent antenna rotation model is established, digital beam control and in-subarray phase shift are carried out on the subarray level, a difference array division high elevation angle maximum maintaining method is adopted, beam coverage of a sensitive area is realized by multi-feed source shaping, and the tracking of a wave control angle tracking loop of the spherical array antenna at the target over-top point is completed.
Compared with the prior art, the invention has the following beneficial effects:
the consumption of hardware resources is small, and the cost is low. Is simple and reliable. The array is divided into a plurality of subarrays by adopting a polar coordinate mode under the spherical phased array antenna coordinate system, and array elements with the same quantization value are divided into one subarray, so that a low sidelobe directional diagram can be obtained, the number of subarrays is small, and grating lobes and grating zero points can be avoided. The method comprises the steps of dividing a spherical array antenna difference array according to azimuth and pitching directions, dividing an array plane azimuth array according to division with a Z-axis tangential plane, dividing an array plane pitching array according to division with an azimuth array orthogonal mode, obtaining a maximum pitch angle threshold of an antenna tracking overhead without losing a target according to a given target tracking overhead characteristic analysis and simulation method through an antenna caliber, taking polarity according to clockwise or counter-clock directions, expressing position information of a space target by azimuth angle, pitch angle and target distance, rotating a coordinate system by taking a Z-axis as a center, rotating an azimuth angle psi to zero degree, and rotating a pitch angle phi to an x-axis as a center to point to the target, so that the x-axis points to the target, completing target overhead tracking design, enabling noise power output by the array to be minimum, having larger flexibility, being capable of arbitrarily controlling beam pointing, enhancing expected signals and inhibiting interference signals, improving resolution capability and angle measurement precision of the space signals and the target, and being less in resource occupation. The method does not need complex equipment, only involves some changes in the wave control software tracking flow, utilizes the original spherical phased array antenna equipment, does not add additional hardware, does not need to additionally add equipment amount and use additional hardware, saves hardware resources and hardware cost, greatly reduces the complexity of the system and saves the cost.
The reliability is high. According to the method, based on a spherical phased array antenna differential array dividing algorithm, under a new rotated coordinate system, a rotation vector A of a target pointing coordinate system under an original coordinate system is calculated, so that a maximum pitch angle threshold value of the spherical phased array antenna differential array is obtained, and the requirement on hardware and the calculation complexity are reduced. And dividing the pitch angle of the differential array according to the obtained pitch angle threshold when the target exceeds a certain elevation angle, and keeping the maximum pitch angle of the differential array on the threshold angle. According to the obtained pitch angle threshold, a method of maximally maintaining the pitch angle of differential array is adopted, so that the spherical phased array antenna can stably track the target in the process of over-jacking of the aerospace vehicle, and the problem of target loss caused by overlarge steady tracking error in the process of tracking the over-jacking target at a high target elevation angle and in the process of tracking the target by limiting the maximum elevation angle of differential array division is avoided.
According to the antenna caliber, the maximum pitch angle threshold of the target which is not lost when the antenna is tracked and overtaken is obtained according to the analysis and simulation of the given target tracking and overtaken characteristics. By utilizing the rotation characteristic of the spherical array antenna tracking overhead target time difference array, an equivalent antenna rotation model is established, and the spherical array antenna tracking is completed by adopting a maximum maintaining method of dividing high elevation angles by a difference array, so that the sum and difference beams obtained after division have good performance, the reliability is improved, the offset defects of high side lobes, grating lobes, gain reduction and pointing angles caused by sub-array designs with the same adjacent size are overcome, and the problem of overlarge azimuth angle and pitch angle dynamics in the process of tracking the overhead of the target high elevation angles in a measurement and control system is solved.
The operation is simple and quick, and the automatic design is convenient. The invention maintains the equipment state of the original system, skillfully utilizes the characteristic of dividing the differential array of the spherical array antenna formed by the character multi-beam, and through the quantitative analysis of the wave control angle tracking dynamic performance of the target during the over-top tracking, the wave control angle tracking with the high elevation limit of the differential array of the spherical array antenna is divided on the basis of the analysis, and the maximum pitch angle threshold value of the differential array division can be obtained according to the index of the analysis and the designed antenna, thereby only relating to the change of the wave control software flow, having no additional mechanical parts and operation and being convenient for the automatic design, operation and management of the equipment. In the subarray division of the digital beam forming, the optimal subarray division scheme is weighed in targets with the mutual restriction of detection probability, target angle estimation precision, side lobe level and the like, the side lobe of the self-adaptive directional diagram is well improved, meanwhile, the direction interference of a subarray-level self-adaptive digital beam forming jammer is obviously restrained, and the requirement that the target is not lost when the antenna is in high elevation self-tracking can be met.
Drawings
The invention is further described below with reference to the drawings and examples of implementation.
FIG. 1 is a schematic diagram of differential array partitioning for a spherical phased array antenna of the present invention; wherein, the coordinate system of the spherical phased array antenna of fig. 1 is schematic; differential array division schematic diagram of spherical phased array antenna;
fig. 2 is a schematic diagram of rotation of the spherical phased array antenna differential array partitioning when the tracking target is over-jacked.
FIG. 3 is a schematic diagram of an equivalent model of the differential array partitioning as it rotates when the tracking target is over-jacked;
FIG. 4 is a simulation of the present invention versus the flight trajectory of an aerospace vehicle, wherein FIG. 4a is a schematic diagram of the angular variation of a spherical phased array antenna tracking satellite when a 73.5 degree elevation angle is over-jacked; fig. 4b is a graph showing the variation of the angular velocity of the tracking satellite of the spherical phased array antenna when the 73.5-degree elevation angle is over-top.
Detailed Description
See fig. 1. According to the invention, an array is divided into a plurality of subarrays by adopting a polar coordinate mode under a spherical phased array antenna coordinate system, array elements with the same quantization value are divided into one subarray, wherein the spherical array antenna difference array is divided according to azimuth and pitching directions, the array plane azimuth difference array is divided according to the section of a Z axis, the array plane pitching difference array is divided according to the orthogonal mode with the azimuth difference array, the polarity is taken in the clockwise or counter clock direction, the azimuth angle, the pitch angle and the target distance are used for representing the position information of a space target, the coordinate system is rotated by taking a Z axis as a center, the azimuth angle phi is rotated to zero degree, and then the pitch angle phi is rotated to an x-axis pointing target by taking a y axis as a center, so that the x axis points at the target; based on a spherical phased array antenna differential array dividing algorithm, under a new coordinate system after rotation, calculating a rotation vector A of a target pointing coordinate system under an original coordinate system to obtain a maximum pitch angle threshold value of the spherical phased array antenna differential array division, dividing the pitch angle of the differential array when the target exceeds a certain elevation angle according to the obtained pitch angle threshold value, and keeping the pitch angle of the differential array to be maximum on the threshold angle; and according to the antenna caliber, obtaining the maximum pitch angle threshold of the target which is not lost when the antenna is tracked and is over-jacked according to the analysis and simulation of the given target tracking and over-jacked characteristics. By utilizing the rotation characteristic of a spherical array antenna tracking over-top target time difference array, an equivalent antenna rotation model is established, digital beam control and in-subarray phase shift are carried out on the subarray level, a difference array division high elevation angle maximum maintaining method is adopted, beam coverage of a sensitive area is realized by multi-feed source shaping, and the tracking of a wave control angle tracking loop of the spherical array antenna at the target over-top point is completed.
Applying a rotation matrix algorithm under a new rotated coordinate system, calculating a pointing coordinate and a target pointing coordinate under an original coordinate system, calculating a rotation angle and a rotation axis, and then calculating a corresponding rotation matrix by using a Rodrign rotation formula to obtain a coordinate system rotation vector matrix A1:
wherein:
F 11 ＝cosθEcosθA；F 12 ＝cosθEsinθA；F 13 ＝sinθE；
F 21 ＝-sinθA；F 22 ＝cosθA；F 23 ＝0；
F 31 ＝-sinθEcosθA；F 32 ＝-sinθEsinθA；F 33 ＝cosθE；
where F11 to F33 denote elements of the rotation vector matrix A1, θe is a pitch angle of the target in the original coordinate system, and θa is an azimuth angle of the target in the original coordinate system.
According to the object coordinates (x) 1 ，y 1 ，z 1 ) Calculating target pointing coordinates in coordinate system transformation
Wherein: x is x 1 Normalized x-axis coordinate value, y for the target in the original coordinate system 1 Is the normalized y-axis coordinate value, z of the target in the original coordinate system 1 And the normalized z-axis coordinate value of the target in the original coordinate system is that the theta E is the pitch angle of the target in the original coordinate system, and the theta A is the pitch angle of the target in the original coordinate system.
Obtained by projection of the target motion trail on the spherical array (x 2 ，y 2 ，z 2 )＝(x 1 ，y 1 ，z 1 )A1′
Wherein x is 2 Is the coordinate value, y, of the target in the new coordinate system of the spherical phased array antenna 2 Z is the coordinate value of the target in the new coordinate system 2 For the coordinate value of the target in the new coordinate system phi Target object Is the pitch angle of the target in a new coordinate system after the spherical phased array antenna coordinate system rotates, and is Target object Is the azimuth angle of the target in the new coordinate system after the coordinate system rotates.
Calculating the coordinates (x) of the array element after the rotation of the coordinate system by using the rotation vector matrix A1 4 ，y 4 ，z 4 )＝(x 3 ，y 3 ，z 3 )A1′
Wherein: x is x 3 ,y 3 ,z 3 Is the coordinate value of the array element under the original coordinate system, x 4 ，y 4 ，z 4 The coordinate value of the array element under the new coordinate system after the coordinate system rotates. Calculating pitch angle array element phi of array element under new coordinate system Array element And azimuth angle psi of array element under new coordinate system Array element
Wherein phi is Target object Is the pitch angle of the array element in the new coordinate system after the coordinate system rotates, ψ Target object Is the azimuth angle of the array element under the new coordinate system after the coordinate system rotates.
A differential array division strategy, wherein the azimuth differential array is divided according to the differential array division strategy: phi (phi) Array element At phi Target object ～φ Target object Taking the positive value of the azimuth difference array within +90°; phi (phi) Array element At phi Target object ～φ Target object Taking the azimuth difference array negative value within 90 degrees; the pitch differential array is partitioned according to the following strategy: phi (phi) Array element At phi Target object ～φ Target object Taking positive values of the pitch difference array within++90°; phi (phi) Array element At phi Target object ～φ Target object Taking the pitch difference array negative value within-90 deg..
See fig. 2. The spherical array antenna differential array division is divided according to azimuth and elevation directions, the array plane azimuth differential array division is divided according to a section of a Z axis, and polarity is taken in a clockwise or reverse clock direction, the array plane elevation differential array division is divided in an orthogonal mode with the azimuth differential array division, the division mode can cause the differential array division to generate rotation phenomenon when the antenna is in a high elevation angle, as shown in figure 2, the larger the antenna elevation angle is, the larger the differential array rotation angular velocity is.
See fig. 3. When the antenna azimuth direction is consistent with the target motion direction at the time 0, the antenna azimuth direction angular velocity component is Ω cos phi t at the time t, and the antenna pitching azimuth velocity is: Ω sin φt. According to the selection characteristic of the difference array division shown in fig. 3 when tracking the target over-top, utilizing the rotation characteristic of the spherical array antenna tracking over-top target time difference array to establish an equivalent antenna rotation model and analyzing the dynamic characteristic of the target over-top, setting the angular velocity of the target in azimuth as omega at the over-top point according to the equivalent antenna rotation model
At the crossThe angular velocity components of the vertex antenna in the azimuth direction are as follows: omega cos phi t t＝0 (1)；
The angular velocity components of the over-peak antenna in the pitching direction are as follows: omega sin phi t t＝0 ＝0 (2)；
The angular acceleration components of the over-peak antenna in the azimuth direction are as follows:
the angular acceleration components of the over-peak antenna in the pitching direction are as follows:
and (3) according to a steady-state error analysis formula of the wave control angle tracking and the target angular acceleration:
wherein: r is angular acceleration omega n Is the loop resonant frequency:
taking tracking loop bandwidth 2B L ＝1H Z Then:
and (3) carrying out formula (4) to obtain the product: θ e pitching ＝1.1236Ω 2 (5)
Wherein R is angular acceleration/s, 2B L To track loop bandwidth for wave control, ω n Omega is the azimuthal velocity of the target at the over-peak for the loop resonant frequency.
Obtaining a maximum difference array division pitch angle threshold of the antenna for target over-top tracking according to design indexes of the spherical antenna and a steady state error analysis formula of the target angular acceleration, and completing the design of a tracking flow of the spherical phased array antenna by adopting a difference array division high elevation maximum maintaining method according to the pitch angle threshold, wherein the process is as follows:
firstly, according to the designed beam width of the spherical array antenna, a steady-state error analysis formula (5) of a wave control tracking loop at an over-fixed point is used for obtaining the target maximum pitch angle acceleration tracked by the spherical array antenna. For example: assuming that the width of the half-wave beam of the antenna is 0.5 degrees, the maximum tolerable over-fixed point azimuth speed can be calculated to be 5.05 degrees/second according to the formula (5); and simulating azimuth acceleration of the spherical array antenna under different over-peak pitch angle conditions according to the track characteristics of the aerospace craft. The simulation sets the orbit height of the aircraft to 300 km, and the target orbit simulation experiment conditions are as follows: the target orbit height is 300 km, and the target flying speed is 7.75 km/s; earth radius: 6.37814×103 km; the method is characterized by comprising the following steps of simulating the flight track of a spacecraft to obtain: when the satellite target is overtopped at 73.5 degrees of elevation, the azimuth speed is greater than 5 degrees/second, and the simulation result is shown in fig. 4. Therefore, according to the conclusion of the analysis, the designed dividing pitch angle threshold value of the spherical phased array antenna difference array is 73.5 degrees.
The method for dividing the high elevation angle by the differential array is adopted in the target tracking process, when the target exceeds a certain elevation angle, the pitch angle of the differential array is divided and kept not to be increased on the threshold angle, so that the steady-state error of the wave control angle tracking loop of the spherical array antenna is ensured not to exceed the half-wave beam width of the antenna, namely the wave control angle tracking loop of the spherical array antenna cannot lose the target.
The foregoing describes in detail embodiments of the present invention, which are described herein using specific embodiments, the description of the embodiments being merely intended to aid in the understanding of the methods and apparatus of the present invention; meanwhile, as those skilled in the art will have variations in the specific embodiments and application scope in accordance with the ideas of the present invention, the present description should not be construed as limiting the present invention in view of the above.
Claims (10)
1. A differential array dividing method for wave control self-tracking of a spherical phased array antenna is characterized by comprising the following steps of: dividing an array into a plurality of subarrays in a polar coordinate mode under a spherical phased array antenna coordinate system, dividing array elements with the same quantization value into one subarray, dividing the spherical array antenna difference array into a plurality of subarrays according to azimuth and pitching directions, dividing the array plane azimuth difference array into a plurality of subarrays according to the azimuth and pitching directions, dividing the array plane pitching difference array into a plurality of subarrays according to the azimuth and pitching directions, taking the polarity in a clockwise or counter-clockwise direction, expressing the position information of a space target by using an azimuth angle, a pitching angle and a target distance, rotating the coordinate system by using a Z axis as a center, rotating the azimuth angle psi to zero degree, and rotating the pitching angle phi to an x axis pointing target by using a y axis as a center, so that the x axis points at the target; based on a spherical phased array antenna differential array dividing algorithm, under a new rotated coordinate system, calculating a rotation vector matrix A1 of a target pointing coordinate system under an original coordinate system to obtain a maximum pitch angle threshold value of the spherical phased array antenna differential array division, and dividing the pitch angle of the differential array when the target exceeds a certain elevation angle according to the obtained pitch angle threshold value, and keeping the pitch angle of the differential array to be maximum on the threshold angle; according to the antenna caliber, according to the given target tracking overhead characteristic analysis and simulation, the maximum pitch angle threshold of the target which is not lost when the antenna tracking overhead is obtained, the rotation characteristic of the spherical array antenna tracking overhead target time difference array is utilized to establish an equivalent antenna rotation model, digital wave beam control and in-subarray phase shifting are carried out on the subarray level, a difference array division high elevation angle maximum maintaining method is adopted, wave beam coverage of sensitive areas is realized through multi-feed forming, and the wave control angle tracking loop of the spherical phased array antenna is completed on the target overhead.
2. The differential array dividing method for wave-controlled self-tracking of spherical phased-array antenna as claimed in claim 1, wherein: applying a rotation matrix algorithm under a new rotated coordinate system, calculating a pointing coordinate and a target pointing coordinate under an original coordinate system, calculating a rotation angle and a rotation axis, and then calculating a corresponding rotation matrix by using a Rodrign rotation formula to obtain a coordinate system rotation vector matrix A1:
wherein:
F 11 ＝cosθE cosθA；F 12 ＝cosθE sinθA；F 13 ＝sinθE；
F 21 ＝-sinθA；F 22 ＝cosθA；F 23 ＝0；
F 31 ＝-sinθE cosθA；F 32 ＝-sinθE sinθA；F 33 ＝cosθE；
where F11 to F33 denote elements of the rotation vector matrix A1, θe is a pitch angle of the target in the original coordinate system, and θa is an azimuth angle of the target in the original coordinate system.
3. The differential array dividing method for wave-controlled self-tracking of spherical phased-array antenna as claimed in claim 1, wherein: according to the object coordinates (x) 1 ，y 1 ，z 1 ) Calculating target pointing coordinates in coordinate system transformation
Wherein: x is x 1 Normalized x-axis coordinate value, y for the target in the original coordinate system 1 Is the normalized y-axis coordinate value, z of the target in the original coordinate system 1 And the angle of incidence of the target in the original coordinate system is theta E, which is the angle of incidence of the target in the original coordinate system.
4. A differential array partitioning method for wave-controlled self-tracking of a spherical phased array antenna as claimed in claim 3, wherein: obtained by projection of the target motion trail on the spherical array (x 2 ，y 2 ，z 2 )＝(x 1 ，y 1 ，z 1 )A1′
Wherein x is 2 Is the x-axis coordinate value, y of the target in the new coordinate system of the spherical phased array antenna 2 For the y-axis coordinate value, z of the target in the new coordinate system 2 Is the z-axis coordinate value phi of the target in the new coordinate system Target object Is the pitch angle of the target in the new coordinate system after the spherical phased array antenna coordinate system rotates,is the azimuth angle of the target in the new coordinate system after the coordinate system rotates.
5. The differential array dividing method for wave-controlled self-tracking of spherical phased-array antenna as claimed in claim 1, wherein: calculating the coordinates (x) of the array element after the rotation of the coordinate system by using the rotation vector matrix A1 4 ，y 4 ，z 4 )＝(x 3 ，y 3 ，z 3 ) A1', calculating pitch angle array element phi of array element under new coordinate system Array element And azimuth angles of array elements in new coordinate system
Wherein: x is x 3 ,y 3 ,z 3 Is the coordinate value of the array element under the original coordinate system, x 4 ，y 4 ，z 4 Is the coordinate value phi of the array element under the new coordinate system after the coordinate system rotates Array element Is the pitch angle of the array element under the new coordinate system after the coordinate system rotates,is the azimuth angle of the array element under the new coordinate system after the coordinate system rotates.
6. The differential array dividing method for wave-controlled self-tracking of spherical phased-array antenna as claimed in claim 1, wherein: the azimuth difference array is divided according to a difference array division strategy: phi (phi) Array element At phi Target object ～φ Target object Taking the positive value of the azimuth difference array within +90°; phi (phi) Array element At phi Target object ～φ Target object Taking the azimuth difference array negative value within 90 degrees; the pitch differential array is partitioned according to the following strategy: phi (phi) Array element At phi Target object ～φ Target object Taking positive values of the pitch difference array within +90°; phi (phi) Array element At phi Target object ～φ Target object Taking the pitch difference array negative value within-90 deg..
7. The differential array dividing method for wave-controlled self-tracking of spherical phased-array antenna as claimed in claim 1, wherein: dividing the spherical array antenna difference array according to azimuth and pitching directions, dividing the array plane azimuth difference array according to a section of a Z axis, taking polarity according to a clockwise or reverse clock direction, and dividing the array plane pitching difference array according to a mode of being orthogonal to the azimuth difference array; when the antenna azimuth direction is consistent with the target motion direction at the time 0, the antenna azimuth direction angular velocity component is Ω cos phi t at the time t, and the antenna pitching azimuth velocity is: Ω sin φt.
8. The differential array dividing method for wave-controlled self-tracking of spherical phased-array antenna as claimed in claim 1, wherein: according to the selection characteristic of the differential array division when tracking the target over-top, utilizing the rotation characteristic of the spherical array antenna to track the over-top target time difference array to establish an equivalent antenna rotation model and analyzing the dynamic characteristic of the target over-top, according to the equivalent antenna rotation model, setting the angular velocity of the target in azimuth at the over-top point as omega, then
The angular velocity components of the over-peak antenna in the azimuth direction are as follows: omega cos phi t t＝0 (1)；
The angular velocity components of the over-peak antenna in the pitching direction are as follows: omega sin phi t t＝0 ＝0 (2)；
The angular acceleration components of the over-peak antenna in the azimuth direction are as follows:
the angular acceleration components of the over-peak antenna in the pitching direction are as follows:
9. the differential array partitioning method for wave-controlled self-tracking of spherical phased-array antenna as claimed in claim 8, wherein: and (3) according to a steady-state error analysis formula of the wave control angle tracking and the target angular acceleration:
wherein: r is angular acceleration omega n Is the loop resonant frequency:
taking tracking loop bandwidth 2B L ＝1H Z Then:
and (3) carrying out formula (4) to obtain the product: θ e pitching ＝1.1236Ω 2 (5)
Wherein R is angular acceleration/s, 2B L Is wave controlledTracking loop bandwidth omega n Omega is the azimuthal velocity of the target at the over-peak for the loop resonant frequency.
10. The differential array partitioning method for wave-controlled self-tracking of spherical phased-array antenna as claimed in claim 9, wherein: and obtaining a maximum difference array division pitch angle threshold of the antenna for target overhead tracking according to the design index of the spherical antenna and a steady-state error analysis formula of target angular acceleration, and adopting a difference array division high elevation angle maximum maintaining method to complete the design of the tracking flow of the spherical phased array antenna according to the pitch angle threshold.
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