CN107783102B - Peak tracking method for height signal of unmanned aerial vehicle - Google Patents

Peak tracking method for height signal of unmanned aerial vehicle Download PDF

Info

Publication number
CN107783102B
CN107783102B CN201610723451.7A CN201610723451A CN107783102B CN 107783102 B CN107783102 B CN 107783102B CN 201610723451 A CN201610723451 A CN 201610723451A CN 107783102 B CN107783102 B CN 107783102B
Authority
CN
China
Prior art keywords
threshold
value
peak point
peak
height
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201610723451.7A
Other languages
Chinese (zh)
Other versions
CN107783102A (en
Inventor
田雨农
王鑫照
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Dalian Roiland Technology Co Ltd
Original Assignee
Dalian Roiland Technology Co Ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Dalian Roiland Technology Co Ltd filed Critical Dalian Roiland Technology Co Ltd
Priority to CN201610723451.7A priority Critical patent/CN107783102B/en
Publication of CN107783102A publication Critical patent/CN107783102A/en
Application granted granted Critical
Publication of CN107783102B publication Critical patent/CN107783102B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S13/00Systems 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
    • G01S13/66Radar-tracking systems; Analogous systems
    • G01S13/70Radar-tracking systems; Analogous systems for range tracking only

Abstract

Unmanned aerial vehicle height signal's peak value tracking method belongs to the radar field, solves the problem of the stability of resolving of plant protection rotor unmanned aerial vehicle radar height, and the technical essential is: the method comprises the steps of tracking the threshold-crossing peak point; and a distance tracking step. The effect is as follows: the stability and the real-time performance are improved.

Description

Peak tracking method for height signal of unmanned aerial vehicle
Technical Field
The invention belongs to the field of radars, and relates to a peak tracking method for an unmanned aerial vehicle height signal.
Background
Plant protection unmanned aerial vehicle, as the name implies is the unmanned aircraft who is used for agriculture and forestry plant protection operation, and this type unmanned aircraft has flight platform (fixed wing, single rotor, many rotors), GPS to fly to control, spraying mechanism triplex, flies to control through ground remote control or GPS, realizes spraying the operation, can spray medicament, seed, powder etc..
Compared with the traditional plant protection operation, the unmanned aerial vehicle plant protection operation has the characteristics of accurate operation, high efficiency, environmental protection, intellectualization, simple operation and the like, and saves the cost of large machinery and a large amount of manpower for farmers. Plant protection unmanned aerial vehicle has the operation height low, and the drift is few, characteristics such as can hover in the air, and the downdraft that the rotor produced helps increasing the air current to the penetrability of crops when spraying pesticide, if height between control plant protection unmanned aerial vehicle that can be stable and the ground vegetation, at the pesticide spray operation in-process, then can be better make the pesticide efficient spray the vegetation on to improve the prevention and cure effect of pesticide etc. make the pesticide reach the biggest utilization ratio.
At present, modes such as kalman tracking, alpha-beta tracking and the like are mainly used for unmanned aerial vehicle altitude tracking, and the kalman method and the alpha-beta method can achieve good tracking effect, but the kalman method has a large amount of matrix changes in the calculation process, so that a large amount of hardware resources are consumed, and the real-time performance of the system is reduced. Compared with the kalman method, the alpha-beta method is much faster, but the calculation time may need to be further reduced for the high real-time performance required by the plant protection unmanned aerial vehicle.
The Kalman method and the α - β method are both methods for tracking the calculated height once, i.e., only data processing is used, and the signal processing part is omitted. Therefore, in order to better improve the tracking effect of the target, the invention carries out a primary peak tracking algorithm and a secondary tracking algorithm on the height during peak searching. The peak tracking algorithm and the altitude tracking algorithm are simpler and more efficient to implement than the Kalman method and the alpha-beta method.
Disclosure of Invention
In order to solve the technical problem of low real-time performance of existing unmanned aerial vehicle height signal tracking, the invention provides the following technical scheme:
a peak tracking method of an unmanned aerial vehicle height signal comprises the following steps: tracking a threshold-passing peak point; and a distance tracking step.
Has the advantages that: the invention carries out primary peak tracking during peak value searching and carries out secondary tracking on the calculated height. The peak value tracking algorithm and the height tracking algorithm are matched for use, so that the operation time of hardware is greatly reduced, the real-time performance of height data is better improved, and the refreshing rate of the height data is improved. Meanwhile, the peak value tracking algorithm and the height tracking algorithm are adopted, so that the abnormal phenomenon of one or more times of height data calculation caused by single or multiple peak value searching errors can be effectively avoided, for example, the height is greatly jumped due to peak value jump, namely, the jump of the height in the period is far greater than the distance change range generated in one period caused by the speed of the unmanned aerial vehicle, and the jump height is considered. Therefore, the abnormal height value caused by the abnormal peak can be effectively avoided by peak tracking and height tracking, and the stability of the tracked height data is effectively improved.
Drawings
FIG. 1 is a graph of frequency variation of a chirped sawtooth FMCW over a frequency sweep period;
fig. 2 is a flow chart of a signal processing method of a radar altimeter system of a vegetation rotor unmanned aerial vehicle in embodiment 2.
Detailed Description
Example 1: a radar signal processing method for a plant protection rotor unmanned aerial vehicle radar altimeter system comprises the following steps:
s1, AD data acquisition;
AD data acquisition, through AD sampling digital processing, the number of data point N that AD gathered, after removing partial data, the number of the surplus point is N _ s.
S2, removing direct current, wherein the step is an optional step;
(1) respectively calculating the average values I _ mean and Q _ mean of respective N _ s data of the I path and the Q path;
Figure BDA0001091806240000021
(2) wherein I is time domain data of the I path, Q is time domain data of the Q path, I _ mean is the mean value of the I path, and Q _ mean is the mean value of the Q path;
(3) subtracting the average value of each path from each data of the path I and the path Q;
(4) the IQ data DC calculation formula is as follows:
Figure BDA0001091806240000031
wherein, I 'is data after direct current removal, and Q' is data after direct current removal.
S3, FFT conversion;
preferably, I, Q data after being subjected to direct current removal are combined into an I + jQ data form, the sawtooth wave I + jQ data are subjected to FFT conversion, time domain data are converted into frequency data, of course, AD acquisition data can also be directly subjected to FFT conversion, I, Q data are combined into an I + jQ data form, and the sawtooth wave I + jQ data are subjected to FFT conversion.
S4, CFAR threshold detection;
and carrying out CFAR threshold detection on the complex modulus value of each point after the FFT.
S5, peak value processing;
the peak processing: after CFAR threshold detection, selecting a maximum point as an output peak value, and executing the following method when threshold peak value extraction is carried out:
setting a peak point threshold factor α for limiting the absolute value of the difference between the detected threshold-crossing maximum peak point and the maximum peak point appearing in the previous cycle, so that the absolute value of the difference is not greater than the peak point threshold factor α:
the expression is as follows:
|L_max(k)-L_max(k-1)|≤α;
Figure BDA0001091806240000032
wherein: l _ max (k) is the maximum peak point coordinate of the threshold passing of the k period, L _ max (k-1) is the maximum peak point coordinate of the last period, and k represents the kth moment; v. ofmaxThe maximum flight speed of the unmanned aerial vehicle is shown, lambda is the wavelength of the millimeter wave radar, fs is the sampling rate, and N is the number of points of FFT;
if the absolute value difference value of the threshold-crossing maximum peak point at the moment k and the threshold-crossing maximum peak point at the moment k-1 is within the set range of the threshold factor alpha of the peak point, the peak point of the kth period is considered to be effective; and if the threshold-crossing maximum peak point exceeds the set peak point threshold factor alpha at the moment k, replacing the peak point output at the moment k with the peak point at the moment k-1.
As a preferable scheme, a peak point sudden change accumulation factor phi is set, and the peak point sudden change accumulation factor phi is defined as that if b periods are continued from the moment k, the value range of b is 5-10, and the threshold crossing maximum peak point is compared with the threshold crossing maximum peak point of the previous period and both exceed the threshold factor a, at the moment k + b, the threshold crossing maximum peak point calculated at the current moment is taken as the threshold crossing maximum peak point at the current moment.
S6, spectrum maximum estimation, wherein the step is an optional step:
obtaining a threshold-crossing maximum peak point for spectrum maximum estimation: setting the coordinates of the threshold-crossing maximum peak point A1 as (a1, k1), wherein a1 represents the value of the threshold-crossing maximum peak point, and k1 represents the amplitude value corresponding to the threshold-crossing peak point; the coordinates of the secondary peak points are A3(A3, k3), the coordinate of the central peak point A is (amax, kmax), and e is amax-a1, the point A1, the coordinate of the point A2 symmetric to the point A is (a2, k1) is (a1+2e, k1), and the zero point A4 of the complex envelope is (a4, k1) is (A3+ e, 0);
wherein: a2, a3 and a4 are the values of the over-threshold maximum peak point of the corresponding point, and k3 and k4 are the amplitude values corresponding to the over-threshold peak point of the corresponding point;
a2, A3 and A4 are approximately a straight line, and the linear relationship is as follows:
Figure BDA0001091806240000041
order to
Figure BDA0001091806240000042
Then
Figure BDA0001091806240000043
Setting error E and deviation E to compare, if | E tint<E, the value of the over-threshold peak point at the moment is the value of the required central peak point, if the deviation E is greater than the set error E,
Figure BDA0001091806240000044
beta is a correction factor, the value range is 1.5-1.9, the value of e is calculated by changing the correction factor, and the value amax of the central peak point is calculated to be a1+ e.
S7, high settlement;
the value amax of the central peak point, and its corresponding frequency value f _ amax, according to the formula
Figure BDA0001091806240000045
Calculating to obtain the height; where T is the modulation period, B is the bandwidth, and c is the speed of light.
Setting an altitude threshold factor epsilon, which is used for limiting the absolute value of the difference between the current altitude data H (k) and the altitude data H (k-1) appearing in the previous period, so that the absolute value of the difference is not larger than the altitude threshold factor epsilon;
the expression is as follows:
the value of | H (k) | -H (k-1) | is less than or equal to epsilon, and the value range of epsilon is 0.8-1.3;
if the absolute value difference value of the height data at the k moment and the absolute value difference value at the k-1 moment are within the range of the set height threshold factor epsilon, the peak point of the k-th period is considered to be effective; if the height data exceeds the set height threshold factor epsilon at time k, the height data output at time k is replaced with the height data at time k-1.
And setting an altitude abrupt change accumulation factor theta, wherein the altitude abrupt change accumulation factor theta is defined as that if b periods continue from the time k, and the altitude data exceeds a threshold factor theta compared with the altitude data of the previous period, the altitude data obtained by resolving the current time is taken as the altitude data of the current time at the time k + b.
Outputting a height value, namely outputting the height value by adopting a sliding window algorithm for the height data output at a single time; the altitude data at time k is equal to N in the sliding windowcThe average value of the maximum height value and the minimum height value of the individual height value is removed and is output as the final height data, and the calculation formula is
Figure BDA0001091806240000051
Wherein N iscIndicating the number of height data points taken by the sliding window.
The improvement of the embodiment is that a peak threshold algorithm and a height threshold algorithm are added when the peak point is processed, through the two steps, the stability of data is improved in a matching mode, and the range finding precision can be improved through a designed spectrum maximum estimation algorithm.
Example 2: application publication No. CN 104678397A's patent application discloses an ultrasonic wave altimeter for unmanned aerial vehicle, has adopted the mode of ultrasonic wave to measure the terrain clearance when unmanned aerial vehicle is near the ground, realizes unmanned aerial vehicle's function of independently taking off and landing, but the ultrasonic wave altimeter biggest range finding that describes in this patent is 11m, and this is far away not enough in spraying the pesticide use to plant protection unmanned aerial vehicle. Therefore, in order to improve the ranging range of the unmanned aerial vehicle altimeter between 30 m and 40m and ensure the ranging precision to be about 0.2m, the invention provides the unmanned aerial vehicle altimeter realized based on the millimeter wave radar. Compared with other detection modes, the millimeter wave radar has the advantages of stable detection performance, good environmental adaptation, small size, low price, capability of being used in relatively severe rainy and snowy weather and the like.
As a supplement to the technical solution of embodiment 1, the millimeter wave radar designed in this embodiment has an operating frequency of 24GHz or 77GHz, and adopts an FMCW continuous wave system, mainly because of the chirp mode, its distance resolution is high. The waveform can adopt a chirp triangular wave FMCW, a sawtooth wave and a constant frequency wave or a combined waveform of the waveforms. Adopt single triangle wave emission waveform, can carry out relative distance's detection to the target, through the relative velocity between the unmanned aerial vehicle that detects out and the vegetation, assume the vegetation is static, then this speed is unmanned aerial vehicle upper and lower flying speed. Accurate settlement of the relative distance of the target can be completed by adopting a single triangular wave. The sawtooth wave can only detect the relative distance of the target, and the constant frequency wave can only detect the speed of the target. Because the Doppler frequency shift that unmanned aerial vehicle vertical flight produced can cause the deviation of certain distance, so can adopt the combination waveform of sawtooth wave and constant frequency wave, realize the compensation to sawtooth wave band distance detection through the constant frequency wave band to the measurement of speed to improve the distance precision between unmanned aerial vehicle and the vegetation. Triangular wave and sawtooth wave and constant frequency wave's combined waveform can all be regarded as the transmission waveform and realize vegetation unmanned aerial vehicle altimeter, can select the transmission waveform according to the application scene of difference to apply to the application field of different vegetation better, in order to reach better distance detection precision.
The range finding scope of the vegetation rotor unmanned aerial vehicle radar altimeter system that this embodiment designed is 1 ~ 50m, and the range finding precision is 0.2 m.
The embodiment mainly provides a design of a vegetation rotor unmanned aerial vehicle anti-collision signal processing part based on a millimeter wave radar and a signal processing method.
The radar center frequency f designed by the embodiment is 24.128 GHz. The emission waveform selects a single sawtooth wave, the period is 1ms, the bandwidth is 250MHz, and the sampling rate fs is 320 KHz. The transmit waveform is shown in fig. 1.
The present embodiment only needs to realize the resolution of the target range speed through one path of IQ data. A processing flow chart of the millimeter wave radar signal for preventing collision of the vegetation rotor unmanned aerial vehicle is given as follows, and is shown in fig. 2;
the method comprises the following concrete steps:
1.AD data acquisition, i.e. data processing
Continuous IQ data with height information is subjected to digital processing through AD sampling, the number N of data points acquired by AD is related to the sampling frequency fs and the sweep frequency period T of the system, namely N is fs T. Because partial data in the front of the collected data is abnormal due to system reasons and cannot be used for subsequent data processing, the time domain data of the remaining points are subjected to subsequent processing after partial data needs to be removed. If the number of points to be removed is N _ q, the number of remaining points is N _ s, and N _ s is N-N _ q. The data to be processed subsequently is N _ s pieces of data.
2. Remove direct current
(1) Respectively calculating the average values I _ mean and Q _ mean of the I path and the Q path and the respective N _ s data,
namely, it is
Figure BDA0001091806240000071
Wherein I is time domain data of the I path, Q is AND data of the Q path, I _ mean is the mean value of the I path, and Q _ mean is the mean value of the Q path.
(2) And subtracting the mean value M obtained by the previous step from each data of the path I and the path Q, thereby finishing the purpose of removing direct current and reducing the influence of a direct current part on target threshold detection.
(3) The IQ data DC calculation formula is as follows:
Figure BDA0001091806240000072
wherein, I 'is data after direct current removal, and Q' is data after direct current removal.
3. Window function processing
I, Q data after direct current removal are combined into an I + jQ data form, then windowing is carried out, a Hanning window or a Hamming window and the like can be selected, side lobes are reduced, and therefore the detection performance of the target is improved; the hanning window will cause the main lobe to widen and decrease, but the side lobes will decrease significantly.
4. FFT transformation
And performing FFT (fast Fourier transform) on the windowed sawtooth wave I + jQ data, and converting time domain data into frequency data.
5. CFAR threshold detection
And carrying out CFAR threshold detection on the complex modulus value of each point after the FFT. The CFAR threshold detection can select a threshold detection method SO-CFAR with an average selected unit, the protection unit can select 1 to 2 points, and the number of window points can select 15 to 20.
6. Peak processing algorithm design
Considering that each peak point corresponds to a corresponding height value in the module value data of the millimeter wave radar altimeter after FFT. After CFAR threshold detection, the maximum point is selected as the output peak. For the characteristic of using single peak point output, it is easy to cause the peak point to jump in a large range, for example, if the output peak point of the previous period is M ═ 5, and the output peak value of the current period is M ═ 30, then the distance jumps by 15 points, and the distance jumps accordingly. In order to improve the stability of the height data output of the unmanned gyroplane, the following new algorithm design is proposed when threshold peak extraction is performed.
Setting a peak point threshold factor α for limiting the absolute value of the difference between the detected threshold-crossing maximum peak point and the maximum peak point appearing in the previous cycle, so that the absolute value of the difference is not greater than the peak point threshold factor α:
the expression is as follows:
|L_max(k)-L_max(k-1)|≤α;
Figure BDA0001091806240000081
wherein: l _ max (k) is the maximum peak point coordinate of the threshold passing of the k period, L _ max (k-1) is the maximum peak point coordinate of the last period, and k represents the kth moment; v. ofmaxThe maximum flight speed of the unmanned aerial vehicle is shown, lambda is the wavelength of the millimeter wave radar, fs is the sampling rate, and N is the number of points of FFT;
if the absolute value difference value of the threshold-crossing maximum peak point at the moment k and the threshold-crossing maximum peak point at the moment k-1 is within the set range of the threshold factor alpha of the peak point, the peak point of the kth period is considered to be effective; and if the threshold-crossing maximum peak point exceeds the set peak point threshold factor alpha at the moment k, replacing the peak point output at the moment k with the peak point at the moment k-1.
And if the absolute value difference value of the threshold-crossing maximum peak point at the moment k and the threshold-crossing maximum peak point at the moment k-1 is within the range of the designed threshold factor, the peak point of the kth period is considered to be effective, and subsequent calculation is carried out, and if the threshold-crossing maximum peak point at the moment k exceeds the designed threshold factor, the peak point output at the moment k is replaced by the peak point at the moment k-1.
As an explanation of the above technical means, in a time unit of an adjacent period, the peak point calculated in the current period and the peak point of the previous period may also remain unchanged if the speed does not change in the adjacent period, but if the vertical flying speed of the drone changes in the adjacent period (here, for the altimeter, if the horizontal flying speed of the drone is in collision avoidance), the peak point of the current period may change to some extent in the previous period, if the drone is close to the ground, the number of the current period may be greater than that in the previous period, and if the drone is far away from the ground, the number of the current period may be less than that in the previous period, and the change range of the peak point is the designed peak threshold factor α, which is the value range selected by the factor, mainly dependent on the maximum flying speed of the drone in adjacent periods, i.e. formula
Figure BDA0001091806240000082
Wherein v ismaxThe maximum flight speed of the unmanned aerial vehicle is shown, lambda is the millimeter wave radar wavelength, fs is the sampling rate, and N is the number of points of FFT.
However, if the height value changes after the flying environment below the plant protection rotor unmanned aerial vehicle changes suddenly, the number of peak points corresponding to the threshold passing may also continuously exceed the designed threshold factor. If the correction is not carried out, after the height is suddenly changed, the threshold-passing maximum peak point detected in each period can exceed the set threshold value factor, and the threshold-passing maximum peak point coordinate can be corrected to be the peak point coordinate at the last moment every time, namely, the height value before the height sudden change can be kept by the same method, and the height value after the sudden change cannot be adapted. In order to improve the adaptability of the radar altimeter of the unmanned aerial vehicle to various environments, a peak point mutation accumulation factor phi is introduced for the adaptability.
The peak point mutation accumulation factor phi is defined as that, if the coordinate value of the threshold-crossing maximum peak point changes suddenly from the time k, continuously for b cycles, that is, the threshold-crossing maximum peak point appearing in the continuously for b cycles is compared with the threshold-crossing maximum peak point in the previous cycle and exceeds the threshold factor a, at the time k + b, the maximum peak point is not replaced by the threshold-crossing maximum peak point in the previous cycle, but the threshold-crossing maximum peak point calculated at the current time is directly used as the threshold-crossing maximum peak point at the current time, so that the task of switching the threshold-crossing maximum peak point in the scene with the height mutation is completed. The value range of b is 5-10.
7. Spectral maximum estimation algorithm
After the threshold-crossing maximum peak point is obtained through the last step, in order to improve the accuracy of height value measurement of the altimeter system of the plant protection rotor unmanned aerial vehicle, a spectrum maximum estimation algorithm for improving the distance measurement accuracy is provided.
Ideally, the frequency spectrum of the echo difference frequency signal has only one spectral line, but actually, in the using process, due to the barrier effect existing in sampling, the spectral line with the maximum amplitude of the discrete frequency spectrum inevitably shifts the position of a spectral peak, so that a certain error exists between the distance value calculated by the peak point and the actual distance. When a spectral peak is shifted, the central spectral line corresponding to the main lobe peak will be shifted to the left or to the right. If the left peak value is larger than the right peak value in the left and right peak values of the threshold-crossing maximum value peak value point, the position of the central spectral line is between the maximum peak value point and the left peak value point, otherwise, the position is between the maximum peak value point and the right peak value point.
Because the spectrum obtained by FFT calculation samples continuous distance spectrum at equal intervals, the maximum point of the spectrum amplitude is necessarily positioned in the main lobe of the curve, and the main lobe has two sampling points. Obtaining a threshold-crossing maximum peak point for spectrum maximum estimation: setting the coordinates of the threshold-crossing maximum peak point A1 as (a1, k1), wherein a1 represents the value of the threshold-crossing maximum peak point, and k1 represents the amplitude value corresponding to the threshold-crossing peak point; the coordinates of the secondary peak points are A3(A3, k3), the coordinate of the central peak point A is (amax, kmax), and e is amax-a1, the point A1, the coordinate of the point A2 symmetric to the point A is (a2, k1) is (a1+2e, k1), and the zero point A4 of the complex envelope is (a4, k1) is (A3+ e, 0);
wherein: a2, a3 and a4 are the values of the over-threshold maximum peak point of the corresponding point, and k3 and k4 are the amplitude values corresponding to the over-threshold peak point of the corresponding point;
a2, A3 and A4 are approximately a straight line, and the linear relationship is as follows:
Figure BDA0001091806240000101
order to
Figure BDA0001091806240000102
Then
Figure BDA0001091806240000103
Setting error E and deviation E to compare, if | E tint<E, the value of the over-threshold peak point at the moment is the value of the required central peak point, if the deviation E is greater than the set error E,
Figure BDA0001091806240000104
beta is a correction factor, the value range is 1.5-1.9, the value of e is calculated by changing the correction factor, and the value amax of the central peak point is calculated to be a1+ e.
The reason for selecting the correction factor is as follows: due to the initial time
Figure BDA0001091806240000105
The coordinate of the point a symmetric point a2 is (a2, k1) — (a1+2E, k1), the abscissa of the point a is symmetric to the abscissa of the point a2 about the maximum peak point under the initial condition, that is, the coordinate of the point a2 is a1+2E, if the deviation E is greater than the set error E, it means that the coordinate of the point a2 is selected too large, that is, the maximum peak point is between a1+2E, and the 2-fold deviation E needs to be reduced. The value principle of the correction factor beta can be selected according to the required E value, if the required precision of E is not high, the correction factor beta can be selected to be 1.9 for correction, if the required precision of E is high, multiple iterations are possibly required to meet the requirement, the correction factor beta needs to be selected to be as small as possible, and 1.5 can be selected for correction.
8. High settlement
Calculating the value amax of the central peak point obtained in the last step, and the corresponding frequency value f _ amax according to a formula
Figure BDA0001091806240000106
Where T is the modulation period, T is 1ms, B is the bandwidth, B is 260MHz, c is the speed of light, and c is 3.0 × 108. Since this embodiment employs sawtooth waves with a very fast period, the difference frequency caused by the maximum speed generated by the vertical ascent and descent of the drone is substantially negligible, so this embodiment does not involve the resolution of the relative speed.
And therefore, the calculation function of the height information of the radar altimeter system of the plant protection rotor unmanned aerial vehicle is completed by single detection.
9. In order to improve the accuracy of altitude information obtained by altimeter calculation and further reduce large-range fluctuation of data, the following data processing algorithm is adopted for further calculation.
The concrete implementation method is as the idea of step 6.
Firstly, an altitude threshold factor epsilon is designed, and the factor is mainly used for limiting the absolute value of the difference between the detected current altitude data H (k) and the altitude data H (k-1) appearing in the previous period not to be larger than the altitude threshold factor epsilon.
I.e., | H (k) | H (k-1) | is less than or equal to epsilon, and the value range of epsilon is generally 0.8-1.3.
And if the absolute value difference value of the height data and the previous time k-1 at the time k is within the range of the designed threshold factor, considering that the peak point of the k-th period is valid, and performing subsequent calculation, and if the height data exceeds the designed threshold factor at the time k, replacing the height data output at the time k with the height data at the time k-1.
Similarly, if the height value changes after sudden change of the flying environment below the plant protection rotor unmanned aerial vehicle, the corresponding height data may also continuously exceed the designed threshold factor. If the height is not corrected, after the height is suddenly changed, the height data detected in each period can exceed the set threshold factor, and each time the height data is corrected into the height data at the previous moment, the height data cannot be well adapted to the suddenly changed height value. To improve the further stability of the altitude output, an altitude jump integration factor θ is introduced for this purpose.
The definition of the height abrupt change accumulation factor theta is that if the height data suddenly changes for b continuous periods from the time k, namely the height data occurring in the b continuous periods is compared with the height data in the previous period and exceeds the threshold factor theta, the height data at the time k + b does not need to be replaced by the height data in the previous period, but the height data calculated at the current time is directly used as the height data at the current time, so that the stability of the height data is improved completely.
For the height data of single output, the sliding window algorithm is adopted to output the height value for the smoothness of the output. I.e. the height data at time k equals N in the sliding windowcThe average value of the maximum height value and the minimum height value of the individual height value is removed and is output as the final height data, and the calculation formula is
Figure BDA0001091806240000111
Wherein N iscIndicating the number of height data points taken by the sliding window.
Example 3: from the technical solutions in the two embodiments, it can be seen that the technical solutions disclosed in the two embodiments further include a peak tracking method for an altitude signal of an unmanned aerial vehicle, and the present embodiment arranges the tracking method, obviously, the tracking method in the present embodiment can be obtained by being supported by the two embodiments, however, the tracking method is a peak tracking method for an altitude signal of an unmanned aerial vehicle that can be independently applied to an unmanned aerial vehicle, and is not limited to the technical solutions in the two embodiments, and the tracking method includes: tracking a threshold-passing peak point; and a distance tracking step.
Wherein: the method for tracking the over-threshold peak point comprises the following steps:
setting a peak point threshold factor α for limiting the absolute value of the difference between the detected threshold-crossing maximum peak point and the maximum peak point appearing in the previous cycle, so that the absolute value of the difference is not greater than the peak point threshold factor α:
the expression is as follows:
|L_max(k)-L_max(k-1)|≤α;
Figure BDA0001091806240000121
wherein: l _ max (k) is the maximum peak point coordinate of the threshold passing of the k period, L _ max (k-1) is the maximum peak point coordinate of the last period, and k represents the kth moment; v. ofmaxFor the maximum flying speed of the unmanned aerial vehicle, lambda is the millimeter wave radar wavelength, and fs is the samplingSample rate, N is the number of points of FFT;
if the absolute value difference value of the threshold-crossing maximum peak point at the moment k and the threshold-crossing maximum peak point at the moment k-1 is within the set range of the threshold factor alpha of the peak point, the peak point of the kth period is considered to be effective; and if the threshold-crossing maximum peak point exceeds the set peak point threshold factor alpha at the moment k, replacing the peak point output at the moment k with the peak point at the moment k-1.
As an explanation of the above technical means, in a time unit of an adjacent period, the peak point calculated in the current period and the peak point of the previous period may also remain unchanged if the speed does not change in the adjacent period, but if the vertical flying speed of the drone changes in the adjacent period (here, for the altimeter, if the horizontal flying speed of the drone is in collision avoidance), the peak point of the current period may change to some extent in the previous period, if the drone is close to the ground, the number of the current period may be greater than that in the previous period, and if the drone is far away from the ground, the number of the current period may be less than that in the previous period, and the change range of the peak point is the designed peak threshold factor α, which is the value range selected by the factor, mainly dependent on the maximum flying speed of the drone in adjacent periods, i.e. formula
Figure BDA0001091806240000131
Wherein v ismaxThe maximum flight speed of the unmanned aerial vehicle is shown, lambda is the millimeter wave radar wavelength, fs is the sampling rate, and N is the number of points of FFT.
However, if the height value changes after the flying environment below the plant protection rotor unmanned aerial vehicle changes suddenly, the number of peak points corresponding to the threshold passing may also continuously exceed the designed threshold factor. If the correction is not carried out, after the height is suddenly changed, the threshold-passing maximum peak point detected in each period can exceed the set threshold value factor, and the threshold-passing maximum peak point coordinate can be corrected to be the peak point coordinate at the last moment every time, namely, the height value before the height sudden change can be kept by the same method, and the height value after the sudden change cannot be adapted. In order to improve the adaptability of the radar altimeter of the unmanned aerial vehicle to various environments, a peak point mutation accumulation factor phi is introduced for the adaptability.
And setting a peak point sudden change accumulation factor phi, wherein the peak point sudden change accumulation factor phi is defined as that if b periods are continuously carried out from the moment k, the value range of b is 5-10, and the threshold-crossing maximum peak point is compared with the threshold-crossing maximum peak point of the previous period and exceeds a threshold factor a, the threshold-crossing maximum peak point calculated at the moment k + b is taken as the threshold-crossing maximum peak point at the moment. In order to ensure the real-time performance of tracking, the value of b is 5-10.
And after the threshold-passing maximum peak point is obtained in the last step, in order to improve the height value measurement precision of the altimeter system, a spectrum maximum estimation algorithm for improving the distance measurement precision is provided.
Ideally, the frequency spectrum of the echo difference frequency signal has only one spectral line, but actually, in the using process, due to the barrier effect existing in sampling, the spectral line with the maximum amplitude of the discrete frequency spectrum inevitably shifts the position of a spectral peak, so that a certain error exists between the distance value calculated by the peak point and the actual distance. When a spectral peak is shifted, the central spectral line corresponding to the main lobe peak will be shifted to the left or to the right. If the left peak value is larger than the right peak value in the left and right peak values of the threshold-crossing maximum value peak value point, the position of the central spectral line is between the maximum peak value point and the left peak value point, otherwise, the position is between the maximum peak value point and the right peak value point.
Because the spectrum obtained by FFT calculation samples continuous distance spectrum at equal intervals, the maximum point of the spectrum amplitude is necessarily positioned in the main lobe of the curve, and the main lobe has two sampling points. Setting the coordinates of the threshold-crossing maximum peak point A1 as (a1, k1), wherein a1 represents the value of the threshold-crossing maximum peak point, and k1 represents the amplitude value corresponding to the threshold-crossing peak point; the coordinates of the secondary peak points are A3(A3, k3), the coordinate of the central peak point A is (amax, kmax), and e is amax-a1, the point A1, the coordinate of the point A2 symmetric to the point A is (a2, k1) is (a1+2e, k1), and the zero point A4 of the complex envelope is (a4, k1) is (A3+ e, 0);
wherein: a2, a3 and a4 are the values of the over-threshold maximum peak point of the corresponding point, and k3 and k4 are the amplitude values corresponding to the over-threshold peak point of the corresponding point;
a2, A3 and A4 are approximately a straight line, and the linear relationship is as follows:
Figure BDA0001091806240000141
order to
Figure BDA0001091806240000142
Then
Figure BDA0001091806240000143
Setting error E and deviation E to compare, if | E tint<E, the value of the over-threshold peak point at the moment is the value of the required central peak point, if the deviation E is greater than the set error E,
Figure BDA0001091806240000144
beta is a correction factor, the value range is 1.5-1.9, and the correction factor is selected from the following reasons: due to the initial time
Figure BDA0001091806240000145
The coordinate of the point a symmetric point a2 is (a2, k1) — (a1+2E, k1), the abscissa of the point a is symmetric to the abscissa of the point a2 about the maximum peak point under the initial condition, that is, the coordinate of the point a2 is a1+2E, if the deviation E is greater than the set error E, it means that the coordinate of the point a2 is selected too large, that is, the maximum peak point is between a1+2E, and the 2-fold deviation E needs to be reduced. The value-taking principle of the correction factor beta can be selected according to the required E value, if the required precision of E is not high, the correction factor beta can be selected to be 1.9 for correction, and if the required precision of E is high, multiple iterations may be neededWhen the requirement is met, the correction factor beta needs to be selected to be a little as possible, 1.5 can be selected for correction, and the invention provides an interval range value of the correction factor for rapidly solving the maximum peak point, namely the correction factor beta is 1.5-1.9. The value of e calculated by the correction factor is changed to calculate the value amax of the central peak point as a1+ e.
The distance tracking comprises the following steps: setting an altitude threshold factor epsilon, which is used for limiting the absolute value of the difference between the current altitude data H (k) and the altitude data H (k-1) appearing in the previous period, so that the absolute value of the difference is not larger than the altitude threshold factor epsilon;
the expression is as follows:
the value of | H (k) | -H (k-1) | is less than or equal to epsilon, and the value range of epsilon is 0.8-1.3;
if the absolute value difference value of the height data at the k moment and the absolute value difference value at the k-1 moment are within the range of the set height threshold factor epsilon, the peak point of the k-th period is considered to be effective; if the height data exceeds the set height threshold factor epsilon at time k, the height data output at time k is replaced with the height data at time k-1.
And setting an altitude abrupt change accumulation factor theta, wherein the altitude abrupt change accumulation factor theta is defined as that if b periods continue from the time k, and the altitude data exceeds a threshold factor theta compared with the altitude data of the previous period, the altitude data obtained by resolving the current time is taken as the altitude data of the current time at the time k + b.
During height output, for height data output at a single time, outputting a height value by adopting a sliding window algorithm;
the altitude data at time k is equal to N in the sliding windowcThe average value of the maximum height value and the minimum height value of the individual height value is removed and is output as the final height data, and the calculation formula is
Figure BDA0001091806240000151
Wherein N iscIndicating the number of height data points taken by the sliding window.
By adopting the peak value tracking algorithm and the height tracking algorithm, the abnormal phenomenon of one or more times of height data calculation caused by single or multiple times of peak value searching errors can be effectively avoided, such as peak value jumping occurs in the single peak value searching process, the peak value difference value between adjacent periods is large, and the height is greatly jumped due to jumping with the peak value, namely, the jump range of the height caused by the peak value jumping is far larger than the distance change range of one period caused by the speed of the unmanned aerial vehicle in the period. Therefore, the abnormal height value caused by the abnormal peak can be effectively avoided by peak tracking and height tracking, and the stability of the tracked height data is effectively improved.
The above description is only for the purpose of creating a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can substitute or change the technical solution and the inventive concept of the present invention within the technical scope of the present invention.

Claims (6)

1.A peak tracking method of an unmanned aerial vehicle height signal is characterized by comprising the following steps:
tracking a threshold-passing peak point; and a step of height tracking;
the method for tracking the over-threshold peak point comprises the following steps:
setting a peak point threshold factor α for limiting the absolute value of the difference between the detected threshold-crossing maximum peak point and the maximum peak point appearing in the previous cycle, so that the absolute value of the difference is not greater than the peak point threshold factor α:
the expression is as follows:
|L_max(k)-L_max(k-1)|≤α;
Figure FDA0002957402520000011
wherein: l _ max (k) is the threshold-crossing maximum peak value of a k period, L _ max (k-1) is the maximum peak value of the last period, and k represents the kth moment;vmaxthe maximum flight speed of the unmanned aerial vehicle is shown, lambda is the wavelength of the millimeter wave radar, fs is the sampling rate, and N is the number of points of FFT;
if the absolute value of the difference value between the maximum threshold-crossing peak value at the moment k and the maximum threshold-crossing peak value at the moment k-1 is within the range of the set peak point threshold factor alpha, the peak point of the kth period is considered to be valid; and if the absolute value of the difference value between the maximum threshold-crossing peak value at the moment k and the maximum threshold-crossing peak value at the moment k-1 exceeds the set peak point threshold factor alpha, replacing the peak point output at the moment k with the peak point at the moment k-1.
2. The peak tracking method for the unmanned aerial vehicle height signal according to claim 1, wherein a peak point sudden change accumulation factor Φ is set, and the peak point sudden change accumulation factor Φ is defined as that, if b cycles continue from the time k, b ranges from 5 to 10, and the threshold-crossing maximum peak point is compared with the threshold-crossing maximum peak point of the previous cycle and both exceed a peak point threshold factor α, the threshold-crossing maximum peak point calculated at the time k + b is used as the threshold-crossing maximum peak point at the current time.
3. The peak tracking method of the altitude signal of the unmanned aerial vehicle of claim 1, wherein the maximum peak point over the threshold is obtained for spectrum maximum estimation: setting the coordinates of the threshold-crossing maximum peak point A1 as (a1, k1), wherein a1 represents the value of the threshold-crossing maximum peak point, and k1 represents the amplitude value corresponding to the threshold-crossing maximum peak point; the coordinates of the secondary peak points are A3(A3, k3), the coordinate of the central peak point A is (amax, kmax), and e is amax-a1, the point A1, the coordinate of the point A2 symmetric to the point A is (a2, k1) is (a1+2e, k1), and the zero point A4 of the complex envelope is (a4, k4) is (A3+ e, 0);
wherein: a2, a3 and a4 are the values of the over-threshold peak points of the corresponding points, and k3 and k4 are the amplitude values corresponding to the over-threshold peak points of the corresponding points;
a2, A3 and A4 are approximately a straight line, and the linear relationship is as follows:
Figure FDA0002957402520000021
order to
Figure FDA0002957402520000022
Then
Figure FDA0002957402520000023
Setting error E and deviation E to compare, if | E tint<E, the value of the over-threshold peak point at the moment is the value of the required central peak point, if the deviation E is greater than the set error E,
Figure FDA0002957402520000024
beta is a correction factor, the value range is 1.5-1.9, the value of e is calculated by changing the correction factor, and the value amax of the central peak point is calculated to be a1+ e.
4. The peak tracking method of the altitude signal of the drone of claim 1, wherein the altitude tracking: setting an altitude threshold factor epsilon, which is used for limiting the absolute value of the difference between the current altitude data H (k) and the altitude data H (k-1) appearing in the previous period, so that the absolute value of the difference is not larger than the altitude threshold factor epsilon;
the expression is as follows:
the value of | H (k) | -H (k-1) | is less than or equal to epsilon, and the value range of epsilon is 0.8-1.3;
if the absolute value of the difference value between the height data at the moment k and the height data at the moment k-1 is within the set height threshold factor epsilon, outputting the height data at the moment k; if the absolute value of the difference between the height data at time k and the height data at time k-1 exceeds the set height threshold factor epsilon, the height data output at time k is replaced with the height data at time k-1.
5. The peak tracking method for the unmanned aerial vehicle altitude signal according to claim 4, wherein an altitude abrupt change accumulation factor θ is set, and the altitude abrupt change accumulation factor θ is defined as that if b cycles are continued from the time k, and the altitude data exceeds the altitude abrupt change accumulation factor θ compared with the altitude data of the previous cycle, the altitude data calculated at the current time is taken as the altitude data at the current time at the time k + b.
6. The peak tracking method of the altitude signal of the drone of claim 1, wherein: during height output, for height data output at a single time, outputting a height value by adopting a sliding window algorithm;
the altitude data at time k is equal to N in the sliding windowcThe average value of the maximum height value and the minimum height value of the individual height value is removed and is output as the final height data, and the calculation formula is
Figure FDA0002957402520000031
Wherein N iscIndicating the number of height data points taken by the sliding window.
CN201610723451.7A 2016-08-25 2016-08-25 Peak tracking method for height signal of unmanned aerial vehicle Active CN107783102B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201610723451.7A CN107783102B (en) 2016-08-25 2016-08-25 Peak tracking method for height signal of unmanned aerial vehicle

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201610723451.7A CN107783102B (en) 2016-08-25 2016-08-25 Peak tracking method for height signal of unmanned aerial vehicle

Publications (2)

Publication Number Publication Date
CN107783102A CN107783102A (en) 2018-03-09
CN107783102B true CN107783102B (en) 2021-04-27

Family

ID=61438867

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201610723451.7A Active CN107783102B (en) 2016-08-25 2016-08-25 Peak tracking method for height signal of unmanned aerial vehicle

Country Status (1)

Country Link
CN (1) CN107783102B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109521433A (en) * 2018-10-31 2019-03-26 歌尔股份有限公司 Determination method, the processing method and processing device of the abnormal frame point cloud data of laser radar

Citations (13)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101980043A (en) * 2010-09-15 2011-02-23 电子科技大学 Anti-receiver phase jump method for measuring directions of interference sources
CN102707271A (en) * 2012-05-31 2012-10-03 武汉大学 System utilizing CMMB (China Mobile Multimedia Broadcasting) signal to detect target and method thereof
KR20130084780A (en) * 2012-01-18 2013-07-26 국방과학연구소 Control method for following vertical profile in the speed-height plane
CN103344218A (en) * 2013-06-18 2013-10-09 桂林理工大学 System and method for measuring altitude of low-altitude unmanned plane
CN103759761A (en) * 2014-01-16 2014-04-30 北京航空航天大学 Unmanned aerial vehicle climbing rate measurement method without acceleration sensor combination compensation
CN203950037U (en) * 2014-05-23 2014-11-19 广东电网公司电力科学研究院 The echo signal treating apparatus of unmanned plane obstacle avoidance system, unmanned plane obstacle avoidance system
CN104238580A (en) * 2014-09-30 2014-12-24 中国航天空气动力技术研究院 Low-altitude flight control method applied to airborne geophysical prospecting of unmanned aerial vehicle
CN104567799A (en) * 2014-11-28 2015-04-29 天津大学 Multi-sensor information fusion-based method for measuring height of small unmanned gyroplane
CN104991245A (en) * 2015-07-29 2015-10-21 杨珊珊 Unmanned aerial vehicle early warning apparatus and early warning method thereof
CN205049136U (en) * 2015-10-21 2016-02-24 零度智控(北京)智能科技有限公司 Unmanned aerial vehicle flight height measuring device
CN105388901A (en) * 2014-08-26 2016-03-09 鹦鹉股份有限公司 Method of dynamic control of a rotary- wing drone in throw start
CN105445714A (en) * 2015-11-24 2016-03-30 大连楼兰科技股份有限公司 Automobile forward direction anticollision system signal processing method
CN105843246A (en) * 2015-11-27 2016-08-10 深圳市星图智控科技有限公司 Unmanned aerial vehicle tracking method, unmanned aerial vehicle tracking system and unmanned aerial vehicle

Patent Citations (13)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101980043A (en) * 2010-09-15 2011-02-23 电子科技大学 Anti-receiver phase jump method for measuring directions of interference sources
KR20130084780A (en) * 2012-01-18 2013-07-26 국방과학연구소 Control method for following vertical profile in the speed-height plane
CN102707271A (en) * 2012-05-31 2012-10-03 武汉大学 System utilizing CMMB (China Mobile Multimedia Broadcasting) signal to detect target and method thereof
CN103344218A (en) * 2013-06-18 2013-10-09 桂林理工大学 System and method for measuring altitude of low-altitude unmanned plane
CN103759761A (en) * 2014-01-16 2014-04-30 北京航空航天大学 Unmanned aerial vehicle climbing rate measurement method without acceleration sensor combination compensation
CN203950037U (en) * 2014-05-23 2014-11-19 广东电网公司电力科学研究院 The echo signal treating apparatus of unmanned plane obstacle avoidance system, unmanned plane obstacle avoidance system
CN105388901A (en) * 2014-08-26 2016-03-09 鹦鹉股份有限公司 Method of dynamic control of a rotary- wing drone in throw start
CN104238580A (en) * 2014-09-30 2014-12-24 中国航天空气动力技术研究院 Low-altitude flight control method applied to airborne geophysical prospecting of unmanned aerial vehicle
CN104567799A (en) * 2014-11-28 2015-04-29 天津大学 Multi-sensor information fusion-based method for measuring height of small unmanned gyroplane
CN104991245A (en) * 2015-07-29 2015-10-21 杨珊珊 Unmanned aerial vehicle early warning apparatus and early warning method thereof
CN205049136U (en) * 2015-10-21 2016-02-24 零度智控(北京)智能科技有限公司 Unmanned aerial vehicle flight height measuring device
CN105445714A (en) * 2015-11-24 2016-03-30 大连楼兰科技股份有限公司 Automobile forward direction anticollision system signal processing method
CN105843246A (en) * 2015-11-27 2016-08-10 深圳市星图智控科技有限公司 Unmanned aerial vehicle tracking method, unmanned aerial vehicle tracking system and unmanned aerial vehicle

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
CFAR Target Detection Based on Gumbel Distribution for HF Radar;Dzvonkovskaya A L , et al;《 International Radar Symposium》;20061231;p1-3 *
一种改进的LFMCW雷达多目标加速度和速度估计方法;吴礼等;《南京理工大学学报》;20111031;第646-651页 *

Also Published As

Publication number Publication date
CN107783102A (en) 2018-03-09

Similar Documents

Publication Publication Date Title
CN107783107B (en) Millimeter wave radar altimeter of plant protection rotor unmanned aerial vehicle
CN107783133B (en) Anti-collision system and anti-collision method for fixed-wing unmanned aerial vehicle of millimeter wave radar
US7633429B1 (en) Monopulse radar signal processing for rotorcraft brownout aid application
CN101825707A (en) Monopulse angular measurement method based on Keystone transformation and coherent integration
CN106291524A (en) LFMCW radar detection movement human mesh calibration method based on anthropometric dummy
CN111965667A (en) Dynamic compensation wind measurement laser radar system and wind measurement method thereof
CN107783128B (en) Multi-target anti-collision system of fixed-wing unmanned aerial vehicle based on millimeter wave radar
CN107783121A (en) Pilotless automobile anti-collision radar system signal processing system and method based on combined waveform
CN105717508B (en) A kind of airborne radar forword-looking imaging method based on the modulation of transmitted waveform orientation
CN113253223B (en) Target detection method for non-stationary clutter suppression based on step frequency signal
CN106019280B (en) FMCW SAR imaging methods and device based on range Doppler correction
CN109655802A (en) A kind of multi-objective particle swarm long time integration detection method based on CLEAN algorithm
CN107783102B (en) Peak tracking method for height signal of unmanned aerial vehicle
CN107783090B (en) Millimeter wave radar-based radar signal processing method for collision avoidance system of fixed-wing unmanned aerial vehicle
CN108445477A (en) The precision distance measurement method of airdrome scene foreign bodies detection radar
CN107783077B (en) Method for processing threshold-passing peak point
CN107783099A (en) Rotor wing unmanned aerial vehicle short distance CAS signal processing system and method based on combined waveform
CN107783132A (en) Autonomous driving vehicle anticollision millimetre-wave radar system and signal processing method
CN107783108B (en) Radar signal processing method for radar altimeter system of plant protection rotor unmanned aerial vehicle
CN110488239B (en) Target detection method based on frequency modulation continuous wave radar
CN107783129B (en) Anti-collision millimeter wave radar signal processing method for rotor unmanned aerial vehicle
CN107783125B (en) Rotor unmanned aerial vehicle anti-collision millimeter wave radar system and signal processing method
CN107783100B (en) Rotor unmanned aerial vehicle short-distance anti-collision system signal processing method based on combined waveform
Li et al. Bistatic forward-looking SAR imaging based on two-dimensional principle of stationary phase
CN115436940A (en) Sparse sliding spotlight SAR imaging mode realization method and device

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant