CN109031275A - A kind of insect horizontal flight VELOCITY EXTRACTION method based on high-resolution polarization radar - Google Patents
A kind of insect horizontal flight VELOCITY EXTRACTION method based on high-resolution polarization radar 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
- 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
- G01S13/50—Systems of measurement based on relative movement of target
- G01S13/58—Velocity or trajectory determination systems; Sense-of-movement determination systems
- G01S13/589—Velocity or trajectory determination systems; Sense-of-movement determination systems measuring the velocity vector
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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
- G01S13/50—Systems of measurement based on relative movement of target
- G01S13/58—Velocity or trajectory determination systems; Sense-of-movement determination systems
- G01S13/581—Velocity or trajectory determination systems; Sense-of-movement determination systems using transmission of interrupted pulse modulated waves and based upon the Doppler effect resulting from movement of targets
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Abstract
The insect horizontal flight VELOCITY EXTRACTION method based on high-resolution polarization radar that the invention discloses a kind of；The present invention observes Migrating Insects using high-resolution polarization radar, obtain the complete polarization information of insect, observation data model and antenna radiation pattern model foundation insect based on polarization radar pass through the echo signal model of wave beam, and the horizontal component of insect flying speed is finally gone out using Least Square Method.It can reduce measurement error using the present invention, improved Parameter Estimation Precision；And the present invention constructs the model for being absorbed in insect horizontal flight VELOCITY EXTRACTION, model is simple and effective, and combines the solution procedure of iteration, so that solution procedure greatly simplifies.
Description
Technical field
The invention belongs to entomological radar technical fields, and in particular to a kind of insect based on high-resolution polarization radar is horizontal
Flying speed extracting method.
Background technique
Entomological radar is a kind of new tool for monitoring high-altitude Migrating Insects population.Entomological radar used at present mainly hangs down
Straight monitoring entomological radar, it is realized by the way of polarization rotation and wave beam nutating to echo from insect quantity, height, orientation angle
Degree, velocity of displacement, direction of displacement, to beam center axle the shortest distance and RCS parameter related with body size extraction.
According to the parameter of acquisition, the category identification of insect can be carried out, predict the direction of migrating of insect, this is for predicting pest and disease damage, grinding
The mechanism of migrating of insect is studied carefully with very great meaning.
With the development of Radar Technology, distance has been increasingly becoming a kind of development trend to high-resolution.Step frequency technology
It is a kind of realization distance to high-resolution important technology.It is by emitting a series of carrier frequency steppings with smaller instant bandwidth
Then signal synthesizes big bandwidth signal by suitably processing in receiving end, to reach higher range resolution.It is high
Distance resolution plays a significant role anti-interference, raising measurement accuracy and fine target following.
As the information such as polarization information in Radar Target Scatter signal and the amplitude of target echo, frequency and phase, it is
Highly useful information.Changeable Polarization Radar System is a kind of new radar system in recent years, it is introduced in the electromagnetic wave of transmitting
Polarization information.The stages such as the development experience of Changeable Polarization Radar System single polarization, dual polarization and complete polarization.Traditional vertical monitoring
Using rotation linear polarization, it realizes rotation linear polarization by the rotation to single linear polarization, thus can entomological radar
The echo from insect intensity in each polarization direction is enough obtained, to obtain all polarization information of insect.And polarization radar is logical
Cross and emit the orthogonal electromagnetic wave of a pair of of polarized state, can directly measure target HH (horizontal polarization transmitting, horizontal polarization receive),
HV (vertical polarization transmitting, horizontal polarization receive), VH (horizontal polarization transmitting, vertical polarization receive) and VV (vertical polarization emits,
Vertical polarization receives) the different polar echo in four tunnels, obtain the complete polarization information of target.
In order to extract the parameter information of Migrating Insects, Smith and Riley et al. are established with rotary polarization and nutating function
The echo signal model of the vertical monitoring entomological radar of energy.Pass through polarization rotation speed and the nutating angle etc. for setting radar
Radar parameter can obtain echo from insect intensity versus time curve during insect passes through wave beam.Insect is returned
Wave amplitude carries out Fourier transformation, so that it may obtain form more simpler than original echo.It can be used in parameter extraction
" three peaks " or " five peaks " approximate method can extract velocity of displacement, direction of displacement, body direction and three and insect ruler
Very little sectional area parameter related with shape.But the radar system resolution ratio is low and solving model is complicated.
Summary of the invention
In view of this, the present invention provides a kind of insect horizontal flight VELOCITY EXTRACTION side based on high-resolution polarization radar
Method observes Migrating Insects using high-resolution polarization radar, obtains the complete polarization information of insect, then establish insect and pass through wave beam
Echo signal model, finally go out the horizontal component of insect flying speed using Least Square Method.Obtain the water of insect
Flat flying speed can provide help to the category identification of insect.
The insect horizontal flight VELOCITY EXTRACTION method based on high-resolution polarization radar, includes the following steps:
Step 1: the observation data model of high-resolution polarization radar is established, specifically:
S11, frequency modulation stepped frequency signal model is established:
Wherein, sHIt (t) is frequency modulation stepped frequency signal；G ' is a constant；N is step frequency number；△ f is carrier frequency stepping
Interval；R is distance of the insect to radar；RminFor starting sample distance；fcFor the centre frequency of entire stepped frequency signal；C is light
Speed；T is the time；
S12, antenna direction graph model is established:
Wherein, E0It is the voltage gain in beam center axle；K=8ln2；D is distance of the insect to beam center axle；L is
The diameter of elevation beam cross section where insect；
S13, frequency modulation stepped frequency signal model and antenna direction graph model according to foundation, establish echo from insect signal mode
Type:
Wherein, Sr,hh(t) be echo from insect signal HH durection component, C is related with antenna gain, signal processing gain
Constant；P is the shortest distance of the insect to radar beam central axis；VhIt is the horizontal component of the insect flying speed to be extracted；τ
Insect and radar beam central axis apart from it is nearest at the time of；θ0.5For half-power beam width；ShhFor horizontal polarization transmitting and water
The insect polarization scattering matrix PSM of flat polarization reception measurement；The echo from insect signal model S of HV, VH and VV componentr,hv(t)、
Sr,vh(t) and Sr,vv(t) with formula (3) model having the same, it is only necessary to by S in formula (3)hhIt is substituted for respective PSM points
Amount.
S14, formula (3) is normalized and is taken logarithm, obtain observation data u (t) model suitable for four road echoes:
Wherein, e is natural logrithm；Two unknown parameter V in data modelhAnd τ, it is expressed as form θ=[V of vectorh,
τ]T, element θ in vectori(i=1,2) it indicates；
Step 2: the four road echo datas that the more same target obtains, take wherein signal-to-noise ratio it is highest all the way, by pre-
Observation data w=[w is obtained after processing0 w1 ... wM-1]T, data length M；The observation data mould obtained using step 1
Type, in R and θ0.5The model data generated under the same conditions is u (θ)=[u1 u2 ... uM-1]T；
Step 3: going out the unknown parameter V in model based on Least Square Method using w and u (θ)hAnd τ, obtain insect
Horizontal flight speed and its estimated value at moment.
Preferably, the step 3 solves unknown parameter using iterative manner, are as follows:
S31, construction cost function J (θ) are as follows:
J (θ)=(w-u (θ))H(w-u(θ)) (2)
Wherein, subscript H indicates complex conjugate transposition；
S32, J is usedkIndicate the cost function of kth time iteration, Jk+1Indicate the cost function of+1 iteration of kth,It is kth
I-th of estimation parameter of secondary iteration,It is i-th of estimation parameter of+1 iteration of kth；Cost function J existsThe second order at place
Taylor expansion are as follows:
S33, in order to make Jk+1Reach minimum, seeks J in formula (3)k+1It is rightDerivative, and enable its be equal to 0, obtain:
S34, selection iteration initial value, are calculated, each iteration finishes judgement solving precision with the iterative formula of formula (4)
Whether meet the requirements:
If being unsatisfactory for requiring, the number of iterations k value adds 1, returns to S33, carries out next iteration；
If meeting the requirements, current value is exactly horizontal velocity VhWith the estimated value of time instant τ.
Preferably, in step 3, start the initial value of θ when iteration are as follows: horizontal velocity VhInitial value range be [0,20],
The initial value range of time instant τ is [0,10].
Preferably, in step 2, the difference for meeting the adjacent value of iterative estimate twice is respectively less than 10-5Be considered as and meet precision and want
It asks.
The invention has the following beneficial effects:
The present invention is a kind of insect horizontal flight VELOCITY EXTRACTION method based on high-resolution polarization radar, is migrated to extract
The horizontal flight speed of insect provides a kind of simple and effective means.Relative to existing insect velocity of displacement extracting method,
The specific advantage of this method is:
(1) present invention is four road available for the same target echo data (two based on polarization radar system
Road same polarization echo data HH and VV, two-way cross polarization echo data HV and VH), compare four tunnel information, takes wherein signal-to-noise ratio
It is highest to be used to extract horizontal velocity all the way, to improve Parameter Estimation Precision.
(2) present invention uses frequency modulation Step Frequency radar synthesized wideband signal, and the more high then distance resolution of bandwidth is higher,
Therefore this system guarantee high resolution range, reduces measurement error to a certain extent.
(3) present invention constructs the model for being absorbed in insect horizontal flight VELOCITY EXTRACTION, and model is simple and effective, and combines and change
The solution procedure in generation, so that solution procedure greatly simplifies.
Detailed description of the invention
Fig. 1 is antenna radiation pattern model schematic.
Fig. 2 (a) is that insect passes through radar beam process schematic, and Fig. 2 (b) is the water of insect flying track and body direction
Flat projection.
Fig. 3 is HH echo data when insect A passes through radar beam.
Fig. 4 is VV echo data when insect B passes through radar beam.
Fig. 5 is the observation data picked out from the HH echo data of insect A and its fitting result
Fig. 6 is the observation data picked out from the VV echo data of insect B and its fitting result.
Wherein, 1- insect, 2- radar, 3- beam center axle.
Specific embodiment
The present invention will now be described in detail with reference to the accompanying drawings and examples.
Initially set up the echo from insect model of high-resolution polarization radar.It needs first to establish frequency modulation Step Frequency in modeling process
Signal model, antenna direction graph model, finally establish echo from insect signal model.
First frequency modulation stepped frequency signal is modeled below.Frequency modulation stepped frequency signal by N number of carrier frequency stepping Chirp signal group
At each Chirp signal bandwidth is B, pulsewidth Tp, carrier frequency stepped intervals be △ f, thus after signal processing can synthetic bandwidth be
The broadband signal of N △ f.If step frequency radar system gradually emits N number of narrowband Chirp signal with identical frequency interval,
Transmitting signal can be written as the sum of N number of Chirp signal, it may be assumed that
Wherein, rect () is rectangular function, andf0It is
The carrier frequency of one subpulse；TrFor the pulse repetition period；Kr=B/TpFor the linear frequency modulation rate of Chirp signal；N=0,1 ..., N-
1 is corresponding frequency point number.B >=△ f is required, in parameter designing to guarantee effective covering of frequency spectrum.
During entomological radar work, antenna alternate emission and reception stepped frequency signal.When demodulation, reference signal is also frequency
Rate stepping.It adjusts the distance and carries out quadrature frequency conversion processing for the echo-signal of the single-point target of R, obtain frequency modulation step after removing carrier wave
Into frequency signal baseband echo model:
Wherein, G is amount related with antenna beam gain and target scattering characteristics.
Obtain that there is high-resolution big bandwidth signal using frequency domain splicing algorithm to frequency modulation stepped frequency signal.It should
Algorithm is that the echo-signal of each subpulse is transformed to frequency domain first, then carries out matched filtering processing respectively, removes through frequency spectrum
It moves, after phase compensation and frequency domain splicing, obtains the frequency-region signal of big bandwidth, finally doing IFFT processing, that high-resolution can be obtained is one-dimensional
Range Profile:
Wherein, G ' is a constant；RminFor starting sample distance；For entire Step Frequency letter
Number centre frequency.
Antenna direction graph model is described below.The gain size of beam main lobe is usually with Gaussian function come approximate:
Wherein, E0It is the gain in beam center axle；K=8ln2；θ0.5For half-power beam width；θ is beam center axle
With target to the angle of beam center line.
It assuming that target is R with distance by radar in beam main lobe, and is D to the distance of beam center axle, schematic diagram is shown in figure
1.For general radar system, beam angle is usually smaller, therefore has tan θ ≈ θ,Root
According to Fig. 1, have:
Therefore, formula (4) can be indicated again are as follows:
The frequency modulation stepped frequency signal model and antenna direction graph model established according to front, establish echo from insect signal mode
Type.As shown in Fig. 2 (a), it is assumed that insect I is that the aerial of H flies at a constant speed along straight line P from height, the folder of straight line P and z-axis positive direction
Angle is α, flying speed V.Due to the influence of wind, insect body direction is often inconsistent with direction of displacement, it is assumed that the body of insect I
Body is towards along straight line Q.Insect flying track, body direction and flying speed are projected on horizontal plane, as shown in Fig. 2 (b), position
The floor projection for moving direction is straight line P ', and the floor projection of body direction is Q ', and the horizontal component of three-dimensional velocity V is Vh.Straight line
P ' and the angle of positive direction of the x-axis are β, and straight line Q ' and the angle of positive direction of the x-axis are φ.A point be that straight line P ' is upper and O ' distances most
Close point, distance are p, and assume that at a time τ, insect I pass through A point.The instantaneous distance of insect I to beam center axle is r.
According to fig. 2 (b), the instantaneous distance r of insect I to beam center axle meets following relationship:
Since beam angle is very narrow, insect during leaping beam main lobe, the distance R of insect to radar and insect
Flying height H is approximately equal, i.e. H ≈ R.Insect polarization scattering matrix PSM are as follows:
Assuming that the signal power that the transmitting of antenna horizontal polarization and horizontal polarization receive the i.e. direction HH is Sr,hh(t), consider day
The gain of line bi-directional voltage, target polarization scattering matrix and Step Frequency synthesis processing, and only consider the variation of signal in the slow time,
Even the sinc function in formula (3) is equal to 1, the form of signal is finally received are as follows:
Wherein, C is and the related constants such as antenna gain, signal processing gain.Similarly, the insect of HV, VH and VV component
Echo signal model Sr,hv(t)、Sr,vh(t) and Sr,vv(t) with formula (9) model having the same, it is only necessary to by S in formula (9)hhIt replaces
Change respective PSM component into, c is the light velocity.
The part that signal formula (9) do not change over time will be received and do normalized, can be obtained:
Logarithm is taken to formula (10), available:
Wherein, e is natural logrithm.This just establishes final echo model, this model is suitable for four road echoes.Model
In there are two unknown parameter VhAnd τ, it is expressed as form θ=[V of vectorh,τ]T, element θ in vectori(i=1,2) it indicates.
Be described below how from actual measurement echo from insect data in estimate horizontal velocity Vh.Polarization radar is at a fixed time
A data are acquired in interval, select valid data and after pretreatment as observation data w=[w0 w1 ...
wM-1]T, data length M；Modular form (11) is in R and θ0.5Data under the same terms are u (θ)=[u1 u2 ... uM-1]T,
So using w and u (θ), the unknown parameter V in model is gone out based on Least Square MethodhAnd τ, obtain the horizontal flight of insect
Speed and its estimated value at moment.
Present embodiment is to solve unknown parameter using iterative manner:
The cost function of construction are as follows:
J (θ)=(w-u (θ))H(w-u(θ)) (12)
Wherein, subscript H indicates complex conjugate transposition.
The data of the signal model and actual observation established are closer, then the value of cost function J is smaller, so adjustment θ
Value, when cost function J reaches minimum, the value of θ is exactly our values to be estimated at this time.Use JkIndicate the mesh of kth time iteration
Scalar functions, Jk+1Indicate the cost function of+1 iteration of kth,It is i-th of estimation parameter of kth time iteration,It is kth+1
I-th of estimation parameter of secondary iteration.Cost function J existsThe second Taylor series formula at place are as follows:
In order to make Jk+1Reach minimum, seeks Jk+1It is rightDerivative, and enable its be equal to 0, can obtain:
Known toIt is meant that the stepped intervals of+1 iteration of kth and kth time iteration, and has:
Solving model formula (11) is for parameter VhWith the first derivative and second dervative of τ:
Suitable iteration initial value is selected, is calculated with the iterative formula of formula (14), each iteration finishes judgement and solves
Whether precision meets the requirements, and carries out next iteration if being unsatisfactory for requiring, if meeting the requirements, current value is exactly horizontal velocity
VhWith the estimated value with time instant τ.
Existing insect velocity of displacement extracting method is the system radar system that polarized based on rotational line, and this method solves ginseng
Number is considerably complicated.The present invention is four road available for the same target echo data (two based on polarization radar system
Road same polarization echo data HH and VV, two-way cross polarization echo data HV and VH), compare four tunnel information, takes wherein signal-to-noise ratio
It is highest to be used to extract horizontal velocity all the way.It follows that the present invention is suitable for polarization radar system, method for solving is simply easy
Row, reduces measurement error using the design of high resolution range to a certain extent.
Therefore, the insect horizontal flight VELOCITY EXTRACTION method based on high-resolution polarization radar that the present invention provides a kind of,
It will illustrate implementation steps below with specific embodiment:
To verify mentioned-above insect horizontal flight VELOCITY EXTRACTION method, it is based on Ku wave band high-resolution complete polarization insect thunder
It reaches, acquires the echo data of aerial Migrating Insects, using a kind of insect based on high-resolution polarization radar of the present invention
Horizontal flight VELOCITY EXTRACTION method, realizes the extraction of its horizontal flight speed.It tests radar system parameters used and is shown in Table 1.
1 complete polarization entomological radar system parameter of table
Step 1, complete polarization entomological radar entomologize echo data:
Complete polarization entomological radar is arranged in the intensive field of insect communities, night opens radar and is at normal work
State, adjustment antenna elevation angle make radar beam vertically to day, start to acquire data.Collected echo data is located in advance
Reason obtains during insect passes through radar beam, the echo-signal that intensity changes over time.For some insect target, compare four
Road echo data picks out the highest echo data all the way of signal-to-noise ratio.The echo data of insect A and insect B are shown in Fig. 3 and figure respectively
4。
Step 2 selects the data of appropriate area as observation data from echo data:
Select area data near echo data wave crest place that observation data are carried out binomial and are intended as observation data
It closes.Observation data and the fitting result difference of the insect A and insect B that pick out are as shown in Figure 5 and Figure 6.The observation that will be singled out
Data normalization obtains the observation data w=[w to match with model0 w1 ... wM-1]T。
Step 3 estimates the horizontal flight speed of insect with iterative algorithm:
Iterative algorithm needs to provide the initial value of parameter θ.For insect target, horizontal velocity VhInitial value range be
[0,20], the initial value range of time instant τ are [0,10].After initial value is selected, by radar observation data w=[w0 w1 ... wM-1
]T, modular form (11) model data and θ under initial value initial value substitute into formula (14) in be iterated operation.Set iteration
Stop condition, for example, when meetingWhen, iteration stopping.
Here, initial value θ=[20 1.5] are selectedT, by the initial value of θ, observation data w=[w0 w1 ... wM-1]TWith
Model data u (θ)=[u1 u2 ... uM-1]TSubstitution formula (14) estimates the horizontal flight speed of insect.Insect A and insect B
Horizontal flight velocity estimation value such as table 2.
2 insect horizontal flight velocity estimation result of table
According to the horizontal flight velocity estimation of above-mentioned actual measurement echo from insect data as a result, it can be concluded that for
Different echo from insect data utilize the insect horizontal flight VELOCITY EXTRACTION method based on high-resolution polarization radar, Ke Yiyou
The horizontal flight speed for estimating insect of effect.
Method of the invention can be applied on complete polarization entomological radar, realize the extraction of insect horizontal flight speed.
In conclusion the above is merely preferred embodiments of the present invention, being not intended to limit the scope of the present invention.
All within the spirits and principles of the present invention, any modification, equivalent replacement, improvement and so on should be included in of the invention
Within protection scope.
Claims (6)
1. a kind of insect horizontal flight VELOCITY EXTRACTION method based on high-resolution polarization radar, which is characterized in that including as follows
Step:
Step 1: establishing echo from insect using the frequency modulation stepped frequency signal model and antenna direction graph model of polarization radar
Signal model normalizes and takes logarithm, obtains observation data model:
Wherein, e is natural logrithm, observes two in data model unknown parameter VhAnd τ, it is expressed as form θ=[V of vectorh,
τ]T, element θ in vectori(i=1,2) it indicates；VhIt is the horizontal component of the insect flying speed to be extracted；τ be insect with
Radar beam central axis apart from it is nearest at the time of；θ0.5For half-power beam width；R is distance of the insect to radar；K=8ln2；
Step 2: acquisition data, the four road echo datas that the more same target obtains, take wherein signal-to-noise ratio it is highest all the way,
Observation data w=[w is obtained after pretreatment0 w1 ... wM-1]T, data length M；The observation number obtained using step 1
According to model, in R and θ0.5The model data generated under the same conditions is u (θ)=[u1 u2 ... uM-1]T；
Step 3: going out the unknown parameter V in model based on Least Square Method using w and u (θ)hAnd τ, obtain the water of insect
Flat flying speed and its estimated value at moment.
2. a kind of insect horizontal flight VELOCITY EXTRACTION method based on high-resolution polarization radar as described in claim 1,
It being characterized in that, the step 3 solves unknown parameter using iterative manner, are as follows:
S31, construction cost function J (θ) are as follows:
J (θ)=(w-u (θ))H(w-u(θ)) (2)
Wherein, subscript H indicates complex conjugate transposition；
S32, J is usedkIndicate the cost function of kth time iteration, Jk+1Indicate the cost function of+1 iteration of kth,It is that kth time changes
I-th of estimation parameter in generation,It is i-th of estimation parameter of+1 iteration of kth；Cost function J existsThe second order Taylor at place
Expansion are as follows:
S33, in order to make Jk+1Reach minimum, seeks J in formula (3)k+1It is rightDerivative, and enable its be equal to 0, obtain:
S34, selection iteration initial value, are calculated, each iteration finishes whether judge solving precision with the iterative formula of formula (4)
It meets the requirements:
If being unsatisfactory for requiring, the number of iterations k value adds 1, returns to S33, carries out next iteration；
If meeting the requirements, current value is exactly horizontal velocity VhWith the estimated value of time instant τ.
3. a kind of insect horizontal flight VELOCITY EXTRACTION method based on high-resolution polarization radar as claimed in claim 2,
It is characterized in that, in step 3, starts the initial value of θ when iteration are as follows: horizontal velocity VhInitial value range be [0,20], time instant τ
Initial value range be [0,10].
4. a kind of insect horizontal flight VELOCITY EXTRACTION method based on high-resolution polarization radar as claimed in claim 2,
It is characterized in that, in step 2, the difference for meeting the adjacent value of iterative estimate twice is respectively less than 10-5Be considered as and meet required precision.
5. a kind of insect horizontal flight VELOCITY EXTRACTION method based on high-resolution polarization radar as described in claim 1,
It is characterized in that, data is acquired described in step 2 are as follows: polarization radar is arranged in the intensive field of insect communities, night opens thunder
Up to normal operating conditions is at, adjustment antenna elevation angle makes radar beam vertically to day, be acquired data.
6. a kind of insect horizontal flight VELOCITY EXTRACTION method based on high-resolution polarization radar as described in claim 1,
It is characterized in that, is pre-processed described in step 2 are as follows: select area data near echo data wave crest place, will as observation data
Data normalization is observed, the observation data w=[w to match with model is obtained0 w1 ... wM-1]T。
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| CN111308435A (en) * | 2019-12-09 | 2020-06-19 | 中国科学院沈阳自动化研究所 | Frequency-variable multi-delay centralized MIMO radar signal processing method |
| CN111551931A (en) * | 2020-05-18 | 2020-08-18 | 西安电子科技大学 | Target length feature extraction method based on polarization high-resolution range profile |
| CN114814818A (en) * | 2022-06-30 | 2022-07-29 | 三亚中国农业科学院国家南繁研究院 | Insect radar monitoring-based pest migration path simulation method |
| US20230194705A1 (en) * | 2021-12-20 | 2023-06-22 | Aptiv Technologies Limited | Movement Compensation for Multi-Dimensional Radar Signal Processing |
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