# Patent

## Title
Wide band clear air scatter doppler radar

## Abstract

Systems and methods for measuring wind speed and direction in clear air conditions using a wide band Doppler radar in accordance with embodiments of the invention are disclosed. In one embodiment of the invention, a wide band Doppler radar system includes an antenna assembly includes at least one transmit antenna and at least one receive antenna; a transceiver connected to the antenna assembly configured to transmit a radar beam includes a transmit signal on a Ka-band carrier frequency and receive a backscattered radar beam includes a carrier frequency that is frequency shifted relative to the transmitted Ka-band carrier frequency of the backscattered radar beam; a data acquisition system connected to the transceiver configured to estimate a wind velocity vector by calculating a Doppler shift between at least one transmitted radar beam and at least one received backscattered radar beam.

## Background
CROSS-REFERENCE TO RELATED APPLICATIONS
The current application claims priority to Provisional Patent Application No. 61/653,882, entitled “WIDE BAND CLEAR AIR SCATTER DOPPLER RADAR”, filed May 31, 2012, the disclosure of which is incorporated herein by reference.


FIELD OF THE INVENTION
The present invention generally relates to radars and more specifically to systems and methods for measuring wind speed and direction using Doppler radars.
BACKGROUND
Wind profilers can detect wind speed and direction (i.e. velocity) at various altitudes using radars and are typically used for meteorological forecasting and flight planning. Radar based wind profilers can measure wind velocity by observing scattering effects on radio waves due to micro-hydrometers including fog, clouds, and/or mist—so called dull weather phenomena and suspended particles including (but not limited to) thick dust and insets.
Further, radar based systems can detect wind speed and direction by observing the so called Bragg Scattering phenomena caused by natural atmospheric turbulence in the atmosphere. Wind profiling radars typically operate at frequencies near 50 MHz, 400 MHz and 900 MHz because Bragg Scattering conditions are dominate at these relatively lower frequencies. However, Bragg Scattering effects are relatively faint even at these lower frequencies and radars have traditionally relied on larger integration times, larger range cells, and larger antenna arrays to make measurements.
Clear air scatterers (CAS) are small turbulent motions of air associated with ever-present hydrodynamic-thermodynamic instabilities in the atmosphere during clear weather conditions. Such small turbulent motions can track the mean velocity of a volume of wind and exist long enough to reliable detected. Further CAS have a defined nature and are prevalent in the convective boundary layer (CBL) where wind speed and direction measurements are particular useful for meteorological forecasting and/or flight planning. However, CAS in the CBL have very small returns (reflected energy), often two orders of magnitude smaller than returns for fog or clouds and conventional thinking has been that radar's operating in the centimeter to millimeter range in clear weather conditions could not obtain a useable return due to the varying and often small concentrations of CAS.
SUMMARY OF THE INVENTION
Systems and methods for measuring wind speed and direction in clear air conditions using a wide band Doppler radar in accordance with embodiments of the invention are disclosed. In one embodiment, a wide band Doppler radar system includes an antenna assembly includes at least one transmit antenna and at least one receive antenna, where each of the at least one transmit antenna is configured to transmit a radar beam includes a transmit signal on a Ka-band carrier frequency and each of the at least one receive antenna is configured to receive a backscattered radar beam includes a carrier frequency that is frequency shifted relative to the transmitted Ka-band carrier frequency of the backscattered radar beam; a transceiver connected to the antenna assembly configured to transmit a radar beam includes a transmit signal on a Ka-band carrier frequency using each of the at least one transmit antenna and receive a backscattered radar beam includes a carrier frequency that is frequency shifted relative to the transmitted Ka-band carrier frequency of the backscattered radar beam using each of the at least one receive antenna; a data acquisition system connected to the transceiver configured to estimate a wind velocity vector by calculating a Doppler shift between at least one transmitted radar beam and at least one received backscattered radar beam.
In a further embodiment, the antenna assembly also includes a horn antenna having waveguide flanges.
In another embodiment, the transceiver operates between 33.3 GHz and 33.5 GHz.
In a still further embodiment, the transceiver operates as a frequency modulated continuous wave (FMCW) radar.
In still another embodiment, the antenna assembly also includes 4 transmit antennas.
In a yet further embodiment, the antenna assembly also includes 4 receive antennas.
In yet another embodiment, the transceiver connected to the antenna assembly is also configured to transmit radar beams that separated by 90 degrees in azimuth.
In a further embodiment again, the transceiver connected to the antenna assembly is also configured to transmit radar beams that tilted 80 degrees up from the horizontal.
In another embodiment again, the wide band Doppler radar system is stationary while in operation.
In a further additional embodiment, the wide band Doppler radar system is pointed north while in operation.
In another additional embodiment, transmitting a radar beam includes a transmit signal on a Ka-band carrier frequency also includes operating between 33.3 GHz and 33.5 GHz.
In a still yet further embodiment, transmitting a radar beam includes a transmit signal on a Ka-band carrier frequency also includes generating a continuous wave.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram of a wide band Doppler radar system for transmitting a radar beam comprising a transmit signal on a Ka-band carrier frequency and receiving a frequency shifted backscattered radar beam and estimating a wind velocity vector by calculating a Doppler shift in accordance with an embodiment of the invention.
FIG. 2 is a flow chart illustrating a process for estimating a wind velocity vector utilizing Doppler shift calculations between at least one transmit radar beam and a backscattered radar beam in accordance with an embodiment of the invention.
FIG. 3 is a flow chart illustrating a process for configuring radar beam directions for collecting data to for Doppler shift calculations in accordance with an embodiment of the invention.
FIG. 4 conceptually illustrates 4 radar beams and respective illuminated volume of wind (point representation) in accordance with an embodiment of the invention.
FIG. 5 is a flow chart illustrating a process for estimating a wind velocity vector under stationary radar conditions in accordance with an embodiment of the invention.
FIG. 6 is a flow chart illustrating a process for generating range-velocity matrices in accordance with an embodiment of the invention.
FIG. 7 is a flow chart illustrating a process for estimating the radar beam Doppler shift velocity using a range-velocity matrix in accordance with an embodiment of the invention.



DETAILED DISCLOSURE OF THE INVENTION
Turning now to the drawings, systems and methods for measuring wind speed and direction in clear air conditions using a wide band Doppler radar are described. A wide band Doppler radar system includes an antenna assembly comprising of at least one transmit antenna and at least one receive antenna. The transmit antennas are configured to transmit a radar beam having a direction and comprising a transmit signal on a Ka-band (27-40 GHz) carrier frequency. The receive antennas are configured to receive a backscattered radar beam comprising a carrier frequency that is frequency shifted relative to the transmitted Ka-band carrier frequency of the backscattered radar beam.
In many embodiments, the system includes a transceiver connected to the antenna assembly and configured to transmit a radar beam comprising a transmit signal on the Ka-band carrier frequency using a transmit antenna. The transceiver is further configured to receive the backscattered radar beam comprising a carrier frequency that is frequency shifted relative to the transmitted Ka-band carrier frequency of the backscattered radar beam using a receive antenna.
In several embodiments, the system includes a data acquisition system connected to the transceiver and configured to estimate a wind velocity vector by calculating a Doppler shift between at least one transmitted radar beam and at least one received backscattered radar beam.
In various embodiments, the system includes using multiple radar beams that can be separated by a predetermined angle with each radar beam tilted relative to the horizontal plane. Each radar beam can illuminate a volume of air in order to determine the wind speed and direction. In several embodiments, the system can be implemented where the radar is stationary or in motion. When the radar is stationary and/or pointing north, the wind velocity vector can be estimated more readily. In many embodiments, the system generates a range-velocity matrix using range measurements (distance between the radar and the illuminated volume of air) and the calculated Doppler shifts between at least one transmit radar beam and backscattered radar beam. In many embodiments, an observed radar beam Doppler shift velocity at various altitudes of interest can be estimated using the range-velocity matrix. Systems and methods for measuring wind speed and direction in clear air conditions using a wide band Doppler radar in accordance with embodiments of the invention are further discussed below.
Wide Band Doppler Radar System Architecture
Wide band Doppler radar systems in accordance with embodiments of the invention can be utilized for measuring wind speed and direction (i.e. wind velocity). A wide band Doppler radar system in accordance with an embodiment of the invention is illustrated in FIG. 1. The wide band Doppler radar system 100 includes an antenna assembly 102 comprising of separate transmit and receive antennas. In many embodiments, the antenna can be a horn antenna with a measured gain of 31 dBi having waveguide flanges. In several embodiments, the receive antenna can have a low noise amplifier on the flange. In various embodiments, the antenna assembly can be replaced with a single antenna solution, combined with a low leakage circulator and a reflected power canceller before the low noise amplifier. In other embodiments, the antenna assembly can be any high gain antenna or antenna system, with an antenna gain near 30 dBi or above. In many embodiments, the antennas can be 150 mm in diameter. Generally, larger antennas can improve the system performance but the maximum size of the antennas can be limited by the applications tolerance for size and weight of the antenna assembly.
In many embodiments, the antenna assembly is connected to a transceiver 104 with waveguide components. In several embodiments, the transceiver operates between 33.3 GHz and 33.5 GHz, with a maximum transit bandwidth of 200 MHz. The operating frequency is not limited to 33.3 GHz to 33.5 GHz as system performance does not significantly alter though the K (18-27 GHz) and Ka (26.5-40 GHz) bands. In various embodiments, a standard operating mode for the transceiver can be 33.4-33.5 GHz for range cells between 3 to 12.5 meters. Additional performance can be gained by using range cells that are smaller than 3 m since the coherence length of CAS are quite small. In many embodiments, the output power of the transceiver can be 34 dBm. In some embodiments, the combination of radar output power and antenna gain can be greater than 50 dB. In several embodiments, the transceiver operates as a frequency modulated continuous wave (FMCW) radar.
The system also includes a low noise oscillator 108 used to generate a system clock and the Ka-band carrier frequency for the transmit signal. In many embodiments, the oscillator produces a 200 MHz system clock that can start with phase noise less than 120 dB at 100 Hz offset from the carrier. The system also includes a multiplier 106 connected to the oscillator 108. In several embodiments, the system clock can be multiplied by five to generate a 1 GHz clock signal. In various embodiments, the 1 GHz clock signal can be further multiplied by 16 to create a 16 GHz clock source where the phase noise of the 1 GHz and 16 GHz clock signals are near theoretical limits with offsets of less than 3 dB+20 log N.
The multiplier is connected to a sweep generator 110. In many embodiments, a direct digital synthesized swept frequency waveform can be created based on a low noise 1 GHz synchronous clock. In several embodiments, the swept waveform starts at 400 MHz and sweeps up to 500 MHz where the signal can then be mixed against the 1 GHz clock signal to 1.4 GHz to 1.5 GHz. In various embodiments, the signal can be filtered and mixed against the 16 GHz clock signal in a sub-harmonic mixer. The output can be selected that sweeps from 33.4-33.5 GHz. Other means for generating the sweep can be employed so long as the sweep linearity is sufficient to resolve the CAS targets in accordance with embodiments of the invention.
The sweep generator is connected to a data acquisition system 112 that is synchronized to the system clock and samples the received backscattered signal waveform. In many embodiments, digital data is generated from sampling the received backscattered signal and the generated transmit signal and presented to a data processor 114 that is connected to the data acquisition system. The data processor processes the data to extract both velocity and range information as further discussed below where the extracted information can provide range and velocity estimates on each radar beam.
Although specific wide band Doppler radar systems for measuring wind speed and direction are discussed above with respect to FIG. 1, any of a variety of wide band Doppler radar systems as appropriate to the requirements of a specific application can be utilized in accordance with embodiments of the invention. Processes for estimating a wind velocity vector using Doppler shift calculations in accordance with an embodiment of the invention are further discussed below.
Estimating a Wind Velocity Vector Using Doppler Shift Calculations
The wind velocity vector Vwind=(vx, vy, vz) provides both wind speed and direction at an observed altitude. A process for estimating a wind velocity vector by utilizing Doppler shift calculations in accordance with an embodiment of the invention is illustrated in FIG. 2. The process 200 includes configuring (202) radar beam directions as further discussed below. The process also includes transmitting (204) a radar beam comprising of a transmit signal on a Ka-band carrier frequency using the antenna assembly as discussed above. In many embodiments, the transmit signal can illuminate CAS in the CBL creating a backscatter reflective signal. The process further includes receiving a backscattered radar beam comprising a carrier frequency that is frequency shifted relative to the transmitted Ka-band carrier frequency of the backscattered radar beam. Using the transmit radar beam and the backscattered radar beam, a Doppler shift is calculated (206). In several embodiments, a Doppler shift is calculated for multiple radar beams as further described below. In many embodiments, a wind velocity vector is estimated (210) using the methods further described below.
Although specific processes for estimating a wind velocity vector by utilizing Doppler shift calculations are discussed above with respect to FIG. 2, any of a variety of processes for estimating a wind velocity vector by utilizing Doppler shift calculations can be utilized in accordance with embodiments of the invention. Processes for configuring radar beam directions in accordance with an embodiment of the invention are discussed further below.
Configuring Radar Beam Directions
Radar beam directions directly impact a Doppler radar system's ability to collect information regarding wind speed and direction. In many embodiments, the individual radar beams work in conjunction in order to create a wind profile comprising of the wind speed and direction at various altitudes. A process for configuring radar beam directions in accordance with an embodiment of the invention is illustrated in FIG. 3. The process 300 includes selecting (302) a number of radar beams corresponding to the number of active pairs of transmit and receive antennas. In many embodiments, four radar beams are selected. The process further includes selecting a degree of separation between the radar beams. In several embodiments, four selected beams are separated by 90 degrees in azimuth. Further, a tilt angle is selected (306) relative to the horizontal plane for each radar beam. In various embodiments, each radar beam is tilted 80 degrees up (or down) from the horizontal. The radar beam directions are configured (308) based on the number of radar beams, degree separation and tilt angles as discussed above.
A 3D conceptual layout depicting 4 radar beams and illuminated volumes of CAS (represented by a point) in accordance with an embodiment of the invention is illustrated in FIG. 4. The layout 400 includes 4 radar beams 402, 404, 406, 408 that are titled up from the horizontal 410. The layout further includes CAS 412, 414, 416, 418 illuminated by the transmit signals and located within each radar beam.
Although specific processes for configuring radar beams are discussed above with respect to FIG. 3, any of a variety of processes for configuring radar beams as appropriate to the requirements of a specific application can be utilized in accordance with embodiments of the invention. Processes for estimating wind velocity when the radar remains stationary and/or pointed north in accordance with embodiments of the invention are further discussed below.
Estimating a Wind Velocity Vector Using a Stationary Radar
In many embodiments of the invention, the radar can be stationary or moving while the system is in operation. In several embodiments of the invention, the system utilizes a four radar beam configuration where four observed beam velocities (V1, V2, V3, V4) are calculated using Doppler shift calculations as discussed above. In order to estimate the wind velocity vector Vwind=(vx, vv, vz) at an altitude of interest, from the four observed beam velocities (V1, V2, V3, V4) at that altitude, a generalized relationship between the observed beam velocities, vector velocity of the radar, and vector velocity of the wind, and the direction that the radar is pointing can be derived.
The relationship can be derived from the observation that a Doppler shift measured on a velocity scale is proportional to the time rate of change of the length of propagation path measured along the radar beam from the radar location to the volume of wind illuminated by the radar. At time t=0, the radar is assumed to be located at a point O=(0,0,0) and an illuminated volume of wind is located at the vector location Rrw measured with respect to O. The radar and wind are respectively moving with velocities Vradar and Vwind. At a short time t later the radar is located at the point Vradart and the illuminated volume of the wind is located at the point Rrw+Vwindt. The distance between these two points is given by the equation:

L(t)=[(Rrw+Vwindt−Vradart)*(Rrw+Vwindt−Vradart)]1/2 

The observed Doppler velocity at time t=0 can be calculated:





  
    V
    obs
  
  =
  
    -
    
      
        [
        
          
            d
            
              L
              ⁡
              
                (
                t
                )
              
            
          
          
            d
            t
          
        
        ]
      
      
        t
        =
        0
      
    
  




Where Vobs can be shown to be:





  
    V
    obs
  
  =
  
    
      (
      
        
          V
          radar
        
        -
        
          V
          wind
        
      
      )
    
    *
    
      
        R
        rw
      
      
        
        
          R
          rw
        
        
      
    
  




A radar system that makes wind velocity measurements on four radar beams where the four radar beams point in the directions as described by:




  
    
      
        η
        ->
      
      rw
    
    =
    
      
        
          R
          rw
        
        
          
          
            R
            rw
          
          
        
      
      =
      
        (
        
          
            
              sin
              ⁡
              
                (
                
                  
                    Ψ
                    r
                  
                  +
                  
                    φ
                    i
                  
                
                )
              
            
            ⁢
            cos
            ⁢
            
              
            
            ⁢
            θ
          
          ,
          
            
              cos
              ⁡
              
                (
                
                  
                    Ψ
                    r
                  
                  +
                  
                    φ
                    i
                  
                
                )
              
            
            ⁢
            cos
            ⁢
            
              
            
            ⁢
            θ
          
          ,
          
            sin
            ⁢
            
              
            
            ⁢
            θ
          
        
        )
      
    
  
  ,
  
    

  
  ⁢
  
    
      for
      ⁢
      
        
      
      ⁢
      i
    
    =
    1
  
  ,
  2
  ,
  3
  ,
  4




where Ψr is the azimuthal orientation of the radar measured clockwise from north, θ is the tilt angle of the radar from the horizontal and the φi is the radar beam steering angle in the horizontal plane relative to the direction of the radar in a clockwise sense.

In many embodiments, the radar can be stationary. A process for estimating a wind velocity vector in the absence of radar motion is illustrated in FIG. 5. The process 500 includes keeping the radar stationary (502) and calculating the Doppler shift using the transmit radar beam and backscattered radar beam for each ith radar beam up to n radar beams such that:

Vi=−sin(Ψr+φi)cos θvx−cos(Ψr+φi)cos θvy−sin θvz, for i=1,2, . . . ,n 

The process further includes estimating (506) the wind velocity vector. The wind velocity vector Vwind can be estimated using the Doppler shift by utilizing the following technique as applied to n number of radar beams (for illustrative purposes only the technique is detailed for 4 radar beams). In the case of 4 radar beams on which the velocities V1, V2, V3, V4 are observed at an altitude of interest, the above equation for Doppler shift calculations create a system of linear equations (4 linear equations with the same set of unknown variables vx, vy, vz). The system of linear equations can be written in matrix equation form:





  
    
      [
      
        
          
            
              
                -
                
                  sin
                  ⁡
                  
                    (
                    
                      
                        Ψ
                        r
                      
                      +
                      
                        φ
                        1
                      
                    
                    )
                  
                
              
              ⁢
              cos
              ⁢
              
                
              
              ⁢
              θ
            
          
          
            
              
                -
                
                  cos
                  ⁡
                  
                    (
                    
                      
                        Ψ
                        r
                      
                      +
                      
                        φ
                        1
                      
                    
                    )
                  
                
              
              ⁢
              cos
              ⁢
              
                
              
              ⁢
              θ
            
          
          
            
              sin
              ⁢
              
                
              
              ⁢
              θ
            
          
        
        
          
            
              
                -
                
                  sin
                  ⁡
                  
                    (
                    
                      
                        Ψ
                        r
                      
                      +
                      
                        φ
                        2
                      
                    
                    )
                  
                
              
              ⁢
              cos
              ⁢
              
                
              
              ⁢
              θ
            
          
          
            
              
                -
                
                  cos
                  ⁡
                  
                    (
                    
                      
                        Ψ
                        r
                      
                      +
                      
                        φ
                        2
                      
                    
                    )
                  
                
              
              ⁢
              cos
              ⁢
              
                
              
              ⁢
              θ
            
          
          
            
              sin
              ⁢
              
                
              
              ⁢
              θ
            
          
        
        
          
            
              
                -
                
                  sin
                  ⁡
                  
                    (
                    
                      
                        Ψ
                        r
                      
                      +
                      
                        φ
                        3
                      
                    
                    )
                  
                
              
              ⁢
              cos
              ⁢
              
                
              
              ⁢
              θ
            
          
          
            
              
                -
                
                  cos
                  ⁡
                  
                    (
                    
                      
                        Ψ
                        r
                      
                      +
                      
                        φ
                        3
                      
                    
                    )
                  
                
              
              ⁢
              cos
              ⁢
              
                
              
              ⁢
              θ
            
          
          
            
              sin
              ⁢
              
                
              
              ⁢
              θ
            
          
        
        
          
            
              
                -
                
                  sin
                  ⁡
                  
                    (
                    
                      
                        Ψ
                        r
                      
                      +
                      
                        φ
                        4
                      
                    
                    )
                  
                
              
              ⁢
              cos
              ⁢
              
                
              
              ⁢
              θ
            
          
          
            
              
                -
                
                  cos
                  ⁡
                  
                    (
                    
                      
                        Ψ
                        r
                      
                      +
                      
                        φ
                        4
                      
                    
                    )
                  
                
              
              ⁢
              cos
              ⁢
              
                
              
              ⁢
              θ
            
          
          
            
              sin
              ⁢
              
                
              
              ⁢
              θ
            
          
        
      
      ]
    
    ⁡
    
      [
      
        
          
            
              v
              x
            
          
        
        
          
            
              v
              y
            
          
        
        
          
            
              v
              z
            
          
        
      
      ]
    
  
  =
  
    [
    
      
        
          
            V
            1
          
        
      
      
        
          
            V
            2
          
        
      
      
        
          
            V
            3
          
        
      
      
        
          
            V
            4
          
        
      
    
    ]
  




which can be rewritten in a more compact form:

AVwind=Vobs 

In many embodiments, the above equation can be solved using the method of least squares for the wind velocity vector Vwind=(vx, vy, vz). In matrix notation the solution becomes:

Vwind=[ATA]−1ATVobs 

Provided that the radar is oriented to the North, then the wind velocity vector Vwind=(vx, vy, vz) can be estimated by:




  
    
      v
      x
    
    =
    
      
        1
        
          2
          ⁢
          cos
          ⁢
          
            
          
          ⁢
          θ
        
      
      ⁢
      
        (
        
          
            V
            4
          
          -
          
            V
            2
          
        
        )
      
    
  
  ,
  
    

  
  ⁢
  
    
      v
      y
    
    =
    
      
        1
        
          2
          ⁢
          cos
          ⁢
          
            
          
          ⁢
          θ
        
      
      ⁢
      
        (
        
          
            V
            3
          
          -
          
            V
            1
          
        
        )
      
    
  
  ,
  
    

  
  ⁢
  
    
      v
      z
    
    =
    
      
        -
        
          1
          
            2
            ⁢
            sin
            ⁢
            
              
            
            ⁢
            θ
          
        
      
      ⁢
      
        (
        
          
            V
            1
          
          +
          
            V
            2
          
          +
          
            V
            3
          
          +
          
            V
            4
          
        
        )
      
    
  




If the observed velocities (V1, V2, V3, V4) are estimated to an accuracy defined by a diagonal covariance matrix:

Mobs=diag(σ12,σ22,σ32,σ42)

then the weighted least squares solution for the wind velocity vector can be provided by:

Vwind=[ATWA]−1[ATW]Vobs 

W=[Mobs]−1 

where the covariance of the wind velocity vector is given by:

Mwind=[ATWA]−1 

and the diagonal elements of Mwind are the variances of the wind velocities (vx, vy, vz).

Although specific processes for estimating a wind velocity vector in the absence of radar motion are discussed above with respect to FIG. 5, any of a variety of processes for estimating a wind velocity vector in the absence of radar motion as appropriate to the requirements of a specific application can be utilized in accordance with embodiments of the invention. Processes for generating range-velocity matrices in accordance with embodiments of the invention are further discussed below.
Formation of Range-Velocity Matrices
In many embodiments, the system can estimate the range and Doppler shift of a CAS by using a form of fast-time slow-time processing that produces a range-velocity matrix. In many embodiments, the range-velocity matrix Crq can be defined corresponding to various slant-range distances from a radar. A process for generating a range-velocity matrix in accordance with an embodiment of the invention is illustrated in FIG. 6. The process 600 includes defining observed slant-ranges away from the radar in the atmosphere. In many embodiments of the invention, the observed slant-range ρr is defined such:




  
    
      ρ
      r
    
    =
    
      r
      ⁢
      
        c
        
          2
          ⁢
          B
        
      
    
  
  ,
  
    

  
  ⁢
  
    r
    =
    0
  
  ,
  1
  ,
  2
  ,
  ...
  ⁢
  
    
  
  ,
  
    N
    ⁢
    
      
    
    ⁢
    F
    ⁢
    
      
    
    ⁢
    F
    ⁢
    
      
    
    ⁢
    
      T
      /
      2
    
  




where c is the speed of light and B is the radar sweep width. The process further includes defining a velocity vq corresponding to each slant-range. In several embodiments, the velocities vq can be defined by:





  
    
      v
      q
    
    =
    
      
        v
        min
      
      +
      
        q
        ⁢
        
          1
          
            Q
            -
            1
          
        
        ⁢
        
          (
          
            λ
            
              
                2
                c
              
              ⁢
              
                T
                m
              
            
          
          )
        
      
    
  
  ,
  
    

  
  ⁢
  
    q
    =
    0
  
  ,
  1
  ,
  2
  ,
  ...
  ⁢
  
    
  
  ,
  
    Q
    -
    1
  




where λ=c/fc is the wavelength of the radar carrier frequency. Further, the altitude above ground level corresponding to the slant range ρr can be calculated:

zr=z0+ρr/sin θ

where λ=c/fc is the radar elevation above ground level. The process further includes generating (606) a range-velocity matrix Crq. In many embodiments, the range-velocity matrix Crq can be defined by:





  
    
      C
      rq
    
    =
    
      
        1
        
          Q
        
      
      ⁢
      
        
          ∑
          
            n
            =
            0
          
          
            Q
            -
            1
          
        
        ⁢
        
          
            wgt
            n
          
          ⁢
          
            B
            rn
          
          ⁢
          
            e
            
              i2π
              ⁢
              
                
              
              ⁢
              
                rn
                /
                Q
              
            
          
        
      
    
  
  ,
  
    

  
  ⁢
  
    q
    =
    0
  
  ,
  1
  ,
  2
  ,
  ...
  ⁢
  
    
  
  ,
  
    Q
    -
    1
  




where:





  
    
      B
      rn
    
    =
    
      
        1
        
          
            N
            ⁢
            
              
            
            ⁢
            F
            ⁢
            
              
            
            ⁢
            F
            ⁢
            
              
            
            ⁢
            T
          
        
      
      ⁢
      
        
          ∑
          
            m
            =
            0
          
          
            NFFT
            -
            1
          
        
        ⁢
        
          
            wgt
            m
          
          ⁢
          
            A
            mn
          
          ⁢
          
            e
            
              i2π
              ⁢
              
                
              
              ⁢
              
                mn
                /
                NFFT
              
            
          
        
      
    
  
  ,
  
    

  
  ⁢
  
    r
    =
    0
  
  ,
  1
  ,
  2
  ,
  ...
  ⁢
  
    
  
  ,
  
    N
    ⁢
    
      
    
    ⁢
    F
    ⁢
    
      
    
    ⁢
    F
    ⁢
    
      
    
    ⁢
    
      T
      /
      2
    
  




where Amn is a matrix of data points with slow time index rows and fast time index columns.

Echoes from strong reflectors can be relatively easy to detect in the range-velocity matrix Crq. However, weaker reflections such as those from CAS and weather events may need more processing gain for detection. The process further includes generating (608) a power spectral averaged range-velocity matrix Prq such that:




  
    P
    rq
  
  =
  
    
      1
      
        N
        avg
      
    
    ⁢
    
      
        ∑
        
          k
          =
          1
        
        
          N
          avg
        
      
      ⁢
      
        
          
          
            
              C
              rq
            
            ⁡
            
              (
              k
              )
            
          
          
        
        2
      
    
  




where k corresponds to a time step of length, QTm equal to the time duration of a data stack. In many embodiments, the averaging used to generate the power averaged range-velocity matrix Prq is performed without overlap in time order to maintain statistical independence. The averaging can reduce the variance of the background noise in the image and allows for more reliable spectral estimation.

Although specific process for generating a range-velocity matrix are discussed above with respect to FIG. 6, any of a variety of processes for generating range-velocity matrices as appropriate to the requirements of a specific application can be utilized in accordance with embodiments of the invention. Processes for estimating radar beam Doppler shift velocities in accordance with an embodiment of the invention are discussed further below.
Estimation of Radar Beam Doppler Shift Velocity at an Altitude of Interest
Radar beam Doppler shift velocities at an altitude of interest can be estimated using a range-velocity matrix. In many embodiments, a power averaged range-velocity matrix Prq can be utilized. A process for estimating radar beam Doppler shift velocity at an altitude of interest in accordance with an embodiment of the invention is illustrated in FIG. 7. The process 700 includes extracting (702) all velocities v1, v2, . . . , vN with corresponding velocity indexes q1, q2, . . . , qN, a at a slant-range distance corresponding to the velocity index r from the range-velocity matrix Prq that satisfies:

10 log10[Prq/Median(Prq)]>K 

where K is a predetermined threshold. In many embodiments, K is chosen to be 2 dB. In several embodiments, smaller values of K can be used if the range velocity matrix Pm was formed with Navg>150.

Due to the turbulent nature of the Ka-band clear air scatter, the observed velocity cannot be reliably estimated by calculating:




  
    V
    obs
  
  =
  
    
      v
      _
    
    =
    
      
        1
        N
      
      ⁢
      
        
          ∑
          
            n
            =
            1
          
          N
        
        ⁢
        
          v
          n
        
      
    
  




due to the presence of high velocity outliers. In order to reject these outliers, a Bayesian approach can be taken. In many embodiments, the velocity vg is upon initial information I can be assumed to be normally distributed with probability density function:





  
    p
    ⁡
    
      (
      
        q
        ❘
        I
      
      )
    
  
  ∝
  
    exp
    [
    
      
        -
        
          
            (
            
              q
              -
              
                Q
                c
              
            
            )
          
          2
        
      
      
        2
        ⁢
        
          σ
          0
          2
        
      
    
    ]
  




where q=0, 1, . . . , Q−1, and Qc=Q/2 is the center velocity index corresponding to zero velocity and σ0=4Qc. This choice of parameters produces an initial velocity distribution that is very nearly uniformly distributed with a slight central tendency towards zero velocity. The symbol ∝ in the foregoing equations indicates a probability distribution that is determined within a simple multiplicative constant. In several embodiments, the constant can be C0=1/(√{square root over (2π)}σ0).

Bayes theorem states that when an observed velocity vn with corresponding velocity index qn from the data v1, v2, . . . , vN, the posterior velocity distribution can be defined as:




  
    p
    ⁡
    
      (
      
        
          q
          ❘
          
            q
            n
          
        
        ,
        I
      
      )
    
  
  ⁢
  
    
      p
      ⁢
      
        (
        
          
            
              q
              n
            
            ❘
            
              q
              n
            
          
          ,
          I
        
        )
      
      ⁢
      
        p
        ⁡
        
          (
          
            q
            ❘
            I
          
          )
        
      
    
    
      
        ∑
        
          q
          =
          1
        
        Q
      
      ⁢
      
        
          p
          ⁡
          
            (
            
              
                
                  q
                  n
                
                ❘
                
                  q
                  n
                
              
              ,
              I
            
            )
          
        
        ⁢
        
          p
          ⁡
          
            (
            
              q
              ❘
              I
            
            )
          
        
      
    
  




In order to reject (704) outlier measurements in the posterior distribution the likelihood of the data p(qn|q, I) is chosen to be:





  
    p
    ⁡
    
      (
      
        
          
            q
            n
          
          ❘
          q
        
        ,
        I
      
      )
    
  
  ∝
  
    
      [
      
        1
        +
        
          
            
              (
              
                q
                -
                
                  q
                  n
                
              
              )
            
            2
          
          
            2
            ⁢
            β
            ⁢
            
              
            
            ⁢
            
              σ
              1
              2
            
          
        
      
      ]
    
    
      -
      β
    
  




where β=1 and σ1=10(Q/256). The posterior distribution due to all the data is:





  
    p
    ⁡
    
      (
      
        
          q
          ❘
          
            q
            1
          
        
        ,
        
          q
          2
        
        ,
        ...
        ⁢
        
          
        
        ,
        
          q
          N
        
        ,
        I
      
      )
    
  
  ∝
  
    
      exp
      [
      
        
          
            (
            
              q
              -
              
                Q
                c
              
            
            )
          
          2
        
        
          2
          ⁢
          
            σ
            0
            2
          
        
      
      ]
    
    ⁢
    
      
        ∏
        
          n
          =
          1
        
        N
      
      ⁢
      
        
          [
          
            1
            +
            
              
                
                  (
                  
                    q
                    -
                    
                      q
                      n
                    
                  
                  )
                
                2
              
              
                2
                ⁢
                
                  βσ
                  1
                
              
            
          
          ]
        
        
          -
          β
        
      
    
  




The radar beam Doppler shift velocities can be estimated (706) via:





  
    V
    obs
  
  =
  
    
      v
      min
    
    +
    
      
        q
        _
      
      ⁢
      
        
          (
          
            
              v
              max
            
            -
            
              v
              min
            
          
          )
        
        
          Q
          -
          1
        
      
    
  




where q is the mean of the posterior probability distribution.

Although specific processes for estimating radar beam Doppler shift velocities at an altitude of interest are discussed above with respect to FIG. 7, any of a variety of processes for estimating a radar beam Doppler shift velocity at an altitude of interest as appropriate to the requirements of a specific application can be utilized in accordance with embodiments of the invention.
Although the present invention has been described in certain specific aspects, many additional modifications and variations would be apparent to those skilled in the art. It is therefore to be understood that the present invention may be practiced otherwise than specifically described without departing from the scope and spirit of the present invention. Thus, embodiments of the present invention should be considered in all respects as illustrative and not restrictive. Accordingly, the scope of the invention should be determined not by the embodiments illustrated, but by the appended claims and their equivalents.

## Claims

1. A wide band Doppler radar system comprising:
an antenna assembly comprising at least one transmit antenna and at least one receive antenna, where:
each of the at least one transmit antenna is configured to transmit a radar beam comprising a transmit signal on a Ka-band carrier frequency; and
each of the at least one receive antenna is configured to receive a backscattered radar beam comprising a carrier frequency that is frequency shifted relative to the transmitted Ka-band carrier frequency of the backscattered radar beam;
a transceiver connected to the antenna assembly configured to:
transmit a radar beam comprising a transmit signal on a Ka-band carrier frequency using each of the at least one transmit antenna; and
receive a backscattered radar beam comprising a carrier frequency that is frequency shifted relative to the transmitted Ka-band carrier frequency of the backscattered radar beam using each of the at least one receive antenna; and

a data acquisition system connected to the transceiver configured to estimate a wind velocity vector in clear air conditions by calculating a Doppler shift between at least one transmitted radar beam and at least one received backscattered radar beam.

2. A wide band Doppler radar system of claim 1, wherein the antenna assembly further comprises a horn antenna having waveguide flanges.

3. A wide band Doppler radar system of claim 1, wherein the transceiver operates between 33.3 GHz and 33.5 GHz.

4. A wide band Doppler radar system of claim 1, wherein the transceiver operates as a frequency modulated continuous wave (FMCW) radar.

5. A wide band Doppler radar system of claim 1, wherein the antenna assembly further comprises 4 transmit antennas.

6. A wide band Doppler radar system of claim 5, wherein the antenna assembly further comprises 4 receive antennas.

7. A wide band Doppler radar system of claim 5, wherein the transceiver connected to the antenna assembly is further configured to transmit radar beams that separated by 90 degrees in azimuth.

8. A wide band Doppler radar system of claim 7, wherein the transceiver connected to the antenna assembly is further configured to transmit radar beams that tilted 80 degrees up from the horizontal.

9. A wide band Doppler radar system of claim 7, wherein the data acquisition system is configured to determine the wind velocity vector from the Doppler shift based on the velocities, Vi of the transmitted and received backscattered radar beams transmitted where i is the number of the radar beam and where:


Vi=−sin(Ψr+φi)cos θvx−cos(Ψr+φi)cos θvy−sin θvz 


where Ψr is the azimuthal orientation of the radar beam, φi is the radar beam steering angle, and θ is the tilt angle of the radar relative to the horizontal.

10. A wide band Doppler radar system of claim 9, wherein the data acquisition system is configured to determine the wind velocity vector


Vwind=(vx,vy,vz)


from the Doppler shift based on transmitted and received backscattered radar beams transmitted where:




  
    
      
        
          v
          x
        
        =
        
        ⁢
        
          
            1
            
              2
              ⁢
              
                
              
              ⁢
              cos
              ⁢
              
                
              
              ⁢
              θ
            
          
          ⁢
          
            (
            
              
                V
                4
              
              -
              
                V
                2
              
            
            )
          
        
      
    
  
  
    
      
        
          v
          y
        
        =
        
        ⁢
        
          
            1
            
              2
              ⁢
              
                
              
              ⁢
              cos
              ⁢
              
                
              
              ⁢
              θ
            
          
          ⁢
          
            (
            
              
                V
                3
              
              -
              
                V
                1
              
            
            )
          
        
      
    
  
  
    
      
        
          v
          z
        
        =
        
        ⁢
        
          
            -
            
              1
              
                2
                ⁢
                
                  
                
                ⁢
                sin
                ⁢
                
                  
                
                ⁢
                θ
              
            
          
          ⁢
          
            (
            
              
                V
                1
              
              +
              
                V
                2
              
              +
              
                V
                3
              
              +
              
                V
                4
              
            
            )
          
        
      
    
  




where V1, V2, V3 and V4 are radar beam velocities and θ is the tilt angle of the radar relative to the horizontal.

11. A method of estimating wind speed and direction using a wide band Doppler radar system comprising:
configuring at least one transmit antenna to transmit a radar beam comprising a transmit signal on a Ka-band carrier frequency;
configuring at least one receive antenna too receive a backscattered radar beam comprising a carrier frequency that is frequency shifted relative to the transmitted Ka-band carrier frequency of the backscattered radar beam;
transmitting a radar beam comprising a transmit signal on a Ka-band carrier frequency using each of the at least one transmit antenna;
receiving a backscattered radar beam comprising a carrier frequency that is frequency shifted relative to the transmitted Ka-band carrier frequency of the backscattered radar beam using each of the at least one receive antenna; and
estimating a wind velocity vector by calculating a Doppler shift between at least one transmitted radar beam and at least one received backscattered radar beam.

12. A method of claim 11, wherein the at least one the transmit antenna and the at least one receive antenna are parts of a horn antenna having waveguide flanges.

13. A method of claim 11, wherein transmitting a radar beam comprising a transmit signal on a Ka-band carrier frequency further comprises operating between 33.3 GHz and 33.5 GHz.

14. A method of claim 11, wherein transmitting a radar beam comprising a transmit signal on a Ka-band carrier frequency further comprises generating a continuous wave.

15. A method of claim 11, wherein configuring at least one transmit antenna to transmit a radar beam further comprises configuring 4 transmit antennas.

16. A method of claim 15, wherein configuring at least one receive antenna too receive a backscattered radar beam further comprises configuring 4 receive antennas.

17. A method of claim 16, wherein the radar beams are separated by 90 degrees in azimuth.

18. A method of claim 17, wherein the radar beams are tilted 80 degrees up from the horizontal.

19. A method of claim 17, wherein the transmitting and receiving are performed at a single location.

20. A method of claim 19, wherein the estimation is calculated from a transmitted radar beam transmitted in the direction of true north.