Dual-polarization radar processing system using time domain method

• US 20090295627A1
• Filed: 05/07/2009
• Published: 12/03/2009
• Est. Priority Date: 05/07/2008
• Status: Active Grant

• Current Assignee: Colorado State University Research Foundation (Colorado State University System)
• Original Assignee: Colorado State University Research
• Inventors: Moisseev, Dmitri N., Venkatachalam, Chandrasekaran, Nguyen, Cuong M.
• Granted Patent: US 8,665,144 B2
• Time in Patent Office: Days
• US Class Current: 342/26.00R
• CPC Class Codes: G01S 13/951 ground based
• CPC Class Codes: G01S 7/025 involving the transmission of linearly polarised waves
• CPC Class Codes: G01S 7/292 Extracting wanted echo-signals
• CPC Class Codes: Y02A 90/10 Information and communication technologies [ICT] supporting adaptation to climate change, e.g. for weather forecasting or climate simulation

Abstract

Embodiments of the present invention provide for improved estimation of environmental parameters in a dual-polarization radar system. In some embodiments, environmental parameters can be estimated using a linear combination of data received in two orthogonal polarization states. In particular, embodiments of the invention improve ground clutter and noise mitigation in dual polarization radar systems. Moreover, embodiments of the invention also provide for systems to determine the differential reflectivity and/or the magnitude of the co-polar correlation coefficient and the differential phase in a dual polarization radar system.

Claims

1. A method comprising:

propagating polarized radar signals to a region of interest using a dual-polarization radar transmitter;

collecting sampled co-polar time series radar data scattered within the region of interest with the dual-polarization radar transmitter, wherein the co-polar time series radar data includes vertically polarized data and horizontally polarized data; and

determining at least one of the differential reflectivity and the co-polar correlation coefficient between the horizontally polarized data and the vertically polarized data from a complex linear combination of the vertically polarized data and horizontally polarized data.

2. The method according to claim 1, wherein the linear combination of the horizontally polarized data and the vertically polarized data can be expressed as

V_α

=V^H+α

V^V.

3. The method according to claim 2, wherein an optimal value for a for the n^th range gate measurement can be estimated as

${\alpha }_{}^{}$

opt n = - ( Z ^ dr n - 1 ) + ( Z ^ dr n - 1 ) 2 + 4 



Re 

( ρ

^ co n - 1 ) 

Z ^ dr n 2 



Re 



( ρ

^ co ( n - 1 ) ) 

Z ^ dr n

4. The method according to claim 2, wherein an optimal value for α

=jβ

for the n^th range gate measurement can be estimated as

${\mathrm{\beta <br><br>}}_{\mathrm{opt}}^n=-\frac{\left({\hat{Z}}_{\mathrm{dr}}^n-1\right)+\sqrt{{\left({\hat{Z}}_{\mathrm{dr}}^n-1\right)}^2+4<br><br><br><br>\mathrm{Im}<br><br>\left({\widehat{\mathrm{\rho <br><br>}}}_{\mathrm{co}}^{n-1}\right)<br><br>{\hat{Z}}_{\mathrm{dr}}^n}}{2<br><br><br><br>\mathrm{Im}<br><br><br><br>\left({\widehat{\mathrm{\rho <br><br>}}}_{\mathrm{co}}^{\left(n-1\right)}\right)<br><br>\sqrt{{\hat{Z}}_{\mathrm{dr}}^n}}$

5. A method of investigating a region of interest with a radar, the method comprising:

propagating polarized radar signals to the region of interest using a dual-polarization radar system;

collecting time series radar data scattered within the region of interest for two polarizations;

calculating a likelihood function for each of the dual-polarization time series data within a parametric model of the region of interest for a defined set of parameters; and

varying the set of parameters to find an extremum of the summed likelihood function.

6. The method according to claim 5, wherein the likelihood function for each polarization is L^h,v(θ

^h,v)=ln(|R^h,v(0^h,v)|)+ir(R^h,v-1(θ

^h,v){circumflex over (R)}_V^h,v), where R^h,v is model covariance matrices for horizontal and vertical polarizations having elements;

$R^{h,v}<br><br>\left[k,l\right]=P_p^{h,v}<br><br>\exp <br><br>\left(-\frac{8<br><br>{\mathrm{\pi <br><br>}}^2<br><br>{{\mathrm{\sigma <br><br>}}_p^{h,v<br><br><br><br>2}<br><br>\left(k-l\right)}^2<br><br>T_s^2}{{\mathrm{\lambda <br><br>}}^2}\right)<br><br>\exp <br><br>\left(-j<br><br>\frac{4<br><br>\mathrm{\pi <br><br>}<br><br><br><br>{\stackrel{\_}{v}}^{h,v}<br><br>\left(k-l\right)<br><br>T_S}{\mathrm{\lambda <br><br>}}\right)+P_c^{h,v}<br><br>\exp <br><br>\left(-\frac{8<br><br>{\mathrm{\pi <br><br>}}^2<br><br>{{\mathrm{\sigma <br><br>}}_c^{h,v<br><br><br><br>2}<br><br>\left(k-l\right)}^2<br><br>T_s^2}{{\mathrm{\lambda <br><br>}}^2}\right)+{\mathrm{\sigma <br><br>}}_N^{h,v<br><br><br><br>2}<br><br>\mathrm{\delta <br><br>}<br><br>\left(k-l\right);<br><br>$

k,l=1, . . . , N

for k, l=1, . . . , N,

wherein;

T_s is a sampling period;

λ

is a wavelength of the radar signal;

j is √

{square root over (−

1)};

δ

is a Kronecker function; and

the set of parameters comprises;

P_p^h,v as a precipitation signal power;

σ

_p^h,v as a precipitation spectrum width;

v^h,v as a mean velocity of precipitation;

P_c^h,v as a clutter power;

σ

_c^h,v as a clutter spectrum width; and

σ

_N^h,v as a noise power.

7. The method recited in claim 5 wherein the extremum is a global extremum.

8. The method recited in claim 5 wherein the extremum is a minimum.

9. The method recited in claim 5 further comprising setting V_α

=V^H+α

V^V and minimizing a log-likelihood function for V_α

, wherein the log-likelihood function is

$L_{\mathrm{\alpha <br><br>}}=\ln <br><br>\left(<br><br>\left(R_c+R_N\right)+{\mathrm{xR}}_p^h<br><br>\right)+\mathrm{tr}<br><br>\left({\left(\left(R_c+R_N\right)+{\mathrm{xR}}_p^h\right)}^{-1}<br><br>{\hat{R}}_{V_{\mathrm{\alpha <br><br>}}}\right),$

where {circumflex over (R)}_Vα

is the sample covariance matrix of V_α

.

10. The method recited in claim 9 wherein

$x=1+\frac{{\alpha }^{}}{}$

2 Z ^ dr + 2 

α





Re 

( ρ

co ) Z ^ dr

when α

is real.

11. The method recited in claim 10 wherein the optimal value for α

for the n^th range gate can be determined from;

${\mathrm{\alpha <br><br>}}_{\mathrm{opt}}^{\left(n\right)}=-\frac{\left({\hat{Z}}_{\mathrm{dr}}^{\left(n\right)}-1\right)+\sqrt{{\left({\hat{Z}}_{\mathrm{dr}}^{\left(n\right)}-1\right)}^2+4<br><br><br><br>\mathrm{Re}<br><br>\left({\widehat{\mathrm{\rho <br><br>}}}_{\mathrm{co}}^{\left(n-1\right)}\right)<br><br>{\hat{Z}}_{\mathrm{dr}}^{\left(n\right)}}}{2<br><br><br><br>\mathrm{Re}<br><br><br><br>\left({\widehat{\mathrm{\rho <br><br>}}}_{\mathrm{co}}^{\left(n-1\right)}\right)<br><br>\sqrt{{\hat{Z}}_{\mathrm{dr}}^{\left(n\right)}}}.$

12. The method recited in claim 9 wherein

$x=1+\frac{{\beta }^{}}{}$

2 Z ^ dr - 2 

β





Im 

( ρ

co ) Z ^ dr

when α

=jβ

.

13. The method recited in claim 12 wherein the optimal value for β

for the n^th range gate can be determined from;

${\mathrm{\beta <br><br>}}_{\mathrm{opt}}^{\left(n\right)}=-\frac{\left({\hat{Z}}_{\mathrm{dr}}^{\left(n\right)}-1\right)+\sqrt{{\left({\hat{Z}}_{\mathrm{dr}}^{\left(n\right)}-1\right)}^2+4<br><br><br><br>\mathrm{Im}<br><br>\left({\widehat{\mathrm{\rho <br><br>}}}_{\mathrm{co}}^{\left(n-1\right)}\right)<br><br>{\hat{Z}}_{\mathrm{dr}}^{\left(n\right)}}}{2<br><br><br><br>\mathrm{Im}<br><br><br><br>\left({\widehat{\mathrm{\rho <br><br>}}}_{\mathrm{co}}^{\left(n-1\right)}\right)<br><br>\sqrt{{\hat{Z}}_{\mathrm{dr}}^{\left(n\right)}}}$

14. A method of investigating a region of interest with a radar, the method comprising:

propagating polarized radar signals to the region of interest using a dual-polarization radar system;

collecting a first time series radar data scattered within the region of interest with a first polarization using a radar;

collecting a second time series radar data scattered within the region of interest with a second polarization using a radar, wherein the first polarization and the second polarization are substantially orthogonal;

estimating spectral moments for the two polarizations; and

estimating at least one of the differential reflectivity, the magnitude of the co-polar correlation coefficient, and the phase of the co-polar correlation coefficient using a linear combination of the first time series radar data and the second time series radar data.

15. The method according to claim 14, wherein at least one of the magnitude of the co-polar correlation coefficient and the phase of the co-polar correlation coefficient are estimated using the first time series radar data and the second time series radar data.

16. The method according to claim 14, further comprising:

creating a summed likelihood function by adding a likelihood function for the first time series radar data and a likelihood function for the second time series radar data; and

maximizing the summed likelihood function to estimate the spectral moments of the first time series radar data and the second time series radar data.

17. The method according to claim 14, wherein the linear combination of the first time series radar data and the second time series radar data comprises V_α

=V^h+α

V^v,

${\mathrm{\alpha <br><br>}}_{\mathrm{opt}}^{\left(n\right)}=-\frac{\left({\hat{Z}}_{\mathrm{dr}}^{\left(n\right)}-1\right)+\sqrt{{\left({\hat{Z}}_{\mathrm{dr}}^{\left(n\right)}-1\right)}^2+4<br><br><br><br>\mathrm{Re}<br><br>\left({\widehat{\mathrm{\rho <br><br>}}}_{\mathrm{co}}^{\left(n-1\right)}\right)<br><br>{\hat{Z}}_{\mathrm{dr}}^{\left(n\right)}}}{2<br><br><br><br>\mathrm{Re}<br><br><br><br>\left({\widehat{\mathrm{\rho <br><br>}}}_{\mathrm{co}}^{\left(n-1\right)}\right)<br><br>\sqrt{{\hat{Z}}_{\mathrm{dr}}^{\left(n\right)}}}$ $\mathrm{and}$ ${\mathrm{\beta <br><br>}}_{\mathrm{opt}}^{\left(n\right)}=-\frac{\left({\hat{Z}}_{\mathrm{dr}}^{\left(n\right)}-1\right)+\sqrt{{\left({\hat{Z}}_{\mathrm{dr}}^{\left(n\right)}-1\right)}^2+4<br><br><br><br>\mathrm{Im}<br><br>\left({\widehat{\mathrm{\rho <br><br>}}}_{\mathrm{co}}^{\left(n-1\right)}\right)<br><br>{\hat{Z}}_{\mathrm{dr}}^{\left(n\right)}}}{2<br><br><br><br>\mathrm{Im}<br><br><br><br>\left({\widehat{\mathrm{\rho <br><br>}}}_{\mathrm{co}}^{\left(n-1\right)}\right)<br><br>\sqrt{{\hat{Z}}_{\mathrm{dr}}^{\left(n\right)}}}$ $\mathrm{where}<br><br><br><br>\mathrm{\alpha <br><br>}=\mathrm{j\beta <br><br>}.$

18. The method according to claim 14, wherein the estimating a magnitude and a phase of the co-polar correlation coefficient can include minimizing the negative log-likelihood function for the linear combination of the first time series radar data and the second time series radar data.

19. A radar system comprising:

a dual-polarization transmitter configured to transmit a signal in two substantially orthogonal polarizations;

a dual-polarization receiver configured to receive a first signal in first polarization and a second signal in a second polarization, wherein the first polarization and the second polarization are substantially orthogonal;

a computer system coupled at least with the dual polarization receiver, the computer system being configured to estimate at least one of the differential reflectivity, the magnitude of the co-polar correlation coefficient, and the phase of the co-polar correlation coefficient using a linear combination of the first signal and the second signal.

20. A radar system comprising:

propagation means for propagating radar into a region of interest;

receiving means for receiving radar backscatter in a first polarization state and radar back scatter in a second polarization state from the region of interest; and

computation means for estimating the spectral moments of the radar backscatter in the first polarization state and the radar backscatter in the second polarization state, and for estimating at least one of the differential reflectivity, the magnitude of the co-polar correlation coefficient, and phase of the co-polar correlation coefficient using a linear combination of the radar backscatter in the first polarization state and the radar backscatter in the second polarization state.