(1)
The ELDORA Radar Processor (RP7) can process radar returns from up to five transmitted frequencies on both fore and aft radars. The data can be from uniform or staggered PRTs. In the case of the latter, real-time velocity unfolding is done. The products computed for a uniform PRT are: reflectivity, velocity, spectrum width, and normalized coherent power (NCP). The products computed for a staggered PRT are: reflectivity, velocity for PRT#1, velocity for PRT#2, unfolded velocity, spectrum width, and NCP. Formal definitions of these parameters and how they are com
puted will be presented.
An autocorrelation is computed on the inphase and quadrature data, using a standard pulse pair algorithm . The output of the standard pulse pair algorithm are the zeroth and first lag of the complex autocorrelation function: Rn(0) and Rn(Ts). The total received power is defined as: Pn = Rn(0), and the resultant vector of the lag one autocorrelation is defined as: Rn(Ts) = An + jBn; where n denotes the frequency number (1 £ n £ 5). The autocorrelation is performed simultaneously on all transmitted frequencies. Vector addition is performed across the frequencies, yielding resultant vector R(Ts) , as given by equation 1:
Scalar addition is performed across the frequencies yielding P:
N is the total number of transmitted frequencies.
The final data products are computed from (1) and (2) as follows:
Reflectivity is given by
where RC is the radar constant and r is the range in km.
Mean velocity is determined by taking the argument of the first autocorrelation lag,
Spectrum width is computed as follows:
where
N is the noise power.
Normalized coherent power is defined as the ratio of the power calculated at lag one and the total received power:
It should be noted that the value of l used is the average of all transmitted frequencies.
Presently ELDORA transmits a staggered PRT in the ratio T2/T1 = 5/4. For a staggered PRT the unambiguous velocity interval becomes:
Data processing for each PRT of the staggered PRT is similar to uniform PRT processing with a notable complication in velocity unfolding.
The inphase and quadrature data is processed independently for each transmitted frequency. Covariance averaging is performed between pairs of pulses separated by T1 and T2 (denoted R1 and R2). This process gives zeroth lag power for both PRT's:
where n denotes the transmitted frequency number (1 £ n £ 5). It also yields two resultant vectors of the covariance averaging:
Vector addition is performed across the frequencies, yielding resultant vectors R1 and R2 for each PRT, as given by the following:
Scalar addition is performed across the frequencies yielding P1 and P2:
Where N is the total number of transmitted frequencies.
The following spectral moments or associated products are computed for the staggered PRT: unfolded velocity, velocity for PRT#1, velocity for PRT#2, reflectivity, spectrum width, and NCP. The phase of each vector is determined as follows:
Velocity unfolding for ELDORA is done in vector space. This is advantageous because the signal processor can unfold the velocity without any knowledge of the PRTs or transmitted frequencies. Given T2/T1 = f 2/f 1 = K2/K1, where K1 and K2 are relatively prime integers and K2 > K1, there exists K1 + K2 regions where the difference, D = (K2/K1)f 2 - f 1 is unique. For K2/K1 = 5/4, nine such regions exist. Associated with each region is a constant phase offset which is added to the average phase, f = ((K2/K1)f 1 + f 2)/2 to place it in the correct Nyquist interval. These phase corrections are stored in a lookup table in the signal processor memory. Averaging the phases associated with each PRT improves the velocity estimate. The phase corrections for the first nine intervals are given in Table 1. Once the absolute phase is determined the unfolded velocity can be calculated as follows:
where l is the average wavelength of the transmitted chips. As the frequency separation on ELDORA is around 10 MHz, this has a negligible effect on the accuracy of the velocity estimate.
|
Region |
D =(K2-K1)f 1-f 2 |
Correction |
|
-5p < f 2£ -3(K2/K1)p |
p |
-2p (1+K2/K1) |
|
-3(K2/K1)p < f 2£ -3p |
-3p /2 |
-p (2+K2/K1) |
|
-3p < f 2£ -(K2/K1)p |
p /2 |
-p (1+K2/K1) |
|
-(K2/K1)p < f 2£ -p |
-2p |
-p |
|
-p < f 2£ p |
0 |
0 |
|
p < f 2£ (K2/K1)p |
2p |
p |
|
(K2/K1)p < f 2£ 3p |
-p /2 |
p (1+K2/K1) |
|
3p < f 2£ 3(K2/K1)p |
3p /2 |
p (2+K2/K1) |
|
3(K2/K1)p < f 2£ 5p |
-p |
2p (1+K2/K1) |
Table 1 Phase Corrections for First 9 Intervals
Estimates for the mean velocities associated with T2 and T1 are given by the following:
Reflectivity is given by
where RC is the radar constant and r is the range in km.
Spectrum width is computed as follows:
(23)
where
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N is the noise power.
Normalized coherent power is defined as the ratio of the power calculated at lag one and the total received power:
(25)
It should be noted that the value of l used is the average of all transmitted frequencies.
