System and method for detecting and estimating the direction of nearstationary targets in monostatic clutter using phase information

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First Claim
1. A system for detecting a target in clutter comprising:
 first means for receiving a complex return signal of an electromagnetic pulse having a real and an imaginary component;
second means for extracting from the imaginary component information representative of the phase component of the return signal; and
third means responsive to the phase component for detecting the target.
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Accused Products
Abstract
A system and method for detecting a target. The inventive method includes the steps of receiving a complex return signal of an electromagnetic pulse having a real and an imaginary component; extracting from the imaginary component information representative of the phase component of the return signal; and utilizing the phase component to detect the target. Specifically, the phase components are those found from the complex rangeDoppler map. More specific embodiments further include the steps of determining a power spectral density of the phase component of the return signal; performing a crosscorrelation of power spectral density of the phase component of the return signal between different antennasubarray (quadrant channels); and averaging the crosscorrelated power spectral density of the low frequency components. In an alternative embodiment, the crosscorrelation is performed on the phase component of the rangeDoppler map directly. This signal can then be averaged to potentially provide improved detection of targets. The crosscorrelations of the power spectral densities derived from the complex valued rangeDoppler map are then used to detect the target in the presence of monostatic clutter. An additional teaching relates to a utilization of the phase component to ascertain a direction of the target and thereby effect target tracking as well as target detection.
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20 Claims
 1. A system for detecting a target in clutter comprising:
first means for receiving a complex return signal of an electromagnetic pulse having a real and an imaginary component;
second means for extracting from the imaginary component information representative of the phase component of the return signal; and
third means responsive to the phase component for detecting the target.  View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10)
 11. A system for detecting a target in clutter comprising:
a radar receiver adapted to receive a complex return signal of an electromagnetic pulse having a real and an imaginary component;
a signal processor for extracting from the imaginary component information representative of the phase component of the return signal; and
a target detector responsive to the phase component for detecting the target.
 12. A method for detecting a target in clutter including the steps of:
receiving a complex return signal of an electromagnetic pulse having a real and an imaginary component;
extracting from the imaginary component information representative of the phase component of the return signal; and
utilizing the phase component to detect the target.  View Dependent Claims (13, 14, 15, 16, 17, 18, 19, 20)
1 Specification
This invention was made with Government support under Contract No. F4962098C0034 awarded by the U.S. Air Force. The U.S. Government therefore has certain rights in the invention disclosed herein.
1. Field of the Invention
The present invention relates to electromagnetic seekers. More specifically, the present invention relates to systems and methods for detecting and tracking targets in clutter.
2. Description of the Related Art
Radio frequency (RF) detection of slowly moving or stationary targets in monostatic clutter is a problem that has recently generated a great deal of interest within the Defense community. Monostatic clutter is naturally produced by ground reflections of the radar'"'"'s transmitted signal. Monostatic clutter is thus largest at zero relative Doppler. Monostatic clutter is particularly troublesome when trying to detect slowly moving target, since there is almost no Doppler difference between the clutter and the target. Exemplary targets include surface vehicles, launchers and loitering UAVs (Unmanned Airborne Vehicles). The root of the difficulty lies in the fact that conventional radar systems use Doppler information for detection and tracking functions. As is wellknown in the radar art, the Doppler shift is a shift in the frequency of radar returns due to the velocity of the target relative to the velocity of the radar receiver. In the presence of clutter, conventional Doppler radar systems lose the ability to use the target'"'"'s Doppler to discriminate it from the clutter. Indeed, the target need not even be nearly stationary for this to be a problem. Even a rapidly moving target can exhibit low Doppler relative to mainlobe clutter if its velocity vector is nearly perpendicular to the velocity vector of the observation platform.
For this reason, most airtoground missiles employ either a highresolution radar seeker or an infrared (IR), electrooptic (EO) or laserradar based (ladar) seeker. However, the inclusion of these seeker modes increases development and production costs of the host platform. Further, IR seekers exhibit more significant atmospheric limitations (smoke, fog, snow, and/or rain, etc.).
While a number of hardware solutions have been proposed, a need remains for an RF based solution that would provide the basis for an allweather, dualmission RF seeker, viz, detection/radarparameterestimation performance with respect to both stationary and nonstationary targets, to significantly extend the capability of currently fielded hardware. More specifically, there is a need in the art for a more effective system or method for detecting targets in clutter without relying on a Doppler shift calculation.
The need in the art is addressed by the system and method for detecting a target of the present invention. The inventive method includes the steps of receiving a complex return signal of an electromagnetic pulse having a real and an imaginary component; extracting from the imaginary component information representative of the phase component of the return signal; and utilizing the phase component to detect the target. Specifically, the phase components are those found from the complex rangeDoppler map.
More specific embodiments further include the steps of determining a power spectral density of the phase component of the return signal; performing a crosscorrelation of power spectral density of the phase component of the return signal between different antennasubarray (quadrant channels); and averaging the crosscorrelated power spectral density of the low frequency components. In an alternative embodiment, the crosscorrelation is performed on the phase component of the rangeDoppler map directly. This signal can then be averaged to potentially provide improved detection of targets. The crosscorrelations of the power spectral densities derived from the complex valued rangeDoppler map are then used to detect the target in the presence of monostatic clutter.
An additional teaching providing by the present invention relates to a utilization of the phase component to ascertain a direction of the target and thereby effect target tracking as well as target detection.
FIG. 1a is a simplified block diagram of a radar system implemented in accordance with the teachings of the present invention.
FIG. 1b shows the clutterscattering coefficient versus incidence angle for grass.
FIG. 2 shows the amplitude of a rangeDoppler map resulting from a simulation of an illustrative embodiment of the present teaching.
FIG. 3 shows real and imaginary values of a point target along the Doppler direction.
FIG. 4 shows amplitude and phase of the point target of FIG. 3.
FIGS. 5(a) and (b) show the amplitude and phase of a clutter return cut at r=85 in the Dopplerdimension, respectively.
FIGS. 5(c) and (d) show the amplitude and phase of a clutter return in addition to a point target and receiver noise.
FIG. 6 shows the effect of crosscorrelating different channels then measuring PSD.
FIG. 7 is a series of graphs which illustrate the results of the first method for target detection of the present invention.
FIG. 8 shows the result of crosscorrelating a measured PSD in different channels then measuring 2^{nd }PSD.
FIG. 9 shows the result of target detection using a method in accordance with the teachings of the present invention.
FIG. 10 shows simulation results with respect to a target with multiple scatterers and multiple point targets.
FIG. 11 show simulation results with reduced SNR in accordance with the present teachings.
FIG. 12 is a diagram showing a simplified view of a planar array antenna with 4 quadrant spatial channels.
FIG. 13 is a graph of simulation results showing the DC component from the PSD of phase functions.
FIG. 14 is a graph of simulation results showing six pairs of distinct crosscorrelation between channels.
FIG. 15 is a diagram showing the returns of two point targets with different Doppler frequencies.
FIG. 16 shows the signals used to detect targets with different Doppler frequencies in accordance with the present teachings.
FIG. 17 shows the linear detrending of complexvalued rangeDoppler map. The detrending algorithm is a standard numerical algorithm taken from MATLAB.
FIG. 18 is a diagram which illustrates target detection before and after detrending in accordance with the inventive method.
FIG. 19 is a diagram showing the rangeDoppler function of illustrative radar clutter return data using a PRI length from 127 to 256.
FIG. 20 shows target detection in amplitude and phasedomains for real clutter data utilizing the teachings of the present invention.
Illustrative embodiments and exemplary applications will now be described with reference to the accompanying drawings to disclose the advantageous teachings of the present invention.
While the present invention is described herein with reference to illustrative embodiments for particular applications, it should be understood that the invention is not limited thereto. Those having ordinary skill in the art and access to the teachings provided herein will recognize additional modifications, applications, and embodiments within the scope thereof and additional fields in which the present invention would be of significant utility.
In conventional monopulse radio frequency (RF) seekers, only the amplitudes of the complexvalued range/Dopplerfilter outputs are used for target detection and/or identification. The randomlike phases of the range/Dopplerfilter output values are seldom considered helpful for this purpose. However, as stated by Rihaczek and Hershkowitz in Radar Resolution and Complex Image Analysis, by A. Rihaczek and S Hershkowitz, Artech House, 1996, it is essential to utilize the whole complexvalued rangeDoppler image rather than only the intensity (amplitude) image because a large part of the information about the target is contained in the phase of the image in addition to the amplitude. Nonetheless, there are two at least two reasons why phase data has not been used for target detection. First, traditionally a window function is used before the Fast Fourier Transform (FFT) of the rangeDoppler image to suppress the sidelobe peaks. The window function will cause low frequency components from the clutter in the phase domain and thus make the extraction of target phase signals much more difficult. As discussed herein, in accordance with the present teachings, an FFT is applied directly on the original RF signals without convolving any window function.
Secondly, the leakage of Doppler FFT will also generate strong low frequency components caused by the clutter leakage in the phase domain. However, as discussed more fully below, a detrending step is used, in accordance with the present teachings, to effectively reduce clutter leakage.
FIG. 1a is a simplified block diagram of a radar system implemented in accordance with the teachings of the present invention. Those skilled in the art will appreciate that the present teachings are not limited to radar applications. The teachings provided herein should also have utility in synthetic aperture radar (SAR), Interferometric SAR (ISAR), LADAR and other imaging applications. The system 10 includes a conventional four quadrant (four channel) radar antenna 12 having radiating elements 13, 15, 17 and 19. The antenna 12 feeds a conventional RF to IF to video analogtodigital converter 14. Baseband video is fed to a conventional radar filter coefficient computer 16 and a set of channel matching adaptive equalization filters 18. The filters 18 provide gain matching signal processing in a conventional manner. The outputs of the filters 18 feed a pulse compression unit 20 which serves to improve the signaltonoise ratio (SNR) in a conventional manner. An FFT 22 then extracts the Doppler signals from each channel for each of a number (e.g. 200) of range gates.
In accordance with the present teachings, a processor 24 operates on the output of the FFTs 22 and provides a set of Doppler range maps as discussed more fully below. The processor 24 outputs conventional target magnitude data to a target detector 26 and target phase data to the detector 26 and a target tracker 28. The target tracker 28 provides signals to a missile guidance system shown generally at 30.
The system 10 of FIG. 1a receives a complex return signal of an electromagnetic pulse having a real and an imaginary component; extracts from the imaginary component information representative of the phase component of the return signal; and utilizes the phase component to detect the target. An additional teaching providing by the present invention relates to the utilization of the phase component to ascertain a direction of the target and thereby effect target tracking as well as target detection.
The teachings of the present invention are best illustrated with respect to the following. In a detection system, skin target data received through the k^{th }channel by the m^{th }pulse in the appropriate nth rangegate are expressed as:
where, R_{0}=range at which signaltonoise ratio (SNR) is 0 dB, R_{t}=range to target, f_{Dt}=Doppler frequency of target, f=transmit frequency, T_{pri}=pulse repetition interval, T_{s}=sample interval, Φ=random starting phase, Φ_{k}=spatial phase at subarray k, and c=speed of light.
Although the skin target is modeled as a “point target”, that is, a single scatterer exhibiting a fixed radar cross section, the model can be easily extended to include multiple distributed scatterers. As an example, a simple extension comprises two closely spaced point scatterers separated by a distance 1<Δn (rangegate resolution) and exhibiting equal Doppler frequency. The observed phase differences, Φ_{d}, is a function of the distance 1 projected along the radar illumination path, and the processor'"'"'s spectral location. Then, the model for a twoscatterer target can be expressed as
where the plus/minus sign depends on the second scatterer being in front of or behind the first scatterer. Similarly, more generalized targets with multiple scatterers (more than two) distributed in a 3D space can be modeled.
Receiver noise is modeled as spatiotemporally white Gaussian noise.
Monostatic Clutter Model
The illustrative clutter model uses scattering coefficients based on calibrated scatterometer data as found in the Handbook of Radar Scattering Statistics for Terrain by Ulaby and Dobson. This data consists of the mean and variance of the co and crosspolarization Radar Cross Section (RCS) magnitude for a variety of terrain types, frequency bands and grazing angles. For this simulation, curvefit parameters for the mean and variance of the RCS were as follows:
where P1, P2, P3, P4, P5, P6, and M1, M2, M3 are coefficients for parameter fits, θ is the angle of incidence in radians, μ is the mean of the RCS, and sd is the standard deviation of the RCS.
FIG. 1b shows the clutterscattering coefficient versus incidence angle for grass. The mean clutterscattering coefficient and the spread corresponding to one standard deviation are shown. The curve fits for the co and crosspolarization clutter backscatter mean and standard deviation are used in the clutter model to provide a geometrydependent clutter power calculation for each rangeDoppler cell. Once the mean and standard deviations are found for the particular clutter cell under consideration, random numbers are drawn from the desired probability distribution in order to obtain a clutter backscatter coefficient (σ)
where, σ is the clutter backscatter coefficient, μ is the mean of the clutter backscatter coefficient for the current clutter geometry, rv is a random number drawn from the appropriate distribution, and sd is the clutter standard deviation. Gaussian, Weibull and Lognormal distributions were used to characterize various types of clutter.
Once the backscatter coefficients have been determined, the clutter model (as shown below) calculates the clutter cell area (A_{i}) based on the current missile/target geometry, rangegate size and antenna beamwidth. The product of this clutter cell area and the backscatter coefficient gives the clutter cell radar cross section which is used in the radar range equation to calculate received clutter power. Clutter data received through the kth channel by the mth pulse in the nth rangegate are expressed as:
where, R_{i}=range to the i^{th }patch, CNR_{0}(R_{i})=cluttertonoise ratio for a 0dBsm patch at range Ri, σ_{i=clutter backscatter coefficient for ith patch=μ}_{i+sd}_{i}*rv, A_{i}=projected area of ith patch, f_{Di}=Doppler frequency associated with the ith patch, f=transmit frequency, T_{pri}=pulse repetition interval, T_{s}=sample interval, Φ=Random starting phase, Φ_{ki}=spatial phase at subarray k, for the ith patch. Clutter demonstrates longterm correlation spreading across PRIs.
The relative geometry for each clutter cell determines its Doppler, range and spatial direction vector all of which are used along with the clutter power to construct a spatial covariance matrix for each rangeDoppler cell. This covariance matrix is then convolved with the pulsecompression, video filter and amplitudeweighted Fourier transform correlation functions. The resulting covariance matrices are used to construct either stochastic rangeDoppler maps or the corresponding stochastic time series data.
Frequency Analysis of Phase Estimates along the Doppler Direction
A representative case where the RF target signal is totally embedded in strong monostatic clutter can be simulated. Illustrative missile radar parameters are listed in Table 1.
FIG. 2 shows the amplitude of a rangeDoppler map resulting from a simulation of an illustrative embodiment of the present teaching. Only the four copolarized antennaquadrant (channel) data are used. The selected rangegate resolution was 40 meters. Within each PRI, there were 200 contiguous range samples with a rangesample interval of 20 meters which represents one half of the rangefilter resolution. A normal level electronic (thermal) noise was also included (noise floor with null limit (dB)=8.69E10). A point target was located 1,700 meters from the missile with a low Doppler frequency of 2.38K Hz. Since the interval between Doppler filters was 258 Hz (=33K Hz/128), the major energy of this point target was centered at the rangeDoppler cell (r=85, d=9).
FIG. 2 shows that a target that is totally embedded in the strong clutter returns would be difficult if not impossible to detect using conventional teachings. The signaltoclutterplusnoiseratio (SCNR) at cell (85,9) was approximately −10 dB. Therefore, the rangeDoppler map in the amplitudedomain could not provide enough information for detecting the target when there is strong clutter returns. The question is what additional information can one gain in the phase domain.
FIG. 3 shows real and imaginary values of a point target along the Doppler direction. The real (solid line) and imaginary (dashdotted line) 1D slices T(85,d) are cut at r=85 along the Doppler direction from the complexvalued 2D rangeDoppler map T(r,d) of a point target centered at cell (85,9). The amplitude and phase can be calculated from the real and imaginary curves in FIG. 3. They are plotted in FIGS. 4a and 4b, respectively.
FIG. 4 shows amplitude and phase of the point target of FIG. 3. The phase is wrapped between π and −π. Note that the phase curve has a πjump at the location of the peak amplitude (d=9), and then gradually increases (or decreases). Obviously from FIG. 4b, the phase function of a point target in the Dopplerdimension will contain strong low frequency components if a spectrum analysis is performed on this function. On the other hand, the phase function of a monostatic clutter return generally contains high frequency components.
FIGS. 5(a) and (b) show the amplitude and phase of a clutter return cut at r=85 in the Dopplerdimension, respectively. There are strong monostatic clutter returns in the amplitude domain from Doppler d=0 to d=20 as shown in FIG. 5(a). However, the phases of the clutter returns are quite random as indicated in FIG. 5(b), and thus contain high frequency components.
FIGS. 5(c) and (d) show the amplitude and phase of a clutter return in addition to a point target and receiver noise. Obviously, the target can not be detected in the amplitudedomain (compare FIG. 5(a) with 5(c)). On the other hand, as indicated in FIG. 5(d), low frequency components caused by the point target can be observed in the phasedomain. These results suggest that one may detect targets by measuring the low frequency components in the phasedomain using spectrum analysis.
Methods for Detecting Targets in PhaseDomain
The present invention provides a system and method for detecting targets in phasedomain. The low frequency components are extracted by PSD (power spectral density) measurements. Clutter returns and receiver noise are further suppressed by crosscorrelation analysis between space (antennaquadrant) channels. Welch'"'"'s method is used for estimating PSD (as used in Matlab Signal Processing tool). Two methods for target detection are disclosed herein.
Method 1 for Target Detection
PSDs are measured in the Dopplerdimension of the rangeDoppler map in the phasedomain.
FIG. 6 shows the effect of crosscorrelating different channels then measuring PSD. FIGS. 6(a) (channel 1) and 6(b) (channel 2) show such PSDs for a point target. It is clear that the point target contains strong low frequency components. For further suppressing clutter and receiver noise, first crosscorrelate the corresponding 1D slices along the Doppler direction between two spacechannels at the same range location:
This operation will suppress clutter and receiver noise since the target signals in different channels have high correlation while the decorrelated clutter (due to distributed nature) and the uncorrelated receiver noise in different channels have much lower correlation. The PSD of the correlated function (Eq. (7)) is then measured. The result with respect to a point target is shown in FIG. 6(c). The first several low frequency components (e.g., from f=0 to f=4) are averaged, and the result is plotted in FIG. 6(d). Clearly, this averaging step can further suppress clutter and receiver noise.
Method 1 was verified using the representative simulated data. The RF signal included a point target, a strong clutter return, and a normal receiver noise. The simulation parameters were given above. The results are shown in FIG. 7.
FIG. 7 is a series of graphs which illustrate the results of the first method for target detection of the present invention. FIG. 7(c) indicates that the crosscorrelation process helped reduce clutter and receiver noise significantly. FIG. 7(d) shows that high SCNR can be obtained in the phasedomain even though the target is totally embedded in the monostatic clutter returns in the amplitudedomain.
Method 2 for Target Detection
In Method 2, PSDs are measured in the Dopplerdimension of the rangeDoppler map for different space channels in the phasedomain. The measured PSD functions in different channels are then crosscorrelated. Finally, a 2^{nd }PSD measurement is taken on the obtained crosscorrelation function. Therefore, the difference between Methods 1 and 2 is that, in Method 1, the original phase functions are used for crosscorrelation, while in Method 2 the PSDs of the original phase functions are used for crosscorrelation. The results using Method 2 are shown in FIGS. 8 and 9.
FIG. 8 shows the result of crosscorrelating a measured PSD in different channels then measuring 2^{nd }PSD.
FIG. 9 shows the result of target detection using a method in accordance with the teachings of the present invention. In FIG. 8, a point target was used as the RF signal, while in FIG. 9 the RF signal included a point target, a strong clutter return, and a normal receiver noise. FIGS. 8(a) and 9(a) show the 1^{st }PSDs of channel 1 and FIGS. 8(b) and 9(b) show the 1^{st }PSDs of channel 2. FIGS. 8(c) and 9(c) show the 2^{nd }PSDs of the crosscorrelations between the 1^{st }PSDs of channels 1 and 2. FIGS. 8(c) and 9(c) show that the power of the target stays high from low PSD frequencies to high PSD frequencies. On the other hand, the power of the clutter and receiver noise does not stretch to higher PSD frequencies. Therefore, the clutter and receiver noise can be suppressed further by averaging the power along the PSD frequency axis starting from a little higher frequency as shown in FIGS. 8(d) and 9(d). The averages in these plots were taken from PSD frequency sample number 6 to number 65.
Improvement of Target Detection Using Phase Estimates
In general, Method 2 can obtain a higher signaltoclutterplusnoiseratio (SCNR) than Method 1 as indicated in FIGS. 7(d) and 9(d). More quantitative analysis on the simulated data shows that in the amplitudedomain the target is undetectable and is totally embedded in the strong monostatic clutter returns with very low SCNR (0.27, or −11.4 dB). Nevertheless, the target can be easily detected in the phasedomain. The SCNR is 25.4 dB (or 18.7) using Method 1 as shown in FIG. 7(d), and is 34.6 dB (or 53.7) using Method 2, as shown in FIG. 9(d). Therefore, a 3040 dB gain in SCNR was achieved when using phases (as opposed to amplitude) estimates.
Targets with Multiple Scatterers and Multiple Point Targets
In this simulation, an extended target with two scatterers separated 10 meters along the range direction was used.
FIG. 10 shows simulation results with respect to a target with multiple scatterers and multiple point targets. This target model was discussed and presented in above with respect to Eq. (2). The target intensity was centered at r=85 and r=86 with Doppler d=9. Other parameters of this simulation are the same as the previous simulation. The results are shown in FIGS. 10(a) (Method 1) and 10(b) (Method 2). Both methods can easily detect the extended target at rangegates r=85 and r=86. This result indicates that the present methods can be applied to more extended targets other than the simple pointtarget.
RF signals containing multiple point targets separated at nearby rangegates have also been simulated. Based on the previous simulation using a single point target located at r=85, another point target located at r=76 was added. Results were obtained and plotted in FIGS. 10(c) (Method 1) and 10(d) (Method 2). It is seen that both Method 1 and 2 can be used for detecting multiple point targets.
Target Detection with Reduced SNR
In the first simulation using the point target described above, the receiver noise was increased intensity by a factor of 5 and 10 to test the robustness of the present methods in reduced SNR (5 and 10 times lower than the normal level).
FIG. 11 show simulation results with reduced SNR in accordance with the present teachings. The results using Method 1 are shown in FIGS. 11(a) (SNR reduced 5 times) and 11(b) (SNR reduced 10 times). Although the noise level is higher, it was still possible to detect the target at rangegate r=85. In general, it was found that Method 1 was more robust than Method 2 in the reduced SNR situation.
For a monopulse radar, after detecting the target the next task will be to estimate the target direction.
FIG. 12 is a diagram showing a simplified view of a planar array antenna with 4 quadrant spatial channels. As shown in FIG. 12, the target direction is measured by the EL (elevation) and AZ (azimuth) angles, which are directly related to the phase differences between the antennaquadrant spatial channels. That is, for the EL direction: θ_{13}=Φ_{1}−Φ_{3}=θ_{24}=Φ_{2}−Φ_{4}, where Φ_{1}, Φ_{2}, Φ_{3}, and Φ_{4 }are the target phases at the 4 antennaquadrant channels. For the AZ direction: φ_{12}=Φ_{1}−Φ_{2}=φ_{34}=Φ_{3}−Φ_{4}. In accordance with the present teachings, the low frequency components used for target detection can be further used for target direction estimation.
As indicated in FIG. 4(b), the low frequency components (e.g., the DC component) depend on the shape of the phase function. Different initial target phases at different channels will change and move the phase functions up or down, and thus change the low frequency components. What is necessary is to scale the measured low frequency components down to the original phase values since the measured values have been scaled up by the crosscorrelation and PSD operations. In accordance with the present teachings, two methods are disclosed to convert the measured low frequency components to phase differences between the spatial channels: the direct method and the crosscorrelation method.
Direct Method
This method uses the low frequency components directly measured from each individual channel. The measured low frequency component values obtained by PSD operation are scaled back by:
Φ_{i}=C_{d}P_{i}^{0.5} (8)
where i=1, 2, 3, 4; C_{d }is a scale constant; and P_{i }is the measured low frequency component values.
CrossCorrelation Method
As discussed above, the crosscorrelation operation between spatial channels can significantly suppress the clutter and receiver noise. As a first step, the measured low frequency component values are obtained first by crosscorrelation then by PSD operations. There are six pairs of distinct crosscorrelation functions, between the four antenna channels: P_{12}, P_{13}, P_{14}, P_{23}, P_{24}, and P_{34}. As per the direct method discussed above, the scaling equation is:
where C_{c }is a scale constant. Therefore, for the elevation (EL) direction: θ_{13}=Φ_{12}−Φ_{32}=Φ_{14}−Φ_{34}, and θ_{24}=Φ_{21}−Φ_{41}=Φ_{23}−Φ_{43}. For the AZ direction: φ_{12}=Φ_{13}−Φ_{23}=Φ_{14}−Φ_{24 }and φ_{34}=Φ_{31}−Φ_{41}=Φ_{32}−Φ_{42}.
The true phase differences of the pointtarget are θ_{13}=θ_{24}=0.46 (radian) and φ_{12}=φ_{34}=−0.13 (radian). For the direct method, P_{i }in Eq.(8) used the values of the DC component at range r=85 of the 4 channels, as shown in FIG. 13.
FIG. 13 is a graph of simulation results showing the DC component from the PSD of phase functions. The scale constant in (8) is estimated as C_{d}=0.25. Channel 3 is quite noisy, and thus we used the other 3 channels to estimate the phase differences. The estimated phase differences are θ_{24}=Φ_{2}−Φ_{4}=0.41 (radian) and φ_{12}=Φ_{1}−Φ_{2}=−0.16 (radian). The estimation error is about 1020%.
For the crosscorrelation method, P_{ij }in Eq.(9) used the average of the DC and the first two harmonic components at range r=85 of the 6 PSD pairs, as shown in FIG. 14.
FIG. 14 is a graph of simulation results showing six pairs of distinct crosscorrelation between channels. The scale constant in Eq.(9) is estimated as C_{d}=0.009. The estimated phase differences are θ_{24}=Φ_{12}−Φ_{14}=0.47 (radian) and φ_{12}=Φ_{14}−Φ_{24}=−0.13 (radian). The estimation error is less than 3%. Therefore, the crosscorrelation method seems to provide better performance than the direct method.
DopplerShifting and DeTrending
For target detection in the amplitudedomain, the optimal case is that the target Doppler frequency is centered at one of the Doppler filters. Otherwise, the target energy will be picked up by several nearby filters causing “leakage”. However, this is not true for target detection in the phasedomain. This is illustrated below with respect the two point targets with different Doppler frequencies shown in FIG. 15.
FIG. 15 is a diagram showing the returns of two point targets with different Doppler frequencies. One has a Doppler frequency of 2.35K Hz (the interval between two Doppler filters is 258 Hz), and thus is 30 Hz away from the number 9 Doppler filter (we call this target T30). The other target has a Doppler frequency of 2.44K Hz, and thus is 120 Hz away from the number 9 Doppler filter (we call this target T120). The real and imaginary functions of T30 and T120 are plotted at FIGS. 15(a) and (b), respectively, and the amplitudes of T30 and T120 are, respectively, plotted at FIGS. 15(c) and (d). T30 has higher amplitude at the center Doppler filter while T120 has more energy spread in nearby filters caused by the leakage. It is this spread energy that generates high values of low frequency components for target detection in phasedomain.
FIG. 16 shows the signals used to detect targets with different Doppler frequencies in accordance with the present teachings. FIG. 16 shows target detection in the phasedomain for two targets: T30 and T60 (Doppler frequency of 2.38K Hz) using Method 2 of the present invention. It is seen that T60 (FIG. 16(b)) can provide much higher values of low frequency components than T30 (FIG. 16(a)) does for target detection. In general, the optimal Doppler frequency for target detection in the phasedomain is the frequency located at the middle of two nearby Doppler filters. Note that this is the worst case for target detection in the amplitude domain.
As can be seen in FIG. 16(b), target T120 has a Doppler frequency close to optimal. To obtain reliable target detection in the phasedomain, Dopplershifting can be used to move the arbitrary target Doppler to the middle of Doppler interval by multiplying a Doppler shift frequency to the received RF signal, that is, by multiplying a phase angle which is linearly increased with the increase of the RF pulse repetition intervals (PRIs) within a Coherent Processing Interval (CPI).
However, Dopplershifting will also increase Fast Fourier Transform (FFT) leakage caused by the clutter and receiver noise. The leakage from clutter will, in turn, generate high values of low frequency components from PSD signal and thus reduces SCNR for target detection in the phasedomain. Detrending can be used here to reduce the leakage caused by clutter while keeping strong low frequency components due to the targets. Note that some different parameter settings can also generate high clutter leakage. For example, a CPI with smaller PRI number (e.g., 32 or 64) will generate higher clutter leakage than a CPI with larger PRI number (e.g., 128 or 256).
As shown in FIG. 5(b), the values of the phase function for a low leakage clutter return change fast around the zero, which means that the trend of the real and imaginary values is close to zero along the Doppler direction. On the other hand, for a signal with high leakage the trends of the real and imaginary functions will linearly or nonlinearly deviate away from the zero. FIGS. 3 and 15(b) showed such an example (a nonlinear trend). To apply the detrending technique, first choose a duration in the Doppler direction where the target trends are almost decayed close to zero. The trends measured in this duration will mostly reflect the trends caused by the clutter leakage. Then linearly or nonlinearly detrend the real and imaginary functions of the whole rangeDoppler map along the Doppler direction. In this way, the clutter leakage is reduced but the high values of low frequency components of the target in the phasedomain are maintained.
A simulation has been conducted using a RF signal with a T30 target, a strong monostatic clutter return, and a normal level receiver noise. The target detection result is shown in FIG. 16(a), where the target phase signal was quite weak. In the 2^{nd }simulation, a 30 Hz Doppler shift was applied to the same RF signal without detrending.
FIG. 17 shows the linear detrending of complexvalued rangeDoppler map resulting from the application of a standard detrending algorithm taken from MATLAB. The real and imaginary functions of five overlapped range slices are plotted in FIGS. 17(a) and (c), respectively. It is seen that the trends of both functions are deviated away from zero. The target detection result is shown in FIG. 18(a).
FIG. 18 is a diagram which illustrates target detection before and after detrending in accordance with the inventive method. Although the target has a relatively high return value, the clutter leakage causes even higher return values by comparing FIG. 18(a) with FIG. 16(a). In the 3^{rd }simulation, a 30 Hz Doppler shift is applied to the RF signal and then a linear detrending is conducted. It is seen in FIGS. 17(b) and (d) that the trends caused by clutter leakage have been corrected towards zero.
The target detection result is shown in FIG. 18(b). The high return values by the clutter leakage as shown in FIG. 18(a) have been significantly suppressed by the linear detrending, and the target return is maintained with a high value as shown in FIG. 18(b). By comparing FIG. 18(b) with FIGS. 16(a) and (b), it is evident that detrending can significantly increase the target phase signal. The result using a T30 target with Dopplershifting and detrending is as good as the result using a T60 target.
TARGET DETECTION USING REAL CLUTTER RETURN DATA
In the simulations discussed above, the monostatic clutter return data were generated based on high fidelity clutter models. The following data relates to the use of real measured radar clutter data to test target detection methods in the phasedomain. The radar clutter data has the following illustrative parameters:
1). Antenna looking up 5 degrees (3 dB pt. on the ground);
2). Antenna sitting approx. 30 ft above water;
3). Antenna scan rate=540 degrees/second;
4). AZ beam width=2 degrees, EL beam width=10 degrees;
5). Rangegate size=approx. 100 ft (0.2 microseconds);
6). PRI=approx. 62 microseconds;
7). Data is coherent over the entire observation interval for more than 2000 PRIs (flexibility to choose CPI time);
8). Data is 12 bits long, and the receiver noise is about 10 counts.
FIG. 19 is a diagram showing the rangeDoppler function of illustrative radar clutter return data using a PRI length from 127 to 256. It is evident that there are strong clutter returns at the low rangegate and low Doppler areas. The Phalanx radar has only single antenna channel, and thus can not conduct spatial crosscorrelation which is the process required for Method 1 and Method 2 developed for radar with multiple antenna channels. Nevertheless, since very long coherent PRIs (more 2000) collected by the Phalanx single antenna channel are available, it is possible to conduct temporal crosscorrelation between different CPIs collected at different time by the same cannel. Therefore, Method 1 and Method 2 as disclosed herein can be applied to this radar data.
FIG. 20 shows target detection in amplitude and phasedomains for real clutter data utilizing the teachings of the present invention. In this embodiment, crosscorrelation is conducted between two CPIs with a PRI length of 128. One is cut from PRI number 128 to 256, the other from 457 to 585. A point target is put at rangegate number 12 with a Doppler frequency of 315 Hz. The PRF is 16.129K Hz, and thus the interval between two nearby Doppler filters is 16.129K Hz/128=126 Hz. Therefore, the target is located at the middle between the number 2 and 3 Doppler filters, and is totally embedded in the strong clutter returns. The SCNR in amplitudedomain is −5.03 dB (0.56) for the first CPI, and is −3.5 dB (0.67) for the second CPI. The 1D slice cut at Doppler d=2 from the clutter amplitude map (FIG. 19) is shown in FIG. 20(a). The 1D slice cut at the same location for the RF signal including the pointtarget discussed above, is shown in FIG. 20(b).
Obviously this target is totally embedded in the clutter and is therefore not detectable in the amplitudedomain. To apply the target detection techniques in the phasedomain in accordance with the present teachings, we first apply the detrending technique to remove some of the clutter leakage and then use Method 1 and Method 2 to detect the target in phasedomain. We only used a small PRI number 128 (out of more than 2000) for a CPI, and thus the FFT leakage is higher than using a lager PRI number. The Doppler duration chosen for measuring the trends is from d=13 to d=35 for the 1^{st }CPI, and from d=10 to d=20 for the 2nd CPI.
The results are shown in FIGS. 20(c) (Method 1) and 20(d) (method 2). The target can be easily detected at range r=12 in the phasedomain. The SCNR in the phasedomain is 23.9 dB (15.7) using Method 1, and is 56.3 dB (654.6) using Method 2.
In the illustrative embodiment, simple correlation and spectrum estimation (periodogram) techniques are used to extract the phase signals. In addition, some simple detrending techniques are used to correct the clutter leakage of Doppler FFT. Further improved results may be expected from the use of more advanced spectrum estimation and FFT leakage correction techniques.
Thus, the present invention has been described herein with reference to a particular embodiment for a particular application. Those having ordinary skill in the art and access to the present teachings will recognize additional modifications, applications and embodiments within the scope thereof.
It is therefore intended by the appended claims to cover any and all such applications, modifications and embodiments within the scope of the present invention.
Accordingly,