Method of generating accurate estimates of azimuth and elevation angles of a target for a phased—phased array rotating radar

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First Claim
1. A method for generating accurate estimates of a radar target'"'"'s azimuth and elevation angles for a rotating monopulse radar comprising the steps of:
 measuring an antenna'"'"'s oneway transmit pattern and three receive antenna patterns;
generating twoway Sum, DeltaAzimuth and DeltaElevation antenna patterns;
translating the coordinates of twoway Sum, DeltaAzimuth and DeltaElevation antenna patterns to center on a sinespace beam steer;
sampling uniformly the twoway antenna patterns at midCPI points of numerous target returns;
coherently integrating over the sinespace trajectories of said target returns;
averaging coherent integration sums of said target returns and plotting said averages at their respective midCPI points to produce average gain antenna patterns;
generating Uoffset and Voffset scan modulated coherently integrated (SMCI) monopulse curves from average gain patterns;
coherently integrating said twoway Sum, DeltaAzimuth and DeltaElevation target returns of said antenna patterns;
calculating the target'"'"'s monopulse ratios from said coherently integrated target return measurements;
calculating the target'"'"'s Uoffset and Voffset monopulse angles in sinespace using said SMCI monopulse curves;
adding said Uoffset and Voffset monopulse angles to a sinespace beam steer to obtain an improved estimate of a target'"'"'s sinespace position denoted as U_{tgt }and V_{tgt}; and
transforming said U_{tgt }and V_{tgt }to azimuth and elevation angles in a nonrotating coordinate system using coordinate system transformations.
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Abstract
A method and apparatus for generating accurate estimates of a radar target'"'"'s azimuth and elevation angles for a phasedphased array rotating radar. Scan modulated coherently integrated (SMCI) monopulse curves are generated from a measured oneway transmit antenna pattern and three receive antenna patterns. The SMCI monopulse curves are calculated in advance for the expected beam steers. To utilize the SMCI monopulse curves, twoway Sum, DeltaAzimuth and DeltaElevation target returns are coherently integrated, the target'"'"'s monopulse ratios calculated, and the SMCI monopulse curves or polynomials used to calculate the target'"'"'s Uoffset and Voffset sinespace angles, which are added to the radar'"'"'s beam steer to get an improved estimate of the target'"'"'s sinespace angular position denoted as U_{tgt }and V_{tgt}. A coordinate system transformation transforms U_{tgt }and V_{tgt }to azimuth and elevation angles in a nonrotating coordinate system.
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14 Claims
 1. A method for generating accurate estimates of a radar target'"'"'s azimuth and elevation angles for a rotating monopulse radar comprising the steps of:
measuring an antenna'"'"'s oneway transmit pattern and three receive antenna patterns; generating twoway Sum, DeltaAzimuth and DeltaElevation antenna patterns; translating the coordinates of twoway Sum, DeltaAzimuth and DeltaElevation antenna patterns to center on a sinespace beam steer; sampling uniformly the twoway antenna patterns at midCPI points of numerous target returns; coherently integrating over the sinespace trajectories of said target returns; averaging coherent integration sums of said target returns and plotting said averages at their respective midCPI points to produce average gain antenna patterns; generating Uoffset and Voffset scan modulated coherently integrated (SMCI) monopulse curves from average gain patterns; coherently integrating said twoway Sum, DeltaAzimuth and DeltaElevation target returns of said antenna patterns; calculating the target'"'"'s monopulse ratios from said coherently integrated target return measurements; calculating the target'"'"'s Uoffset and Voffset monopulse angles in sinespace using said SMCI monopulse curves; adding said Uoffset and Voffset monopulse angles to a sinespace beam steer to obtain an improved estimate of a target'"'"'s sinespace position denoted as U_{tgt }and V_{tgt}; and transforming said U_{tgt }and V_{tgt }to azimuth and elevation angles in a nonrotating coordinate system using coordinate system transformations.  View Dependent Claims (2, 3, 4, 5)
 6. A method for generating scan modulated coherently integrated (SMCI) monopulse curves comprising the steps of:
measuring an antenna'"'"'s oneway transmit pattern and three receive antenna patterns; generating twoway Sum, DeltaAzimuth and DeltaElevation antenna patterns by performing a point by point multiplication of the antenna gain of the oneway transmit pattern with the antenna gains of the three receive patterns; translating the coordinates of twoway Sum, DeltaAzimuth and DeltaElevation antenna patterns to center on a sinespace beam steer; sampling uniformly the twoway antenna patterns at midCPI points of numerous target returns; coherently integrating over the trajectories of said target returns; averaging coherent integration sums of said target returns and plotting said averages at their respective points; and generating scan modulated coherently integrated (SMCI) monopulse curves from the Sum, DeltaAzimuth and DeltaElevation average gain antenna patterns as follows; generating a Uoffset SMCI monopulse curve by taking the real parts of the DeltaAzimuth Ucardinal plane gains divided pointbypoint by the Sum Ucardinal plane gains; and generating a Voffset SMCI monopulse curve by taking the real parts of the DeltaElevation Vcardinal plane gains divided pointbypoint by the Sum Vcardinal plane gains.  View Dependent Claims (7, 8, 9)
 10. A method for applying SMCI monopulse polynomials to target returns and determining azimuth and elevation angles in a nonrotating coordinate system comprising the steps of:
coherently integrating twoway Sum, DeltaAzimuth and DeltaElevation target returns; calculating the target'"'"'s Uoffset and Voffset monopulse ratios from said coherently integrated target return measurements; calculating the target'"'"'s Uoffset and Voffset monopulse angles in sinespace using said SMCI monopulse polynomials; adding said Uoffset and Voffset monopulse angles to a sinespace beam steer to obtain an improved estimate of a target'"'"'s sinespace position denoted as U_{tgt }and V_{tgt}; and transforming said U_{tgt }and V_{tgt }to azimuth and elevation angles in a nonrotating coordinate system using knowledge of the antenna'"'"'s yaw and tilt angles and coordinate system transformations.  View Dependent Claims (11)
 12. A method of producing an average gain pattern for a rotating radar employing coherent integration comprising the steps of:
storing a measured twoway antenna pattern with U and V sinespace coordinates; translating said antenna coordinates to center on a beam steer; calculating a W component of said antenna pattern coordinates; calculating the number of samples in a coherent processing interval (CPI); calculating a yaw angle scanned in a sampling period; calculating said yaw angle scanned in said CPI; calculating a starting yaw angle with respect to the NWU Xaxis; calculating midCPI points of numerous target returns in a NWU frame; coherently integrating over trajectories of said target returns for integration steps one to number of samples in a CPI; and averaging said coherently integrated pattern of said target returns to obtain an average gain pattern.  View Dependent Claims (13)
 14. A phasedphased array rotating radar system comprising:
a phasedphased array rotating antenna; an antenna electronics unit for sending and receiving signals to and from said phasedphased array rotating antenna wherein the direction of radar beams transmitted by said antenna are electronically controlled; means connected to said antenna electronics unit for processing target return signals and generating transmit command signals; a signal and data processor for generating estimates of a target azimuth angle and elevation angle including means for pulse compression of target return signals; means for coherent integration of compressed pulses; means for detection processing of said coherently integrated compressed pulses; means for monopulse processing of detected signals; means for target tracking; means for generating array beam steering commands; a beam steering generator connected to said signal and data processor for generating beam steering commands for said antenna electronics unit; said signal and data processor for generating estimates of a target azimuth angle and elevation angle comprises means for generating scan modulated monopulse curves from average gain patterns, means for calculating a target'"'"'s monopulse ratios, means for calculating said target'"'"'s Uoffset and Voffset monopulse angles, means for adding said Uoffset and said Voffset monopulse angles to a sinespace beam steer obtaining estimates of said target'"'"'s angular position (U_{tgt }and V_{tgt}); and means for transforming said estimates U_{tgt }and V_{tgt }to said azimuth and elevation angles in a nonrotating coordinate system.
1 Specification
1. Field of the Invention
This invention relates generally to a rotating phasedphased array radar, and in particular to a method of generating accurate estimates of azimuth and elevation angles of a radar target using precalculated monopulse curves for a rotating monopulse radar using coherent integration of pulse returns.
2. Description of Related Art
An antenna of a mechanically rotating radar moves in azimuth relative to a target as pulses are transmitted and received. As a result, the pulse returns are scanmodulated by the radar'"'"'s twoway antenna patterns. In other words, the pulses experience dissimilar antenna pattern gains as the array rotates. Coherent integration of the pulse returns is done to increase the signaltonoise ratios (SNRs) of the received signals prior to detection and target angle estimation. Nonrotating radars frequently employ the monopulse method for angle measurement. This process involves forming monopulse ratios and mapping those ratios to a target angle estimate using a precalculated monopulse curve or polynomial. The monopulse process has not been employed for rotating radars using coherent integration because the monopulse ratios do not map to the correct target angles when curves developed for a stationary array are used.
The performance of an angle estimation technique can be gauged by its beamsplitting ratio (BSR). The BSR is defined as the antenna pattern'"'"'s twoway 3dB beamwidth divided by the standard deviation of the angle error at 20 dB SNR. Previous rotating radars employing coherent integration, such as the U.S. Government'"'"'s AN/SPS49 LongRange Air Surveillance Radar, have measured target azimuth angle using an algorithm to locate the centroid of the detected signal envelope. However, centroiding algorithms require multiple detections using minidwells and are characterized by small BSRs on the order of 2 to 4. The technique described herein is applicable for radars that want to coherently integrate the whole dwell for optimum performance and achieves BSRs on the order of 8 to 10 which is over twice the typical BSR of a centroiding
U.S. Pat. No. 5,017,927, issued May 21, 1991 to Ashok K. Agrawal et al., and assigned to General Electric Co. of Morristown, N.J., discloses a technique for using phase shifters and variable gain amplifiers within the transmitreceive (TR) processor of each antenna element to compensate for errors in the internal circuitry of the sum, azimuth difference and elevation difference beam formers. This invention is designed for a nonrotating radar and is an improved hardware implementation of the original monopulse method. However, it does not correct for the effects of rotation on a radar employing coherent integration (CI).
U.S. Pat. No. 5,986,605, issued Nov. 16, 1999 to Leslie A. Priebe et al., and assigned to Raytheon Company of Lexington, Mass., discloses a new method of monopulse processing that only requires two receiver channels and does not form the traditional monopulse ratios. The antenna is still subdivided into four quadrants. Quadrant pairs are formed from the top two quadrants, the bottom two quadrants, the left quadrants and the right quadrants. The signals received on the quadrant pairs are multiplied together to form two correlation beams. The estimated elevation and azimuth angles are the phase angles of the correlation beams. Target detection is performed by thresholding the magnitude of either correlation beam. This patent disclosure is an entirely new method of monopulse processing that was designed for a nonrotating radar, and does not correct for the effects of rotation on a radar employing CI.
U.S. Pat. No. 6,618,008, issued Sep. 9, 2003, to John Arthur Scholz and assigned to Nederlandse Organisatie of Delft, Netherlands, discloses a variation on the traditional monopulse antenna architecture. The antenna is still subdivided into four quadrants and the signals received on these quadrants are still summed, differenced and divided to form monopulse ratios. However, the antenna quadrants in this invention are not fixed in place. Instead, the quadrants rotate so that the difference pattern nulls are either aligned or perpendicular to the returns from the target tracks. The inventors claim these “virtual” quadrants reduce the complication and expense of the RF hardware required and allows the target to be tracked along any angle instead of the traditional azimuth and elevation angles. This invention is designed for a nonrotating radar and is an architectural variation on the original monopulse method. However, it does not correct for the effects of rotation on a radar employing CI.
U.S. Pat. No. 6,680,687 issued Jan. 20, 2004 to Michel Phelipot and assigned to Thales of Paris, France discloses a variation on the traditional centroiding algorithm used by 2dimensional (2D) rotating radars for estimating target azimuth. A transmitted Npulse burst is split into two N/2pulse halfbursts. These halfbursts are then processed to associate a signal amplitude and azimuth angle with each halfburst. Coherent integration is used to determine amplitude and centroiding is used to determine azimuth. The two halfburst measurements of amplitude and azimuth are then combined using a mathematical formula to generate an improved estimate of target azimuth. However, coherently integrating halfbursts result in a factor N/2 improvement in SNR. Coherently integrating the entire N pulse burst, as the present invention does, results in a factor N improvement in SNR. Thus, the present invention achieves 3dB more SNR. Furthermore, U.S. Pat. No. 6,680,687 is intended for a 2D radar. A 2D radar measures only range and azimuth as opposed to a 3D radar which measures range, azimuth and elevation. The present invention will work for either a 2D or 3D radar and takes into account any crosscoupling between the azimuth and elevation measurements.
Accordingly, it is therefore an object of this invention to provide a method for determining accurate estimates of a radar target azimuth angle and elevation angle for a rotating monopulse phasedphased array radar using coherent integration of target pulse returns.
It is another object of this invention to provide a method for generating scan modulated coherently integrated (SMCI) monopulse curves, and to use these curves to accurately calculate the radar target'"'"'s sinespace offset from the beam steer. The target'"'"'s sinespace position is then transformed to azimuth and elevation angles in a fixed nonrotating coordinate system.
These and other objects are further accomplished by a method for generating accurate estimates of a radar target'"'"'s azimuth and elevation angles for a rotating monopulse radar comprising the steps of measuring an antenna'"'"'s oneway transmit pattern and three receive antenna patterns, generating twoway Sum, DeltaAzimuth and DeltaElevation antenna patterns, translating the coordinates of twoway Sum, DeltaAzimuth and DeltaElevation antenna patterns to center on a sinespace beam steer, sampling uniformly the twoway antenna patterns at midCPI points of numerous target returns, coherently integrating over the sinespace trajectories of the target returns, averaging coherent integration sums of the target returns and plotting the averages at their respective midCPI points to produce average gain antenna patterns, generating Uoffset and Voffset scan modulated coherently integrated (SMCI) monopulse curves from average gain patterns, coherently integrating the twoway Sum, DeltaAzimuth and DeltaElevation target returns of the antenna patterns, calculating the target'"'"'s monopulse ratios from the coherently integrated target return measurements, calculating the target'"'"'s Uoffset and Voffset monopulse angles in sinespace using the SMCI monopulse curves, adding the Uoffset and Voffset monopulse angles to a sinespace beam steer to obtain an improved estimate of a target'"'"'s sinespace position denoted as U_{tgt }and V_{tgt}, and transforming the U_{tgt }and V_{tgt }to azimuth and elevation angles in a nonrotating coordinate system using coordinate system transformations and knowledge of the antenna'"'"'s yaw and tilt angles. The method comprises the step of fitting polynomials to the SMCI monopulse curves using a method of least squares.
The objects are further accomplished by a method for applying SMCI monopulse polynomials to target returns and determining azimuth and elevation angles in a nonrotating coordinate system comprising the steps of coherently integrating the twoway Sum, DeltaAzimuth and DeltaElevation antenna patterns target returns, calculating the target'"'"'s Uoffset and Voffset monopulse ratios from the coherently integrated target return measurements, calculating the target'"'"'s Uoffset and Voffset monopulse angles in sinespace using the SMCI monopulse polynomials, adding the Uoffset and Voffset monopulse angles to a sinespace beam steer to obtain an improved estimate of a target'"'"'s sinespace position denoted as U_{tgt }and V_{tgt}, and transforming U_{tgt }and V_{tgt }to azimuth and elevation angles in a nonrotating coordinate system using knowledge of the antenna'"'"'s yaw and tilt angles and coordinate system transformations. The step of transforming the estimates of a target'"'"'s sinespace position U_{tgt }and V_{tgt }to azimuth and elevation angles in a nonrotating coordinate system comprises the steps of transforming the target'"'"'s sinespace coordinates to normalized northwestup (NWU) coordinates (X_{n}, Y_{n}, Z_{n}), and calculating the target'"'"'s NWU azimuth (Az_Tgt) and elevation (El_Tgt) using the following relationships
The objects are further accomplished by a method of producing an average gain pattern for a rotating radar employing coherent integration comprising the steps of storing a measured twoway antenna pattern with U and V sinespace coordinates, translating the antenna coordinates to center on a beam steer, calculating a W component of the antenna pattern coordinates, calculating the number of samples in a coherent processing interval (CPI), calculating a yaw angle scanned in a sampling period, calculating the yaw angle scanned in the CPI, calculating a starting yaw angle with respect to the NWU Xaxis, calculating midCPI points of numerous target returns in a NWU frame, coherently integrating over trajectories of the target returns for integration steps one to number of samples in a CPI, and averaging the coherently integrated pattern of the target returns to obtain an average gain pattern. Coherently integrating over the trajectories of the target returns comprises the steps of determining the antenna yaw angle at each integration step, calculating sinespace trajectories of the target returns, interpolating the twoway antenna patterns at the trajectory points, and coherently integrating by summing the antenna pattern gains at each point in the sinespace trajectories of the target returns and plotting the sums at the midCPI points of their respective sinespace trajectories, and averaging the coherently integrated antenna patterns by dividing the antenna pattern gains by the number of samples in a CPI to produce an average gain twoway antenna pattern.
The objects are further accomplished by a phasedphased array rotating radar system comprising a phasedphased array rotating antenna, an antenna electronics unit for sending and receiving signals to and from the phasedphased array rotating antenna wherein the direction of radar beams transmitted by the antenna are electronically controlled, means connected to the antenna electronics unit for processing target return signals and generating transmit command signals, a signal and data processor for generating estimates of a target azimuth angle and elevation angle including means for pulse compression of target return signals, means for coherent integration of compressed pulses, means for detection processing of the coherently integrated compressed pulses, means for monopulse processing of detected signals, means for target tracking, means for generating array beam steering commands, a beam steering generator connected to the signal and data processor for generating beam steering commands for the antenna electronics unit, the signal and data processor for generating estimates of a target azimuth angle and elevation angle comprises means for generating scan modulated monopulse curves from average gain patterns, means for calculating a target'"'"'s monopulse ratios, means for calculating the target'"'"'s Uoffset and Voffset monopulse angles, means for adding the Uoffset and the Voffset monopulse angles to a sinespace beam steer obtaining estimates of the target'"'"'s angular position (U_{tgt }and V_{tgt}), and means for transforming the estimates U_{tgt }and V_{tgt }to the azimuth and elevation angles in a nonrotating coordinate system.
Additional objects, features and advantages of the invention will become apparent to those skilled in the art upon consideration of the following detailed description of the preferred embodiments exemplifying the best mode of carrying out the invention as presently perceived.
The appended claims particularly point out and distinctly claim the subject matter of this invention. The various objects, advantages and novel features of this invention will be more fully apparent from a reading of the following detailed description in conjunction with the accompanying drawings in which like reference numerals refer to like parts, and in which:
Referring to
An antenna 14 of the phasedphased array rotating radar system 10 moves in azimuth relative to a target as pulses are transmitted and received. As a result, the target returns are scanmodulated by the radar'"'"'s twoway antenna patterns as the antenna 14 rotates through a dwell, the dwell being the interval of time during which pulses are transmitted and received. Not all of the pulses transmitted are coherently integrated. A small number of the initial pulses are used to fill and settle the signal processing filters. These pulses are called fill pulses. Pulses received after the fill pulses are coherently integrated. The portion of the dwell during which the pulses to be coherently integrated are transmitted and received is called the coherent processing interval or CPI. Scan modulation causes the target return pulses to experience dissimilar sum and difference pattern gains as the antenna 14 moves relative to the target. Coherent integration of the pulse returns increases the signaltonoise ratios of the sum and difference channel signals prior to detection and target angle refinement. The rotating radar system 10 employs a method of generating monopulse curves for the rotating phasedphased array radar system 10 and also employs coherent integration. The monopulse measurements are combined with array position and rotation rate information to generate estimates of the target'"'"'s azimuth and elevation angles.
Referring to
The phasedphased array antenna 14 receives and transmits RF signals 30, 39 into and from space, respectively. The phasedphased array antenna 14 comprises many individual array elements with a transmit/receive (T/R) module (not shown) connected to each array element. These array elements are combined into transmit/receive integrated microwave modules (TRIMMs). The TRIMMs are combined to form subarrays. The subarrays are combined to form the array antenna 14. The direction of the transmit and receive radar beams is electronically controlled by changing the phase shifts, attenuation and polarization settings (if applicable) of the T/R modules and the timedelays of the individual subarrays. The AEU 15 comprises the T/R modules, the TRIMMs, the subarrays and their interconnections, as well as the interfaces to the REX 16 and the BSG 19. The AEU 15 sends RF target returns 31 to the REX 16 and receives RF transmit waveform signals 36 from the REX 16. The REX 16 comprises an exciter portion which generates the RF transmit waveform signals 36 and sends them to the AEU 15, and a receiver portion which receives RF monopulse signals from the AEU 15, digitizes said RF monopulse signals, and provides them to the SDP 17.
The SDP 17 comprises a signal processing portion which performs pulse compression, coherent integration, detection processing, monopulse processing, clutter suppression and RF interference cancellation. A data processing portion of the SDP 17 provides automatic target tracking which includes the selection of the beam position and waveform for the next target update. The SDP 17 sends radar video 33 to the RDCU 18. The BSG 19 receives array beam steering commands 37 from the SDP 17 and provides time delay commands to the subarrays, and phase shift, attenuation and polarization commands to the T/R modules in the AUE 15 in order to position the radar beam. The RDCU 18 provides radar video signals 33 regarding target location in polar coordinates (range and azimuth) using a PPI (plan position indicator) display. This RDCU 18 also allows a radar operator or external control unit to issue radar commands 34 to change various parameters and functions of the radar system 10 in order to optimize performance in accordance with environmental conditions. The radar system 10 features that may be controlled include RF frequency, types of signal processing, transmitted waveform, clutter suppression, and RF interference cancellation.
Referring to
Monopulse angle refinement follows target detection, and begins by forming the real parts of the complex ratios of the pulse compressed sum and difference channel target returns. These quantities are called monopulse ratios and are mathematically defined as:
where
 r_{U}=the Uoffset monopulse ratio
 r_{V}=the Voffset monopulse ratio
 Δ_{AZ}=pulse compressed azimuth difference signal
 Δ_{EL}=pulse compressed elevation difference signal
 Σ=pulse compressed sum signal
 φ_{AZ}=phase angle between the sum and azimuth difference channels
 φ_{EL}=phase angle between the sum and elevation difference channels
Usually φ_{AZ }and φ_{EL }are zero or 180 degrees, and r_{U }and r_{V }are frequently called the azimuth and elevation difference channel monopulse ratios, respectively. The r_{U}, r_{V }monopulse ratios are mapped to offset angles in sinespace using precalculated curves or polynomials. The offsets are added to the beam steer to produced refined target angle estimates. This refinement is expressed mathematically as:
U_{tgt}=U_{beam}+U_{offset }
V_{tgt}=V_{beam}+V_{offset }
where U_{tgt}, V_{tgt }are the refined target angle estimates in sinespace, U_{beam}, V_{beam }are the beam steer coordinates in sinespace, and U_{offset}, V_{offset }are the U, V offset angles obtained from the monopulse curves or polynomials.FIGS. 910 are graphs showing Uoffset and Voffset monopulse curves, and they are described hereinafter.
Coherently integrating the pulse returns is frequently done to increase the signaltonoise ratios of the sum and difference channel signals prior to target detection and angle refinement. For nonrotating radars this has no impact on the monopulse process as the individual pulse returns experience the same sum and difference pattern gains. However, target returns received by a rotating radar are scanmodulated by the antenna'"'"'s twoway patterns as the radar rotates through the dwell. In other words, the pulses experience different sum and difference pattern gains as the antenna face moves relative to the target. Consequently, the mean gains of the coherently integrated pulses are the coherent average of the antenna pattern gains that cut across the target, and the monopulse ratios are ratios of average not point gains. For the monopulse process to work accurately, the monopulse curves should be calculated from average gain farfield patterns. Antenna patterns should be coherently averaged over the radar'"'"'s coherent processing interval (CPI) and should take into account rotation rate, antenna tilt, beam steer and CPI length. The process for calculating the average gain farfield patterns of a rotating radar are described herein.
The coordinate systems used in this description are the NorthWestUp (NWU) coordinate system, the Radar Face Coordinate (RFC) system, and the NWU or SineSpace Coordinate system.
The NWU system is a righthanded Cartesian coordinate system with its origin located at the intersection of the antenna'"'"'s axis of rotation and its boresight vector. The boresight vector is the antenna face normal originating at the face center. The NWU positive Zaxis points up and is defined as being perpendicular to the reference ellipsoid and defines the local level plane. The positive Xaxis points north and is defined as the projection of the Earth rotation angular rate vector onto the local level plane. The positive Yaxis points west and completes the righthanded orthogonal set.
The RFC system is a righthanded Cartesian coordinate system with its origin located at the antenna face center. The RFC positive Yaxis is oriented vertical and points upward, parallel to the antenna face. The positive Zaxis is pointed outward and normal to the antenna face. The positive Xaxis is defined to complete the righthanded coordinate system.
The UVW coordinate system is a straightforward extension of the RFC system. A coordinate point expressed in the RFC system is converted to the UVW (sinespace) system by normalizing the range to 1. For example, if (X_{RFC}, Y_{RFC}, Z_{RFC}) is a RFC coordinate, the corresponding UVW coordinate is
u=x_{RFC}/Range
v=y_{RFC}/Range
w=z_{RFC}/Range
where Range=√{square root over (x_{RFC}^{2}+y_{RFC}^{2}+z_{RFC}^{2})}.
Since range is always unity in the UVW system, only two coordinates are necessary to communicate the underlying information. The third coordinate can be determined by solving the equation
√{square root over (u^{2}+v^{2}+w^{2})}=1.
Typically, only the UV coordinates of the UVW system are used. Beam steers and antenna patterns are expressed in coordinates because with the exception of scan loss, antenna patterns expressed in UV coordinates are invariant with respect to the beam steer. Although sinespace coordinates are unitless, they are often expressed with the unit of “sine” to identify what they are.
Referring to
Strictly speaking, the NWU and RFC systems do not share the same origin. The antenna face center of a rotating radar is typically about half a meter from the antenna'"'"'s axis of rotation and the NWU origin. However, for the purpose of calculating average gain farfield patterns we shall assume that the NWU and RFC systems share the same origin. Since the range of a radar target is characteristically anywhere from a few kilometers to hundreds of kilometers, this small approximation should not be a problem.
The coordinate system transformation from the NWU to RFC frame is presented below. In the transformation, (x_{NWU}, y_{NWU}, z_{NWU}) denotes a point in the NWU frame, and (x_{RFC}, y_{RFC}, z_{RFC}) denotes a point in the RFC frame. The two frames are assumed to share the same origin. To transform from the NWU frame to the UVW frame, simply normalize the point'"'"'s range to unity either before or after the transformation.
The RFC to NWU coordinate system transformation is shown below. To transform from the UVW frame to the NWU frame, simply multiply the sinespace point by the target'"'"'s range either before or after the transformation.
Referring to
Range=√{square root over (x_{NWU}^{2}+y_{NWU}+z_{NWU}^{2})}
Azimuth=arctan(y_{NWU}/x_{NWU})
Elevation=arctan(z_{NWU}/√{square root over (x_{NWU}^{2}+y_{NWU}^{2})})
Referring to
Referring to
Referring again to
The method includes in step 52 averaging the coherent integration sums, and plotting these coherent averages at their respective midCPI points. At this point the average gain twoway Sum, DeltaAzimuth and DeltaElevation antenna patterns have been generated for the given beam steer. In step 54, generate the SMCI monopulse curves from the average gain pattern in exactly the same manner as generating normal monopulse curves from a normal gain pattern. Uoffset monopulse curves are calculated by dividing the DeltaAzimuth Ucardinal plane gains by the Sum Ucardinal plane gains. Voffset monopulse curves are calculated by dividing the DeltaElevation Vcardinal plane gains by the Sum Vcardinal plane gains. In step 56, polynomials are fitted to the monopulse curves using the method of least squares for efficient implementation of the monopulse process.
Application of the SMCI monopulse process results in an estimate of the target'"'"'s angular position in sinespace. However, sinespace is centered on the antenna face and therefore rotates with the antenna. The ultimate goal of the process is to express the target'"'"'s angular position in a nonrotating coordinating system. The nonrotating coordinate system used herein is the NorthWestUp (NWU) coordinate system; however, any nonrotating coordinate system may be used. The steps for implementing the SMCI monopulse process are described below. The radar'"'"'s Signal Data Processor (SDP) unit 17 performs the implementation and all coordinate system transformations.
The SMCI monopulse curves are a function of the radar'"'"'s beam steer and must be calculated in advance for the expected beam positions. Referring now to
A pseudocode description of the algorithm for coherently averaging the antenna patterns is provided in Tables 1, 2 and 3. Table 1 defines the required inputs, Table 2 defines the required functions, and Table 3 lists the steps of the algorithm. Statements beginning with a percentage sign (%) are descriptive comments and are not executed. Statements that do not start with a percentage sign are mathematical operations that are executed. The notation used is similar to that used by the MATLAB programming language and should be familiar to one of ordinary skill in the art.
Uoffset monopulse curves for the normal and average gain patterns are calculated by taking the real part of the DeltaAzimuth Ucardinal plane gains divided by the Sum Ucardinal plane gains. Voffset monopulse curves are calculated by taking the real part of the DeltaElevation Vcardinal plane gains divided by the Sum Vcardinal plane gains. The curves are calculated over the 6dB beamwidth of the oneway Sum pattern. Mathematically, the monopulse curves can be expressed as:
where
 ΔAz(U_{offset})=DeltaAzimuth Ucardinal plane gains as a function of U_{offset }
 Sum(U_{offset})=Sum Ucardinal plane gains as a function of U_{offset }
 ΔEl(V_{offset})=DeltaElevation Vcardinal plane gains as a function of V_{offset }
 Sum(V_{offset})=Sum Vcardinal plane gains as a function of V_{offset }
 φ_{AZ}=phase angle between the sum and azimuth difference channels
 φ_{EL}=phase angle between the sum and elevation difference channels
A resolver transducer is a rotary position sensor that is used to measure an antenna'"'"'s Rotate angle also known as a Yaw angle (see
RotateMidCPI=RotateMeasured+(T_Mid_{—}CPI−T_Measured)×Scan_Rate
Where
 RotateMidCPI=The estimated midCPI Rotate angle in radians.
 RotateMeasured=The Rotate angle, in radians, measured by the resolver just prior to executing the dwell.
 T_Mid_CPI=The midCPI time of the dwell in seconds.
 T_Measured=The time at which RotateMeasured was measured in seconds.
 Scan_Rate=The antenna'"'"'s rotation rate calculated from recent resolver measurements in radians per second.
The target'"'"'s NWU azimuth and elevation angles, denoted as Az_Tgt and El_Tgt, respectively, can be calculated in the following manner:
 1) Use SMCI monopulse curves or polynomials to generate accurate estimates of the target'"'"'s U, V coordinates in sinespace, denoted as U_{Tgt }and V_{Tgt}, respectively. Calculate W_{Tgt }as
W_{Tgt}=√{square root over (1−U_{Tgt}^{2}−V_{Tgt}^{2})}  2) Estimate RotateMidCPI using resolver measurements taken just prior to executing the dwell.
 3) Transform the target'"'"'s sinespace coordinates to normalized NWU coordinates, denoted as (X_{n}, Y_{n}, Z_{n}), using the following coordinate system transformation:
 1) Use SMCI monopulse curves or polynomials to generate accurate estimates of the target'"'"'s U, V coordinates in sinespace, denoted as U_{Tgt }and V_{Tgt}, respectively. Calculate W_{Tgt }as

 4) Calculate the target'"'"'s NWU azimuth (Az_Tgt) and elevation (El_Tgt) using the equations below:
Az_{—}Tgt=arctan(Y_{n}/X_{n})
El_{—}Tgt=arctan(Z_{n}/(X_{n}^{2}+Y_{n}^{2})
 4) Calculate the target'"'"'s NWU azimuth (Az_Tgt) and elevation (El_Tgt) using the equations below:
Computer simulations were performed in the MATLAB programming language to compare the performance of the SMCI monopulse curves against conventional monopulse curves when both are used by a rotating radar. The antenna that was simulated was a rectangular array. The following parameters were used to simulate the radar:
 Antenna Scan Rate=30 RPM
 Antenna Tilt=20 degrees
 Center Frequency=10 GHz
 CPI Length=2.34 msecs
 Sampling Period=0.02 msecs
 Number of Array Element Columns=128
 Number of Array Element Rows=128
 ElementtoElement Spacing=1.5 cm
The simulated oneway antenna patterns had the following array weights:
 Transmit Pattern: Uniform weights on azimuth and elevation.
 Sum Pattern: 30 dB,
n =5 Taylor weights on azimuth and elevation.  DeltaAzimuth Pattern: 30 dB,
n =5 Bayliss weights on azimuth, and uniform weights on elevation.  DeltaElevation Pattern: 30 dB,
n =5 Bayliss weights on elevation, and uniform weights on azimuth.
The beam was steered to the following position in sinespace:
U_{beam}=0 sines
V_{beam}=−0.3 sines
Twoway normal gain antenna patterns were simulated with the specified array parameters and weights. These simulated antenna patterns along with the specified scan rate, antenna tilt, center frequency, CPI length, sampling period and beam steer provided the inputs to the algorithm described in Tables 1, 2 and 3. The output of the algorithm was a set of twoway average gain Sum, DeltaAzimuth and DeltaElevation antenna patterns.
Referring to
Ninthorder polynomials of the following forms were fit to the monopulse curves:
U_{offset}=a_{0}+a_{1}r_{U}+a_{2}r_{U}^{3}+a_{3}r_{U}^{5}+a_{4}r_{U}^{7}+a_{5}r_{U}^{9 }
V_{offset}=b_{0}+b_{1}r_{V}+b_{2}r_{V}^{3}+b_{3}r_{V}^{5}+b_{4}r_{V}^{7}+b_{5}r_{V}^{9 }
The method of least squares was used to calculate the polynomial coefficients a_{0}, a_{1}, . . . , a_{5 }and b_{0}, b_{1}, . . . , b_{5}. To generate noisy monopulse ratios, 100,000 targets were uniformly distributed over the 6dB beamwidth of the receive Sum pattern. These noiseless targets were then tracked through the twoway sum and difference patterns and coherently integrated. Gaussian noise was added to the SMCI sum and difference channel returns to produce a desired, average SNR ratio. Monopulse ratios were formed and inserted into the monopulse polynomials to calculate the U, V offsets. Measurement error is defined and calculated as the difference between the measured U, V offsets and the true U, V offsets. The mean and standard deviation of the measurement errors are computed and plotted as a function of SNR. Mean measurement error is also called the bias error, and the error'"'"'s standard deviation is commonly called the onesigma accuracy.
Referring to
This invention has been disclosed in terms of a preferred embodiment. It will be apparent that many modifications can be made to the disclosed method without departing from the invention. Therefore, it is the intent of the appended claims to cover all such variations and modifications as come within the true spirit and scope of this invention.