1. Field of the Invention
The present invention relates to a technique for mitigating multipath impacts on azimuth accuracy in a monopulse interrogator.
2. Description of Related Art
Identification Friend or Foe (IFF) monopulse interrogators are typically used to determine an azimuth bearing of a target such as an aircraft. The target azimuth bearing is determined by processing magnitudes of monopulse ratio measured by a horizontally rotated beam of two-channel monopulse antenna.
In the presence of multipath signals arising from target images on nearby reflectors, the IFF monopulse ratio becomes complex having a real part and an imaginary part. The real part of the complex monopulse ratio has been used to obtain an estimate for the target azimuth, hereinafter it is called the traditional target azimuth.
The standard deviation of traditional target azimuth has been used as a flag to indicate the presence of multipath signals. Processing either the magnitude or the real part of the complex monopulse ratio yields inaccurate values for the target azimuth which can lead to target trajectories experiencing a bias and wandering azimuth.
The present invention provides a method for mitigating multipath impacts on azimuth accuracy of a monopulse interrogator. Samples of monopulse ratio for samples of antenna boresight angle within an antenna scan are calculated from an interrogation of a target. Samples of traditional target azimuth are calculated from the samples of monopulse ratio. A mean of the samples of traditional target azimuth is calculated. An alternative target azimuth is calculated from the samples of monopulse ratio within target's region which will be defined later. Whether a multipath signal exists is determined from a standard deviation of the samples of traditional target azimuth. The mean of the samples of traditional target azimuth is supplied as an output if a multipath signal does not exist. The alternative target azimuth is supplied as an output if the multipath signal does exist.
It is contemplated that the present invention could also be embodied in a payload of monopulse radar to mitigate impacts of multipath signals.
The exact nature of this invention, as well as the objects and advantages thereof, will become readily apparent from consideration of the following specification in conjunction with the accompanying drawings in which like reference numerals designate like parts throughout the figures thereof and wherein:
In
In step 402, a target, such as target 102, is interrogated by a two-channel antenna 106. In step 404, the antenna receives replies from the interrogation of target 102. In step 406, a monopulse ratio is calculated. The monopulse ratio is
V1 is a voltage in one of the antenna channels and V2 is a voltage in the other antenna channel.
In the presence of multipath signals, the monopulse ratio is complex and can be expressed as having a real part u an imaginary part v, and a phase Θ. The imaginary part of the monopulse ratio is referred to as the quadrature angle, in steps 408, 418, and 422, the real part, the magnitude, and the quadrature angle, of the monopulse ratio are calculated.
The real part of the monopulse ratio can be expressed from S. M. Sherman; Complex indicated angles applied to unresolved radar targets and multipath, IEEE Transaction on Aerospace and Electronic Systems, Vol. AES-7, No. 1, 1971 as
Where φ0 is the antenna boresight angle; κφ is the antenna slope which equated to unity for simplicity; and χ and ψ are amplitude and phase of the ratio between the target field and image field at the antenna 106.
The quadrature angle of the monopulse ratio is expressed from S. M. Sherman; Complex indicated angles applied to unresolved radar targets and multipath, IEEE Transaction on Aerospace and Electronic Systems, Vol. AES-7, No. 1, 1971 as
The quadrature angle is calculated in step 422.
The phase of the monopulse ratio (1) can be expressed as
The phase is calculated in step 408 along with the real part of the monopulse ratio.
The magnitude of the monopulse ratio is expressed as
and it is calculated in step 418.
The magnitude of the ratio between the image field and the target field is expressed as
Γ is the magnitude of reflection coefficient at the surface of reflector 104, G(α−φ0) is the antenna radiation pattern along the image azimuth α, and G(φ−φ0) is the antenna radiation pattern along the target azimuth φ.
In the case of either a conducting reflector or a grazing incidence, where Γ=1, and an antenna with a Gaussian radiation pattern, the magnitude of the ratio between the image field and the target field at the antenna (6) can be expressed as
In (8), 2θ0 is the 3 dB antenna beam width. With some direct mathematical manipulations, the magnitude of the ratio between the image field and the target field at the antenna (7) can also be expressed as
χ=exp(−2a{φm−φ0}{α−φ0}) (9)
where φm is the arithmetic mean of the target azimuth and the image azimuth.
The image azimuth can use the following identity:
The distance h is shown as a distance 124 in
To exclude non physical values for the image azimuth, the image azimuth (11) should be subjected to the following conditions: sgn(α)=sgn(h)
|α|>|φ| (12)
wherein sgn(x) is the sign function and stands for the polarity of the parameter x. The sign function can be expressed as:
In the special case of both an aircraft target flying in the antenna far field_and azimuth angles (α,φ, φ0) measured from the reflector plane, α=−φ. Thus the real part (2) and imaginary part (3) of the monopulse ratio can be expressed as
These two equations are used in an embodiment of the present invention.
Calculation steps 408, 418, and 422 of
To derive a traditional target azimuth in step 410, the real part of monopulse ratio is used. The target azimuth φ0 is expressed as
In the case of a single path, the phase of monopulse ratio is either 0 or ±π and gives real values for target azimuth with a polarity depending on target location with respect to antenna boresight.
In step 412, the mean of the traditional target azimuth and the standard deviation σ of the traditional target azimuth are calculated. Upon calculating values of the traditional target azimuth within an antenna scan, the mean and standard deviation σ of those values are calculated and stored. To reduce processing time a moving window technique is used for calculating the mean and standard deviation of traditional target azimuth.
The moving window technique can be illustrated by consulting N samples within each antenna scan. For a window of n+1 samples (n+1≦N), the first moment <φ>n+1 and second moment <φ2>n+1 of target azimuth can be expressed as
where < >n is the ensemble average over n samples.
The number of samples is increased until it encounters all the N samples within the antenna scan. In this case the first moment and the second moment can be used to obtain the mean
ν=√{square root over (<φ>N−
In step 414, the standard deviation is compared to a predetermined threshold value. If the standard deviation is greater than a predetermined threshold value, then multipath signals exist. If the standard deviation is not greater than a predetermined threshold value, then multipath signals do not exist.
The predetermined threshold value is dependent on noise level in the system. An explanation for deriving the predetermined threshold value can be found in W. D. Blair & M. Brandt-Pearce, Statistical Description of Monopulse Parameters for Tracking Rayleigh Targets, IEEE Transaction on Aerospace and Electronic Systems, Vol. 34, No. 2, 597 (1998); and A. D. Seifer, Monopulse-Radar Angle Measurements in Noise, IEEE Transaction on Aerospace and Electronic Systems, Vol. 30, No. 3, 950 (1994) which are hereby incorporated by reference.
In step 416, the mean of the target azimuth is stored. In step 430 the mean of the target azimuth is outputted.
In step 420, a search for the minimum of the magnitudes of the monopulse ratio is performed. To accomplish this, at an arbitrary antenna boresight angle φ0n the difference An between magnitude of monopulse ratio |D/S|n and its counterpart |D/S|n−1 measured at the preceding boresight angle φ0(n−1) is calculated.
Δn−|D/S|n−|D/S|n−1 (19)
If the difference Δn changes its polarity from − to + the preceding antenna boresight φ0(n−1) can be considered the boresight at which a minimum of the magnitude of the monopulse ratio occurs. This procedure is repeated to find other minima for the monopulse ratio. The minima of the magnitude of the monopulse ratio and the corresponding boresight angles are used in step 426 to search for a target azimuth region, which will be described more fully in detail hereinafter.
In the case of a double path signal, where there is only one image, there may be one or two minima for the magnitude of the monopulse ratio. If there is only one minimum value, it may be associated with either the target or the image depending on the angular distance between the target and its image. If there are two minima, one of them is associated with the target and the other is associated with the image. The minimum value associated with the target is deeper than its counterpart associated with phantom image, as seen in
Alternatively, the minimum of the magnitude of the monopulse ratio (5) can be calculated by first rewriting the monopulse ratio as:
D/S=|D/S| exp(jΘ) (20)
The differential of the logarithm of the monopulse ratio can then be taken to get
The prime (′) over any quantity stands for the first order derivate with respect to the antenna boresight angle φ0. The above identity provides a tool for getting the first order derivative of magnitude and phase monopulse ratio from the first order derivative of such a ratio.
In obtaining the first order derivative of the monopulse ratio and hence the first order derivatives of the ratio magnitude and phase, the monopulse ratio can be rewritten as
D/S=u+jv (22)
Then the differential of the logarithm of the rewritten monopulse ratio can be taken as follows
Multiplying the numerator and the denominator in the right hand side of (23) by u−jv yields
which can then be compared to the equation (21) resulting in the first order derivative of the monopulse ratio
The first order derivative can then be equated to zero to find the relationship governing the antenna boresight angles of the minima or maxima of the monopulse ratio. In doing so, we get
uu′+vv′=0 (26)
The differential u′ can be found by differentiating (14) yielding:
The differential v′ can be found by differentiating (15) yielding:
Introducing explicit expressions of u(14), v(15), u′(27), and v′(29) into (26) leads to a nonlinear equation for antenna boresight. Some special cases, however, need to be discussed with respect to solutions for the equation.
In the first special case, the target is separable from its image. In this case, the minimum of the magnitude of the monopulse ratio associated with the target occurs at very small values of χ where χ<<1. Thus, from (14) we get
u≈−φ
0m+φ
v≈0 (30)
Introducing (30) into (26) results in φ0m=φ implying that the above boresight angle coincides with the target azimuth. This can also be inferred from
Next, the minimum magnitude value associated with the image is found. Such a value occurs at large values for the field ratio χ where χ>>1. Accordingly from (14) we get,
Introducing (31) into (26) results in φ0m=−φ which coincides with the image azimuth, as seen in
When the target and its image are within the antenna beam width no simple analytic solution is available. In this case numerical simulations could be used to search for the minimum of the magnitudes of the monopulse ratio as shown in
In step 424, a search for the maximum of the magnitudes of quadrature angle is considered. To accomplish this, at an arbitrary antenna boresight angle φ0n the difference Δvn between magnitude of quadrature angle |vn| and its counterpart |v(n−1) measured at the preceding antenna boresight angle φ0(n−1) is calculated
Δvn=|−|v(n−1)| (32)
If the difference Δvn changes its polarity from + to −, the antenna boresight angle φ0(n−1) is considered as the antenna boresight angle where a maximum of the magnitude of the quadrature angle occurs. This procedure is repeated to find other maxima of the magnitude of the quadrature angle. The maximum of the magnitudes of the quadrature angles and the corresponding antenna boresight angles are then stored for use in step 426, which will be described more fully in detail later.
In the case of only one image such as in the case of a double-path signal, there is only one maximum for the quadrature angle. The maximum occurs at an azimuth located between the target azimuth and the image azimuth. If the quadrature angle has zero values within any antenna scan, the above step could be skipped.
If the phase ψ=mπ(m=0,1, . . . ) the quadrature angle described by either (4) or (15) reduces to zero. This justifies not using the quadrature angle as a flag for investigating the presence of multipath signals.
Alternatively, to obtain the antenna boresight angles at which the maximum of the magnitude of the quadrature angle occur, the first order derivative of the quadrature angle (15) is used:
For non trivial location, where a maximum of the magnitude of the quadrature angles occur, χ=1, which can be substituted into the above formula. Solving the resultant gives the antenna boresight of the maximum of the magnitude of the quadrature angle which occurs at the arithmetic mean φmq described by (10).
This indicates that in the presence of double-path signals, there is only one boresight angle at which the magnitude of the quadrature angle is a maximum. Such a boresight angle is equal to the arithmetic mean of the target azimuth and the image azimuth. So it is located within the target-image azimuth region as seen in
In step 426, a search for a target azimuth region is conducted. In the presence of multipath signals, an angular zone scanned by a monopulse antenna can be divided into three azimuth regions: (1) target azimuth region; (2) image-target azimuth region; and (3) image azimuth region. The target azimuth region is less affected by multipath signals and is located near the minimum of the magnitude of the monopulse ratio associated with the target, as seen in
To search for the target azimuth region, antenna boresight angles of the minimum for the magnitude of the monopulse ratio are compared to each other and then compared to the corresponding boresight angles at which the maximum of the magnitude of the quadrature angle occurs. If there are two minima for the magnitude of the monopulse ratio, the region between the two minima is excluded as the target azimuth region, and the region near the deepest minimum which is not excluded is chosen as the target azimuth region. If there is only one deep minimum for the magnitude of the monopulse ratio and one maximum for the magnitude of the quadrature angle, the region between the minimum of the magnitude of the monopulse ratio and the maximum of the magnitude of the quadrature angle is excluded as the target azimuth region, and the region near the minimum of the magnitude of the monopulse ratio which is not excluded is chosen as the target azimuth region.
The alternative target azimuth is then calculated in step 428 from within the target azimuth region since the target azimuth region is less affected by the multipath signals. The slope of the magnitude of the monopulse ratio may be used to calculate the target azimuth by projecting where the target azimuth would be. If the difference between the target azimuth and image azimuth is larger than the antenna beam width, values of the monopulse ratio are similar to their counterparts in the absence of multipath signals. However, if the difference between the target azimuth and image azimuth is in the order of, or less than the beam width, the slope governing the linear relation between the magnitude of the monopulse ratio and antenna boresight angle may be slightly different from the corresponding slope, in absence of the multipath signals. Thus, the residual azimuth may still wander slightly after the impacts of the multipath signals are mitigated.
In both
In one embodiment, the region to the left of line 512 can be considered the target azimuth region, the area to the right of line 508 can be considered the image azimuth region, and the area between line 508 and line 512 can be considered the interference azimuth region or target-image azimuth region for both graphs 5 and 6.
The mitigating of the multipath impacts in
The errors and the standard deviation σ are not totally eliminated because of the behavior of the monopulse ratio when the target and its image are not resolved. In that case, the antenna boresight angle of the minimum of the magnitude for the monopulse ratio does not coincide with the exact target azimuth and it varies as the target azimuth varies.
In
In both
In one embodiment, the region to the left of line 1012 can be considered the target azimuth region, the area to the right of line 1008 can be considered the image azimuth region, and the area between line 1008 and line 1012 can be considered the interference azimuth region or target-image azimuth region for both graphs 15 and 16.
The monopulse ratio calculation module 1106 then calculates samples of monopulse ratio for samples of antenna boresight angles using the replies from the interrogation of the target. It also calculates the real part for each of the samples of the monopulse ratio, the magnitude for each of the samples of the monopulse ratio, and the magnitude for each quadrature angle for each of the samples of the monopulse ratio. The monopulse ratio calculation module 1106 is connected to the traditional target azimuth calculation module 1108 by connection 1116 and to the alternative target azimuth calculation module 1110 by connection 1118 for transferring some or all of the calculations.
The traditional target azimuth calculation module 1108 receives the samples of monopulse ratio, the real part of the samples of monopulse ratio, the magnitude of the samples of monopulse ratio, or any combination thereof, from the monopulse ratio calculating module 1106 and calculates a mean of samples of traditional target azimuths using the samples of monopulse ratio. It can also calculate a standard deviation of the samples of traditional target azimuth. The traditional target azimuth calculation module is connected to the azimuth selection module 1112 by connection 1120 to output the mean of the samples of traditional target azimuth and also the standard deviation of the samples of traditional target azimuth.
The alternative target azimuth calculation module 1110 receives the samples of monopulse ratio, the magnitudes of the samples of the monopulse ratio, the quadrature angels, or any combination thereof. It can determine the minima of the magnitude of the samples of monopulse ratio and the maxima of the magnitudes of the quadrature angles of the samples of monopulse ratio. Furthermore, it can determine the target azimuth region and calculate an alternative target azimuth from the monopulse ratio within the target azimuth region. The alternative target azimuth calculation module 1110 can be connected to azimuth selection module 1112 by connection 1122 to output the alternative target azimuth.
The azimuth selection module 1112 receives the mean of the samples of traditional target azimuth and the standard deviation of the samples of traditional target azimuth from the traditional target azimuth calculation module 1108 by connection 1120 and the alternative target azimuth from the alternative target azimuth calculation module 1110 by connection 1122. The azimuth selection module 1112 compares the standard deviation of the samples of traditional target azimuth with a threshold value. If the standard deviation of the samples of first target azimuths is greater than the threshold value, then the azimuth selection module 1112 outputs the alternative target azimuth by connection 1124. If the standard deviation of the samples of traditional target azimuth is not greater than the threshold value, then the azimuth selection module 1112 outputs the mean of the samples of traditional target azimuth by connection 1124.
The alternative target azimuth calculation module 1110 performs its calculations substantially in parallel with the first target azimuth calculation module 1108. However, the alternative target azimuth calculation module 1110 could also perform its calculations in serial, or partially in serial with traditional target azimuth calculation module 1108. The alternative target azimuth calculation module 1110 could also wait to perform its calculations until the azimuth selection module has determined that the standard deviation of samples of traditional target azimuth is greater than the threshold value.
Those skilled in the art will appreciate that various adaptations and modifications of the just described preferred embodiments can be configured without departing from the scope and spirit of the invention. Therefore, it is to be understood that, within the scope of the appended claims, the invention may be practiced other than as specifically described herein.