Abstract:
A system includes an antenna array consisting of a plurality of antenna elements, a plurality of receivers to process the signals from the antenna elements of the antenna array, and a combiner to combine receiver outputs so as to minimize the effect of undesirable signals such as multipath or interference while maintaining a nominal gain in the direction of the desired signal. The combiner takes into account variation or uncertainty in the assumed antenna array response, such as imprecise knowledge of the angle of arrival and uncertainty in the array manifold and multiplicative uncertainties due to gain variations between receivers, as well as non-uniformity in the response due to coupling between elements and coupling with the antenna structure. This system is applicable to antenna arrays with non-uniform responses, such as closely spaced arrays in which the coupling between elements is significant.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS AND CLAIM OF PRIORITY  
       [0001]     The present invention is a continuation of Provisional Application Nos. 60/326,522 and 60/352,716, respectively filed in the U.S. Patent and Trademark Office on Oct. 1, 2001 and Jan. 28, 2002 and priority is hereby claimed under 35 USC 119 with respect to these two provisional applications. 
     
    
     APPENDIX  
       [0002]     The attached appendix contains an article entitled: “Robust Beamforming in GPS Arrays” by Robert G. Lorenz and Stephen P. Boyd, ION National Technical Meeting, Jan. 28-30, 2002, San Diego, Calif. The contents of this article, omitted from the Detailed Description below for the sake of brevity, include very detailed analyses of some of the features of the present invention and are incorporated by reference herein in its entirety.  
       BACKGROUND OF THE INVENTION  
       [0003]     1. Field of the Invention  
         [0004]     The present invention relates to processing signals, such as GPS signals, received by a plurality of antenna elements for the purpose of rejecting interference from undesired signals.  
         [0005]     2. Description of the Related Art  
         [0006]     Multi-path and interference frequently limit the performance and availability of carrier phase-based relative positioning and precision navigation techniques. There are a number of ways of rejecting multipath and, to a lesser extent, interference. When the earth below the antenna contains appreciable moisture, it becomes a good reflector of L-band RF energy. Reflections from the ground below the antenna are commonly the largest source of multipath in GPS survey systems.  
         [0007]     A RHCP (Rights Hand Circularly Polarized) wave, incident at an arbitrary angle on a dielectric discontinuity, can be resolved into two linearly polarized parts, namely, a transverse magnetic (TM) component and a transverse electric (TE) component. The reflection coefficients for each of these components are generally different. However, the reflected signal will be elliptically polarized with roughly a left hand circular polarization, i.e., the opposite of the incident wave.  
         [0008]     An antenna element designed to receive a RHCP wave from above the horizon, such as a turnstile antenna, will generally have a strong response to left-hand elliptically polarized radiation arriving from below the horizon. A ground plane or slow-wave structure, such as a choke-ring, is typically employed to shield the antenna element from reflections arriving from below the horizon.  
         [0009]     A high degree of isolation typically requires a physically large structure. For example, in U.S. Pat. No. 4,647,942, entitled “Circularly Polarized Antenna for Satellite Positioning Systems,” Counselman and Steinbrecher describe the use of a circularly polarized antenna for satellite position systems making use of a turnstile antenna element, namely a quadrifilar combiner in conjunction with 4 monopoles equally spaced in a horizontal plane above a large ground plane structure. While the antenna is reported to have excellent multi-path performance, the use of a large ground plane structure limits its utility for man-portable systems. For methods that attempt to control the radiation pattern of an antenna using choke rings (slow-wave structures) or ground planes, there is normally a tradeoff between physical size and efficacy.  
         [0010]     Because the GPS signals are bandlimited, multi-path mitigation techniques that discriminate between the direct signal path and reflections based on differences in time-of-arrival are of little utility in mitigating close in multi-path.  
         [0011]     U.S. Pat. No. 4,809,005, entitled “Multi-Antenna GPS Receiver for Seismic Survey Vessels” by Counselman introduces the idea of an antenna array system making use of post-correlation beamforming, that is, controlling the radiation pattern of a collection of antennas after each of them has performed satellite specific operations on the GPS signals. In this and subsequent patents, Counselman does not teach how are the outputs of the antennas combined.  
         [0012]     The idea of minimizing the weighted power output from an antenna array was first described by J. Capon in an article entitled: “High Frequency-wave Number Spectrum Analysis”, Proceedings of the IEEE, Volume 57, Number 8, August 1969, Pages 1408-1418. While the method described therein may be viewed as optimal, its performance can degrade to arbitrarily poor levels in the presence of uncertainty in the array response, also known as an array manifold.  
         [0013]     In his paper entitled “Array Antennas for DGPS”, Proceedings of the IEEE 1998 Position Location and Navigation Symposium, Palm Springs, Calif., Apr. 22, 1998, Pages 352-357, Counselman describes an antenna array making use of three turnstile antennas whose outputs are combined with fixed weights so that the antenna&#39;s amplitude response is approximately the Heaviside step function of the received signals elevation. The described antenna array has three vertically stacked turnstile antennas. Again, this antenna array is an excellent compromise. However, due to the fixed weights, the antenna system cannot adapt to additional knowledge.  
         [0014]     In the paper entitled “GPS Code and Carrier Multipath Mitigation Using a Multi-Antenna System,” IEEE Transactions on Aerospace and Electronic Systems, Volume 37, Number 1, January 2001, Pages 183-195, Ray et al. describe a system that makes use of an antenna array in which antenna elements are oriented circularly around a centrally located antenna. The lack of vertical aperture limits the performance of this method.  
         [0015]     In the present invention, the antennas forming the array, such as turnstile antennas, are not isolated from reflected signals arriving from below the horizon. Instead, a linear combination of the turnstile antenna outputs having a small response in the direction of the reflected signal is chosen. With such an antenna array arrangement, the usual trade-off between antenna size and multipath performance need not apply.  
       SUMMARY OF THE INVENTION  
       [0016]     The present invention includes an antenna array for mitigating multi-path based on angle-of-arrival differences. It also includes a signal processor to process signal processing algorithms to combine the output of the array elements to minimize the effect of interferences and multi-path.  
         [0017]     The combining technique explicitly takes into account variation or uncertainty in the assumed array response. Sources of this uncertainty include imprecise knowledge of the angle of arrival and uncertainty in the array manifold. In one example embodiment of the present invention, uncertainty in the array manifold is modeled explicitly via an uncertainty ellipsoid that gives the possible values of the array for a particular look direction. Weights are chosen to minimize the total weighted power output of the array, subject to the constraint that the gain exceeds unity for all array responses in this uncertainty ellipsoid. Hence, the present invention can guarantee performance of a robust method in the presence of uncertainties. The present invention extends naturally to the case where the aggregate uncertainty arises from more than one component in the signal path, e.g., the array manifold, the radio frequency (RF) electronics, etc.  
         [0018]     It is therefore an object of the present invention to provide a signal processing method and apparatus having an accurate response to the desired received signal in the presence of multi-path or interferences.  
         [0019]     It is another object of the present invention to provide a method and apparatus employing a plurality of antenna elements for mitigating the effect of undesired signals and interference.  
         [0020]     Briefly, these and other objectives are accomplished by providing a method and apparatus to process a plurality of signals received from individual antenna elements and to combine the processed outputs to reduce the effect of undesired signals. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0021]     Further objects and advantages of the present invention and will become apparent from the following detailed description and drawings in which:  
         [0022]      FIG. 1  is a block diagram of a system in accordance with an example embodiment of the present invention consisting of an antenna array, a plurality of GPS receivers, and a timebase common to all of the GPS receivers.  
         [0023]      FIG. 2  is a drawing showing an earlier disadvantageous GPS beamforming system.  
         [0024]      FIG. 3  is a drawing showing an example embodiment in accordance with the present invention.  
         [0025]      FIG. 4  is a schematic drawing showing a turnstile antenna element.  
         [0026]      FIG. 5  is a drawing showing a wire model of an antenna used in conjunction with an example embodiment of the present invention. 
     
    
     DETAILED DESCRIPTION  
       [0027]     Referring to  FIG. 1 , the system embodying the present invention is shown. Signals are received at an antenna array  101  consisting of a plurality of antenna elements  102 ,  103 , and  104 . The outputs of antenna elements  102 ,  103 , and  104  are respectively connected to a plurality of receivers (such as GPS receivers)  105 - 107 . The GPS receivers  105 - 107  are additionally connected to a common timebase  108 . The stability of the timebase  108  is not critical. For example, the timebase  108  may comprise a temperature compensated crystal oscillator.  
         [0028]     Antenna elements  102 ,  103 , and  104  of array  101  are, for example, identical turnstile elements arranged in a vertical collinear fashion. The turnstile antennas  102 ,  103 , and  104  are optimally spaced apart at approximately a ½ of a wavelength at the highest frequency of use. A spacing of greater than a half of a wavelength creates ambiguity in the received number of carrier cycles. Closer spacing reduces the effectiveness of the antenna and increase the coupling between antennas. The spacing between turnstile antenna elements in an example embodiment of the present invention is 3 inches, which corresponds to approximately {fraction (1/3)} of a wavelength at the GPS L1 frequency. This topology is well suited for kinematic surveying applications. The array phase center is taken to be the phase center of the center element. Unlike an array in a horizontal plane, a vertically stacked array affords strong discrimination between signals arriving from above and below the horizon due to its large vertical aperture.  
         [0029]     The outputs of receivers  105 - 107  are connected to a measurement combiner  109 . The function of the measurement combiner  109  is to combine the outputs of receivers  105 - 107  to produce measurement data  110  of aspects of the signal characteristics such as pseudorange and carrier phase. For exemplary purposes, three antenna elements and multipliers have been shown. However, the present invention is not limited thereto and a different number of antenna elements may be employed. Generally speaking, increasing the number of antenna elements increases the cost, the power consumption, and performance of the system.  
         [0030]     In the illustrative example of the present invention, three separate receivers are used along with a common timebase. Alternately, a single receiver containing multiple receiver sections may be employed. In addition, the relative gains of the different receiver sections must be estimated. This matter will be addressed in the discussion of  FIG. 3 .  
         [0031]     In another variation of the present invention, the antenna elements are be connected to a multiplexer that selectively connects one of the antenna elements to a single receiver. In this case, the receiver processing acts in synchronism with the multiplexer to allow a single receiver to process signals from all of the antenna elements. An advantage of this approach is that the complexity of this solution is lower. In addition, signals from each of the antenna elements are processed by a single receiver and hence are not subject to different gains or phases. This approach incurs a loss of sensitivity relative to the multiple receiver architecture.  
         [0032]     In  FIG. 2 , a controlled radiation pattern antenna typical of an earlier disadvantageous GPS systems employing beamforming is shown. A receiving antenna array  201  comprises antenna elements  202 ,  203 , and  204  respectively. The antenna elements  202 - 204  are connected to a beamformer  209  via a covariance estimator  208  and to multipliers  205 ,  206 , and  207  respectively. An estimate of the covariance of the array element outputs of array  201  is computed in covariance estimator  208 . Beamformer  209  uses this covariance estimate and computes complex weights that are applied to multipliers  205 ,  206 , and  207  respectively. The outputs of multipliers  205 ,  206 , and  207  are added together in an adder  210 . The output of the adder  210  is applied to a GPS receiver  211  that outputs measurement data  212 . The reception pattern of the antenna array may be controlled in this manner to mitigate the effect of strong interfering signals.  
         [0033]     While this approach works well at mitigating the effect of strong interfering sources, it is not well suited for precise relative positioning systems for two reasons. First, this system usually has high power consumption and a high cost. The increased cost is due to the fact that traditionally it has been expensive to precisely weight radio frequency (RF) signals. Second, a single set of weights is used for the combining of the outputs of the antenna elements. As a result, the weights used represent a compromise that is used for all satellites.  
         [0034]     What differentiates the present invention from previous approaches to beam forming is that the complex amplitudes are combined after correlating with locally generated replicas of the pseudorandom code and carrier for each received satellite signal. The correlation process is a linear, time-varying operation; hence, the reception pattern of the antenna array may be controlled by forming combinations of the correlation coefficients. One significant advantage of the present invention is that the antenna response can be adjusted on a satellite-by-satellite basis. This allows the system to choose an optimal radiation pattern for each satellite instead of a compromise for all satellites. Since the weights are applied after correlation, the multipliers may be implemented in software and do not require additional hardware.  
         [0035]      FIG. 3  shows the architecture of the post-correlation beamformer that constitutes a portion of the example embodiment of the present invention. For clarity, a single beamformer is shown. In practice, separate beamformer weight vectors may be used for each satellite. Antenna array  301  comprises a plurality of antenna elements numbered  302 ,  303 , and  304 . Antenna elements  302 ,  303 , and  304  are respectively connected to an equal number of GPS receivers  305 ,  306 , and  307 .  
         [0036]     Parameter estimator  311  makes use of inputs  312  that provide a-priori information, outputs of the GPS receivers  305 ,  306 , and  307 , and outputs of the measurement processor  315 . A-priori information  312  may consist of the array manifold and its uncertainty, antenna orientation, and receiver gains. The outputs of the GPS receivers includes pseudoranges, carrier phases, correlation coefficients, and optionally pre-correlation sample data. The outputs of parameter estimator  311  comprise information about the orientation of the antenna array  301 , the relative gains of the GPS receive paths, and an estimate of the desired covariance measurement. As it is desirable to minimize the number of estimated parameters, one of the receiver gains may be considered to be unity. Parameter estimator  311  makes use of nonlinear estimation techniques, for example. As some of the parameters are well-modeled as evolving according to a linear stochastic model, the parameter estimator  311  may be implemented as an extended Kalman filter.  
         [0037]     The aggregate uncertainty in the response of the antenna array and the receiver paths for each satellite is the set of possible values of the element-wise product of the array manifold and the receiver gains, wherein each of the above quantities can take on any value in their uncertainty region. A further output of the parameter estimator  311  comprises an outer approximation of the uncertainty region of the element-wise product of the array manifold and the receiver gains. In this example embodiment of the present invention, an ellipsoidal approximation is used. The output of the parameter estimator  311  is applied to a beamformer  313 .  
         [0038]     Two different covariance estimates are of utility. In the presence of strong interfering signals that are uncorrelated with the received GPS signal, a covariance estimate based on the intermediate frequency (IF) samples of each GPS receiver is computed. In the case where the undesired signal is correlated with the desired signal, such as multipath, samples of the correlation coefficients for each satellite, computed in receivers  302 ,  303  and  304 , are used to estimate the covariance for each satellite&#39;s beamformer computation.  
         [0039]     The beamformer  313  weight vector is chosen to minimize the time-averaged weighted power output of the array subject to the constraint that the real part of the gain in the direction of the satellite is greater than unity for all possible values of the array manifold or receiver gain in accordance with the respective uncertainty descriptions. Mathematically, the time averaged power out of the array is given by the quantity w*Rw, where w is the beamformer weight vector, (·)* denotes the conjugate transpose, and R corresponds to the estimate of the covariance. The beamformer  313  may use regularization methods or may make use of the fact that if the aggregate uncertainty description is an ellipsoid, the beamformer weight vector can be efficiently calculated using convex optimization techniques.  
         [0040]     Outputs of receivers  305 - 307  are also respectively inputted to multipliers  308 - 310 . Outputs of the beamformer  313  are respectively inputted to multipliers  308 - 310 . The outputs of multipliers  308 - 310  are inputted to an adder  314  whose output is inputted to a measurement processor  315 . The measurement processor  315  outputs measurement data  316  and also feeds back an output to the parameter estimator  311 .  
         [0041]     The operation of the turnstile antenna element can be better understood by referring to  FIG. 4 . Each turnstile antenna element consists of a quadrifilar combiner  401  and four identical monopoles numbered  402 ,  403 ,  404 , and  405 .  
         [0042]     Quadrifilar combiner  401  may consist of a strip-line circuit. Commercially available quadrifilar combiners have a loss of approximately {fraction (1/2)} dB. The magnitudes of the outputs match within a few percent and the phases, relative to ideal quadrature, to within ±5°.  
         [0043]     The monopoles radiate from the quadrifilar combiner at equally spaced angles in a nominally horizontal plane.  
         [0044]     When the elements are infinitesimal dipoles, the magnitudes are equal, and the phases are in quadrature, the antenna produces a circular pattern in the plane on the turnstile antenna elements. In the preferred embodiment, the length, taper, and diameter of the antenna elements  402 - 405  were chosen to match the input impedance of the elements to 50 Ω, the characteristic impedance of the quad hybrid. As a result, the pattern of the prototype antenna is slightly different due to the geometry of the elements and the non-ideal performance of the quad hybrid. The deviation from the idealized response creates no significant problems.  
         [0045]     The GPS satellites transmit RHCP radiation. An electric field vector of constant length characterizes RHCP radiation that rotates around a circular path. If the wave is traveling toward the observer and the vector rotates counterclockwise, it is right-hand polarized. The operation of the quadrifilar combiner can be understood in terms of the four inputs being multiplied by weight factors  406 ,  407 ,  408 , and  409  and summed in a summer  410  having an output  411 . The phasing is chosen such that the outputs of the dipoles add constructively when illuminated with RHCP radiation from the zenith. The weights shown correspond to those in the antenna when viewed from above.  
         [0046]      FIG. 5  shows a simulation model of an antenna. Both the array manifold and the input impedances of the antenna array elements may be simulated with the Numerical Electromagnetics Code (NEC), version 4. It is possible to design the shape and size of the monopole elements so as to approximately match the characteristic impedance of the quadrifilar combiners.  
         [0047]     The wire grid model used in the NEC simulation consists of approximately 2000 segments. The diameter of each wire element has approximately the same surface area as the portion of the antenna it is being used to model. Though the turnstile antenna elements are identical, the responses of the turnstile antenna elements to plane wave excitation differ as the array manifold and the impedances presented to the quadrifilar combiners are strongly affected by coupling between elements and other parts of the antenna structure.  
         [0048]     Various changes may be made in the structure and embodiments shown herein without departing from the concept of the present invention. Further, features of the embodiments shown in the various figures may be employed with the embodiments shown in the other figures. Therefore, the scope of the present invention is to be determined by the terminology of the following claims and the legal equivalents thereof.