Abstract: System and method for resolving phase ambiguities of various transducer arrays, including non-coplanar interferometer antennas on an aircraft skin, in order to determine the direction of arrival of a signal received by the array and emitted by a source remote from the array.

Abstract: An apparatus comprising an array of antenna elements, a beamformer for adjusting signals to and from the elements to form a first beam pattern and a second beam pattern, and wherein the first beam pattern is a sum pattern and the second beam pattern is a null pattern. A method of beamforming for sidelobe cancellation is also provided.

Abstract: A long baseline interferometer antenna system and method for determining the location of an emitter. The long baseline interferometer antenna system comprises a first antenna, a second antenna, an inertial navigation system, an antenna baseline measurement system, a multi-channel receiver and a processor. The first and second antenna elements are positioned on a platform and are both configured to receive signals from the emitter. The first and second antenna elements form a long baseline antenna pair. The inertial navigation system measures the platform position and attitude; and the antenna baseline measurement system measures the antenna baseline vector between the first and second antenna elements. The multi-channel receiver measures the differential phase between antenna pairs, and the processor computes the emitter location. Additional antenna elements can be included and some can be configured as squinted beam pair and make use of amplitude difference of arrival measurements.

Abstract: A Moving Transmitter Correlation Interferometer Geo-Location (MT-CIGL) system is disclosed that permits locating both moving and stationary transmitters from moving DF equipment. A conjugate gradient based search routine is utilized which solves for the location of moving and stationary transmitters at the start of each measurement sequence and then solves for the velocity and direction of motion of the moving transmitter. This information is used to track the moving transmitter. Received signals are sampled, digitized and stored in covariance matrices. They are then summed and normalized using an equation that has velocity terms that are set to zero to minimize extraneous correlation peaks, and a maximum correlation peak is developed. A conjugate gradient search routine is used to find the correlation peak of the summed data. The value of the peak is then analyzed to see if it is above or below a predetermined value.

Abstract: Method of arranging transducers, including non-coplanar interferometer antennas on the outer surface of an aircraft, to minimize phase ambiguities when determining the direction of arrival of a signal received by an array of the transducers and emitted by a source remote from the array.

Abstract: System and method for resolving phase ambiguities of various transducer arrays, including non-coplanar interferometer antennas on an aircraft skin, in order to determine the direction of arrival of a signal received by the array and emitted by a source remote from the array.

Abstract: An antenna comprised of a plurality of identical subarrays each having N antenna elements. The antenna elements of a core of subarrays all contribute outputs which are used for forming sum and difference beams. A peripheral area surrounding the core has subarrays which have a lesser number of antenna elements which participate in the signal processing operation to derive the sum and difference beams. The antenna elements of each subarray are combined in a manifold having one output, for the peripheral subarrays, and three outputs for the core subarrays. The manifold outputs are provided to various digital receivers which process the manifold signals with predetermined weighting functions. A digital beamformer processes the digital receiver outputs to derive the sum and difference beams which are used by a radar processor for tracking targets.

Abstract: An interferometer arrangement includes an antenna array that receives radiation from a plane wave emitted by a transmitter, the radiation being incident on the array at an angle (?). The array includes a plurality of antennas that provide output signals to a switching unit. The switching unit selects pairs of signals and passes them to a processor for processing. The processor is configured to produce an output signal that unambiguously indicates the value of the angle (?).

Abstract: A method for antenna tracking includes providing a central feed element in an antenna focal region with additional feed elements in an azimuth coordinate to provide a multitude of feed elements that each have a static beam position, and varying ratios of amplitudes of adjacent feed elements of the multitude of feed elements to electronically steer a beam between the static beam positions.

Abstract: Methods and systems are provide for precision direction finding capabilities for a sensing system, the method comprising providing a sensing system that utilizes an amplitude direction finding scheme, receiving a received signal in at least two receivers of the energy wave sensing system, the received signal generated by a first object, comparing the received signal at each receiver in a processor of the sensing system utilizing an amplitude direction finding technique to produce amplitude direction finding technique data, the amplitude direction finding technique data indicative of course direction of the first object, processing the received signal further to determine angle of arrival data based on an interferometric technique to produce interferometric technique data, the interferometric data indicative of a more precise direction of the first object than provided by the amplitude direction finding technique and determining the direction finding data of the first object based on a residual phase error of

Abstract: Methods and apparatus are disclosed for measuring position and motion of a “marker” antenna (14), disposed on a subject (12) at a physical location to be tracked. Relative distance of the marker antenna (14) from receiving antennas (18) is measured by phase differences of its microwave signals (40) at the receiving antennas (18) for at least two successive marker positions. Alternatively, actual distances (104, 106) are calculated by choosing a source position (102) and iterating the distances (104, 106) until the calculated phase differences match those measured. Four to six receiving antennas (18) are positioned at edges of a volume (16) where activity is conducted. Each received signal (40) is amplified and down-converted in a mixer (44). A single reference oscillator (46) feeds all the mixers (42) to preserve phase relationships of the received signals. Received signals (40) are digitized and presented to a multi-channel digital tuner (50).

Abstract: An interferometer array system and method for processing pulse signals from a target emitter includes an n element interferometer array of radiator elements for producing radiator signals in response to the pulse signals from the target emitter. M processing channels process radiator signal elements, where m<n. A switch matrix is connected between the array and the processing channels, switching different combinations of the radiator elements to the channels within a single pulse to achieve processing of all radiator signals within a single pulse of said pulse signals from the target emitter.

Abstract: An interferometer array system for processing pulse signals from a target emitter includes an n element interferometer array of radiator elements for producing radiator signals in response to the pulse signals from the target emitter. M processing channels process radiator signal elements, where m<n. A switch matrix is connected between the array and the processing channels, switching different combinations of the radiator elements to the channels within a single pulse to achieve processing of all radiator signals within a single pulse of said pulse signals from the target emitter.

Abstract: Method and device for space-time estimation of one or more transmitters based on signals received using an antenna network. Signals received using the antenna network are separated in order to obtain signals s(t). Signals s(t) are grouped by transmitter, where the signals s(t) are from more than one transmitter, and arrival angles &thgr;mi of the multipaths pm transmitted by each transmitter are determined.

Abstract: A system and method for detecting and tracking a target object, including the calculation of the target object's altitude, is disclosed. During the processing of signals received by a receiver, the system selectively calculates the altitude of the target object from signals modified by an interference effect pattern formed by the signals broadcast by a transmitter, or from the calculation of geometric shapes associated with three or more transmitters and determining the intersection point of those shapes.

Abstract: For interferometric and/or tomographic remote sensing by means of synthetic aperture radar (SAR) one to N receiver satellites and/or transmitter satellites and/or transceiver satellites with a horizontal across-track shift the same or differing in amplitude form a configuration of satellites orbiting at the same altitude and same velocity. Furthermore, a horizontal along-track separation, constant irrespective of the orbital position, is adjustable between the individual receiver satellites. In this arrangement one or more receiver satellites orbiting at the same altitude and with the same velocity are provided with a horizontal across-track shift varying over the orbit such that the maximum of the horizontal across-track shift occurs over a different orbital position for each satellite, the maxima of the horizontal across-track shifts are positioned so that the baselines are optimized for across-track interferometry.

Abstract: A method and apparatus for tracking a target. A signal from the target is received using a directional antenna and is digitized to provide a time series of samples. The samples are transformed, preferably by a wavelet transform. A signature of the target is identified in some of the transformed samples and a direction to the target is determined from others of the transformed samples. Target identification and target direction determination are iterated, with the identification being based on the most recently determined direction, and with the direction determination being based on the most recent identification, until a termination criterion is satisfied. Using wavelet transforms gives the antenna an effective beamwidth twenty percent narrower than the antenna aperture.

Abstract: The location of a cellular telephone handset relative to the sites of two pairs of fixed cellular transceivers is determined by responding to the phase difference of radio waves the handset emits, as coupled to the sites. The phase difference is detected by supplying replicas of the waves received at the first and second sites to first and second electro-acoustical transducers at opposite ends of a Bragg cell. One Bragg cell is thus associated with each pair of cellular transceivers. A laser beam incident on each Bragg cell is deflected by a moving optical grating resulting from the interaction of acoustic waves applied by the electro-acoustical transducers to the particular Bragg cell. The laser beam deflection angle for each Bragg cell determines the relative phase angle of the acoustic waves in that cell.

Abstract: An antenna array of “n” individual parabolic dishes is arranged about a center in subarrays extending in North, East, South and West rows. Signals received by the antennas are combined into representations of the electromagnetic environment as viewed with various simultaneous beam geometries, through a combination of analog signal summation, and digital implementation of aperture synthesis techniques. All antennas monitor the same portion of sky. The array is able to scan the sky without physically moving the antennas. The angular resolution of the array greatly exceeds that of the individual antennas. A variety of different research objectives, such as targeted searches, all-sky surveys, sky mapping, interference studies, the study of a variety of natural astrophysical phenomena, and the search for intelligently generated microwave emissions of possible extraterrestrial origin, may be realized simultaneously.

Abstract: Spatial profile creation section 102 creates an intensity distribution, that is, a spatial profile or spatial information of reception signals with respect to the directions of arrival of signals using reception signals prior to despreading received via antenna elements 101-1 to 101-4. Direction of arrival estimation section 103 estimates the directions of arrival of signals sent from other parties of communication from the spatial information created by spatial profile creation section 102 and divides and outputs the information of the directions of arrival to reception units 104-1 to 104-4 according to the direction of arrival. Beam formers 111 in reception units 104-1 to 104-4 each rotate the phase of the output reception signals from antenna elements 101-1 to 101-4 at predetermined angles based on the information of directions of arrival and combines these rotated reception signals so as to increase the reception levels of the signals sent from the directions of arrival.

Abstract: A method and apparatus for mitigating multipath signal distortion using a multi-element antenna array is provided. The multi-element antenna array is used to discriminate between the desired signal and its multipath components based on spatial angle of arrival. A reference signal, provided by the positioning system receiver, is used to compute element weightings that are utilized to null out the multipath components before they reach the receiver.

Abstract: A method for resolving interferometric ambiguities for an interferometer system with antenna elements employs multiple interferometric elements within the baseline. The overall accuracy of the interferometer system results from the interferometric elements with the longest baseline dimension; the remaining interferometric elements provide a means to correctly resolve ambiguities. According to the method, the baseline locations of additional elements are determined by using an integer fractional location. By so doing, the ambiguities of the overall baseline correspond to a limited number of ambiguities of the fractional baseline so that many of the ambiguities of the overall baseline can be eliminated. According to a preferred method, baseline values are selected to obtain a high probability of correct ambiguity resolution with a minimum number of additional interferometric elements. In this way, the design complexity is reduced.

Abstract: The present invention relates to a device for measuring the movements of a moving object, especially in a hostile environment, starting from a predetermined initial position, comprising:

Abstract: The present invention uses feedback 300 from RF carrier frequency measurements 301 to disassociate the emitter angle-of-arrival component 313 in the ambiguous phase measurement 312 from the initially unknown phase measurement integer ambiguities 314; to then process 302 resolve the ambiguities; and finally to process 303 to obtain the correct emitter AOA. The present invention does this by converting the actual interferometer baselines 315 on which the unassociated pulse 308 phase measurements 304 were made at different emitter frequencies to a baseline set 305 for a single-frequency equivalent interferometer array. This conceptual array has the following property: the phase measurement 306 that would be made on it at the fixed frequency for a signal at the same direction-of-arrival 307 are identical to the actual phase measurements made on the physical array. Because of this equivalency the conceptual array is called the E(equivalent)-array.

Abstract: A system for determining the direction that an object is pointing is disclosed. The pointing direction is calculated by determining phase differences between signals arriving at different positions on the object from a single source. Preferably the signals are received from Global Positioning System satellites and multiple antennae are positioned appropriately on the object. A number of methods are disclosed to obtain both the integer and fractional parts of the phase difference. Once the absolute value of the phase difference is determined and the satellite positions are known, it is possible to determine the direction that the object is pointing. A number of possible applications are disclosed including aerial imaging, artillery weapons aiming and satellite receive dish alignment.

Abstract: The invention described here concerns the use of GPS (Global Positioning System) interferometry, or any similar satellite constellation, to estimate the attitude of a vehicle, and is particularly suited for LEO (Low Earth Orbit) satellites. The invention is based on a system of gyroscopic and interferometric sensors and a piece of software to process the data received by such sensors. The invention can be applied to any type of vehicle (terrestrial, naval, aircraft or spacecraft) to determine the attitude of the vehicle with respect to an inertial reference system.

Abstract: A passive system for locating a distant source of radio frequency energy, for example a pulsed radar transmitter, from a portable platform such as a moving aircraft. The disclosed system is non ambiguous in locating ability by way of using time difference of arrival and time difference of arrival-rate processing of signals received from the distant source. This is in contrast with phase-based locating wherein location ambiguities are inherent. The disclosed system is supported by an included recalibration subsystem enabling practical maintenance of time difference of arrival system algorithm accuracy notwithstanding physical component and signal delay changes attributable to thermal or other environment effects. Maintenance of delay measurements accurate into the tens of picosecond range by this recalibration arrangement are employed to obtain usefully precise energy source locations. Mathematical equation-based disclosures of signal delay algorithms and their recalibration are included.

Abstract: An interferometer antenna system (32) for measuring the angle of arrival of RF signals. The interferometer antenna system (32) includes a plurality of interferometer antenna elements (36) coupled to a first switching network (42). The first switching network (42) is coupled to only two interferometer receivers (44, 46). The first switching network (42) selectively connects the plurality of interferometer antenna elements (36) in pairs to the two interferometer receivers (44, 46) in a sequential manner, so that a phase difference is measured between the received signal for several of the pairs of the interferometer elements (36). Additionally, a plurality of guard antenna elements (38) are coupled to a second switching network (48). A single guard receiver (50) is coupled to the second switching network (48), where the second switching network (48) selectively connects one of the guard antenna elements (38) to the guard receiver (50) in a sequential manner.

Abstract: An integrated receiver includes an Instantaneous Frequency Measurement (IFM) device, an interferometer and switches. The IFM receives signals from a target and determines the frequency of the signals. The IFM includes the shared N-channel phase receiver. The interferometer also receives the signals from the target and determines the angle-of-arrival (AOA) of the signals. The interferometer includes the shared N-channel phase receiver and shares the shared N-channel phase receiver with the IFM. The switches selectively connect the shared N-channel phase receiver to the IFM when the IFM is determining the frequency of the signals, and selectively connect the shared N-channel phase receiver to the interferometer when the interferometer is determining the AOA of the signals. The shared N-channel phase receiver determines phase information indicative of the frequency of the signals and the AOA of the signals.

Abstract: An apparatus and method for determining the angles-of-arrival and the polarization states of incoming RF signals of unknown polarization using five or more RF sensing antenna elements of differing yet known orientations of polarization.

Abstract: An algorithmic technique which allows antenna arrays that are used for interferometric direction finding to have elements with arbitrary orientation. This technique allows the phase errors associated with non-identical element orientation to be estimated, without explicit knowledge of either the polarimetrics of the array elements or the polarimetrics of the source. It relies upon the fact that there exists a single number which describes the polarimetric interaction, and that this number can be estimated and then utilized to remove the phase component due to polarimetric interaction. This technique makes it feasible to incorporate direction finding arrays into articles that could benefit from such arrays, but because of size or shape constraints, were previously not able to do so.

Abstract: A method of geoid measurement and/or earth imaging, characterized in that at least one directional antenna (2) is used to pick up a radio signal from a satellite and reflected on the ground, and said signal is processed using a reference signal that corresponds to the radio signal from the satellite in order to obtain a geodesic measurement and/or an image of the zone (Z) towards which the directional antenna (2) is pointed.

Abstract: An antenna and system for determining two-dimensional angle-of-arrival includes circular array interferometers for azimuth, linear interferometers for elevation, and a mast for positioning the interferometers in a vertically stacked orientation. The circular array interferometers exhibit azimuth constant-phase-difference contours orthogonal to elevation constant-phase-difference contours exhibited by the linear interferometers. An antenna and system for determining azimuth of input signals includes ambiguous and non-ambiguous circular array interferometers. The non-ambiguous circular array interferometer resolves ambiguities introduced by the ambiguous circular array interferometer, the at least one ambiguous circular array interferometer operatively coupled to a low-order Butler matrix and power divider/combiner such that a high order Butler matrix is not required to generate omnidirectional phase modes from the ambiguous circular array interferometer.

Abstract: A linear interferometer antenna for making azimuth angle measurements and elevation angle measurements of an identified target. The antenna includes six radiating elements which receive signals sent from the target, a beam forming network, and a processing unit. Four of the six radiating elements are positioned on a first plane and the remaining two radiating elements are positioned on a second plane. The second plane is parallel to and positioned at a predetermined distance from the first plane.

Abstract: A spread spectrum signal detection system comprising two spatially separated receivers, a correlator, such as a time integrating correlator employing acousto-optic cells, which is connected to the outputs from the two receivers to produce a signal representative of the cross correlation function of the two spread spectrum signals, a filter arranged to transmit only the central portion of the cross correlation function and a signal processor to produce the cross spectral density and thereby determine the presence of the spread spectrum signal. The direction of arrival of the spread spectrum signal can be determined by measurement of the angle of the phase slope of the cross spectral density. The acousto-optic cells can be Bragg cells.

Abstract: An apparatus and method for determining the angles-of-arrival and the polarization states of incoming RF signals of unknown polarization using three or more RF sensing antenna elements of differing yet known orientations of polarization.

Abstract: Gravitation in three dimensions is measured using an accelerometer attached to a carrier, a satellite navigation receiver and a computer. The satellite navigation receiver determines a position and attitude, and changes in the position and attitude over time. The computer calculates complete kinematics in inertial space from the timely changes of the determined position and attitude and calculates the gravitation by subtracting the kinematic acceleration from the one observed by the accelerometer. In a preferred embodiment the accelerometer is connected tightly to the carrier. At most, damping elements may be mounted between the accelerometer and the carrier. The accelerometer can be a single accelerometer or a triplet of non-parallel accelerometers. The satellite navigation receiver may be one instrument equipped with three or more antennae or a set of three or more single instruments connected to each other.

Abstract: An attitude determination system uses multiple antenna inputs which are time-multiplexed into a multi-channel receiver. Each channel tracks one incoming signal from a known or ascertainable source. For each of the incoming signals being tracked, digital processing can be used to determine range differences between the different antenna elements for that incoming signal, and to compute attitude based on the range differences and the known configuration of the attenna elements relative to each other.

Abstract: A method for determining the geolocation--i.e., the latitude, longitude, and altitude--of a stationary emitter emitting an RF signal. The method employs at least one moving observer to measure electrical phase change of the emitter over two or more successive dwell intervals, and at least two observers, moving or stationary and of known position, to determine the pulse time of arrival of the emitter signal. The phase change measurements are taken using a long baseline interferometer (LBI), and the pulse time of arrival measurements are calculated using short baseline interferometers (SBI). Circles of position are generated from bearing change measurements ascertained from the LBI phase change measurements, and hyperbolic lines of position are generated based on the SBI measurements. The position of the emitter is then determined from the intersection of the circles and lines of position.

Abstract: A system is disclosed for estimating the position and velocity of a moving transmitter making use of both Doppler frequency measurements and LBI phase measurements. The frequency measurements and the LBI phase measurements are made from a platform moving through said measurement path. The estimation is based on equation models ##EQU1## These equation models are used in cost evaluations in grid searches to provide initial estimates of parameters defining the position and velocity of the transmitter and the initial estimates are used in nonlinear least squares calculations based on the equation models to provide an estimate of the position and velocity of the transmitter.

Abstract: A method for estimating the number of emitters of intermittent or periodic pulsed energy waveforms received at a sensor location and the parameters of the intermittent or periodic energy waveforms, including: accumulating over a selected period of time output of the sensor, the output consisting of a set of vectors, each of the vectors consisting of at least one element of parameters of direction, frequency, and amplitude, and which element(s) specify(ies) a point in a space defined by the element(s) for each of the waveforms received when at least the parameter of direction is included; dividing the space into a plurality of bins, considering each vector in turn, and apportioning weight of each vector to be accumulated within at least some of the plurality of bins; determining at the end of the selected period of time which of the bins exceed a threshold strength and are, therefore, the emitters; and calculating the at least one element of parameters for each emitter as appropriate for the vector elements se

Abstract: An antenna system is made up by a main antenna and a sub antenna which is adjacent the main antenna in a direction not perpendicular to the direction of beam scan of the main antenna and which has a beam axis coincident with a beam axis of the main antenna. Antenna beams of the antenna system are scanned by a scan device. Received signals of both the antennas are subjected to a multiplication process under phase coherent condition in a phase-coherent multiplying device. A signal corresponding to a maximum frequency component in the output signal of the phase-coherent multiplying device is output by a frequency discriminating device and then subjected to a signal conversion process in a signal converting device. Information about a radio wave source only in the direction of the antenna beams is thus obtained.

Abstract: An autotracking antenna system operable to cause a steerable antenna assembly to automatically track a moving RF video signal source has a reflector, a rotator for positioning the reflector at any desired position in azimuth and elevation, a primary antenna element positioned to receive an RF video signal reflected from the center of the reflector, and a series of offset antenna elements each positioned to receive an RF video signal reflected from a different off-center location on the reflector. A tracking control processor is operable to select and receive video signals from the primary antenna element and the offset antenna elements and to control the rotator, and a signal receiver receives video signals from the antenna element and has a video signal output.

Abstract: In a long base line interferometer system for determining the position of a transmitter, the phase differences between the signal received by the antennas at each end of the base line are monitored as the interferometer moves through a measurement path to obtain phase difference measurements distributed along the measurement path. A cost function involving measuring the sum of the squares of the differences between measured values and predicted values is determined for each of a set of trial location grid points and the grid point with the lowest cost function is selected as a starting point for determining the transmitter location by least squares convergence. In evaluating the cost function, the predicted values are obtained from the equation: ##EQU1## in which .o slashed..sub.0 is unknown phase offset and the X and Y coordinates of the transmitter are unknown. The least squares convergence is carried out by iteratively adding corrections to predicted values for the unknowns until convergence occurs.

Abstract: An antenna array for radio interferometry uses three equi-spaced triplets set vertically above the ground with different respective spacings, the center antenna of each triplet being at a different height. Signal processing circuits provide for each triplet a signal which is a function of the elevation angle .theta. but is independent of the ground reflection coefficient, P. the signals are weighted to give the optimum value of .theta., e.g., by selecting the signal varying most rapidly with .theta.. Some antennae can be shared and for example three triplets may be provided by seven antenna elements.

Abstract: This invention provides a method and apparatus for determining position from code modulated, suppressed carrier signals received from satellites, in which a digital composite of the signals received from a plurality of satellites is formed at a first point, the digital composite is processed to measure the carrier phase of the signal from each of the plurality of satellites to derive computer data, and said computer data are combined with data derived from measurements of signals received from the same plurality of satellites at another point, to determine position data.

Abstract: A beam sharpened, low sidelobe antenna is obtained by segmenting the antenna to provide two sub-antennas, one of which is arranged as an interferometer. The output signals of the two antennas are added and subtracted to provide sum and difference signals. The sum and difference signals and the output signals are then utilized to provide the desired beam sharpened, low sidelobe antenna.

Abstract: A precision direction finding system for making precision angle of arrival estimates for a signal received through two antenna elements separated in space. Phase interferometry is used to determine a precise angle of arrival, with multiple ambiguities due to the periodic nature of the phase difference related to geometric angle. The interferometric ambiguities are resolved using the time difference of arrival (TDOA) of the signal at the two antenna elements. TDOA is measured using leading edge envelope detection for simple pulsed signals, and predetection correlation for phase and frequency modulated signals.

Abstract: Radar emitter carrier frequency or pulse time-of-arrival measurements are used to resolve the differential phase measurement ambiguities on a long baseline interferometer (LBI) used to passively locate the emitter. The LBI requires only two pulses to precisely measure the change in signal angle of arrival caused by observer motion relative to the emitter, whereas frequency Doppler needs tens of pulses, and time Doppler may need hundreds of pulses, to estimate the same change to the same accuracy. Therefore Doppler measurements are made only to the accuracy needed to estimate the angle change accurately enough to differentially resolve the LBI.

Abstract: A method for use with a long baseline interferometer that unambiguously estimates the angle of arrival of an RF agile signal produced by an emitter. The angle of arrival estimate provided by the method may be used to resolve phase ambiguities inherent in the long baseline interferometer, thereby providing for the unambiguous estimation of the angle of arrival of the RF signal from the emitter. The RF agile signals processed to determine the phase thereof. The phase information contained in the energy radiated by the emitter is then processed to estimate the angle of arrival of the energy. The phase information contained in the RF agile signal is processed using the equations .phi.=(2.pi.fL/c) sin .theta., and .delta. sin .theta.=(c/2.pi.fL).delta..phi., where the phase (.phi.) is measured to a given error (.delta..phi.) to determine the direction of arrival (.theta.) of the energy radiated by the emitter.