the essential problems of determining the angle of arrival of an emitter signal with an adaptive interferometer and a short baseline can perhaps be best described with fig1 . let it be assumed that a distant emitter signal is received by two sensors , 1 and 2 . for a monochromatic signal , one may write the signal received by the two sensors as : where a 1 and a 2 denote signal amplitudes , ω is the angular frequency of the emitter signal being equal to 2πf where f is the frequency of the signal , t is time , λ is the wavelength of the signal , φ is an arbitrary phase and θ and d are respectively the &# 34 ; angle - of - arrival &# 34 ; of the signal and the separation distance between the sensors 1 and 2 . in the adaptive interferometer , the signal s 2 , which is the output of the sensor 2 , is led to a 90 ° hybrid 3 , having 0 ° phase and 90 ° phase outputs . signal controllers 4 and 5 provide attenuations k 1 and k 2 at the 0 ° and 90 ° outputs , respectively , such that the output 6 of the signal controller 4 is : ## equ1 ## similarly , because of the 90 ° phase difference , the output 7 of the signal controller 5 is : ## equ2 ## if the two signal controller output signals 6 and 7 are first summed and then this sum is subtracted from s 1 , the residue signal s e , following the subtraction , which will be referred to as the error signal , can be written as : ## equ3 ## if , now , the values of k 1 and k 2 are so adjusted that : ## equ4 ## the error signal s e will approach zero . in an adaptive interferometer , the values k 1 and k 2 are automatically adjusted so that s e is driven to a zero value by two closed - loop controls . if for any reason the values of k 1 or k 2 or both are not exactly what is needed for a null , the nonzero s e will be placed at the input of a synchronous detector 8 referenced to the signal s 2 . the characteristic of this synchronous detector is such that there will be a dc output of the detector as long as there is any nonzero input signal having the same waveform as that of the reference signal . since , in this case , the reference signal has the same waveform as the input signal , there will be dc signals at the output of the synchronous detector whenever s e is nonzero . these dc signals are used to adjust the values of k 1 and k 2 through controls 11 and 12 until these values make s e = 0 . thus , the closed - loop controls in the adaptive interferometer shown in fig1 will always create a null of the error signal for which : ## equ5 ## that is , if d / λ ≦ 1 , ## equ6 ## eq . ( 7 ) shows how the angle - of - arrival θ of the emitter signal can be determined when k 2 , k 1 , d and λ are known . the signal processor 9 provides the value of θ in accordance with eq . ( 7 ). to avoid an ambiguity , the baseline d must be short , that is d / λ ≦ 1 . however , a short baseline causes the resolution problem during the angle measurement , particularly for small values of θ . thus , from eq . ( 6 ): ## equ7 ## and when θ is very small , sin θ ≅ θ and ## equ8 ## the resolution and accuracy with which θ can be determined by an adaptive interferometer , then , will depend on the resolution and accuracy with which the ratio ( k 2 / k 1 ) can be measured . if the control loops are such that one can obtain a 60 db null initially and maintain a 60 db , then the resolution and accuracy of θ will be on the order of 10 - 3 / 2π , or about 1 / 6 of a milliradian when d / λ = 1 . the next problem for the determination of the angle - of - arrival of the emitter signal is the lack of knowledge of the emitter signal frequency . normally this can be remedied by an additional loop as shown in fig2 . here the first cancellation loop 16 involving signal controllers k 1 and k 2 is the same as shown in fig1 . the second cancellation loop 17 , containing a delay line 13 of length l and the 2 additional signal controllers 14 and 15 providing attenuations of k 3 and k 4 , respectively , also creates a null for the signal received by sensor 1 . for the equilibrium condition for both loops , one obtains : ## equ9 ## thus , with the knowledge of the signal controller values k 1 , k 2 , k 3 and k 4 and those of the parameters d and l , one can determine the angle of arrival θ and the wavelength λ of the emitter signal . the signal processor and display unit which is at the output of the system in this case , provides information on the angle - of arrival , theta , and the wavelength , lamda , and their display . the provision of an additional loop to determine the emitter signal frequency , however , does not make the adaptive interferometer operation independent of frequency . more specifically , when the emitter signal is a carrier suppressed , or a broadband signal or a pseudo noise modulated signal , there is no specific value of λ for the signal and , hence , an adequate null may not be obtainable by adjusting the amplitude and phase of the signal received by one sensor and subtracting this adjusted signal from that received by the other sensor , as described above . for such a case , a time domain interferometer , where the signal controllers provide an amplitude and a time delay adjustment , instead of a phase adjustment , will be necessary . since , in the absence of multipaths , the emitter signal , as received by the two sensors , must differ only by an amplitude factor and a time delay , regardless of the complexity of its frequency spectrum of the emitter signal , a time domain adaptive interferometer will make the angle measurement independent of the frequency spectrum of the emitter signal . such an interferometer also avoids the problem of phase ambiguity when the baseline is more than a wavelength . this advantage , however , may not be relevant when a long baseline is not practical for other reasons . also , no separate frequency determination is necessary since the angle of arrival θ is dependent only on the differential time of arrival , regardless of the frequency spectrum of the emitter signal . fig3 shows a schematic arrangement for a time - domain interferometer . in this case , the emitter signal received by the two sensors 1 and 2 is of the form ks ( t - t ) and s ( t ). that is , in the absence of a multipath , the emitter signal , regardless of its frequency , modulation , etc ., as received by the two sensors , can only differ by an amplitude factor k and a time delay t . for a null , the signal s ( t ) has to be modified in amplitude by a factor k and delayed by a time delay t . when the signal ks ( t - t ) is cancelled by an adaptive closed - loop control containing the signal controller 18 , the adjustment of time delay t will be a measure of the angle - of - arrival of the signal . thus , the angle - of - arrival of the signal , in that case , may be obtained from the relation : where c is the velocity of propagation of the emitter signal and d is the baseline length . the angle determination by a time domain adaptive interferometer , shown schematically in fig3 then , is independent of frequency since no frequency or modulation related term appears in eq . ( 12 ). the values of k and t needed to create a signal null is processed in accordance with eq . ( 12 ) to obtain the value of θ or the angle - of - arrival of the signal at the signal processor and display unit which also may provide a display of the value of the angle - of - arrival . the synchronous detector 20 and the control for the variable amplitude and time delay 19 are similar to those shown in fig1 . perhaps the most severe limitations on the measurement of angles from a distant emitter by an interferometer result from the low signal level of the emitter signal and due to the presence of multiple signals at the sensors . to illustrate these problems , one may consider eq . ( 5 ), where the signal controller parameters k 1 and k 2 are always of fractional values . since the amplitudes , a 1 and a 2 , of the emitter signal at the sensors are about the same , the signal amplitude a 1 has to be reduced by about 6 - 10 db for the equality requirement in eq . ( 5 ). now if the signal level of the emitter is low to begin with , a further reduction of the signal and , hence , the signal - to - noise ratio , may cause the interferometer to be ineffective . unfortunately , as said earlier , the amplification of the signal at the signal controller path , or amplifications of both signals received by the two sensors , are not permissible because of the inherent nonphase tracking characteristics of the amplifiers . any phase error or time delay of the signal at the signal controller path , or any differential phase or time delay error when both sensor signals are amplified , causes a direct error in angle measurement by an interferometer . the angle measurement problem arising from the presence of multiple signals at the sensors can be avoided if a signal selectivity is provided at the sensors . such a selectivity is readily obtained by a tuned circuit at each sensor . however , the differential phase or time delay introduced by two separate tuned circuits is unacceptable , since it introduces a direct error in angle measurement . also , a selectivity by tuned circuit is not feasible for co - channel interferences in the form of multipath signals . fig4 is a simplified illustration of direction finding for weak signals and for signals in the presence of interferences . here the same signals received by the two sensors 51 and 52 are led to the two power dividers 53 and 54 . the output in one branch of the power dividers 53 and 54 are summed in the summer 55 to create a reference signal . this reference signal is then amplified by amplifier 56 and tuned if necessary . the reference signal then is split into two parts at the power divider 57 . one of the two output ports of the power divider 57 provides the reference signal for the control loop 58 which nulls the signal at the second branch of the power divider 53 by a means similar to that shown and explained in fig1 . similarly , the second output port of the power divider 57 provides the reference signal for the control loop 59 which cancels the signal at the second branch of the power divider 54 . the adjustment of phase made in control loop 58 is the phase difference between the reference signal and the signal received by sensor 51 . similarly , the adjustment of phase made in control loop 59 is the phase difference between the reference signal and the signal received by sensor 52 . finally , the difference in phase adjustments made in control loops 58 and 59 gives the phase difference between the signals received by sensors 51 and 52 . thus , any phase introduced at the reference line , including the amplifier or tuned circuit , does not affect the determination of the relative phase between the signals received by sensors 51 and 52 . the arrangement shown in fig4 therefore permits amplification and tuning the reference signal to enable direction finding of weak signals and signals in the midst of co - channel and adjacent channel interferences . the signal processor and display unit , which may be regarded as the system output , processes the value of the angle - of - arrival from the difference in phase angles as obtained from the control loops 58 and 59 . if it is intended to determine the angle - of - arrival θ as well as the frequency of the signal f , one may combine the features of fig2 and 4 . such an arrangement is shown in fig5 . it is seen that fig5 is very similar to fig4 except that two 3 - way power dividers , 64 and 67 in fig5 replace the 2 - way power dividers 54 and 57 respectively , in fig4 . also , a delay line 62 and a third control loop 60 are introduced in fig5 . thus , in fig5 the reference signal is created in three parts . the first and second parts of the reference signal are used to create countersignals that null the signals received by the sensors 51 and 52 and present at the second outputs of the power dividers 53 and 64 through control loops 58 and 59 respectively . the third part of the reference signal from the third output port of the power divider 67 is used to create a countersignal to null the signal at the third output port of the power divider 64 and the delay line l by the control loop 60 . finally , from the adjustments made in control loops 58 , 59 and 60 , the signal processor 61 computes and displays the frequency and angle - of - arrival of the signal . the remainder of the operation of fig5 is the same as that described in fig4 . in some cases , the determination of the direction of an emitter signal may require the measurement of two orthogonal angles such as θ and φ corresponding to azimuthal and elevation angles . for such cases , at least three sensors , not all being on the same plane , are required . again , the sum of the signals received by the sensors can be amplified and tuned to the particular frequency of interest to create the reference signal and to determine the electrical phase angle between the reference signal phase and that of the signal received by each sensor . from these measurements , the common phase of the refertence signal can be eliminated to obtain the differential electric phase between signals received by any pair of sensors and to determine therefrom the two orthogonal angles for the emitter . the above described embodiments , methods , and operational explanations are furnished as illustrations of the principles of the invention and are not intended to define the only embodimentsd possible in accordance with the teachings of the invention . rather , protection under the united states patent law shall be afforded to the invention , as further defined in the claims .