TCAS bearing measurement receiver apparatus with phase error compensation method

A TCAS receiver, including a relative bearing measurement radio receiving apparatus for use with an antenna array having four antennas where each antenna has associated with it, its own receiver capable of demodulating both I and Q components of transmissions from an intruding aircraft.

BACKGROUND OF THE INVENTION 
 This invention relates to a direction finding antenna system. More 
 specifically, it relates to a receiver system in a Traffic/Alert Collision
 Avoidance System (TCAS) which is particularly suited for determining the 
 bearing of a target aircraft relative to a protected aircraft and methods 
 of operation. 
 The TCAS equipment located aboard a protected aircraft periodically 
 transmits interrogation signals which are received by transponders located
 aboard other aircraft, hereinafter referred to as target aircraft, in the 
 vicinity of the protected aircraft. Mode S altitude reporting transponders
 are preferred so that TCAS capabilities can be fully exploited. In reply 
 to the interrogation signals, the target aircraft's transponder transmits 
 a response signal. The TCAS equipment aboard the protected aircraft 
 determines the range of the target aircraft in accordance with the round 
 trip time between transmission of the interrogation signal and receipt of 
 the response signal. Relative bearing to the target aircraft is determined
 from differences in the time to different elements in the TCAS antenna. In
 addition, if the target aircraft is equipped with a Mode C or Mode S 
 transponder, the protected aircraft can determine the altitude of the 
 target aircraft from the content of the response signal. 
 Information in the response signal, as well as information derived from the
 response signal, is used by the TCAS equipment to determine whether there 
 is a threat of collision between the protected aircraft and the target 
 aircraft. The response from each target aircraft is processed individually
 to determine the degree of threat and then, if necessary, an appropriate 
 advisory is issued by the TCAS equipment to the pilots of the protected 
 aircraft to minimize the degree of threat. 
 Relative bearing to the target aircraft may be determined from the response
 signal by a multi-element antenna array, for example, by a four-element 
 antenna array and an associated receiver system. Typically, a TCAS antenna
 consists of an array of four vertically polarized elements. The elements 
 are preferably spaced equally about the circumference of the antenna 
 array, that is geometrically at 90.degree. intervals. A first pair of 
 elements, therefore, is aligned on an axis which is perpendicular to an 
 axis on which the second pair of elements are aligned. Adjacent elements 
 are those which are circumferentially spaced apart by 90.degree. 
 geometrically. Opposite elements are those which are circumferentially 
 spaced apart by 180.degree. geometrically. 
 Conventionally, the relative bearing to the target aircraft is determined 
 by measuring the phase difference of the response signal between opposite 
 element pairs. If both pairs of opposite elements are used, for example, 
 then the phase difference between one opposite element pair is K sin 
 (.beta.) and the phase difference between the other opposite element pair 
 is K cos (.beta.), where K is the maximum phase excursion of the response 
 signal between the elements in the respective opposite pair, and .beta. is
 the angle of the target signal incidence with respect to the axes 
 connecting antenna elements within an element pair. The actual relative 
 bearing is then calculated as follows: 
EQU .beta.=tan.sup.-1 (K sin (.beta.)/K cos (.beta.)) 
 Such a system functions properly as long as K is less than 180.degree. 
 electrical degree in space at the operating frequency. K is related to 
 element spacing. When K is greater than or equal to 180.degree., an 
 ambiguity exists as phase detectors in the receive system are unable to 
 properly distinguish phase differences. In such cases, for example, the 
 phase detector cannot differentiate between measured phase differences of 
 180.degree. and -180.degree.. Under these circumstances, the relative 
 bearing to the intruder aircraft cannot be determined with certainty. This
 ambiguity conflicts with a desire to utilize an antenna which has the 
 greatest phase excursion between opposite elements (i.e. large element 
 spacing) in order to maximize the signal to noise ratio of the system. 
 Also, in a phase only measurement system, the phase error of the 
 measurement means cannot be ignored. For example, some of the receive 
 system induced phase errors cannot be corrected by factory calibration of 
 system equipment since phase variations occur in the system components 
 with varying temperature, age and other variables. 
 Several methods of addressing these phase errors have been proposed in the 
 past. U.S. Pat. No. 5,122,808 issued on Jun. 18, 1992, to Constantinos S. 
 Kyriakos entitled "PHASE ONLY BEARING MEASUREMENT WITH AMBIGUITY 
 CORRECTION IN A COLLISION AVOIDANCE SYSTEM", is one of such methods. 
 While this approach has enjoyed considerable use in recent years, it has 
 several drawbacks. One drawback with this approach is its inability to 
 determine the bearing of an intruding aircraft without receipt of at least
 two or more transmissions from the intruding aircraft. 
 In prior TCAS bearing implementations using phase measuring techniques, two
 or more transmissions were often necessary before a bearing value could be
 computed. Between the transmissions, hardware reconfigurations were 
 required that could introduce errors that could result in errors in 
 relative bearing calculations. 
 When more than one transmission is required to obtain the data needed to 
 calculate the relative bearing, target data points in one transmission 
 must be paired up with corresponding target data points, target for 
 target. Any error in pairing could result in considerable error in bearing
 calculations. One method of reducing the probability of incorrect pairing 
 is to implement digital filtering that operates on several transmissions, 
 but this further extends the time delay before valid relative bearing can 
 be determined. 
 Within a TCAS system, interrogations often occur at the rate of 1 per 
 second. In prior inventions, relative bearing determination is often made 
 after two or more interrogations. Thus, bearing update is often after a 
 delay on the order of a few seconds. Each message transmission from a 
 transponder unit is typically 64 uSec or 120 uSec in length, and is made 
 up of several pulses that are typically 0.5 uSec each in duration. 
 Consequently, there exists a need for improved receiver systems for 
 measuring the bearing of an intruder aircraft. 
 SUMMARY OF THE INVENTION 
 It is an object of the present invention to provide for an improvement in 
 bearing determinations of an intruding aircraft. 
 It is a feature of the present invention to include a four-element antenna 
 array where each antenna element in the array has associated with it, its 
 own receiver. 
 It is an advantage of the present invention to provide for bearing 
 determination without the need for "swap switches" which have been common 
 in prior art TCAS receiver systems. 
 It is another object of the present invention to provide for bearing 
 determinations of intruding aircraft with the reception of a single 
 transmission from the intruding aircraft. 
 It is another feature of the present invention to include receivers 
 dedicated to the antenna elements where each receiver is capable of 
 reception and demodulation of both in-phase (I) and quadrature (Q) 
 components of transmissions incident thereon from an intruding aircraft. 
 It is another advantage of the present invention to eliminate the need for 
 receiving multiple transmissions from an intruding aircraft before a 
 bearing calculation can be made. 
 It is an objective to make all four I and all four Q measurements at the 
 same time to avoid errors that can be introduced when only two I and two Q
 measurements are made at one time and the other two I and two Q 
 measurements are taken at another time, possibly with hardware 
 reconfigurations that can introduce errors. 
 The present invention is a method and apparatus for determining the 
 relative bearing of an intruding aircraft which is designed to satisfy the
 aforementioned needs, provide the previously stated objects, include the 
 above-listed features and achieve the already articulated advantages. The 
 present invention is carried on in a "multiple reception-less" system, in 
 the sense that the requirement to receive multiple transmissions from an 
 intruding aircraft before making a bearing determination of such intruding
 aircraft is eliminated. 
 The present implementation reduces the time delay required to determine 
 relative bearing. 
 With the present invention, relative bearing determination can be made 
 during a reception with only a delay on the order of microseconds. That 
 is, all of the data to provide a full accuracy bearing determination is 
 obtainable from one reception of one pulse. 
 The present invention is capable of acquiring all the data needed to 
 determine relative bearing to full accuracy on one of the 0.5 uSec pulses 
 including the first one. Delay in the digital processing of the data may 
 be a few milliseconds using the digital processing of present day 
 computers resulting in a much shorter delay time to provide an accurate 
 relative bearing measurement output. 
 Because the four phase detectors are in effect connected around the circle 
 of the antenna array, and because I and Q measurements are taken 
 essentially simultaneously, the phase measurement system is a 
 closed-system. This causes cancellation in certain errors. For example, 
 differences in phase of mutual coupling of opposite elements pairs 
 cancels. That is, an antenna array that is not square, but moderately 
 "diamond" in shape, may be used in the system without introducing 
 significant bearing errors. 
 The closed-system resulting from the loop connection of phase detectors 
 allows for considerable variation in antennas from one to another without 
 significantly affecting the accuracy of the system in measuring bearing. 
 For example, the array radius (element spacing) can be changed 
 considerably and the auto calibration algorithm will properly calibrate 
 the system. Thus, TCAS antennas from different manufacturers will function
 in the system even though they may have considerably different design 
 parameters. Software lookup antenna compensation tables are not required 
 to meet the bearing accuracy required for TCAS bearing output. 
 Accordingly, the present invention is a relative bearing measurement radio 
 receiving apparatus for use with an antenna array having four antennas 
 where each antenna has associated with it, its own receiver capable of 
 demodulating both I and Q components of transmissions from an intruding 
 aircraft.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
 Now referring to the drawings, wherein like numerals refer to like matter 
 throughout, and more particularly to FIG. 1, there is shown a highly 
 simplified TCAS receiver/antenna combination, generally designated 100, 
 having a multi-element antenna array 102 which includes antennas 1021, 
 1022, 1023, and 1024. These antennas may be arranged in a circular pattern
 with the antennas being separated by an angular distance of 90.degree. 
 geometrically. Antennas 1021, 1022, 1023, and 1024 are designed to receive
 signals from transponders on board intruding aircraft and to transmit 
 interrogations to transponders. These antennas and others similar to them 
 have been used extensively in the past and are generally well known. The 
 orientation and element spacing of this array of elements can be varied 
 depending upon particular requirements of a system. 
 The set of antenna elements can be oriented with any angular orientation 
 with the offset referenced to the basic square orientation. The angular 
 offset set from the basic square orientation can be removed in the digital
 processing. Increasing the element spacing will increase the accuracy with
 which the bearing can be estimated. But increasing the element spacing 
 creates ambiguities that must be removed to obtain proper calculation of 
 the bearing. Typically, the element spacing will be less than 180 
 electrical degrees in space between adjacent elements, at the operating 
 frequencies of 1030 MHz or 1090 MHz. 
 Also shown in FIG. 1 is a TCAS bearing receiver system generally designated
 106 having receivers 1061, 1062, 1063, and 1064 disposed therein. Disposed
 between antenna 102 and receiver system 106 is a plurality of connection 
 lines 104. Connection lines 104 include individual connecting lines 1041, 
 1042, 1043, and 1044, which connect the antenna/receiver pairs 1021 and 
 1061, 1022 and 1062, 1023 and 1063, and 1024 and 1064. Connecting lines 
 104 should be understood to include all transmission paths between the 
 antenna 102 and the receiver 106 which would include connecting cables, 
 their associated connectors, and signal paths on any circuit cards 
 associated with the system 100 which are disposed between antenna 102 and 
 receiver 106. 
 Receiver 106 includes radio frequency sources 110. Source 110 may be used 
 to calibrate the phase errors in the system 100. Source 110 includes 
 transmitter source 1030 and calibration source 1090 which through switch 
 111 are selectively coupled with antennas 1021, 1022, 1023, and 1024 
 through switches 1081, 1082, 1083, and 1084 respectively. For receiver 
 calibration, the receiver calibration source 1090 is selected. For normal 
 transmit, the transmitter 1030 source is selected. Receivers 1061, 1062, 
 1063, and 1064 are selectively coupled to antennas 1021, 1022, 1023, and 
 1024 respectively. Receivers 1061, 1062, 1063, and 1064 may be any type of
 known receiver architecture which is capable of receiving and demodulating
 both I and Q components of any received signal. Receiver 106 includes 
 intermediate frequency (IF) calibration sources 112 and 114, which may be 
 local oscillators operating at predetermined frequencies. Disposed between
 receiver 1061 and 1062 is phase detector 12. Disposed between receiver 
 1062 and 1063 is phase detector 23. Disposed between receiver 1063 and 
 1064 is phase detector 34. Disposed between receiver 1064 and 1061 is 
 phase detector 41. Phase detectors 12, 23, 34, and 41 are used to measure 
 the relative phase between the outputs of the receivers 1061, 1062, 1063, 
 and 1064 for both their I and Q components. Phase detectors 12, 23, 34, 
 and 41 may be accomplished using various different types of devices; 
 typical circuits that might be used as phase detectors include double 
 balanced diode mixers and Gilbert cell integrated circuit mixers. Phase 
 detector 12 provides an output I.sub.12 and Q.sub.12. Similarly, phase 
 detector 23 provides an 123 output and a Q.sub.23 output. Phase detectors 
 34 and 41 provide I.sub.34 and Q.sub.34 and I.sub.41 and Q.sub.41 outputs 
 respectively. Frequency conversion to the typical IF frequency of 60 MHz, 
 while present, is not shown in simplified diagram FIG. 1. 
 Now referring to FIGS. 1 and 2, there is pictorially shown a signal flow 
 diagram 200 of the process of bearing determination for the present 
 invention which shows phase detector inputs 202, which are output from 
 phase detectors 12, 23, 34, and 41 of FIG. 1. The signals 202 are first 
 processed through the step 204, which makes corrections for bias and gain 
 balancing. This first step 204 may be preceded by an analog to digital 
 conversion. Once step 204 is completed, the following step 206 computes 
 the raw phase difference between the compared receiver adjacent channels. 
 This computed raw phase difference includes phase errors therein which 
 could come from several sources, including errors in the phase detectors 
 themselves and errors relating to transmission path differences between 
 the channels also referred to at times as phase alignment or receiver and 
 antenna cable alignment. Computed raw phase differences is then processed 
 through step 208, which is designed to correct for phase errors resulting 
 from characteristics of the phase detectors. Then in step 210, errors 
 associated with transmission path link differences between the compared 
 transmission paths are corrected. A corrected phase signal is then output 
 for each of the four receiver comparisons. The outputs of the various 
 steps 210 are combined through summer 212 and summer 214 and ultimately an
 angle of arrival of the incident transmission from an intruding aircraft 
 .beta. is determined through step 216. .beta. is the relative bearing of 
 the intruding aircraft. Summer 212 and 214 compute the differences. 
 In the normal operational mode, the processing of the signals from the four
 receivers 1061, 1062, 1063, and 1064 of FIG. 1 is done in parallel and may
 be accomplished from a single transmission from an intruding aircraft. 
 A more detailed review of the steps 204, 206, 208, and 210 follows. The 
 step 204 bias correction and gain adjustment can be accomplished in 
 various ways, using techniques well known in the art. One way of 
 approaching this step may be to consider the following relationships: 
 IBias=.SIGMA.IData(n)/N, QBias=.SIGMA.QData(n)/N. 
 This is the bias offset that is subtracted as a bias correction such that 
 the resulting bias offset is 0. 
EQU I to Q Gain ratio=.SIGMA.[IData(n)-IBias)/.SIGMA.(QData(n)-Qbias] 
 where n=one sample of I or Q data, N=number of samples in one cycle, where 
 one cycle is from the approximately 50 kHz beat note between the 50.975 
 MHz and 60.025 MHz oscillators. Gain ratio between I and Q of the I and Q 
 pairs is then scaled to 1 in the gain correction process. 
 Mathematically, the gain adjustment calculation is the sum of the ratios 
 rather than ratios of the sum. The sum of ratios is used to produce an 
 averaged estimate of the gain difference between the I and Q channels. 
EQU I to Q Gain ratio=SUM[(Idata(n)-Ibias)/(Qdata(n)-Qbias)] 
 for one cycle of I or Q data. 
 During this calibration process, one cycle of each phase detector is 
 sampled into separate buffers so that each buffer starts at 0 degrees of 1
 and 0 degrees of Q. The gain difference is then used to perform the gain 
 correction. 
 The bias offset and gain correction relationships may be facilitated by the
 use of two oscillators 112 and 114 (FIG. 1) which may be turned on to 
 create a 50 kHz beat note at all four I/Q phase detectors. Sweeping the 
 phase detectors 12, 23, 34, and 41 in this manner allows the offset of 
 each I and Q channel to be removed and the gain of each pair of I and Q to
 be set equal. 
 This is done with the phase detector being swept with the 59.975 MHz and 
 60.025 MHz oscillators. The 50 kHz beat note was chosen as a compromise to
 both minimize errors associated with short term and long term drift of the
 oscillators, while allowing enough sampling resolution to achieve a high 
 degree of correction accuracy. The beat frequency is not a critical issue.
 There is a wide range of beat frequencies that could have been chosen that
 would result in proper performance. Low beat frequencies would require 
 excessive time to sample a full cycle of the beat frequency while possibly
 introduce errors from oscillator drift. 
 After bias offset and compensation, the arc tangent of the ratio of each 
 I/Q pair is computed at block 206. Once the uncorrected computed phase at 
 block 206 is generated, the next step is to correct for phase detector 
 response or linearity errors in accordance with step 208. Any method of 
 correcting for phase errors due to the phase detectors 12, 23, 34, and 41 
 themselves could be utilized. 
 Because the phase detectors do not output perfect sine and cosine waves 
 when swept, a phase detector linearity compensation must be made. This is 
 accomplished at block 208 in FIG. 2. Since the phase detectors are sampled
 at constant intervals, the output of each Arctan process should be a 
 linear slope from 0 to 360.degree.. That is, if the phase detectors were 
 perfect and output sine and cosine waves, the output would be a constant 
 slope. Any differential from the constant slope is then the correction 
 needed for each Arctan result. 
 To perform the phase detector correction for phase detector linearity, 208,
 oscillators 112 and 114 are turned on. Oscillators 112 and 114, when 
 turned on, generate phase signals at the I/Q phase detector outputs which 
 sweep the detectors with a constant rate of change (nominal 50 kHz). 
 Characterizing the phase error in the phase detectors may be accomplished 
 by analyzing the error between the actual phase detector response relative
 to an ideal response. One method of doing this is to use the zero degree 
 crossing of the 50 kHz beat note to synchronize the actual phase curve 
 with the ideal curve, store the error (actual minus ideal) from 0 to 360 
 degrees (one cycle of the beat note), perform inverse interpolation on the
 error data such that the error data may be indexed using the uncorrected 
 phase, and performing averaging on the error curves to lessen the affects 
 of phase discontinuities in the raw measurements. 
 The hardware following the I and Q detectors consists of an analog to 
 digital converters on each I and each Q channel output from the receivers 
 with the resulting numerical digitized values operated on by a digital 
 signal processor computer. This signal processor consists of the typical 
 components of the CPU (Central Processor Unit) random access memory (RAM) 
 and the program memory in read only memory (ROM). 
 Computing the raw phase between adjacent elements is a digital operation. 
 Software techniques apply in this case. To compute raw phase between 
 adjacent elements perform the following for each adjacent element pair. 
EQU .phi..sub.12 (n)=UNWRAP(ARCTAN(I(n)/Q(n))) 
 Where (I(n) and Q(n) are gain and bias balanced and the UNWRAP function 
 takes the {-90, 90} degree ARCTAN result in conjunction with the signs of 
 I(n) and Q(n) to produce a phase sample which is unambiguous from {0, 360}
 degrees. This approach provides a concise result and avoids the use of a 
 phase correction table. NOTE: The unwrap function is well known in the 
 art, including a definition such as: 
 UNWRAP (P) unwraps radian phases P by changing absolute jumps greater than 
 pi to their 2 *pi complement. It unwraps along the first non-singleton 
 dimension of P. P can be a scalar, vector, matrix, or N-D array. 
 A well-known software package, "Mathlab", could be used, but others could 
 be used as well. This approach provides a concise result and avoids the 
 use of a phase correction table. 
 Since I(n) can be related to a sine function and Q(n) to a cosine function 
 because of quadrature, the division results in a tan function since 
 tan=sine/cosine. The fundamental concept is that of performing the arctan 
 while preserving the quadrant information. This is similar to the ATAN2 
 function employed in several software programs. 
 Once the corrections are made for the phase detector errors, then the 
 channel-to-channel phase offset or phase misalignment corrections are made
 in accordance with step 210. This phase offset is due to pair-to-pair time
 delay differentials in the sum of the antenna feed line coaxial delays 
 plus the internal receiver channel time delays. Time delays result in 
 corresponding phase shifts. Various methods of performing phase correction
 could be applied. One method of performing step misalignment 210 is as 
 follows: 
 The following determines the difference in time delay from an antenna 
 element to a corresponding phase detector in relation to the delay from an
 adjacent antenna element to the same phase detector. 
 Assume the antenna is symmetrical with equal element-to-element spacing and
 that the two opposite-to-opposite spacings are equal. 
 Step 1. Transmitter/receiver/calibration switches 1071-1074 and 1081-1084 
 are set so antenna element 1024 transmits a calibration signal at 1090 MHz
 to antenna elements 1021 and 1022. Assume the special case where 
 L1=L2=L3=L4 where L1, L2, L3, and L4 are the cable lengths for cables 
 1041-1044 respectively. Additionally, assume that the four receivers 
 1061-1064 have identical phase delays (can also be described as time 
 delays) therein which are denoted as RL1, RL2, RL3, and RL4 respectively. 
 Also assume that for this special case, the difference in transmission 
 paths between opposite and adjacent elements of the antenna is 60 
 electrical degrees for signals at 1090 MHz. 
 Step 2. Read the output of phase detector 12. 
 Step 3. With the switches set for antenna element 1024 to transmit to 
 antenna elements 1021 and 1022, then phase detector 12 will read 
 -60.degree.. 
 Step 4. Switch the transmitter/receiver/calibration switches so that 
 antenna element 1024 is off and element 1023 is now transmitting. 
 Step 5. Read the output of phase detector 12 which will be +60.degree. in 
 the example. 
 Step 6. Determine the average of readings. The difference (L1+RL1)-(L2+RL2)
 is then the average of the two readings at the phase detector 12 which in 
 this special case is 0.degree.. 
 Step 7. Now assume that the same procedure is repeated except that L1 is 
 20.degree. longer than L2 at 1090 MHz and RL1 is 10.degree. longer than 
 RL2 at 1090 MHz. With antenna element 1024 transmitting, phase detector 12
 would have a reading of -30.degree.. Then switching to transmitting from 
 antenna element 1023 with antenna element 1024 off, the reading on phase 
 detector 12 would be +90.degree.. The average of these phase readings is 
 +30.degree., and this corresponds to (L1+RL1)-(L2+RL2). 
 Step 8. This average is used as a phase reference point for receptions on 
 antenna element 1021 with respect to receptions on antenna element 1022. 
 This +30.degree. reading is the same that would be produced if a 
 calibration element were located at the very center of the antenna array 
 and driven at 1090 MHz. This 30.degree. bias is removed by digital signal 
 processing carried on in step 210 of the angle of arrival computation 
 shown in FIG. 2. 
 ##EQU1## 
 Where, .PHI. is phase detector corrected angle and .PSI. is phase detector 
 center. 
 Regrouping 
 ##EQU2## 
 where, SinOffset :=.PSI.41-.PSI.23 CosOffset :=.PSI.34-.PSI.12 
 The estimate of the angle of aircraft of .beta. in step 216 is then 
 calculated using well-known techniques, such as the following: 
 Refer to FIG. 1 Looking at J1-J2 cable pair 
EQU .PSI.12.sub.A :=(M.sub.31 +L.sub.1 +RL.sub.1)-(M.sub.23 +L.sub.2 +RL.sub.2)
EQU .PSI.12.sub.B :=(M.sub.41 +L.sub.1 +RL.sub.1)-(M.sub.42 +L.sub.2 +RL.sub.2)
 Assuming adjacent mutual coupling phases are equal gives, 
EQU .PSI.12:=1/2.multidot.[(M.sub.31 -M.sub.42)+2.multidot.[(L.sub.1 
 +RL.sub.1)-(L.sub.2 -RL.sub.2)]] 
 Looking at J3-J4 cable pair 
EQU .PSI.34.sub.A :=(M.sub.31 +L.sub.3 +RL.sub.3)-(M.sub.41 +L.sub.4 +RL.sub.4)
EQU .PSI.34.sub.B :=(M.sub.23 +L.sub.3 +RL.sub.3)-(M.sub.42 +L.sub.4 +RL.sub.4)
 Assuming adjacent mutual coupling phases are equal gives, 
EQU .PSI.34:=1/2.multidot.[(M.sub.31 -M.sub.42)+2.multidot.[(L.sub.3 
 +RL.sub.4)-(L.sub.3 -RL.sub.4)]] 
 CosOffset :=.PSI.34-.PSI.12 
EQU CosOffset :=[(L.sub.3 +RL.sub.3)-(L.sub.4 +RL.sub.4)]-[(L.sub.1 
 +RL.sub.1)-(L.sub.2 +RL.sub.2)] (Equation 3) 
 By symmetry, a similar equation results for SinOffset. 
 Equation 2 provides a comprehensive description of operation providing 
 bearing information from all element pairs. CosOffset is obtainable from 
 equation 3 and SinOffset is obtainable from a similar equation. The path 
 phase differences, for example (L1+RL1)-(L2+RL2), which is needed to 
 determine CosOffset in equation 3, are obtainable from the calibration 
 process described earlier in relation to FIG. 1. 
 Once all of the path phase differences are determined, SinOffset and 
 CosOffset can be determined, and equation 2 is then used to calculate 
 corrected angle of arrival (AOA) or relative bearing. Once SinOffset and 
 CosOffset are known, the system is switched from Calibration mode to 
 normal bearing measurement mode. At that point, with SinOffset and 
 CosOffset known, incoming reading from the four phase detectors are fed in
 this equation in the signal processor. The IBias and QBias offsets are 
 applied to each corresponding phase detector reading as is the Gain 
 corrections, and the phase detector linearity corrections, before 
 application to the process of equation 2. 
 It is thought that the method and apparatus of the present invention will 
 be understood from the foregoing description and that it will be apparent 
 that various changes may be made in the form, construction, steps and 
 arrangement of the parts and steps thereof, without departing from the 
 spirit and scope of the invention or sacrificing all of their material 
 advantages. The form herein described being a preferred or exemplary 
 embodiment thereof.