"""Strapdown"" induction compass transmitter with compensation for heading errors due to the vertical component of the Earth's magnetic field and due to two cycle error during turns and during climbing and diving maneuvers"

The invention relates to an apparatus for compensating a "strapdown" induction compass transmitter to eliminate heading errors during turns and during climbing and diving maneuvers which are due to the vertical component of the Earth's magnetic field and those due to the horizontal component of the Earth's field perpendicular to the axis of tilt. Instabilities and anomalies such as "Northerly Turning Error" which are due to the vertical component of the Earth's magnetic field are thus eliminated or minimized as is two cycle error which is due to the Earth's horizontal field during these same maneuvers. The vertical field roll compensating signal, to compensate for turn induced errors, is made proportional to the product of the Earth's magnetic field M, the sine of the dip angle D, and the sine of the bank or roll angle .phi.. The vertical field pitch compensating signal, to compensate for errors induced by climbing or diving maneuvers, is made proportional to the product of the sine of the angle .phi., the Earth's magnetic field M, and the sine of the dip angle D. The roll compensating signal is combined by summation with the demodulated signals from the sine .psi. signal processing channel (i.e., the signal from the compass transmitter windings which sense the field along the athwartships axis. The pitch compensating signal is combined by summation with the demodulated signal from the cos .psi. channel (i.e., the signal from the compass transmitter windings which sense the field along the fore/aft axis). Since pitch angle .theta. and bank angle .phi. (as well as their trigonometric functions sin .phi. and sin .theta.) can be readily obtained from the aircraft vertical (roll and pitch) gyroscopes and dip angle D is known for any latitude and longitude, the compensating signals can be easily generated and applied to the signal processing channel coupled to the output signal processing channels from the compass transmitter to cancel vertical field error. In an alternative embodiment compensation for two cycle error is provided by generating signals proportional to the cosine of the roll angle .phi. and the cosine of the pitch angle .theta.. The two cycle compensating signals are combined with the vertical field error corrected signals from the compass transmitter by multiplication to cancel two cycle error.

The instant invention relates to a magnetic heading reference system and 
more particularly, to one utilizing a "strapdown" induction compass 
transmitter which is compensated to minimize or eliminate heading errors 
during turns, climbs and dives due to vertical field error and two cycle 
error. 
Normally, the heading output for an aircraft compass system is obtained 
from a directional gyro whose heading is slowly corrected to agree with 
the heading provided by induction compass transmitter. This type of 
directional heading output system is complementary in that the short term 
stability and accuracy of the gyroscope is combined with the long term 
accuracy of the compass transmitter so that the overall system 
incorporates the best features of each. One class of induction compass 
transmitters used as aircraft magnetic references are pendulous in order 
to assure that the sensing element (i.e., the magnetometer windings) 
remains horizontal during non-accelerating straight flight within the 
pendulous tilt freedom of the device (which is normally in the range of 
.+-. 27.degree.). Under these conditions the induction compass is 
insensitive to the vertical component of the Earth's field. 
In a typical induction compass transmitter, the horizontal component H of 
the Earth's magnetic field M is resolved along the ship's axes and can 
then be sensed and utilized to produce an output signal which represents 
the heading of the aircraft with respect to magnetic North. Thus, the 
Earth's horizontal component H can be resolved along the aircraft fore/aft 
(roll) and athwartships (pitch) axes so that the heading indicated by the 
compass transmitter is then represented by the arc-tangent of the 
athwartships component H.sub.P of the Earth's horizontal field divided by 
the fore/aft component H.sub.R as sensed in the plane of the sensing 
elements. 
However, because of the pendulous suspension, the induction compass 
transmitter is susceptible to tilt during turns and during linear 
acceleration of the aircraft. This, in turn, produces errors in the sensed 
direction of magnetic North and in indicated heading. That is any 
acceleration due to speed change, or the centripetal acceleration imposed 
during a turn, causes the plane of the sensing element of the compass 
transmitter to be displaced from the horizontal. Thus, during a 
coordinated turn, the pendulous element assumes a lateral tilt angle which 
agrees with the bank angle of the aircraft; or becomes some other lateral 
angle if the turn is not coordinated. In the case of acceleration or 
deceleration due to speed changes, the pendulous element is tilted in a 
vertical plane so as to simulate the effects of rotation about the pitch 
axis. Because of the tilting of the plane of the compass transmitter under 
these conditions, not only is the sensed horizontal component normally 
reduced, but in addition, a component of the Earth's vertical field is 
sensed. If the compass is "strapped down," i.e., non pendulous and rigidly 
secured to the aircraft frame, on the other hand, there is no tilt during 
acceleration due to speed changes, but the compass also tilts during 
climbs and dives. The vertical Earth's field component is therefore sensed 
along the athwartships axis during turns and along the fore/aft axis 
during climbs or dives. This sensed vertical component adds vectorially to 
the sensed horizontal field component and, in the general case, results in 
erroneously sensing of magnetic North. 
Tilt of the induction compass sensing element produces errors from a 
combination of two causes. 
The first of these is a two cycle error which is developed whenever there 
is a component of the Earth's horizontal magnetic field perpendicular to 
the axis of tilt together with a component along the axis of tilt. The 
perpendicular component is reduced in magnitude as a function of the angle 
of tilt when projected on to the plane of the sensing coil. This reduced 
component when recombined with the unchanged horizontal component measured 
along the axis of tilt produces an apparent vectorial shift in the sensed 
direction of the field in the plane of the coil. Two cycle error is a 
function of both the heading angle .psi. and the angle of tilt (bank angle 
.phi. or pitch angle .theta.). It has the same magnitude for all magnetic 
field dip angles D and is normally small. 
The other tilt induced error occurs because the vertical component of the 
Earth's magnetic field projects on the plane of the tilted coils and adds 
vectorially to the sensed horizontal component. This vertical field error, 
however, varies with magnetic field dip angle D and as a result can vary 
widely. An angular tilt about the aircraft axis during turns causes this 
second error source to produce what is termed "Northerly Turning Error" 
and can induce heading anomalies and ambiguities as well as a continuous 
oscillation when attempting to straighten out on a northerly heading when 
in the Northern Hemisphere, and similarly, when attempting to straighten 
out on a southerly heading in the Southern Hemisphere. The nature of this 
error which is due to the vertical component of the Earth's magnetic field 
as the aircraft turns, may be understood better by considering the 
following. 
Assume that an aircraft in a coordinated right turn attempts to level out 
on a North heading using the induction compass transmitter, whether 
pendulous or "strapdown," as a reference. The compass transmitter tilts to 
the same right wing down attitude as does the aircraft. When on a North 
heading, a portion of the Earth's vertical field vector now passes from 
West to East in the plane of the compass transmitter, vectorially adding 
to the actual sensed horizontal component and making it appear that 
magnetic North is to the East of its actual location. Consequently, the 
aircraft continues to turn beyond North before levelling off. Once level, 
North is now correctly indicated to be to the West and the aircraft must 
to into a left bank for a heading correction. A portion of the Earth's 
vertical field vector now passes from East to West in the plane of the 
compass transmitter, vectorially adding to the actual sensed horizontal 
component in the opposite sense thereby making it appear as if North is to 
the West of its actual location. Again, the aircraft continues to turn 
beyond true magnetic North before levelling off. This situation continues 
making it virtually impossible to obtain or maintain the desired constant 
North heading. 
It is customary, therefore, in conventional slaved aircraft compass systems 
to interrupt compass slaving during turns in order to avoid the 
oscillating condition about the northerly heading. This vertical field 
error often causes the compass mode of operation (available on some 
compass systems for emergency use when a directional gyro has failed) to 
become literally useless during turns unless dip angle is relatively 
small. Since dip angle in the middle of the Continental U.S. is 
approximately 70.degree., it can be seen that this is a serious problem in 
aircraft navigation. 
Similar errors are also developed in pendulously mounted compass 
transmitters during acceleration due to speed changes because the 
pendulous compass transmitter tilts about the aircraft pitch axis. For 
most aircraft large tilt angles which are associated with large 
accelerations are of a relatively short duration so that the problem is 
normally somewhat less severe than that which occurs during turns of the 
aircraft. Even so, compass slaving is frequently disconnected on aircraft 
during acceleration to prevent error buildup. Again, compass mode 
operation during acceleration may also be severely affected. 
A "strapdown" induction compass transmitter, as pointed out previously, is 
not tilted because of acceleration due to speed changes. It is, however, 
affected by the Earth's vertical field component while climbing or diving. 
During a climb, a portion of the Earth's vertical field vector passes from 
fore to aft in the plane of the compass transmitter, vectorially adding to 
the actual horizontal component sensed along the fore/aft axis thereby 
making it appear that magnetic North is to the East of its actual location 
when heading West in the Northern hemisphere. During a dive, on the other 
hand, a portion of the Earth's vertical field passes from aft to fore in 
the plane of the compass transmitter vectorially adding to the actual 
sensed horizontal component in the opposite sense. As a result, indicated 
heading shows North to the West of its actual location. 
In a recently filed application entitled "A Strapdown Induction Compass 
Transmitter with Compensation for Heading Errors due to the Vertical 
Component of the Earth's Magnetic Field During Turns and During Dives or 
Climbs" Ser. No.: 729,411, Filed: Oct. 4, 1976, in the name of Gerald L. 
Sullivan, and assigned to the General Electric Company, the assignee of 
the present invention, a compensating system for a "strapdown" compass 
transmitter is described in which a control signal equal to the product of 
the sine of the magnetic field dip angle (sin D) the tilt or bank angle 
(sin .phi.) and the Earth's magnetic field (M) is generated and utilized 
to drive a current directly through the sensing windings of the compass 
transmitter or through auxiliary windings to generate a flux field which 
cancels out the sensed flux due to the vertical component of the Earth's 
field during turns. As a result, the output from the induction compass 
during a turn is essentially free of errors due to the vertical component 
of the Earth's magnetic field, thereby minimizing or eliminating 
hemispherical turn errors of the type usually referred to as "Northerly 
Turning Errors" during turns. A further control signal equal to the 
product of the magnetic field angle (sin D), the pitch angle (sin .theta.) 
and the Earth's magnetic field M is generated and utilized to drive a 
current directly through the sensing windings of the compass transmitter 
which sense the fore/aft component of the Earth's horizontal field or 
through auxiliary windings to generate a flux field which cancels the 
sensed flux due to the vertical field during climbs and dives. The output 
from the induction compass during a climb or during a dive is thus 
essentially free of errors dur to the vertical component of the Earth's 
magnetic field, thereby minimizing or eliminating hemispherical turn 
errors during such maneuvers. This, in turn, makes it possible to use the 
magnetic compass for heading purposes without the need for a directional 
gyro. 
While the arrangements shown in the aforesaid Sullivan application are very 
effective in compensating a "strapdown" compass transmitter for errors due 
to the vertical component of the Earth's magnetic field, both during turns 
and during climbs and dives, there are some practical problems associated 
therewith. By applying the compensation current directly to the induction 
compass transmitter windings or to a separate compensating winding, 
blocking capacitors must be provided between the compass transmitter and 
the signal receiver elements leading to the heading indicator or control 
components of the system. Furthermore, there is also a need for 
maintaining a high impedance source for the compensation signal in order 
to avoid scale errors due to loading. The instant invention is based on 
the recognition that the desired compensation both for a vertical field 
error and two cycle errors can be achieved by injecting the DC 
compensation signals into the transmitter sin .psi. and cos .psi. output 
channels, i.e., the signal processing channels in which the signals 
representing the field sensed along the athwartships and the fore/aft axis 
of the aircraft are processed. By combining the DC compensating signal 
with a demodulated DC signal, the effects of vertical field error and two 
cycle error can easily be cancelled. This arrangement avoids problems 
associated with direct injection of currents into the compass induction 
transmitter sensing windings or associated compensation windings. 
It is therefore a principal objective of the invention to provide an 
arrangement for compensating a "strapdown" induction compass transmitter 
to eliminate heading error turns and during climbs and dives caused by the 
vertical component of the Earth's magnetic field by compensating the 
demodulated signal from the transmitter in its signal processing channel 
exterior to the induction compass transmitter. A further objective of the 
instant invention is to provide a compensated "strapdown" induction 
compass transmitter in which heading errors caused by tilting of the 
sensing elements are minimized or reduced entirely. 
Still another objective of the invention is to provide a compensated 
"strapdown" induction compass transmitter in which heading errors in turns 
and during climbs and dives due to two cycle error are eliminated by 
compensating demodulated signals from the compass transmitter in a signal 
processing channel outside of the transmitter. 
Yet a further objective of the invention is to provide a compensated 
magnetic compass heading system having roll and pitch compensation to 
eliminate vertical field errors and two cycle errors and produce an 
accurate heading indication without the need for a directional gyroscope, 
in which compensation is achieved outside of the induction compass 
transmitter. 
Other objectives and advantages of the instant invention will become 
apparent as the description proceeds. 
Briefly, in accordance with one aspect of the invention, roll and pitch 
compensation of a "strapdown" induction compass transmitter during turns 
and while climbing and diving is realized through compensation in a signal 
channel external to the induction compass transmitter. Compensating 
signals are generated which are proportional to the errors induced by the 
Earth's vertical field during these maneuvers without sensing the vertical 
field directly are used to cancel the effect of the Earth's vertical field 
component. The compensating signals are derived from the Earth's magnetic 
field M (a known quantity) the magnetic dip angle D (a known quantity for 
any given latitude and longitude and the tilt angle (roll and pitch) which 
is a sensed quantity readily obtainable from the aircraft vertical 
gyroscope. The turn compensating signal has a magnitude M sin D sin .phi. 
which by definition, is equal to V sin .phi. the vertical feild error due 
to tilting of the compass transmitter windings during turns. This DC 
compensating signal is combined with the demodulated signal from the sin 
.psi. (heading) output channel, i.e., the signal representing the output 
from those windings which sense the Earth's magnetic field along the 
athwartships axis. The compensating signal for vertical field error during 
climbs or dives has a magnitude equal to M sin D sin .theta. which, by 
definition, is equal to V sin .theta. (the vertical field error in climbs 
and dives). This DC compensating signal for vertical field errors during 
climbs and dives is combined with the demodulated signal from the cos 
.psi. output channel of the compass transmitter, i.e., the output from 
those windings of the compass transmitter which sense the Earth's magnetic 
field along the fore/aft axis of the vehicle. Thus, errors introduced 
during climbing or diving due to a vertical component of the Earth's field 
are eliminated eliminating instabilities such as "Northerly Turning 
Errors" during these maneuvers. The compensated, demodulated, DC compass 
transmitter signals may then be remodulated in any suitable fashion to 
provide a suitable output signal for a heading indicating or a control 
system. 
In an alternative embodiment, the compensated, demodulated signal in both 
the sin .psi. and cos .psi. channels may be processed further to 
compensate for two cycle errors by introducing DC signals proportional to 
the cosine the cos of the roll and pitch angles (cos .phi., cos .theta.). 
The two cycle error compensating signals are combined, with the signal 
which has been previously compensated for vertical field errors. The twice 
compensated signal is free of two cycle error and free of errors due to 
the vertical component of the Earth's magnetic field.

In order to understand the manner in which the instant invention is used to 
compensate a "strapdown" induction compass transmitter to reduce or 
eliminate heading errors caused by the vertical component of the Earth's 
magnetic field, it will be revealing to discuss initially the relationship 
between the Earth's magnetic field and the magnetic field components 
sensed by a "strapdown" induction compass both in level flight, during 
level turns, and during climbs and dives when tilting of the aircraft axes 
and of the compass transmitter produces changes in the sensed field. Thus, 
FIG. 1 illustrates an aircraft 10 in level flight in a horizontal plane 
(illustrated generally at 11) in a direction shown by the arrow 12 which 
in the particular instance, is the direction of the aircraft with respect 
to the North directed horizontal domponent H of the Earth's magnetic field 
M. The Earth's magnetic field M is a vector quantity shown at 13 
consisting of a North directed horizontal component H shown at 14 and a 
vertical component V shown at 15. The angle measured from the horizontal 
component H to the Earth's magnetic field vector M is termed the dip angle 
D, with the dip angle being considered positive when the Earth's magnetic 
field dips below the horizontal, as it does in the Northern Hemisphere. 
Consequently, the vertical component of the Earth's magnetic field is 
considered positive when directed downward. The direction of the Earth's 
magnetic field M, i.e., the dip angle D varies with latitude with the dip 
angle being zero (0.degree.) at the magnetic equator and becoming 
90.degree. at the North magnetic pole. The analytical relationship between 
the Earth's magnetic field and the horizontal and vertical components of 
that field are therefore as follows: 
EQU H = M cos D (1) 
EQU v = m sin D (2) 
EQU tan D = V/H (3) 
aircraft magnetic heading is defined as a horizontal angle .psi. (positive 
in a clockwise direction from magnetic North) shown generally at 16, 
between the horizontal projection of the aircraft fore/aft or roll axis 
shown at 17, and magnetic north. The horizontal component of the Earth's 
magnetic field may, in turn, be resolved along the aircraft axes into two 
orthogonal horizontal components H.sub.R and H.sub.P which are functions 
of magnetic heading angle .psi.. H.sub.R is a component parallel to the 
horizontal projection 17 of the aircraft fore/aft or roll axis and is 
shown by the arrow 18 and is considered positive when directed forward, as 
illustrated. H.sub.P is a component parallel to the horizontal projection 
19 of the aircraft athwartships or pitch axis. H.sub.P is shown by the 
arrow 20 and is considered positive when directed to port. With the 
westerly heading shown in FIG. 1, the sensed athwartships component 20 is 
directed to starboard and is therefore considered to be negative. 
The analytical relationships between the orthogonal components H.sub.R and 
H.sub.P along the aircraft axes, the heading angle .psi. and the 
horizontal component H of the Earth's magnetic field may be defined as 
follows: 
EQU .psi. = actual magnetic heading 
EQU H.sub.P = H sin .psi. (4) 
EQU H.sub.R = H cos .psi. (5) 
EQU Tan .psi. = (H.sub.P /H.sub.R) (6) 
the heading indicated by an induction compass transmitter which has a 
plurality of windings to sense the athwartships and the fore/aft component 
of the horizontal component of the Earth's magnetic field may generally be 
represented by the arc tangent of the athwartships (positive to port) 
component A of the Earth's magnetic field divided by the fore/aft 
(positive forward) component F of the Earth's field as sensed in the plane 
of the coils or windings of the compass transmitter. When the aircraft is 
in level flight in the horizontal plane as shown in FIG. 1, the two 
orthogonal components of the horizontal field H are sensed accurately and 
produce an accurate magnetic heading indication. Furthermore, with the 
aircraft in level flight, the vertical component V of the Earth's field as 
illustrated at 15 is not sensed in the plane of the compass transmitter 
sensing windings and has no effect on the magnetic output heading. 
With a "strapdown" induction compass transmitter, the transmitter, of 
course, is rigidly fastened to the frame of the aircraft. The plane of the 
transmitter sensing windings therefore tilts with the aircraft. That is, 
with a "strapdown" compass transmitter, the plane of the transmitter is 
tilted in a vertical plane as the aircraft rotates about its pitch axis 
while climbing or diving and is rotated about the roll axis and tilts to 
the aircraft bank angle as the aircraft goes into rotation about its pitch 
axis as in the case of a climb or a dive, is illustrated in perspective in 
FIG. 2. The aircraft 10 is still flying with a westerly heading with 
respect to magnetic North N as shown by the arrow 12. The aircraft is 
shown as having been rotated about its pitch axis so as to be in a 
climbing attitude. That is, aircraft 10 is shown with its fore/aft axis 17 
rotated through an angle .theta. in the plane DECF so that it is no longer 
in level flight in the horizontal plane ACBD. The fore/aft component 
H.sub.R of the horizontal field component H of the Earth's magnetic field, 
which is shown at 18, is sensed by the induction compass transmitter which 
has also been rotated through the angle .theta.. The sensed fore/aft 
component is reduced as a function of the cos .theta.. The fore/aft 
component due to the horizontal component of the Earth's field is thus: 
EQU F.sub..theta.H = H.sub.R cos .theta. (7) 
With the compass transmitter tilted to the pitch angle .theta., it can be 
seen that the Earth's vertical field component is no longer perpendicular 
to the plane of the sensing windings and a component of the Earth's field, 
shown at 21, is sensed along the fore/aft axis 17 of the aircraft and is 
equal to V sin .theta.. In a climb the vertical field component is 
directed rearward and thus negative in the Northern Hemisphere, as 
illustrated. 
Thus,, F.sub..theta.V = -V sin .theta.. The total fore/aft component sensed 
in the tilted plane of the compass transmitter for a positive (climb) 
pitch angle .theta. is therefore: 
EQU F.sub..theta. = F.sub..theta.H + F.sub..theta.V = H.sub.R cos .theta. - V 
sin .theta. (8) 
EQU F.sub..theta. = H cos .psi. cos .theta. - V sin .theta. (9) 
The athwartships component A sensed by the compass transmitter is not 
affected by the vertical component of the Earth's field during a climb (or 
dive) and remains: 
EQU A.sub..theta. = H.sub.P sin .psi. (10) 
If the aircraft also goes into a turn rotates through a bank angle .phi. 
the vertical component of the Earth's field is no longer perpendicular to 
the plane of the compass transmitter windings which measure the 
athwartships axis and a component of the vertical field is sensed which is 
proportional both to the roll or bank angle .phi. as well as to the pitch 
angle .phi.. A component of the horizontal field along the fore/aft axis 
is sensed along the athwartships axis. The following relationships fully 
define F and Ain terms of H.sub.R, H.sub.P, .phi., .theta. and V for a 
"strapdown" induction compass transmitter during non-level turns: 
EQU F = H.sub.R cos .theta. - V sin .theta. (11) 
EQU A = - H.sub.R sin .phi. sin .theta. +H.sub.p cos .phi. - V sin .phi. cos 
.theta. (12) 
Equation (12) may be rewritten in terms of H, V, .theta. and .phi. as 
follows: 
EQU F = H cos .psi. cos .theta. - V sin .theta. (13) 
EQU A = -H cos .psi. sin .phi. sin .theta. + H sin .psi. cos .phi.- V sin .phi. 
cos .theta. (14) 
Using the subscript .phi. to designate F, A and .psi. during a level turn, 
i.e., .theta.= 0 then the field sensed by a "strapdown" transmitter is 
defined by the following equations: 
EQU F.sub..phi. = H cos .psi. (15) 
EQU A.sub..phi. = H sin .psi. cos .phi. -V sin .phi. (16) 
##EQU1## 
EQU Tan.psi..phi. = Tan.psi.cos.phi. - (Vsin.phi./Hcos.psi.) (18) 
But V/H - Tan D 
Hence: 
##EQU2## 
.psi..sub. 
The first expression on the right hand side, tan .psi. cos .phi. represents 
the two cycle error in that it is a function of both the heading angle 
.psi. and the bank or roll angle .phi.. The second expression on the right 
hand side represents the vertical field error and is a function of the dip 
angle D, i.e., vertical field error = tan D (sin .phi./cos .psi.). 
Since dip angle varies with latitude from zero (0.degree.) at the equator 
to 90.degree. at the magnetic north pole, this vertical field error can 
vary substantially and produce heading errors which manifest themselves as 
turning problems. These problems, generally referred to as "Northerly 
Turning Errors," include heading anomalies and ambiguities if the bank 
angle equals or exceeds a critical value and results in oscillations about 
the desired heading if the bank angle is below the critical value. 
Briefly, if the bank angle exceeds the complement of the dip angle, it is 
not possible to find and indicate all headings since the compass 
transmitter will then only indicate headings in a limited range no matter 
what the actual heading is. The problem is at its most severe when 
attempting a turn while on a direct East ((9.degree.) or West 
(270.degree.) heading. On such an East or West heading, if the bank angle 
exceeds the complement of the dip angle, there can be a complete reversal 
of the heading indication. Thus, on an East (90.degree. ) heading, a right 
wing down turn in which the bank angle exceeds the complement of the dip 
angle, causes the compass transmitter indication to reverse 180.degree. 
and indicate a West (270.degree.) heading. Similarly, while on a West 
(270.degree.) heading a left wing down turn in which the bank angle 
exceeds the complement of the dip angle causes the compass transmitter to 
indicate an East (90.degree.) heading. 
If the bank angle is exactly equal to the complement of the dip angle then 
the output of the compass transmitter becomes indeterminate on these 
headings since it no longer senses any magnetic field and all heading 
indication is lost. The manner in which these anomalies and ambiguities 
occur when the bank angle equals or exceeds the critical angle (i.e., the 
complement of the dip angle) will be illustrated in connection with an 
aircraft on an East or West heading since this represents a "worst case" 
situation. 
For an East and West heading, the sensed for/aft component F of the Earth's 
horizontal field obviously goes to zero, i.e., F.sub..phi. = 0. For an 
East heading (East = 90.degree.) the value of the sin of heading angle, 
i.e., sin .psi. = sin 90.degree. = +1. For a West heading (West = 
270.degree.) sin .psi. = sin 270.degree. = -1. Thus, on an East heading 
the sensed athwartships component A.sub.100, as defined in Equation (16) 
becomes zero, when V sin .phi. = H sin .psi. cos .phi.; i.e., when the 
vertical field error equals and is in an opposite direction to the sensed 
horizontal component. 
Since sin = +1 for an East heading, A.sub..phi. = 0 when: 
EQU V sin .phi. = H cos .phi. (20) 
Transposing Equation (20) becomes 
EQU H/V = (Sin .phi./Cos .phi.) (21) 
By trigonometric transformation, Equation (21) becomes: 
EQU (H/V) = Tan .phi. (22) 
However, since (H/V) = COT D then COT D = Tan .phi.. But COT D = Tan 
(90.degree.-D) 
EQU therefore, Tan .phi. = Tan (90.degree.-D) (23) 
EQU or .phi. = 90.degree.-D. (24) ps 
In other words, for a given dip angle the induction compass transmitter 
heading becomes indeterminate in an East heading in the Northern 
Hemisphere when the bank angle is to the right and is equal to the 
complement of the dip angle. If .phi. &gt; 90-D then the indicated heading 
actually reverses 180.degree.. 
In a similar fashion, for a West heading with sin .psi. = -1, then 
EQU Tan .phi. = - (H/V) = - COT D = - Tan (90.degree.) = Tan - (90.degree.-D) 
or 
EQU .phi. = - (90.degree.-D) 
in summary, in the Northern Hemisphere, indicated headings become 
indeterminate when flying East with a right (positive) bank angle equal to 
the complement of the dip angle or when flying West with a left (negative) 
bank angle equal to the complement of the dip angle. Increasing the bank 
angle so that it exceeds the complement of the dip angle results in a 
reversal of the polarity of the athwartships component A.sub..phi. and 
produces 180.degree. error in indicated heading for the above conditions. 
Consequently, the indicating heading appears to modulate around West 
(270.degree.) during a right turn, and to modulate around East 
(90.degree.) during a left turn. This results in not being able to turn to 
indicated headings near North or South without first levelling down to a 
bank angle which is lower than the complement of the dip angle. For the 
mideastern U.S., where dip angle is +70.degree., the bank angles must 
therefore be less than .+-.20.degree. to avoid this problem on the 
East/West heading. 
For headings other than East or West any turns in which the bank angle 
exceeds the complement of the dip angle, the compass transmitter will 
indicate only a limited and erroneous range of headings. The nature of the 
problem may be discerned from Tables I and II which tabulate the indicated 
heading vis-a-vis the actual heading in case of Table I and the magnitude 
and direction of the heading error in Table II for bank angles of 
.+-.15.degree. (below the critical angle) and .+-.30.degree. (above the 
critical angle) for a dip angle D = +70.degree. which represents a dip 
angle typical of the Eastern United States. 
TABLE I 
______________________________________ 
INDICATED HEADING (DEG) 
Actual 
Hdg (.degree.) 
+15.degree. Bank 
+15.degree. Bank 
+30.degree. Bank 
-30.degree. Bank 
______________________________________ 
0 324.58 35.42 306.05 53.95 
45 357.73 63.11 312.88 70.40 
90 90.00 90.00 270.00 90.00 
135 182.27 116.89 227.12 109.60 
180 215.42 144.58 233.95 126.05 
225 243.11 177.73 250.40 132.88 
270 270.00 270.00 270.00 90.00 
315 296.89 2.27 289.60 47.12 
______________________________________ 
TABLE II 
______________________________________ 
INDICATED HEADING ERROR (DEG) 
Actual 
Hdg (.degree.) 
+15.degree. Bank 
-15.degree. Bank 
+30.degree. Bank 
-30.degree. Bank 
______________________________________ 
0 -35.42 35.42 -53.95 53.95 
45 -47.27 18.11 -92.12 25.40 
90 0.00 0.00 +180.00 0.00 
135 47.27 -18.11 92.12 -25.40 
180 35.42 35.42 53.95 -53.95 
225 18.11 -47.27 25.40 -92.12 
270 0.00 0.00 0.00 .+-.180.00 
315 -18.11 47.27 -25.40 92.12 
______________________________________ 
As may be seen from Table I for a right wing down turn where the bank angle 
is in excess of the complement of the dip angle (i.e., +30.degree.) the 
compass transmitter indications are limited to the range from 227.degree. 
to 312.degree.. Thus, for any actual heading from 0.degree. to 360.degree. 
the indicated headings from the compass transmitter vary over a limited 
(and mostly erroneous) range; i.e., limited range, roughly between a 
South-West (225.degree.) and Northwest (315.degree.) heading. Similarly, 
for a left wing down turn (i.e., -30.degree.) the compass transmitter 
indications are limited to the range from 47.degree. to 132.degree.. The 
indicated headings in this instance are limited to a range roughly between 
North-East (+45.degree.) to South-East (135.degree.) even though the 
actual headings may vary through 360.degree.. Thus, it can be seen that 
due to vertical field error, serious ambiguities and anomalies exist on 
all indicated headings from a compass transmitter when in a turn in which 
the bank angle exceeds the complement of the dip angle. 
The indicated headings and heading errors shown in Tables I and II have 
values characteristic of the exemplary dip and bank angles described in 
connection therewith (i.e., D = + 70 = .+-.15 and .phi. .+-. 30.degree.). 
Obviously for different combinations of dip angles and bank angles, the 
actual indicated heading and heading error values will vary with actual 
dip and bank angles but the "Northerly Turning Error" ambiguities and 
anomalies of the type just described exist to varying degrees as long as 
the bank angle equals or exceeds the complement of the dip angle. 
In addition to the "Northerly Turning Error" anomalies and ambiguities 
which occur during a turn when the bank angle equals or exceeds the 
complement of the dip angle, "Northerly Turning Error" also results in 
continuous oscillations about a desired heading when attempting to 
straighten out on a northerly heading in the Northern Hemisphere even 
though the bank angle is less than the complement of the bank angle. 
Again, it must be stressed that the term "Northerly Turning Error" is 
somewhat of a misnomer as it is really a hemispherical turning error 
produced during turns by the Earth's vertical field and is by no means 
limited to the Northern Hemisphere since the same problem exists in the 
Southern Hemisphere when attempting to straighten out a Southerly heading. 
The nature of this oscillatory "Northern Turning Error" can also be 
illustrated by reference to Table I. Let it be assumed that the system is 
being operated in the compass mode, i.e., not slaved to a directional 
gyro. For a +15.degree. bank [i.e., a right hand turn towards North with a 
bank angle less than the complement of the dip angle], the plane must turn 
to an actual heading of approximately 45.degree. for the compass to have 
an indicated heading of approximately 0.degree. (i.e., 357.73.degree.). 
Upon levelling out, however, the compass indicates the actual heading is 
45.degree. to the East of true magnetic North. This informs the pilot that 
a left bank turn is needed to obtain a North heading. During a subsequent 
-15.degree. bank, the aircraft turns to an actual heading of approximately 
315.degree. because at that heading the indicated for a -15.degree. bank 
is approximately 0.degree. (i.e., 2.27.degree.). Upon levelling out, the 
now correct indication of 315.degree. will inform the pilot that he is 
now to the West of magnetic North and that a right bank turn is needed to 
obtain a North heading. Thus, an oscillatory condition exists which makes 
it very difficult to turn to and level out on a North heading in turns 
where the bank angle is less than the complement of the dip angle. 
The oscillatory condition which exists as the pilot tries to turn to a 
northerly heading in the Northern Hemisphere is not present when turning 
to a southerly heading in the Northern Hemisphere. That is, the data from 
Table I makes it clear that this oscillatory or overshoot instability does 
not exist since for a southerly heading the compass indicator will show 
180.degree. before that heading is actually reached. That is, while trying 
to turn to a southerly heading in a Northern Hemisphere, the error 
introduced by the vertical component of the Earth's field causes an 
undershoot rather than an overshoot. As a result, although the compass 
transmitter gives erroneous indications which introduce some difficulties, 
the fact that the error results in undershoot allows the pilot, by 
continuing to bank, to reach the southerly heading in the Northern 
Hemisphere. 
As has been shown previously by Equation (16) the vertical field error 
along the athwartships axis during a turn is -V sin .phi.. As a result, 
the indicated heading which is represented by the arc tangent of the 
athwartships component A.sub..phi. divided by the fore/aft component 
F.sub.100, has an error term which is proportional to Tan D, i.e., the 
tangent of the dip angle. Since magnetic dip angle D varies substantially 
with latitude, substantial errors in indicated heading, as shown in Table 
I and II are present in "Northerly Turning Error." 
Applicant has found that the vertical field error can be substantially 
eliminated by adding a compensating signal to the compass transmitter in 
the form of a varying D.C. compensation signal which cancels out the 
vertical field error. 
The Earth's vertical magnetic field component is defined as V = M sin D, 
where M is the Earth's magnetic field and D is the dip angle. The vertical 
field error, -V sin .phi. is therefore equal to: 
EQU -V sin .phi. = -M sin D sin .phi. (25) 
Thus, by adding a signal equal to M sin D sin .phi. to the athwartships 
component A.sub..phi., A.sub..phi. is modified to become A.sub..phi.C. 
This compensated signal A.sub..phi.C is then equal to: 
EQU A.sub..phi.C = (H sin .psi. cos .phi. - V sin .phi.) + M sin D sin 
.phi.(26) 
EQU A.sub..phi.C = H sin .psi. cos .phi. (27) 
Substituting Equation (27) which is the magnetic heading in Equation (17), 
the tan of .psi..sub..phi. becomes: 
EQU Tan .psi..sub..phi.C = Tan .psi. cos .phi. (28) 
It can be seen from Equation (28) that the compensated indicated heading 
only contains a two cycle error proportional to .psi. and .phi.. This 
error is relatively small and does not vary with latitude. As a result, 
there is no error due to the Earth's vertical field component and 
"Northerly Turning Error" is eliminated. 
Table III, below shows the indicating heading error for various bank angles 
and a dip angle of +70.degree. with the introduction of a compensating 
signal equal to M sin D sin .phi.: 
TABLE III 
______________________________________ 
TURN 
COMPENSATED INDICATED HEADING ERROR (.degree.) 
Actual 
Hdg (.degree.) 
+15.degree. Bank 
-15.degree. Bank 
+30.degree. Bank 
-30.degree. Bank 
______________________________________ 
0 0.00 0.00 0.00 0.00 
45 -0.99 -0.99 -4.11 -4.11 
90 0.00 0.00 0.00 0.00 
135 0.99 0.99 4.11 4.11 
180 0.00 0.00 0.00 0.00 
225 -0.99 -0.99 -4.11 -4.11 
270 0.00 0.00 0.00 0.00 
315 0.99 0.99 4.11 4.11 
______________________________________ 
As may be seen from Table III, by eliminating the vertical field errors 
during a turn, the only errors still present in the output of the 
induction compass transmitter are those due to two cycle error. However, 
as pointed out previously, two cycle errors tend to be relatively small 
and do not have the major effects that vertical field errors do. It will 
be apparent therefore that by providing a compensating signal which is 
equal to M sin D sin .phi., that the overall errors produced by a 
"strapdown" induction compass transmitter are reduced substantially and 
"Northerly Turning Error" has been effectively eliminated. 
Compensation of a "strapdown" induction compass transmitter for tilt about 
the pitch axis while climbing or diving during straight flight, i.e., no 
rotation about the roll axis, may be similarly achieved. That is, in a 
climb or a dive during straight flight, the bank or roll angle .phi. = 
.theta. = aircraft pitch angle relative to the horizontal. For this 
condition, using the subscript .theta. for the the sensed fore/aft and 
athwartships components during a climb or dive, F.sub..theta. and 
A.sub..theta. may be defined as follows: 
EQU F.sub..theta. = H cos .psi. cos .theta. - V sin .theta. (29) 
EQU A.sub..theta. H = sin .psi. (30) 
It will be apparent from Equations (29) and (30) that in a straight climb 
or a dive (where the bank angle .phi. = 0) the sensed athwartships 
component A.sub..theta. is not affected by the Earth's vertical field 
component V but the sensed fore/aft component is. As pointed out 
previously, the arc tangent of, the indicated compass transmitter heading 
then becomes .sub..theta.. 
##EQU3## 
From Equation (33) it is apparent that again, there is a two cycle error 
and a vertical field error 
##EQU4## 
which varies with dip angle and can introduce various heading anomalies. 
The heading anomalies during climbs and dives are similar in nature to 
those introduced during a turn but occur on different headings. These 
heading anomalies and ambiguities occur if the pitch angle during a climb 
or dive equals or exceeda a critical value. Briefly, if the pitch angle 
exceeds the complement of the dip angle, it is not possible to find and 
indicate all headings since the compass transmitter will then ohn only 
indicate headings in a limited range no matter what the actual heading is. 
The problem is at its most severe when on a direct North (0.degree.) or 
South (180.degree.) heading. On such a North or South heading, if the bank 
angle exceeds the complement of the dip angle, there can be a complete 
reversal of the heading indication. Thus, on a North (0.degree.) heading, 
a positive pitch angle (i.e., a climb) which exceeds the complement of the 
dip angle, causes the compass transmitter indication to reverse 
180.degree. and indicate a South (180.degree.) heading. Similarly, while 
on a South (180.degree.) heading a negative pitch angle (i.e., a dive) 
which exceeds the complement of the dip angle causes the compass 
transmitter to indicate a North (0.degree.) heading. 
If the pitch angle is exactly equal to the complement of the dip angle then 
the output of the compass transmitter becomes indeterminate on these 
headings since it no longer senses any magnetic field and all heading 
indication is lost. 
The manner in which these anomalies and ambiguities occur when the pitch 
angle equals or exceeds the critical angle (i.e., the complement of the 
dip angle) will be illustrated in connection with an aircraft on a North 
or South heading since this represents a "worst case" situation. 
For a North and South heading, the sensed athwartships component A of the 
Earth's horizontal field obviously goes to zero, i.e., A.sub..theta. = 0. 
For a North heading (North = 0.degree.) the value of the cos of the 
heading angle i.e., cos.psi. = cos 0.degree. = +1. For a South heading 
(180.degree.) cos .psi.= cos 180.degree. = -1. Thus, on a North heading, 
the fore/aft component F.sub..phi. as defined in Equation (29) becomes 
zero when V sin .theta. = H cos .psi.cos .theta.. 
Since cos .mu. = +1 for a North heading, F.sub..theta. = 0 when 
EQU V sin .theta. = H cos .theta. (34) 
Transposing, Equation (34) becomes 
EQU H/V = (sin .theta./cos .theta.) (35) 
By trigonometric transformation, Equation (35) becomes: 
EQU (H/V) = Tan .theta. (36) 
However, since (H/V) = COT D then COT D = Tan .theta.. But COT D = Tan 
(90.degree.-D) 
Therefore, 
EQU Tan .theta. = Tan (90.degree.-D) (37) 
or 
EQU .theta. = 90.degree.-D (38) 
in other words, for a given dip angle the induction compass transmitter 
heading becomes indeterminate in a North heading in the Northern 
Hemisphere when the aircraft is in a climb and the pitch angle .theta. is 
equal to the complement of the dip angle. If .theta. &gt;90-D then the 
indicated heading actually reverses 180.degree.. 
In a similar fashion, for a South heading with cos .psi. = -1, then 
EQU Tan .theta. = 1 H/V = - COT D = - Tan (90.degree.-D) = Tan - (90.degree.-D) 
(39) 
or 
EQU .theta. = - (90.degree.-D) 
in summary in the Northern Hemisphere, indicated headings become 
indeterminate when flying North and climbing with a pitch angle (positive) 
equal to the complement of the dip angle or when flying South and diving 
with a pitch angle (negative) equal to the complement of the dip angle. 
Increasing the pitch angle so that it exceeds the complement of the dip 
angle results in a reversal of the polarity of the fore/aft component 
F.sub..theta. and produces 180.degree. error in indicated heading for the 
above conditions. Consequently, the indicated heading appears to modulate 
around South (180.degree.) during a climb and North (0.degree.) during a 
dive. This results in not being able to obtain a heading indication 
without first levelling down to a pitch angle which is lower than the 
complement of the dip angle. For the mideastern U.S., where the dip angle 
is approximately +70.degree., the pitch angle for climbs and dives must 
therefore be less than .+-.20.degree. to avoid this problem on a North or 
South heading. 
In addition to the problems encountered during dives and climbs when on a 
North or South heading, other anomalies exist at other headings. Table IV 
(below) shows indicated headings and Table V below shows indicating 
heading errors for exemplary pitch angle values of .+-.15.degree. and 
.+-.30.degree. for a dip angle of 70.degree.. 
TABLE IV 
______________________________________ 
INDICATED HEADING (DEG) 
Actual 
Hdg (Dg) 
+15.degree. Pitch 
-15.degree. Pitch 
+30.degree. Pitch 
-30.degree. Pitch 
______________________________________ 
0 0.00 0.00 180.00 0.00 
45 92.27 26.89 137.12 19.60 
90 125.42 54.58 143.95 36.05 
135 153.11 87.73 160.40 42.88 
180 180.00 180.00 180.00 0.00 
225 206.89 272.27 199.60 317.12 
270 234.58 305.42 216.05 323.95 
315 267.73 333.11 222.88 340.40 
______________________________________ 
TABLE V 
______________________________________ 
INDICATED HEADING ERROR (.degree.) 
Actual 
Hdg (.degree.) 
+15.degree. Pitch 
-15.degree. Pitch 
+30.degree. Pitch 
-30.degree. Pitch 
______________________________________ 
0 0.00 0.00 +180.00 0.00 
45 47.27 -18.11 92.12 -25.40 
90 35.42 -35.42 53.95 -53.95 
135 18.11 -47.27 25.40 -92.12 
180 0.00 0.00 0.00 +180.00 
225 -18.11 47.27 -25.40 93.12 
270 -35.42 35.42 -53.95 53.95 
315 -47.27 18.11 -92.12 25.40 
______________________________________ 
It can be seen from Table V that for a positive pitch angle (climb) in 
excess of the complement of the dip angles (i.e., +30.degree., the compass 
transmitter indicated headings are limited to the range .about.137.degree. 
to 222.degree.. Similarly, for a negative pitch angle (dive) in excess of 
the complement of the dip angle (i.e., -30.degree.), the indicated 
headings are limited to the range 317.degree. to 43.degree.. This 
obviously introduces severe heading indication errors when in a climbing 
or a diving maneuver with the pitch angle exceeding the complement of the 
dip angle. 
Applicant has found that the vertical field error can be substantially 
eliminated during climbs and dives by adding a DC compensating signal to 
the compass transmitter which cancels the effect of the Earth's vertical 
field on the compass sensing windings. The Earth's vertical field V is 
defined as V = M sin D, where M is the Earth's magnetic field and D is the 
dip angle. Vertical field error -V sin .theta. therefore is equal to: 
EQU -V sin .theta. = - m sin D sin .theta. (40) 
Thus, by adding a signal equal to M sin D sin .theta. the fore/aft 
component F.sub..theta., F.sub..theta. is modified to become 
F.sub..theta.C. The compensated fore/aft component F.sub..theta.C is 
therefore defined as: 
EQU F.sub..theta.C = (H cos .psi. cos .theta. - V sin .theta.) + M sin D sin 
.theta.) (41) 
Hence, 
EQU F.sub..theta.C = H cos .psi. cos .theta. (42) 
As a result, the arc tangent of .psi. becomes: 
##EQU5## 
It will be apparent from Equation (43) that the compensated indicated 
heading only contains a two cycle error. 
By adding such a compensating signal, the indicated heading error for 
various bank angles at a dip angle of +70.degree. is reduced substantially 
as may be seen from Table VI below: 
TABLE VI 
______________________________________ 
PITCH 
COMPENSATED INDICATED HEADING ERROR (DEG) 
Actual 
Hdg (.degree.) 
+15.degree. Pitch 
-15.degree. Pitch 
+30.degree. Pitch 
-30.degree. Pitch 
______________________________________ 
0 0.00 0.00 0.00 0.00 
45 0.99 0.99 4.11 4.11 
90 0.00 0.00 0.00 0.00 
135 -0.99 -0.99 -4.11 -4.11 
180 0.00 0.00 0.00 0.00 
225 0.99 0.99 4.11 4.11 
270 0.00 0.00 0.00 0.00 
315 -0.99 -0.99 -4.11 -4.11 
______________________________________ 
Table VI shows that by eliminating vertical field errors, the only errors 
in the output of the induction compass transmitter are those due to two 
cycle error. However, as may be seen from this tabulation, these errors 
tend to be relatively small and do not have the major effects on the 
heading indication that vertical field errors do. It will be apparent 
therefore that the overall errors produced in the output of a "strapdown" 
induction compass transmitter during climbs and dives are reduced 
substantially along with the anomalies and ambiguities associated with 
this condition. 
Although two cycle error is relatively small since it does not vary with 
latitude, there may be occasions when there is a need to eliminate even 
this relatively minor source of heading error. This may be achieved by 
processing the athwartships and fore/aft signals A.sub..phi.C and 
F.sub..theta.C which have been compensated for errors due to the Earth's 
vertical field component by modifying the corrected signal (by 
multiplying) to cancel the cos .phi. and cos .theta. terms. 
A.sub..phi.C is modified to become A.sub..phi.CC in the following fashion: 
EQU A.sub..phi.CC = A.sub..phi.C .multidot. (1/cos) .phi.; A.sub..phi.C = H sin 
.psi. cos .phi. (44) 
EQU .thrfore. A.sub..phi.CC = sin .psi. cos .phi. .multidot. (1/cos) .phi. = H 
sin .psi. (45) 
As a result the arc tangent .sub..phi.C according to Equation (28) becomes: 
EQU Tan .sup..psi..sub..phi.CC = (H sin.psi./H cos.psi.) = Tan .psi.(46) 
Similarly: 
F.sub..theta.C according to Equation (42) becomes 
EQU F.sub..theta.CC = F.sub..theta.C .multidot. (1/cos) .sub..theta. ; 
F.sub..theta.C = H cos .psi. cos .theta. (47) 
EQU .thrfore. F.sub..theta.CC = H cos .psi. cos .theta. = .multidot. (1/cos) = 
H cos .psi. (48) 
As a result, the arc tangent of .psi..sub..theta.C according to Equation 
(43) 
becomes: 
##EQU6## 
As will be described in detail later, cancellation of the two cycle error 
terms cos .phi. and cos .theta. may be most readily achieved by 
multiplying the DC negative feedback signal in the null balancing, 
demodulating networks for the respective output signals from the induction 
compass transmitter windings by the compensating signals cos .phi. and cos 
.theta.. 
FIG. 3 illustrates one embodiment of an arrangement for compensating the 
output of a "strapdown" induction transmitter of the synchro type for 
errors due to the vertical component of the Earth's field both during 
turns and during climbs or dives. The system of FIG. 3 involves the 
developing of a DC compensating signal of magnitude M sin D sin .phi. and 
combining this signal with the demodulated output signal from the 
induction compass transmitter windings which sense the athwartships 
magnetic field component of the aircraft to compensate for turn induced 
errors due to the vertical field. Similarly, a DC compensating signal of 
magnitude M sin D sin .theta. is generated and combined with the 
demodulated output signal from those windings of the compass induction 
transmitter which sense the fore/aft component of the Earth's magnetic 
field. This compensating signal is combined with the demodulated output 
signal to compensate for any errors due to the vertical component of the 
Earth's magnetic field during climbs or dives. Sin .phi. and sin .theta. 
can easily be supplied from the aircraft vertical gyros and signals 
proportional to sin D may be readily set by means of a potentiometer or 
automatically programmed as a function of latitude and longitude. The 
apparatus illustrated in FIG. 3 can be easily adapted to an existing 
compass system that uses a synchro type output from the compass 
transmitter and thus may be utilized without affecting impedance matching 
between the transmitter and slaving system. Compensation of the output 
from the induction compass transmitter is external to the transmitter 
itself and is realized by combining the compensating signals with the 
demodulated output signals in the signal processing channel for the sensed 
athwartships and fore/aft components of the Earth's magnetic field 
respectively. 
Thus, in FIG. 3, a "strapdown" compass transmitter is illustrated 
schematically at 30. Transmitter 30 includes an excitation winding 31 
having a sinusoidal excitation voltage (commonly at 400 Hz) applied 
thereto to saturate a magnetic core structure twice during each excitation 
voltage cycle. A plurality of magnetometer sensing windings 32-34 are 
mounted on the magnetic core structure. Saturation of the core twice 
during each excitation voltage cycle results in the Earth's field inducing 
second harmonic voltages in these windings proportional to the magnitude 
of the Earth's field along the axes on which the windings are mounted. 
Windings 32, 33 and 34 are connected in a grounded Y or synchro 
configuration. Windings 32 and 33 sense the athwartships component A of 
the Earth's horizontal magnetic field and winding 34 sensed the fore/aft 
component F. The second harmonic, double sideband, carrier suppressed, 
output signals from compass transmitter 30 are supplied via leads 35-38 to 
a Scott-Tee transformer shown at 39. The Scott-Tee has a Y connected 
synchro type primary winding, not shown, to which the three phase signals 
from the induction compass transmitter are coupled. The secondary of the 
Scott-Tee transformer, also not shown, has a pair of orthogonally wound 
windings so that the three phase output signals from the synchro type 
induction compass transmitter are converted therein to produce a pair of 
output signals which are respectively representative of the sin .psi. and 
cos .psi. functions of the Earth's magnetic field H, i.e., the fore/aft 
and athwartships components of the field as sensed by the induction 
compass transmitter. Scott-Tee transformers are well-known devices for 
transforming either a two phase input to a three-phase output or, 
conversely, a three-phase input to a two-phase output as is the case in 
FIG. 3. Reference is hereby made to textbook "Alternating Current 
Machinery" - LV Dewley, MacMillan Co., N.Y. (1949) and particularly pages 
89 through 91 thereof which describe the basic characteristics of the 
so-called Scott-Tee connection. 
The output signals from Scott-Tee transformer 39 are therefore second 
harmonic, double sideband, carrier suppressed signals representative of 
the sine and cosine of the heading angle .psi. and therefore represent the 
Earth's field as sensed along the athwartships axis of the aircraft and 
along the fore/aft axis of the aircraft respectively. This signal, 
representative of the sine of the heading angle .psi., i.e., .about. H sin 
.psi. from induction transmitter is applied to a sin.psi. signal 
processing channel 40. The output from the Scott-Tee proportional to the 
cosine of the heading angle, (i.e., .about. H cos .psi.) and therefore the 
field sensed along the fore/aft axis of the vehicle is applied to a cos 
.psi.signal processing channel shown generally at 41. The two signals are 
processed in the respective channels to produce demodulated, DC signals 
which are therefore representative respectively, of the Earth's magnetic 
field components sensed along these axes. The signal representative of the 
athwartships components includes errors due to the Earth's vertical field 
component as well as two cycle errors during any aircraft turns when the 
"strapdown" induction compass transmitter is tilted to the bank or roll 
angle .phi. of the aircraft. Similarly, the "strapdown" induction compass 
transmitter is tilted to the pitch angle .theta. during climbs or dives 
produces sensing errors in the windings of the induction compass 
transmitter due to these tilt angles. As pointed out previously, in 
connection with Equation (15) during turns the Earth's magnetic field as 
sensed along the fore/aft axis F.sub..phi. which is proportional to 
cosine of the heading angle, is not subject to errors induced by the 
vertical component of the Earth's magnetic field, nor does it include any 
two cycle error. It is only the component sensed along the athwartships 
axis, as shown by Equation (16), that is subject to vertical field and two 
cycle error during turns. Similarly, as may be seen from Equation (30) 
during non-turning climbs or dives, the signal representative of the 
Earth's field along the athwartships axis is not subject to errors due to 
the vertical component of the Earth's field nor is it subject to two cycle 
errors. Only fore/aft sensed signal, as shown in Equation 29 is subject to 
errors due to the vertical component of the Earth's field and two cycle 
error. 
The second harmonic, double sideband, carrier suppressed signals at the 
output of Scott-Tee 39 are applied, respectively, through coupling 
capacitors 42 and 43 to amplifiers 44 and 45 in the respective processing 
channel. The amplified second harmonic signals are applied as one input to 
synchronous demodulators 46 and 47. A second harmonic carrier signal from 
local reference carrier signal source 48 is applied as the other input to 
synchronous demodulators 46 and 47. That is, if the excitation voltage for 
induction compass transmitter 30 is a 400 Hz alternating voltage, then the 
output signals are second harmonics of the excitation frequency (i.e., 800 
Hz). By inserting a carrier at twice the excitation frequency, i.e., 800 
Hz, demodulators 46 and 47 demodulate the signals to produce varying DC 
outputs that represent the variations of the Earth's magnetic field as 
sensed by the windings of the induction compass transmitter along the 
athwartships and fore/aft axes. 
The output from demodulator 46 in sin .psi. channel 40 which represents the 
Earth's field sensed along the athwartships axis of the vehicle is 
processed to compensate for errors due to the Earth's vertical field 
during turns. The output from demodulator 47 in the cos .psi. channel 41 
which measures the component of the Earth's magnetic field sensed along 
the fore/aft axis of the vehicle, is then processed to compensate the 
signal for errors due to the vertical component of the Earth's magnetic 
field during dives and climbs. 
The output from the sin .psi. channel demodulator 46 is therefore applied 
to a summing network 49 in which the demodulated signal from the induction 
compass transmitter representative of the athwartships of the Earth's 
magnetic field is summed with the compensating signal from a vertical 
field compensation network shown generally at 50 which generated a DC 
compensating signal used to cancel the effects on the sin .psi. output 
signal of the vertical component of the Earth's magnetic field due to 
tilting of the induction compass transmitter sensing windings during 
turns. Compensating network 50 thus generates a signal proportional to M 
sin D sin .phi. and couples this signal to the other input of summing node 
49 to add the DC compensating signal to the demodulated DC signal from the 
induction compass transmitter. 
One input to network 50 is a varying DC input voltage from the vertical 
roll gyro which signal is proportional to the sine of the turn or bank 
angle .phi. and hence represents the bank or tilt of the compass 
transmitter during a turn. The signal from the roll gyro is applied to an 
amplifier 51 which produces an amplified sin .phi. signal and also 
introduces a scale factor representative of the Earth's magnetic field M 
so that the amplified output is proportional to M sin .phi.. This 
amplified output is applied as the DC supply voltage for potentiometer 52 
which has a movable wiper 53 which is controlled by a shaft 54. Wiper 53 
is set by shaft 54 to insert sin D term. The voltage at wiper is therefore 
proportional to the product of the sine of the bank angle .phi. the 
Earth's magnetic field M and the sine of the dip angle D (i.e., V.sub.53 = 
M sin D sin .phi.). Potentiometer wiper 53 may be set manually or 
alternatively, sin D may automatically be programmed as a function of the 
latitude and longitude. If the aircraft is to traverse a relatively small 
distance in latitude, so that the dip angle D remains relatively constant, 
potentiometer 52 may be adjusted initially by positioning the wiper so 
that for any given bank angle the output exactly cancels the vertical 
field error and no further adjustment is required. If the aircraft is 
likely to fly over a large distance so that the dip angle D changes 
substantially, changes in the wiper position by the pilot will be 
necessary to maintain proper compensation. Potentiometer 52 may be a 
linear potentiometer which has a sinusoidal scale calibration so that the 
wiper is adjusted to provide the required sin D adjustment. Alternatively, 
a sinusoidally wound potentiometer with a linear scale may be utilized 
instead. 
The output from potentiometer wiper which is M sin D sin .phi. is applied 
to the other input of summing node 49. This signal which is equal to V sin 
.phi. or the error due to the vertical component of the Earth's field is 
thus added algebraically to the demodulated DC signal from the windings of 
the induction compass transmitter which sense the athwartships component 
of the Earth's field and as a result, error due to the vertical component 
of the Earth's field during turns is cancelled. The output from summing 
node 49 is therefore H sin .psi. cos .phi. and thus contains only the two 
cycle error due to the bank or tilt angle .phi.. The corrected signal may 
be applied to the heading indicator system directly or may be remodulated 
for utilization in any suitable manner in a heading indicating or control 
system. 
Simlarly, the output from demodulator 47 in the cos .psi. channel 41 which 
represents the component of the Earth's magnetic field sensed along the 
fore/aft axis of the aircraft, is processed to compensate the signal for 
errors due to the Earth's vertical field during climbs or dives. The 
output from demodulator 47 is therefore applied to summing network 55 in 
which the demodulated DC signal from the induction compass transmitter 
representing the cos .psi. or fore/aft signal is combined by summation 
with a compensating signal from a vertical field compensation network 
shown generally at 56 which generated a compensating signal which cancels 
the effects of the output signal from the compass transmitter of the 
vertical component of the Earth's magnetic field during climbs or dives. 
Compensating network 56 generates a signal proportional to M sin D sin 
.theta. and couples this signal to the other input of summing node 55. One 
input to network 56 is a varying DC input voltage from the vertical pitch 
gyro which is proportional to the sine of the pitch angle .theta. and 
hence, represents the pitch or tilt of the compass transmitter while 
climbing or diving. The signal from the gyro is applied to an operational 
amplifier 57 which produces an amplified sin .theta. signal. The amplified 
sin .theta. signal may also include a scale factor for the Earth's 
magnetic field M, i.e., M sin .theta. and is applied as the DC supply 
voltage for a potentiometer 58. Movable wiper 59 is also controlled by 
shaft 54 to the set position of wipers 59 to insert a sin D term. The 
voltage at wiper 59 is therefore proportional to the product of the sine 
of the pitch angle .theta., the Earth's magnetic field M and the sine of 
the dip angle, (i.e., V.sub.59 = sin D sin .theta.). As pointed out in the 
description of the compensating channel 40, the potentiometer wipers may 
be set manually or automatically programmed as a function of latitude and 
longitude. Thus, depending on the distance to be traversed the sin D term 
may be set in the potentiometer and not changed throughout the whole 
voyage whereas if the vehicle is to cover a large distance and such a 
change in latitude so that the dip angle D changes substantially, changes 
in wiper position may be necessary to maintain proper compensation. Again, 
the potentiometer may be linear with the sinusoidal scale calibration or 
sinusoidally wound with a linear scale. 
The voltage at potentiometer wiper 59 is supplied directly to the other 
input to summing node 55. The signal M sin D sin .theta. is equal to V sin 
.theta.. V error due to the vertical component of the Earth's field is 
thus added algebraically to the demodulated DC signal from the induction 
compass transmitter windings which sense the fore/aft component of the 
Earth's magnetic field. As a result, the error due to the vertical 
component of the Earth's field is cancelled. The output from summing node 
55 is therefore H cos .psi. cos .theta. and thus contains only the two 
cycle error due to the tilt or pitch angle .theta.. This corrected signal 
representing the cos .psi. term may be applied to the heading indicator 
heading directly or demodulated for utilization in any suitable manner in 
a heading indicating or control system. 
The compensated "strapdown" induction compass transmitter system shown in 
FIG. 3 was one in which the sensing windings are connected in a grounded Y 
or synchro configuration which require transformation through a Scott-Tee 
transformer or the like to produce output signals which are respectively 
proportional to the sine and cosine of the heading angle .psi., prior to 
demodulation and compensation. The synchro type of connection for 
induction compass transmitter is quite common so that the compensation 
arrangement illustrated in FIG. 3 is very useful and has applicability to 
existing systems. The instant invention is however, not limited thereto 
since it is equally applicable to induction compass transmitters using 
other winding configurations. FIG. 4 illustrated an arrangement in which 
an induction compass transmitter having a typical resolver winding 
configuration is compensated according to the instant invention. Because 
the sensing windings of the transmitter are connected in a resolver 
configuration, the output from the windings may be demodulated and 
compensated directly without requiring the use of Scott-Tee transformers 
or the like since the output from the sensing windings directly represent 
the components of the Earth's magnetic field sensed along the fore/aft and 
athwartships axis. That is, the output from the windings are directly 
proportional to sin .psi. and cos .psi.. Thus, in FIG. 4, a "strapdown" 
induction compass transmitter of the resolver type is illustrated 
schematically at 60. Compass transmitter 60 includes an excitation winding 
61. An alternating excitation voltage (commonly at 400 Hz) is applied 
thereto to saturate a magnetic core structure on which magnetometer 
sensing windings 62 and 63 are wound. The excitation voltage saturates the 
core twice during each excitation voltage cycle so that the Earth's 
magnetic field induces second harmonic voltages proportional to the 
fore/aft and athwartships components of the Earth's horizontal field in 
these windings. Windings 62 and 63 are connected in a typical resolver 
configuration so that winding 62 senses the fore/aft component F of the 
Earth's horizontal magnetic field H and the winding 63 senses the 
athwartships component A. The output from winding 63 is therefore 
proportional to the product of the horizontal component of the Earth's 
magnetic field H and the sine of the heading angle .psi. while the output 
from winding 62 is proportional to the product of the horizontal component 
H of the Earth's magnetic field and cosine of the heading angle .psi.. The 
output from windings 62 and 63 are thus applied to signal processing 
channels 65 and 66 in which the signals are demodulated and thereafter 
compensated to cancel the effects of the vertical component of the Earth's 
magnetic field on the output of the transmitter during turns and while 
climbing or diving. 
These second harmonic signals representing the fore/aft and athwartships 
components of the Earth's magnetic field, i.e., are applied through 
suitable coupling capacitors and amplifiers 67 and 68 as one input to 
synchronous demodulators 69 and 70. The other input to each of the 
demodulators 69 and 70 is a second harmonic carrier signal from reference 
carrier signal source 71. By reinserting a carrier signal of twice the 
frequency of the excitation voltage applied to the transmitter, 
demodulators 69 and 70 demodulate the second harmonic carrier suppressed, 
double sideband signal from the transmitter windings to produce a varying 
DC output which represents the variations of the Earth's magnetic field as 
sensed by the windings of the compass transmitter. 
The second harmonic reference carrier signal is again shown as being 
supplied from a separate source of carrier signal 71. It will be obvious, 
however, that the second harmonic carrier signal applied to demodulators 
69 and 70 may be obtained directly from carrier excitation voltage source 
by multiplying a signal to produce the second harmonic reference carrier 
signal. The demodulated output signals from demodulators 69 and 70 are DC 
signals proportional respectively to the sensed athwartships and fore/aft 
components of the Earth's magnetic field. During a turn as pointed out 
previously, the horizontal component of the Earth's field as sensed 
athwartships is affected by the vertical component of the Earth's magnetic 
field which introduces errors proportional to V sin .phi.. Demodulated 
output signal from modulator 70 is a DC signal proportional to the sensed 
fore/aft component of the horizontal component of the Earth's magnetic 
field and is affected by the vertical component of the Earth's magnetic 
field during non-turning climbs and dives which introduces errors 
proportional to V sin .theta.. 
The outputs from demodulators 69 and 70 are applied as one input to summing 
nodes 72 and 73. The other input to summing node 72 is a compensating 
signal proportional to M sin D sin .phi. from a vertical field turn 
compensating network shown generally at 74. The other input to summing 
node 73 is a compensating signal proportional to M sin V sin .theta. from 
a pitch compensating network shown generally at. 
Network 74 generates a compensation signal which is used to cancel errors 
due to vertical components of the Earth's magnetic field due to tilting of 
the compass transmitter during turns. Network 75, on the other hand, 
generates a compensation signal which is used to cancel errors due to the 
vertical component of the Earth's magnetic field due to tilting of the 
compass transmitter during nonturning dives or climbs. Compensating 
network 74, as pointed out above, generates a signal equal to M sin D sin 
.phi. which is exactly equal to the turn induced vertical field error V 
sin .phi. and is used to cancel the error due to the Earth's field 
component. One input to network 74 is a varying DC input voltage from the 
vertical roll gyro which is proportional to the sine of the roll or bank 
angle .phi. and hence represents the bank angle or tilt of the compass 
transmitter. 
This signal from the roll gyro is applied to an amplifier 76 which 
amplifies the sin .phi. signal and introduces a scale factor equal to the 
Earth's magnetic field M. The amplified output from amplifier 76 is thus a 
signal proportional to the product of the Earth's magnetic field and the 
sine of the bank angle, i.e., M sin .phi. and is applied as the DC supply 
voltage for potentiometer 77. A movable potentiometer wiper 78 is manually 
controlled by a shaft 79 to set the wiper and insert a sin D term. The 
voltage at wiper 78 is therefore equal to the product of the sin of the 
bank angle .phi., the Earth's magnetic field, M, and the sine of the dip 
angle D (i.e., V.sub.78 = M sin D sin .phi.). 
As pointed out previously, potentiometer wiper 78 may be set manually or 
may be automatically programmed as a function of latitude. In the case of 
small distances in which small or no variations of latitude are traversed, 
the position of the wiper may be preset. If the aircraft is to fly over a 
large distance and the dip angle changes substantially, changes in wiper 
position by the pilot may be necessary to maintain proper compensation. 
Furthermore, potentiometer may be linear with sinusoidal scale 
calibrations or it may be a sinusoidally long potentiometer with a linear 
scale. 
The output from wiper 78 is applied as the other input to summing node 72 
to cancel the vertical field error in the demodulated DC output from the 
sin .psi. signal processing channel of the compass transmitter. The 
compensated output signal from summing node 72 is then applied from output 
terminal 80 so that the compensated sin .psi. component may be applied to 
a heading indicator, control network or the like. That is, the demodulated 
compensated signals may be remodulated if desired and then applied to 
heading indicator or utilized for control purposes. 
Pitch compensating network 75 generates a DC compensation signal which is 
equal to the vertical field error during non-turning climbs and dives and 
is proportional to V sin .theta.. This compensating signal is applied to 
summing node 73 to compensate the sensed fore/aft component of the Earth's 
horizontal field. This network generates a singal proportional to M sin D 
sin .theta. which cancels vertical field error introduced during climbs 
and dives, i.e., it cancels the vertical field error term V sin .theta.. 
One input to network 75 is a varying DC input voltage from the vertical 
pitch gyro which is proportional to the sine of the pitch angle .theta. 
and hence, represents the angle of tilt of the compass transmitter during 
a non-turning climb or dive. The DC signal from the vertical ptich gyro is 
applied to an amplifier 81 in which the sin .theta. signal is amplified 
and a scale factor proportional to the magnitude of the Earth's magnetic 
field M is introduced. The output from amplifier 81 is thus a signal 
proportional to M sin .theta. which is applied as a DC supply voltage to a 
potentiometer 82. A movable wiper 83 is manually controlled by common 
shaft 79 to set the position of the wiper and insert a sin D term. The 
voltage at wiper 83 is therefore the product of the sine of the pitch 
angle .theta., the Earth's magnetic field M and the sine of the dip angle 
D (i.e., V.sub.83 = M sin D sin .theta.). The voltage at potentiometer 
wiper 83 is applied as the other input to summing node 73 to cancel the 
vertical field error in the demodulated DC signal. The compensated output 
signal from summing node 74 is applied to an output terminal 84 where it 
may be applied to heading indicator or control network for utilization 
there. That is, the demodulated compensated signals may be remodulated and 
applied to heading indicator or utilized in whatever form is necessary for 
performing the function desired. 
FIGS. 3 and 4 show arrangements for compensating the outputs from an 
induction compass transmitter to eliminate or cancel the effects of the 
vertical component of the Earth's magnetic field during turns and while 
climbing and diving. However, as pointed out previously, signals after 
compensation for vertical field error is still subject to two cycle error 
equivalent. That is, during turns, the horizontal component of the Earth's 
field H sin .psi. as sensed by the athwartships sensing windings still 
includes an error component proportional to the cosine of the bank angle; 
i.e., the sensed field is H sin .psi. cos .phi.. In most instances, this 
error factor which is proportional to cos .phi. is small as compared to 
errors to the vertical field error which varies with the sin of the dip 
angle. However, in some circumstances, it is desirable to compensate the 
output signal from the induction compass transmitter to eliminate even the 
small two cycle error. 
FIG. 5 illustrates an arrangement in which the signals proportional to the 
athwartships and fore/aft components are sensed by the induction 
transmitters, are initially compensated to eliminate the error component 
due to the Earth's vertical field both during turns and during climbs and 
dives and are thereafter further compensated to eliminate two cycle error. 
In FIG. 5, the signal after being compensated for vertical field error is 
remodulated and compensated for two cycle error in a null balancing, 
closed loop, remodulating circuit. The remodulated signal is fed back in a 
negative feedback path to the input of the remodulating circuit. In the 
negative feedback, the signal is demodulated and also multiplied by two 
cycle compensation signals proportional to cos .phi. and cos .theta. 
respectively, to cancel two cycle error in the sin .psi. and cos .psi. 
channels respectively. The demodulated and compensated signals from the 
negative feedback paths are fed back to the inputs of the remodulating 
channels to be summed with the incoming DC signal which is used as the 
modulating signal in the remodulating channel. As a result, the closed 
loop remodulation circuits are driven until the outputs are modulated 
signals which are proportional respectively to H sin .psi. and H cos .psi. 
thereby eliminating both the vertical field and two cycle error. 
The signals representing the Earth's field sensed by the induction compass 
transmitter windings along the fore/aft and athwartships axes of the 
vehicle are compensated for vertical field error, in the manner shown in 
either FIG. 3 or 4, i.e., by converting the output from a synchro type 
compass transmitter to the sin and cos signals through a Scott-Tee 
transformer or by utilizing a resolver type of induction compass sensing 
windings. Thus, two signals obtained from the transmitter not shown, are 
applied to input terminals 100 and 101 of vertical field and two cycle 
error and compensation networks to compensate both for the effect of the 
Earth's vertical field during turns and during climbs and dives and also 
for two cycle error. The signal representing the Earth's field as sensed 
by the transmitter windings along the athwartships axis of the vehicle are 
applied to input terminal 100. The signal is first demodulated and then 
processed to compensate for errors due to the Earth's vertical field 
during turns. Thereafter, this compensated demodulated DC signal is 
applied to a null balancing, closed loop remodulating network in which the 
signal is remodulated and fed back via a negative feedback loop to the 
input of the network. The negative feedback signal is further processed by 
multiplying the signal by a signal proportional to cos .phi. to cancel two 
cycle error. 
The signal representing teh Earth's field as sensed by the induction 
compass transmitter windings along the fore/aft axis of the aircraft are 
applied to input terminal 101 and applied to a vertical field compensating 
signal processing network, in which the signal is demodulated and 
processed to compensate for errors due to the vertical component of the 
Earth's field during climbs and dives. This compensated DC signal is then 
applied to a null balancing, closed loop, remodulating network in which 
the signal is remodulated and fed back through a negative feedback loop to 
the input of the network. The negative feedback signal is processed by 
multiplying the signal by the compensating signal proportional to cos 
.theta. to cancel two cycle error introduced into the fore/aft sensed 
field during climbs and dives. 
The signals from the compass transmitter representing the Earth's 
horizontal field sensed along the athwartships axis of the vehicle is 
impressed on input terminal 100. It is thereafter applied to signal 
processing channel 102 after suitable amplification in amplifier 103 as 
one input to a demodulator 104. The second harmonic, double sideband, 
carrier suppressed signal is demodulated in demodulator 104. To this end, 
a second harmonic carrier signal from carrier signal source 105 which is 
applied as the other input to the demodulator. The output from demodulator 
104 is therefore a varying DC voltage which is proportional to horizontal 
component of the Earth's field as sensed along the athwartships axis of 
the vehicle. This signal as pointed out previously, includes an error term 
equal to V sin .phi. during turns. This latter error factor represents the 
error induced into the vertical by the vertical component of the Earth's 
field during turns. The demodulated signal is therefore compensated for 
vertical field error by applying the demodulated signal as one input to a 
summing node 106 where it is combined with a compensating signal from the 
vertical field compensating network 107. This compensating signal cancels 
the vertical field error term V sin .phi.. Compensating network 107 
generated, as described previously in connection with FIGS. 3 and 4, a 
signal proportional to M sin D sin .phi. which is equal to the vertical 
field error V sin .phi.. Vertical field compensating network 107, in a 
manner similar to that described previously in connection with FIGS. 3 and 
4, include a potentiometer 108. The supply voltage to potentiometer 108 is 
from the output of amplifier 109 and is proportional to M sin .phi.. The 
input to amplifier 109 is a signal from the vertical roll gyro which is 
proportional to the sine of the bank or tilt angle, i.e., sin .phi.. 
Amplifier 109 not only amplifies the sin .phi. signal but also introduces 
a scaling factor proportional to the magnitude of the Earth's field so 
that output from amplifier 108 is equal to M sin .phi.. Potentiometer 109 
has a movable wiper 110 that is controlled through shaft 111. Shaft 111 
moves wiper 110 so that a sin D term is inserted. The voltage at wiper 110 
is therefore proportional to the product of the sine of the bank angle 
.phi., the Earth's magnetic field M and the sine of the dip angle D, 
(i.e., V.sub.110 = M sin V sin .phi.). This voltage at wiper 110 is 
therefore equal to the error introduced by the vertical component of the 
Earth's magnetic field, i.e., V sin .phi. and is applied as the other 
input to summing node 106. The output signal from summing node 106 is 
therefore a signal which has been compensated for vertical field errors. 
In other words, the output of summing node 106 is a DC signal proportional 
to H sin .psi. cos .phi.. Thus, while the DC output signal from summing 
node 106 is a signal proportional to the Earth's magnetic field sensed 
along the athwartships axis of the vehicle, it does include a two cycle 
error proportional to cos .phi. due to banking or tilting of the vehicle 
on which the compass transmitter is mounted during turns. 
The output signal from summing node 106 which now includes only a two cycle 
error is applied to summing node 112 at the input of a close loop 
remodulating network 113 in which the signal is remodulated and the two 
cycle error proportional to cos .phi. is eliminated. Remodulating network 
113 consists generally of a modulation path in which the varying DC output 
signal from summing node 112, which is a DC voltage proportional to sin 
.psi. cos .phi. is remodulated. The output of node 112 is applied to 
amplifier 114. The amplified output signal is supplied to modulator 115 
the other input to which is from a reference carrier source 116 which may 
be a second harmonic of the transmitter excitation frequency. The output 
of modulator 115 may thus be a double sideband, carrier suppressed, second 
harmonic signal proportional to H sin .psi. cos .phi.. This remodulated 
signal is applied to an output terminal and is also coupled to a negative 
feedback path 117 in which the second harmonic, modulated signal is 
corrected to compensate for cos .phi. to eliminate two cycle error. The 
signal compensated for two cycle error is also demodulated in negative 
feedback path 117 to provide a varying DC signal proportional to the 
corrected signal. This signal is applied as the second input to summing 
node 112 to allow the Remodulating Network to produce a modulated output 
signal at null balance condition which is H sin .psi.. 
The signal from modulator 115 is applied as one input to a multiplier 118 
in negative feedback path 117. The other input to multiplier 118 is a 
signal from the vertical roll gyro terminal 119 which is proportional to 
cos .phi.. The output from multiplier 118 is therefore a second harmonic, 
double sideband, carrier suppressed signal which is now reduced in 
magnitude since cos .phi.&lt; 1. By By reducing the negative feedback (sin 
cos .phi.&lt; 1), the output from the closed loop is correspondingly 
increased thereby cancelling the cos .phi. error term in the output from 
the athwartships sensing windings. 
In any closed loop with negative feedback, the transfer function 
(output/input) (C/R) is a function of the loop gain G and the negative 
feedback H. Thus, (C/R) = (G/1+GH). If G &gt;&gt;&gt; 1, which is the case if the 
amplifier gain is large, then GH &gt;&gt;&gt; 1 and the transfer function becomes: 
EQU (C/R) = (1/H) (i.e., (C/R) = (G/GH) = (1/H). 
if the negative feedback is reduced by the factor cos .phi. and cos .phi. 
&lt;1, a condition that exists if the plane is not in level flight since 
.phi. - 0.degree. and cos .phi. = 1 only in level flight. For any angle of 
bank cos .phi.&lt; 1. Since the transfer function is inversely proportional 
to negative feedback H, reduction of H by multiplying by cos .phi. which 
is &lt;1, obviously results in increasing cos .phi. by a corresponding cos 
.phi. factor thereby cancelling two cycle error. 
The output of multiplier 118 is a modulated signal which is proportional to 
H sin .psi... This signal is applied as one input to synchronous 
demodulator 119 in the negative feedback path. The other input to 
demodulator 119 is a second harmonic carrier signal from carrier signal 
source 116. This carrier signal is reinserted to demodulate the 
compensated, second harmonic, double sideband carrier to produce a varying 
DC voltage at the output of demodulator 119 which is proportional to H sin 
.psi.. This DC signal is the other input to summing node 112. When output 
from summing node 112 is at the null balance condition then the output of 
modulator 115 in a second harmonic, double sideband modulated signal which 
is proportional to H sin .psi.. Therefore, the signal at the output 
terminal is proportional to the Earth's magnetic field as sensed by the 
induction compass transmitter windings along the athwartships axis with 
errors due to the vertical component of the Earth's field and two cycle 
errors eliminated. 
Similarly, the component of the Earth's magnetic field as sensed by the 
winding of the transmitters along the fore/aft axis, i.e., proportional to 
H cos .psi., are compensated to eliminate errors due to the vertical 
components of the Earth's field during turns, climbs and dives and to 
eliminate two cycle errors. Thus, the incoming signal at terminal 101 is 
amplified in amplifier 120 and applied to demodulator 121. This second 
harmonic carrier signal from carrier signal source 105 is applied to 
demodulator 121 which synchronously demodulates the suppressed carrier, 
double sideband signal to produce a varying DC voltage which is 
proportional to the horizontal component of the Earth's field as sensed 
along the fore/aft axis of the vehicle. This signal, as pointed out 
previously, is equal to the H cos .psi. cos .theta. - V sin .theta.. The 
latter term, of course, represents the error introduced by the vertical 
component of the Earth's magnetic field during climbs and dives. 
The output of demodulator 121 is applied as one input to summing node 122 
and is summed with a compensating signal from a vertical field 
compensation network shown generally at 123. This compensating signal has 
a magnitude such that it cancels the vertical field error term V sin 
.theta.. Compensating network 123 generated a signal proportional to M sin 
D sin .theta. which exactly equals the vertical field error V sin .theta.. 
Network 123, in a manner similar to that described in connection with 
channel 102 includes a potentiometer 124 which has a voltage supplied 
thereto from an amplifier 125 which is proportional to M sin .theta.. The 
input signal to amplifier 125 is a signal from the vertical pitch gyro 
which is proportional to the pitch angle during climbs and dives, i.e., 
sin .theta.. Amplifier 124 not only amplifies the sin .theta. signal but 
introduces a scaling factor proportional to the magnitude of the Earth's 
magnetic field M so that the output from amplifiers equal to M sin .theta. 
Potentiometer 124 has a movable wiper 126 which is controlled by common 
shaft 111 to insert a sin D term. The voltage at wiper 126 is therefore 
proportional to the product of the sine of the pitch angle .theta., the 
Earth's magnetic field M and the sine of the dip angle D, (i.e., V.sub.126 
= M sin D sin -). This signal which is therefore equal to the error due to 
the vertical component of the Earth's magnetic field. This signal is 
impressed as the other input to summing node 121 so that the output from 
summing node 122 is a DC signal which has been compensated for vertical 
field errors. In other words, the output of summing node 122 is a DC 
signal proportional to H sin .psi. cos .theta.. 
This signal which, however, does include a two cycle error term 
proportional to cos .theta. is applied as one input to a summing node 127 
at the input to a closed loop remodulating network 128 in which the signal 
is remodulated and the two cycle error due to cos .theta. is eliminated. 
Remodulating network 128 consists of a remodulating path in which the DC 
voltage proportional to H sin .psi. cos .theta. from node 127 is amplified 
in amplifier 128 and applied as one input to modulator 129, the other 
input to which is from reference carrier source 116. The carrier which may 
be second harmonic of the transmitter excitation voltage frequency is 
remodulated and applied to an output terminal 130 and is also applied to a 
negative feedback path 132 in which the modulated signal is corrected to 
compensate for cos .theta. to eliminate two cycle error. The compensated 
negative feedback signal is demodulated in feedback path 132 and the 
demodulated DC signal is applied to summing node to drive the closed loop 
network to produce a modulated output signal at null balance which is 
proportional to H cos .psi.. That is, corrected for two cycle error as 
well as vertical field error. The output from modulator 129 is applied as 
one input to a multiplier 133 in the negative feedback path. The other 
input to multiplier 133 is a signal from the vertical pitch gyro terminal 
which is proportional to cos .theta.. The output from multiplier 134 is 
therefore a second harmonic, double sideband, carrier suppressed signal 
which is now proportional to H cos .psi.. By reducing the negative 
feedback by cos .theta. (since cos .theta. &lt;1) the output from the closed 
loop is correspondingly increased, thereby cancelling the cos .theta. 
error term in output from the fore/aft sensing windings. The compensated 
signal from multiplier 133 is applied as one input to a demodulator 136 in 
the negative feedback loop, the other input to which is a second harmonic 
carrier signal from the carrier source 116. The output from demodulator 
136 is a DC voltage proportional to H cos .psi.. At zero or null 
condition, the output of modulator 129 and at terminal 130 is a modulated 
signal which is proportional to H cos .psi.. Therefore, the output signal 
at terminal 130 is proportional to the Earth's field as sensed by the 
compass transmitter windings along the fore/aft axis with errors due to 
the vertical component of the Earth's field as well as two cycle error 
eliminated. 
From the foregoing description, it can be seen that vertical field induced 
errors during turns as well as during non-turning climbs and dives have 
been eliminated. Furthermore, if desired, two cycle errors due to these 
various maneuvers may be eliminated also by further processing of the 
signal after initial compensation for vertical field errors. 
In the arrangements illustrated in FIGS. 3, 4 and 5, and exact compensation 
signal, i.e., M sin D sin .phi. or sin .theta. is generated by obtaining a 
signal proportional to the sine of the tilt angle during turns and during 
climbs and dives from the vertical roll or vertical pitch gyro which form 
part of an aircraft system. For some applications, however, compensation 
will be sufficiently accurate if a linear function of the bank angle 
.theta. or the pitch angle .theta. is used in place of the geometric 
function. This approximation becomes quite accurate as the bank angle or 
the pitch angle becomes small which automatically occurs when the aircraft 
is levelling out on a desired heading after turn or after climb or dive. 
Similarly, in correcting two cycle errors, a compensating signal equal 
either to cos .phi. or cos .theta. is utilized to cancel the two cycle 
error. For some applications, the angle itself rather than the 
trigonometric function thereof may be used with equal facility. Hence, it 
will be understood and appreciated that the instant invention is not 
limited to an arrangement in which sompensation for the vertical field 
errors or two cycle errors is achieved by utilizing a signal which is a 
trigonometric function of either the bank or pitch angles but that the 
pitch or bank angles may be utilized directly. 
It will be seen therefore that applicant has provided an arrangement and 
method for compensating a "strapdown" induction compass transmitter in the 
signal processing channels associated with the output of the transmitter 
to eliminate the effects of vertical field error and two cycle errors to 
eliminate turning instabilities such as northerly turning error. 
While a number of specific embodiments of this invention have been shown 
and described above, it will, of course, be understood that the invention 
is not limited thereto since many modifications both as to the circuit 
arrangement and the instrumentalities employed therein may be made. It is 
contemplated by the appended claims to cover any such modifications which 
fall within the true spirit and scope of this invention.