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Inertial Navigation System (INS) & Inertial Reference System (IRS )


The fundamental element of this complex system is the Inertial Sensor System (ISS). To make up this system we have a stable platform consisting of high quality gyros and accelerometers and a computer.

The purpose of the computer is to integrate the accelerometer outputs with time to give velocity and then integrate velocity with time to give distance travelled. From this is available pitch and roll attitude, true heading, true track, drift, present position in latitude and longitude, ground speed and wind. To change all this information from ISS to Inertial Navigation System (INS) we have a further computer which allows us to inject and store waypoints and then compute track angle error, distance and time to go to reach them. This information can be used by the autopilot, flight director or for normal manual flying of the aircraft.

The modern INS was the first self-contained single source of all navigation data; now joined by the similar IRS, laser gyro system which will be discussed later. The current state-of-the-art engineering has enabled production of INS with performance, size and weight characteristics which far exceed other older navigation systems.

Navigation Fundamentals

Great circle

This is a circle on the surface of a sphere whose centre and radius are those of the sphere itself. Relating this to the earth, the equator and all the lines joining the north and south cardinal points (the earth's poles) are examples of great circles.

On a plane surface, the shortest distance between two points is: of course, a straight line which joins them. On a sphere, the shortest distance between two points is the smaller arc of the great circle which passes through both points.

Small circle

This is a circle on the surface of a sphere whose centre and radius are not those of the sphere. With the exception of the equator, all lines of latitude are small circles; they do not represent the shortest distance between two points.

Great Circle and Small Circle.jpg


Longitude and latitude

These fonn a reference system for the position of points on the earth's surface, and in determining the in-flight position of an aircraft with respect to the earth.

Firstly, the datum is established by a great circle through the north and south poles which passes through Greenwich. That half of the circle which passes through Greenwich is known as the prime or Greenwich meridian and is 000°. The other half is called the anti- meridian and is 180°. Other great circles in the form of meridians,
or lines of longitude as they are called, are established to the east and to the west of the prime meridian.

The next step is to have a datum point for positions in the direction north and south. This is obtained by dividing the earth by a great circle midway between the poles. This circle is the equator and is 0° latitude.

Longitude: The longitude of any point is the shortest distance in the arc along the equator between the prime meridian and the meridian through the point. It is expressed in degrees and minutes and is annotated east or west according to whether the point lies east or west of the prime meridian.

Latitude: The latitude of any point is the arc of the meridian between the equator and the point. It is also expressed in degrees and minutes, and is annotated north or south according to whether the point lies north or south of the equator.

Heading (HDG)

The direction in which the nose of an aircraft is pointing; it is measured in degrees (000-360) clockwise from true, magnetic, or compass north, designated as Hdg (T), Hdg (M), and Hdg (C). Hdg (T) is the only one of the three which is plotted.

Track (TK)

The direction in which an aircraft is moving over the earth; it is also measured in degrees from true or magnetic north. Only true TK is plotted. If there were no wind, there would be no drift and TK would be the same as HDG; also the case with a direct head- or tail-wind.

Drift (DA)

The angle between HDG and TK due to the effect of wind. The direction of drift is always from HDG to TK. Each may be true or magnetic but never mixed. If TK is less than HDG, drift is to the left, and if TK is greater than HDG, it is to the right

Heading, Track and Drift.jpg


Ground speed (G/S)

The actual speed (in knots) of an aircraft over the ground, i.e. speed relative to the earth. If there were no wind, GS would be equal to true airspeed (TAS).

Wind direction (W/D)

The angle, measured in degree!: clockwise from true north, with respect to the direction from which the wind is blowing.

Wind speed (W/S)

The speed, in knots, at which the air is moving relative to the ground.

Wind Correction Angle (WCA)

The angle between the desired track and the heading of the aircraft necessary to keep the aircraft tracking over the desired track.

Ground Speed and True Airspeed.jpg


Parts of an Inertial Navigation System (INS) & Inertial Reference Unit (IRU)

An INS system consists of the four principal units as follows


Inertial navigation unit (INU)

This unit contains an inertial section consisting of accelerometers, gyroscopes and gimballed platforms, a digital computer and all associated circuit module cards, and a battery charger unit.


Control and display unit (CDU)

This allows all associated data to be inserted into the computer, and to be read out from it by means of segmented LED displays.


Mode selector unit (MSU)

This unit controls all the modes in which the system can be operated.


Battery unit

This unit provides dc power for turning the system on, and is also used as back-up in the event that power from an aircraft's system is interrupted.

Parts of INS.jpg


The inertial reference system (IRS) performs the same basic navigational functions as an INS, but, as its fully digital computer can also be pre-programmed with other relevant reference data. The system consists of only two principal units. The outputs are supplied to a greater number of interfacing systems. The inertial reference unit (IRU) also contains accelerometers, gyroscopes and the computer.

Inertial Navigation System (INS) vs Inertial Reference System (IRS)

The major differences of IRS from INS are as follows

  • the gyroscopes are of the ring laser type instead of the spinning rotor type.

  • the complex mechanical arrangement of a gimbal system and synchronous transmission loops is replaced by a mathematical equation program so that acceleration and attitude signals required for navigation are directly computed.

  • the unit is directly mounted to an airframe, i.e. it is of the 'strapdown' type so that the aircraft itself becomes the inertial platform.

  • magnetic and true headings are derived from a program of known data related to the position data loaded into the computer, so that headings can be computed without the aid of MHRS flux detector units.

  • no battery "unit and charger is used.

Basic Principle

The IN/IR system work on the principle of measurement of acceleration and integrating it with respect to time obtain velocity signal and integrating the velocity signal with respect to time to to obtain distance.

INS basic Principle.jpg


If the latitude and longitude of the starting point of its flight are fed into the computer, the computer would be able to display the present position and the ground speed, with inputs from the accelerometer and integrators


The accelerometer is basically a pendulous device. When the aircraft accelerates, the pendulum, due to inertia, swings off the null position. A signal pick-off device tells how far the pendulum is off the null position. The signal from this pick-off device is sent to an amplifier and current from the amplifier is sent back into a torque motor located in the accelerometer.


A torque is generated which will restore the pendulum to the null position. The amount of current that is going into the torquer is a function of the acceleration which the device is experiencing.



Two accelerometers are mounted at the heart of the inertial system. One of the accelerometers measures the aircraft‘s acceleration in the north- south direction and the second in the east-west direction.

Rate Gyroscopes

The gyroscopes are of the integrating rate type, meaning that they sense movement about only one axis, and that the rate changes are integrated to give distance changes.


The input and output axes of the gyroscopes are positioned so that they relate directly to the north and east coordinate system of 'X' and 'Y' accelerometer positioning. They are designated as north ('Y') and east ('X') gyroscopes.


The 'Y' gyroscope has its input axis aligned with an aircraft's roll axis, while that of the 'X' gyroscope is aligned with the pitch axis; the manner in which they sense attitude changes depends on aircraft heading.


Thus, if an aircraft and its INS platform are heading north, the 'X' gyroscope senses pitch attitude changes, and the 'Y' gyroscope senses roll attitude changes. The converse of this is true, however, when an aircraft and platform are heading east.

A third gyroscope is also provided and is mounted on a second platform. Its purpose is to sense changes about the local vertical (designated 'Z') and to keep the X-Y platform in the same position relative to space and the N-E coordinates, i.e. to maintain its north datum. This gyroscope and its platform are also designated 'Z'. Any change of platform or azimuth relative to the inner gimbal ring corresponds to an equivalent heading change, and so by connecting a signal pick-off element to the 'Z' gyroscope signals corresponding to such change can be produced. These signals are supplied to an azimuth torque motor which rotates the 'Z' platform in the opposite direction to the heading change

The Schuler Tuned Platform

For precision operation of an INS, it is essential for the 'X' and 'Y' acceleration-sensing axes to be maintained normal to a local vertical with the earth's centre at all times. If this were not done, false gravitational forces would be sensed, giving rise to errors in the computed distance flown and in the present position of an aircraft. These forces and errors are overcome by mounting the accelerometers in such a way that any displacements are detected by gyroscopic-type sensors.

There are two mounting arrangements:

  • the gyro-stabilized platform

  • the 'strapdown'

The principle of both is based on the Schuler theory which states that when a pendulum whose bob is at the centre of the earth, and suspended from a point above its surface.


If, the suspension point were accelerated around the earth, the bob, being at the centre of the earth's gravity, would always remain vertically below its suspension point. A platform mounted on the suspension point tangential to the earth's surface would, therefore, also remain horizontal irrespective of acceleration.

If, for any reason, the pendulum bob became displaced from the earth's centre, it would start to oscillate with a period of 84.4 minutes; this is the value obtained by substituting the earth's radius (in feet) for the pendulum length I in the basic formula for calculating the time period of a pendulum.


Thus, by mechanizing an INS platform to remain horizontal, an analogue of the Schuler earth pendulum with a period of 84.4 minutes is produced, and the platform is then said to be Schuler tuned.

The gyro-stabilised (gimballed) Plafform

Three gyroscopes are mounted on the stable platform, filed so that their sensitive axis are aligned with north-south, east-west and earth vertical, respectively. 


The platform is pivoted to inner and outer gimbals and each gimbal axis is connected  to a servo motor; the two horizontal-axis motors are known as the pitch and roll motors and the vertical axis motor is known as the azimuth motor.


The north gyro sensitive axis is aligned north-south and the east gyro sensitive axis is aligned east-west. Similarly, the north-south accelerometer pendulous mass axis is aligned north-south and the east-west accelerometer mass axis is aligned east-west. The sensitive axis of the azimuth gyro is aligned with earth vertical.

Gryo Stabilised Platform.jpg


Let us assume that the aircraft is stationary on the ground on a northerly heading and with the platform levelled (i.e. earth horizontal) and aligned with north and accept for the moment that the system will maintain the platform both level and aligned. 


If the pilot now takes the aircraft away from its stand, still on a northerly heading, the north-south accelerometer will sense the northerly acceleration as the aircraft moves away and the integrators will convert this to speed and distance for the computer and its cockpit display. 


The east-west accelerometer senses no acceleration and so the system continuously computes distance travelled north from the starting point.


On arrival at the eastern end of the east-west runway, the pilot turns the aircraft left onto a heading of 270°T. The frame of the stable platform, being attached to the airframe, will have turned through 90° with the aircraft. Any tendency of the stable platform to turn away from its north-south alignment will be immediately sensed by the azimuth gyro, which will precess and send an error signal to the azimuth servo motor. The platform is therefore turned relative to the airframe to maintain north-south alignment. The amount by which it is turned gives the change of aircraft heading for the INS computer.


As the aircraft accelerates along the east-west runway on the take-off roll, the acceleration is sensed by the east-west accelerometer and integrated to show increasing velocity and distance travelled westward. The aircraft nose is pitched up and this nose-up pitch is maintained during the climb, which for simplicity we will assume continues on a westerly heading.


Any tendency of the stable platform to tilt in pitch will be immediately sensed by the north gyro, since on this heading the pitch alis is coincident with the north-south axis. The north gyro will send an error signal to the pitch servo motor to correct the tilt until the north gyro signal is nullified.


Let us now assume that the aircraft levels out at the top of the climb at constant speed (i.e. no acceleration) and turns left onto a heading of 225°T. During the turn the aircraft will, of course, bank and any tilting of the stable platform will be sensed by both north and east gyros, which will signal the pitch and roll servo motors to maintain the platform level. 


North alignment during the turn is again maintained by the azimuth gyro and azimuth servo motor, turning the platform relative to the airframe and generating the heading change for the INS computer whenever the aircraft is on a non-cardinal heading, control of platform levelling is shared by the north and east gyros and the pitch and roll servo motors. North-south alignment is at all times maintained by the azimuth gyro and its servo motor.

Strapped-down Systems

The disadvantages of the gyro stabilised platform INS are that the gyroscopes are expensive to manufacture and they inevitably suffer to some extent from random wander, however small, due to manufacturing imperfections.  These, of course, lead to inaccuracies in the INS output.

The gyroscopes take some time to warm up and reach their operating speed, and platform alignment is a relatively slow process with the vast improvements in computer technology and the introduction of the ring laser gyro it became possible to develop inertial systems that do not require a stabilised, earth horizontal platform, but which can be mounted directly to the aircraft structure. Hence the term ‘strapped down’. 


These systems typically use three ring laser gyros with their sensitive axes aligned to the aircraft roll, pitch and yaw axes. Since the accelerometers are also attached to the airframe and move with it, it follows that they will sense gravitational accelerations. 

The INS computer must differentiate between the accelerations that occur in the earth horizontal plane and those that occur in the aircraft horizontal plane in order to eliminate gravitational accelerations. Alignment is achieved during an alignment phase with the aircraft stationary on the ground.


The INS computer is able to discriminate between the accelerometer outputs due to gravity, since aircraft attitude is filed, and those due to earth rotation and to compute the angle between the aircraft fore and aft (roll) axis and true north.

In the navigation mode the INS computer receives input of aircraft manoeuvres from the ring laser gyros and uses these to identify accelerometer outputs due to aircraft movement in the earth horizontal plane. 


These are then related to the north-south, east-west and azimuth ales to compute speed and direction of  movement, distance travelled, current position, etc.


Corrections for earth rate, transport wander and coriolis effect are computed in much the same way as previously described, from the calculated angular differences between aircraft and earth horizontal and between true north and the aircraft longitudinal axis.


Some strapped-down systems use an alternative type of ring laser gyro that has four sides as opposed to three and some military systems incorporate a third accelerometer to measure vertical acceleration.

Position Calculation

The ultimate function of an inertial navigation system is to provide the pilot with navigational data such as track, ground speed and present position in terms of latitude and longitude.


Track and speed

The track calculated by the INS is a great circle track. The speed calculated at any instant is groundspeed, because the INS bases its calculations upon accelerations of the aircraft over the surface of the earth.


Latitude and longitude

Distance travelled north-south in nautical miles converts directly to change of latitude, since each nautical mile along a meridian equates to one minute of latitude. Distance travelled east-west is known as departure and is calculated using the equation:


Departure E-W(nm) = change of longitude × cosine latitude 


Since, in the case of the INS computation, departure is known the calculation carried out by the INS computer to determine change of longitude is therefore:


Change of longitude = departure (nm) × secant latitude

INS Self-alignment

The stable element in an INS must be accurately aligned in both azimuth and attitude to allow the accelerometers to measure accelerations along their chosen axes.

  • Warm up period - the first stage in any alignment sequence is to bring the fluid-filled components to the correct operating temperature. This phase normally takes between 3 to 4 minutes.

  • Coarse alignment - the platform is roughly levelled and aligned in azimuth; this removes gyro alignment errors and cuts the time to a minimum.

  • Coarse levelling - pitch and roll driven until they are at 90° to each other. The platform is then roughly levelled using either the aircraft frame as reference, or using the outputs from gravity switches or the horizontal accelerometers.

    • Coarse azimuth alignment - is achieved by turning the platform until the heading output agrees with the aircraft’s best known True Heading.

    • Coarse alignment level and aligns the platform within 1°- 2° in a few seconds.

  • Fine levelling - with zero output from the accelerometers fine levelling is achieved. The process takes anything up to 1 to 1.5 minutes, levelling the platform to within 6 seconds of arc.

  • Gyro compassing - the platform can be aligned in azimuth by connecting the gyro normally used to stabilize the platform about an east-west axis, to the azimuth gimbal motor. With the platform correctly aligned in azimuth the east gyro should not be subject to rotation of its input axis due to earth rotation; when the platform is out of alignment the east gyro will detect a component of earth rotation and the resultant output signal can be used to torque the azimuth gyro until the table is aligned.

  • Accelerometers must be levelled (velocity set to zero).

  • Platform must be orienteded to true north - gyro compassing (position verified).

Mode selector Panel

The various modes of operation of the stable platform INS are selected by means of a simple panel, similar to that illustrated in Figure 3.9. The rotary switch shown has five positions and there are two illuminated annunciators.



This is the mode selected to switch the system on, which is for ground use only . In this mode power is supplied to the system and the gyros are warmed and spun up to operating speed. Whilst this is taking place it is usual to insert the current position to the nearest 6 seconds of arc. The aircraft's present latitude and longitude are inserted in the CDU when in this mode, and an auto-alignment sequence commences. The INS is not affected by movements of the aircraft while in this mode.



This selects the alignment mode, during which the levelling and alignment procedure described above takes place. When alignment is completed the 'READY NAV' light illuminates green to indicate that the system is ready to go into the 'NAV' mode. The aircraft must remain stationary in the 'ALIGN' mode.


This is the navigation mode, used throughout the period of ground movement and flight and during which the INS will make all its navigation calculations and display them as required on the control and display unit. It must be selected before the aircraft moves from its parked position. The 'READY NAV' light is extinguished on selection. 


Selects pitch, roll and platform heading stabilization outputs only; no display is presented on the CDU. This mode disables the navigational capability of the computer for the remainder of a flight, because once turned off, the computer cannot be switched on again. Normally, this selection is only made when a computer failure has occurred.


The selector switch is provided with two mechanical stops: one between the 'STBY' and 'ALIGN' mode positions, and the other between the 'NAV' and 'ATT' mode positions. In order for the selector knob to move over the stops, it must be pulled out. The reason for having the stops is to prevent the 'NAV' mode from being inadvertently switched out.

The INS has its own internal battery, which is capable of supplying power to the system for a limited period, typically about 15 minutes, in the event of loss of the normal power supply. The BATT annunciator will illuminate red when the battery power falls to a predetermined level (typically 18 V), warning the pilot that the INS is about to fail.

The mode control panel for IRS is similar to the INS except that a 'STBY' mode is not required for the reason that the application of comprehensive digital signal- processing techniques, and of ring laser gyroscopes, eliminates the need to allow for 'warm-up' and gyroscope 'run-up'.

INS Control Panel.jpg


Four mode and status annunciators lights are provided for each system as follows:


Illuminates white when a system is in the alignment mode. In the event of alignment procedure failure, it flashed on and off.


This illuminates amber to indicate that power to the system has automatically changed over from the normal 115 V ac to 28 V dc power from the battery system.


Illuminates amber when the battery power source drop below 18V.


Illuminates amber when failure in the system are detected.

Control and display unit (CDU)

The unit comprises an alphanumeric light-emitting diode (LED) display, a rotary selector switch and a keyboard for the insertion of data. In addition, there is the facility to set up a route by inserting waypoint latitudes and longitudes at which track changes are to be made.

Waypoints are identified in numerical sequence using the selector wheel, starting with waypoint 1 as the departure airfield. Each waypoint is entered using the keyboard to set its latitude in the left alphanumeric display and its longitude in the right alphanumeric display. Insertion is made by pressing the INSERT button.

If a change of track is authorised en-route, say direct from waypoint 5 to waypoint 8, this is made using the TK CHG pushbutton.

INS:IRS Control and Display Unit (CDU).j


CDU selections

The functions of the CDU buttons are as follows

Display Selector Switch

The Display select switch consist of the following position:

TK/GS (track and groundspeed)

The INS computed track, usually referenced to magnetic north, is displayed to the nearest tenth of a degree in the left display and the ground speed in knots in the right display. For example, a current track of 135ºM and a ground speed of 467 knots would appear as 135.08 and 0467.

HDG/DA (heading and drift angle)

The heading obtained from the angle between the platform frame and north reference is displayed to the nearest tenth of a degree in the left display. The angular difference between heading and track (drift angle) is displayed to the nearest tenth of a degree in the right display, preceded by the letter R or L to indicate whether drift is right or left. Thus, a heading of 137ºM on a track of 135ºM would be presented as 137.08 and L 02.08.

XTK/TKE (cross track distance and track error angle)

Cross track distance is the distance by which the aircraft is displaced right or left of the desired great circle track and is displayed in the left display to the nearest tenth of a nautical mile. The track error angle is the angular difference, right or left, between the desired great circle track and the actual track being made, to the nearest tenth of a degree. If the aircraft were displaced 112 nm to the left of the desired track of 135ºM, the left display would read L 01.5. If the track being made good happened to be 130ºM, the right display would read L 005.08.

POS (present position)

The aircraft's current latitude and longitude are shown to the nearest 6 minutes of arc in the left and right displays, respectively. Suppose it happens to be at 51.15.7N, 04.23.6W, this would appear as 51815.7'N in the left display and 04823.6'W in the right display.

WPT (waypoint positions)

The position of each inserted waypoint is shown as latitude in the left display and longitude in the right display by selecting WPT on the rotary selector switch and scrolling through the waypoint numbers with the waypoint selector wheel.

DIS/TIME (distance and time to the next waypoint)

The distance in nautical miles from the present position to the next waypoint is shown in the left display and the time at present groundspeed to the nearest tenth of a minute in the right display.

WIND (wind speed)

The INS is able to compute wind direction and speed and these are displayed in the left and right displays, respectively, to the nearest degree of arc and knot.

DSR TK/STS (desired track and status)

The great circle track from one waypoint to the next changes as the aircraft progresses between the two and the INS computes the present desired magnetic track based upon distance from the waypoints, magnetic variation and the assumption that the aircraft is on track. This will appear in the left display to the nearest tenth of a degree and the right display will be blank. The status function is for use only whilst the INS is in ALIGN mode and it shows a numerical display in the right window that indicates the status of the alignment procedure. The display typically shows 99 at the start of alignment and counts down to 0, when alignment is completed and READY

NAV is illuminated.

WPT Selector Switch

This Switch is of the thumbwheel type, and when the 'Data Selector Switch' is set to 'WPT', it enable WPT's 1 to 9 to be selected for latitude and longitude insertion, or selection of WPT's 0 to 9 for presentation of their coordinates on the upper display. It is also used for inserting and displaying latitude, longitude, altitude and frequency of up to nine DME stations.

TK CHG Switch

The track change (TK CHG) push button is used when altering the pre-planned sequence of waypoints. Conventionally waypoint 0 is the aircraft's current position. Suppose ATC has cleared you to fly direct to, say, waypoint 5 then the TK CHG button is pressed until 0±5 appears in the display. The DIM thumbwheel adjusts the brightness of the LED displays.


This rotary switch is used to select the type of flight control to be used in flying from waypoint to waypoint. In AUTO the INS will automatically change the from/to display as each waypoint is over- flown and would normally be used in conjunction with automatic flight. In MAN (manual) the pilot is required to enter the from/to display as each waypoint is reached. The RMT (remote) position is used when two or more INS are fitted and enables the waypoint information to be transferred from one INS to the other(s).


Operation of this button transfers entered data into the the computer

Data Keyboard

This contains ten push-button keys switches (0-9) fro entering present position and WPT coordinates,'FROM/TO' WPTs. desired XTK effects, and TK hold. Each key illuminates white when pressed. For the Display of DME station latitude, longitude, altitude and frequency, the following key selection are made 3 and 9 enable altitude and frequency display. 2 or 8 enable altitude to be loaded. 4 or 6 enables frequency to be loaded. 7 and 9 enables latitude and longitude to be loaded.


This push- button switch is used to erase data loaded into display but not yet loaded into the computer, when presses it illuminates white.


This permites a position check and update to be made, and also a display of malfunction codes. It also illuminates white when pressed.

There are three Annunciators of the CDU as follows


This illuminates amber two minutes before reaching a 'TO' WPT. The operation of this annunciator also depends on the setting of the 'AUTO/MAN/RMT' switch. In the 'AUTO' mode the annunciator is extinguished when the 'FROM/TO' display changes to the next two WPT number. If the switch is in "MAN' =, the light flashed as the aircraft flies over the WPT. The annunciator is operable as a G/S greater than 250 knots.


Illuminates amber when the INS is operating on Battery power.


Illuminates red when the system malfunction occurs, or during 'ALIGN' mode it flashes to indicate system degradation, or that an alignment failure has occurred. It will not extinguish unless the fault is corrected or the INS is switched off. 

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