Inertial Navigation System
Introduction to Inertial Navigation Systems
- INS is an accurate navigational aid for pilots
- The instrument is independent of any ground installation
- INS is capable of world-wide operations
- Advanced form of deduced reckoning is used in INS
- Inertial Navigation System comprises of three parts
- inertial navigation unit
- Mode selector unit
- Control and display unit
Principle of Inertial Navigation Systems
- Accelerometers and Integrators are the core of Inertial Navigation Systems
- High grade accelerometers provide acceleration or deceleration
- Acceleration Integrators integrates acceleration to obtain velocity
- Velocity integrators further integrates velocity to obtain distance gone
- INS knows the distances travelled in North-South and East-West directions
- Change in position of aircraft can be deduced by distance travelled
Principle of Accelerometers
- Accelerometers are used to measure acceleration of aircraft
- E-I bar pendulous suspension is the heart of an accelerometer
- High magnetic permeability materials are used in E-I bar
- Acceleration swings the pendulum off the null position due to inertia
- E-I bar detects acceleration by measuring variation of magnetism
- Variation signal is detected in the E bar which is sent to pick-off device
- Current is amplified is sent to the torque motor of accelerometer
- Torque generated restores the pendulum to the null position
- Acceleration is calculated from the amount of restoration current
First Stage Integrators
- Integrators are time multipliers which multiplies any value with time
- First stage integrators calculate velocity by multiplying acceleration with time
- Acceleration integrated in N-S gets velocity component in N-S direction
- Acceleration integrated in E-W gets velocity component in E-W direction
- The velocities can be compounded to get distance travelled
Second Stage Integrators
- Second stage Integrators are also time multipliers
- Second stage integrators calculate distance by multiplying velocity with time
- Velocity integrated in N-S gets distance travelled in N-S direction
- Velocity integrated in E-W gets distance travelled in E-W direction
- Distances travelled in the N-S and E-W directions provides new position
New Latitude and Longitude
- Latitude of new position obtained by simple addition of nautical miles
- Considering earth to be a perfect sphere latitude calculation is simple
- One minute corresponds to one nautical mile
- Longitude of new position has to be obtained by finding the departure
- Departure is the distance in nautical miles along a parallel of latitude
- Change in longitude is a product of departure and secant of latitude
- Secant multiplier is used to calculate the new longitude
- Accurate latitude information is required to find the new longitude
Platform Stabilisation of INS
- Accelerometers require a stabilised platform for accurate results
- Non-stabilised platform will tilt the E and I bars of the accelerometer
- Incorrect acceleration would be sensed
- Gyro stabilised platform is used to mount the accelerometers
- The platform keeps the accelerometers stable during aircraft manoeuvrers
- Pitch, roll as well as the yaw movements are compensated
- Gyro stabilisation maintains the INS platform horizontal to the surface of earth
Construction of Stabilised Platform
- Gyro stabilised platform uses three horizontal axis gyroscopes
- Spin axis of the gyros are mutually perpendicular to each other
- Gyros have single degree of freedom and are connected to motors
- Rate integrating space gyroscopes are used in the stabilised platform
- Gimbals are shaped like sealed cans floating within each other
- Viscous liquid is used to reduce the bearing torques
- Gyros act like two degree of freedom gyroscopes
- Accelerometers on the platform are maintained horizontal to earth surface
- Stable platform corrects for apparent wander due to earth rate and transport
Correction for Gyro Wander
- Errors due to real as well as apparent gyro wander have to be corrected
- Gyro wander is also classified as drift and topple
- Real wander is caused due manufacturing imperfections
- Real drift is almost eliminated in a perfect gyroscope
- Platform stabilisation corrects for aircraft manoeuvres
- Apparent drift and topple are to be corrected for correct functioning
- Earth rate and Transport are the causes of apparent wander
Earth Rate Correction
- Gyro stabilised platform has to be maintained horizontal to earth surface
- Computed earth rate has to be corrected using a feed back mechanism
- Feed back provides inputs to gyro stabilised platform
- Earth rate wander can be resolved into two components
- Horizontal component is 15 times sin of latitude in degrees per hour
- Vertical component is 15 times cos of latitude in degrees per hour
- These values ate fed to the platform to correct for earth rate
Transport Wander Correction
- Transport wander corrections are applied due to movement of aircraft
- Horizontal component of transport wander is equal to product of
- One sixtieth of easterly component of aircraft velocity and tan of latitude
- Vertical component is corrected using an electro-mechanical feedback loop
- North south component of velocity divided by the radius of earth
- Schuler tuning is used to correct vertical component of transport wander
Coriolis Force and Central Acceleration
- INS computer computes and corrects for Coriolis and centripetal forces
- Coriolis force and central acceleration errors have to be corrected
- Coriolis force is caused due to acceleration of along curved meridians
- Central acceleration is caused due centripetal force on gyroscope
Caging or Warm Up
- Alignment of INS comprises of caging, levelling and gyro compassing
- Caging or warm up is the first step in initial alignment, it lasts for 3 minutes
- Frame, inner and outer gimbals are brought at 90 degrees to each other
- Fluid filled components are heated to correct operating temperature
Coarse and Fine Levelling
- Levelling or coarse alignment is the next in initial alignment, lasts 3 minutes
- Levelling brings the velocity detected by accelerometers to zero
- INS platform is made horizontal to earth surface with aircraft on chocks
- Local gravity vector is sensed by inbuilt accelerometers
- Feedback mechanism is used to transmit correction to levelling motor
- Coarse levelling of the platform roughly leveling platform
- Gravity switches and horizontal accelerometers provide inputs
- Platform is turned within 1 to 2 degrees of aircraft heading
- Fine levelling aligns the platform to an accuracy of 6 seconds of arc
Gyro – Compassing
- Gyro compassing is the third step of initial alignment lasting 11 minutes
- Spin axis of earth is sensed and platform rotated to orientate with true north
- Earth rate provides required inputs to detect spin axis of earth
- Gyro compassing is impossible at high latitudes higher than 70 degrees
- Earth rate which is a factor of cosine latitude is quite low at high latitudes
- Correct azimuth alignment would result in zero acceleration in east or west
- Platform moves at the same velocity as earth in east west directions
- Initial alignment is sensitive to incorrect latitude entry only
- Incorrect longitude entry does not affect initial alignment
Schuler Period
- Consider a pendulum suspended from earth’s surface and bob at earth’s centre
- Length of pendulum will be equal to the radius of the earth
- Acceleration of suspension point around the surface would keep bob vertical
- Vertical position of the bob is due to centre of gravity of earth
- Consider a platform mounted on the suspension point tangential to surface
- Tangential to surface could also be called horizontal to surface
- The pendulum would remain horizontal irrespective of the acceleration
Schuler Oscillations
- If the bob is displaced from earth’s centre the pendulum would oscillate
- The period of oscillation is called Schuler Period which is 84.4 minutes
- Schuler Oscillations cause errors in the which increase and reduce with time
- Calculated position varies from a minimum to maximum error in 84.4 minutes
Bounded Errors
- Bounded errors increase to maximum and return to zero in a schuler cycle
- One Schuler cycle is 84.4 minutes
- Bounded errors are caused due to three reasons
- Platform tilt due to initial misalignment of platform
- Inaccurate measurement of acceleration by accelerometers
- Integrator errors in the first stage of integration
- Bounded errors do not increase with time but causes schuler oscillations
- Distances measured oscillates from its mean position in a sin wave form
Un-bounded Errors
- Unbounded or Ramp errors are outside the feedback loop
- Ramp errors continuously increase with time in a ramp formation
- Initial azimuth misalignment of the platform during gyro compassing
- Acceptable misalignment is within 0.1 degrees
- Real wander of the azimuth gyro
- Drift rate of 1 over 100 of degree is acceptable
- Topple rate of 1 over 100 of a degree is acceptable
- Second stage distance integrator error
- Calculates in correct distances for a given velocity
Cumulative Errors
- Inertial navigation system suffers from both bounded as well as ramp errors
- Inherent errors like the shape of earth also add up to the errors
- The cumulative effect of all the errors would result in a sine wave pattern
- The sine wave increases with time or distance flown
- Better quality of manufacturing reduce errors
- Laser Ring Gyroscopes have reduced the amount of errors