Integration of Inertial Navigation System and Global Positioning System Using Kalman Filtering

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Integration of Inertial Navigation System and
Global Positioning System Using Kalman Filtering

• By
• Vikas Kumar N. 99D01010
• Under the guidance of
• Prof. K. Sudhakar

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Overview

• Inertial Navigation System (INS)
• Global Positioning System (GPS)
• Kalman Filtering
• Simulation work
• Hardware Implementation

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Strap Down INS

• Body fixed gyroscopes accelerometers

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INS module

p
Flight Dynamics Control
Euler parameter integration
Euler angle computation
DCM
q
r

ax
Gravitation Centrifugal correction
U V W integration
VN VE VD calculation
Latitude Longitude Altitude integration
H
ay
az
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FDC States
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Euler angle integration
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Euler parameters - Quaternions
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Euler angle computation
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Direction Cosine Matrix

• From local earth or navigation frame to body
  frame.

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Navigation frame
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Acceleration Corrections

• Centrifugal
• Gravitational

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Navigation Frame
Body Frame
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• Latitude integration
• Longitude integration
• Height integration

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INS module

p
Flight Dynamics Control
Euler parameter integration
Euler angle computation
DCM
q
r

ax
Gravitation Centrifugal correction
U V W integration
VN VE VD calculation
Latitude Longitude Altitude integration
H
ay
az
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INS Errors

• Alignment roll pitch yaw errors
• Gyroscope
• Bias or drift constant gyro output
• Scale factor error
• Accelerometer
• Bias (changes randomly after each turn-on)
• Scale factor error
• Nonorthogonality of gyro and accelerometer
• Random measurement noise
• Navigation errors position velocity

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GPS

• Space segment
• 24 satellites
• Control segment
• Ground control
• User segment
• Receiver
• Civil military
• Gives position in terms of latitude longitude
  and altitude

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GPS (contd.)

• L1 primary signal at 1575.42 MHz
• Clear Acquisition Code (C/A) civilian use
• Unencrypted signal
• Precise Code (P) military use
• Encrypted higher bandwidth more precise
• L2 secondary signal at 1227.6 MHz
• C/A can be degraded intentionally Selective
  Availability

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GPS errors

• Ephemeris error
• Incorrect satellite location transmitted by GPS
• Affects ranging accuracy
• Satellite Clock errors
• Multipath reflection errors
• Atmospheric delays
• Ionospheric
• Tropospheric
• Random measurement noise
• Dilution of Precision (DOP)

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GPS module
Flight Dynamics
X
H
Latitude Longitude Altitude conversion
Y
Z
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Conversion using WGS-84

• Distance corresponding to a degree change in
  latitude is given by
• Distance corresponding to a degree change in
  longitude is given by

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• Where a and b are the equatorial and polar radius
  of the earth respectively.
• Latitude at current location
• Longitude at current location

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Accelerometer Modelling

• Ideally
• Actually
• C is the scale factor in mV/g
• D is the 0 g offset in V
• 16-bit ADC modelling
• Finally

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Gyroscope Modelling

• Ideally
• Actually
• C is the scale factor in mV//s
• D is the constant drift in /s
• 16-bit ADC modelling
• Finally

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• Errors due to temperature effects ignored
• Errors due to non-orthogonality of gyros and
  accelerometers ignored
• GPS Random error introduced with standard
  deviation of 20m.

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Error Implementation

p
Sensor modelling
Flight Dynamics
Euler parameter integration
Euler angle computation
DCM
q
r

ax
Gravitation Centrifugal correction
U V W integration
VN VE VD calculation
XY Height Integration
l m H
ay
az
l
m
Kalman Filter
H
Corrected position
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Aim

• To reduce the effect of errors in the sensors so
  that INS can give out correct values of the
  position of the aircraft
• To use the GPS output as a tool to estimate the
  error in the INS and to correct the error as much
  as possible by using the method of Kalman filters

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Kalman Filter

• Stochastic estimator
• Estimate a state x with a measurement z

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• wk and vk represent process and measurement
  white noise with covariances Q and R.
• If is the a priori estimate of the process at
  time tk then the error covariance matrix is
  defined as

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Prior estimate
Compute Kalman Gain
Update estimate with measurement
Project Ahead
Compute error covariance for update estimate
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Feedback aided INS
Feedforward aided INS
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9 State Filter Model

• Position Velocity Attitude and Gravity
  perturbation equations

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Position Dynamics Equation
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Velocity Dynamics Equation
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Attitude Dynamics Equation
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State Space Model
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Discrete Kalman Filter
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Correction Algorithm
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Hardware Implementation
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Overview

• Description of target hardware
• System flow
• DSP simulator
• Future Work

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Target Hardware

• Requirements
• Compact
• Light weight
• Single voltage supply operated
• Speedy accurate calculations
• INS data acquisition computations within 10ms
• GPS data acquisition and Kalman filter
  computation within 10ms (preferred)
• Two blocks
• GPS INS Data Acquisition Card (GIDAC)
• Navigation Processor Card (NPC)

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GIDAC

• GPS data acquisition thru Field Programmable Gate
  Array (FPGA) based chip
• Only 1 chip required
• Faster than micro-controller
• Accelerometer Gyroscopes
• Acquisition using a 2nd order Butterworth filter
• Digitizing using 16-bit 6 channel ADC

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INS acquisition

• Sensor signals are signal conditioned
• Filtered for noise
• Scaled to 0 - 5V
• 6 channel 16 bit parallel output ADC (ADS8364)
  chosen
• Simultaneous sampling is done
• Digitized signals sent to NPC

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GPS acquisition FPGA chip

• Reads data from GPS receiver in SIRF
  (proprietary) sentence format
• One chip faster processing due to presence of
  internal DPRAM
• Stores calculates the positions given by the
  GPS in SIRF format extremely fast
• Internal DPRAM stores the final calculated
  position NPC every 1 s
• Asynchronous communication maintained to save
  processor time

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NPC

• DSP TMS320VC33
• Supporting Hardware
• Parallel port for connectivity
• PAL chip 22V10
• DPRAM 7130
• JTAG connector to download emulator
• Other required peripherals

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DSP TMS320VC33

• Floating point DSP
• Max. Instruction cycle time 13ns or 150MHz
• 75MIPS 150MFlops
• Parallel multiplication ALU operations in a
  single cycle
• 2 timers
• 50 pin connector interface with external
  circuitry
• 34K words dual access SRAM
• Inexpensive

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Supporting Hardware

• DPRAM for parallel data transfer storing output
• Control signals to select peripheral chips given
  by Programmable Array Logic chip
• Provides output for control of dataflow hold
  read signals to ADC

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System Flow

• Initialization of DSP peripherals
• 2 interrupts /INT0 /INT1 defined
• Timer0 Timer1 configured
• Software reset given to ADC by program operate
  in CYCLE mode
• Timer0 provides clock to ADC at 5MHz
• Timer1 interrupts every 10ms or 100Hz
• Start_INS 0 GPS_available 0

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• 6 channels of ADC A0 A1 B0 B1 C0 C1
  grouped 2 at a time
• EOC signal in 3 pulses
• Variable count 2 used to count these signals
• /HOLDx signals are made low whenever Timer1
  overflow occurs 6 channels of ADC are sampled
• Main program waits in IDLE mode

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Interrupt Service Routines

• EOC of ADC (/INT1) occurs
• Data from 6 channels stored
• Start_INS 1
• Return to main program
• Reading of GPS by FPGA (/INT0) occurs
• Data from internal DPRAM read by NPC
• GPS_available 1
• Return to main program

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DSP simulator

• Code Composer Studio 3x4x
• Simulates actual DSP target hardware not
  required
• C assembly source codes can be interfaced and
  debugged
• Inputs from C program read every 10ms from a file
  on PC (actual sensors not used)
• Voltages from sensors in hexadecimal format
• GPS data in hexadecimal format as would be given
  by SIRF sentence position along NED in m
  GPS modelling
• Initial state at t 0 was hardcoded in the
  program

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Features of CCS3x4x

• Probe points
• File reading
• File writing
• Similar to sensor reading
• Output in COFF format
• Assembly language code to be loaded in TMS320C3x
  assembler
• Profile points
• Enable clock
• Count cycles
• Time taken by program on a real DSP can be
  computed

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• Tested for 50s running of the program
• Memory consumed 17K words no external RAM
  required
• Accuracy upto 3-4 decimal places as matched with
  the MATLAB output

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Future Work

• Emulator to run assembly code on target hardware
  required
• Results timing to be checked on target hardware
  for consistency
• Sensor board can be designed
• Sensor modelling in program to be modified
  according to sensors being used
• Calibration to be done to calculate scale factors
  biases of sensors.
• Initial state at t 0 currently hardcoded or
  read from a file better method to be devised
• Output currently written on DPRAM a
  simultaneous display interface to be created
• More number of states can be implemented on
  Kalman filter for higher accuracy of output

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THANK YOU !
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