1. EE 495 Modern Navigation Systems INS Error Mechanization Mon, March 21 EE 495 Modern Navigation Systems Slide 1 of 10

2. INS Error Mechanization Introduction Mon, March 21 EE 495 Modern Navigation Systems Why do errors in PVA grow as we perform dead reckoning?  Some due to errors in the PVA “mechanization” equations o Also, other sources such as imperfect gravity models  Most due to errors in the IMU measurements Can we model the process by which these errors evolve?  YES – INS Error Mechanization Later these error models will allow us to combine other navigation sensors with the INS Slide 2 of 10

3. ECI Error Mechanization Notation Mon, March 21 EE 495 Modern Navigation Systems True Value of the vector: Measured value of the vector: Estimated value of the vector: Error in the vector:  Truth - estimate Slide 3 of 10

4. INS Error Mechanization Background - Linearization Mon, March 21 EE 495 Modern Navigation Systems For all three INS frame mechanizations ( i, e, & n ) we developed a vector differential eqn. of the form:  where the state vector  is defined in terms of the PVA and  contains the ideal IMU measurements (i.e., gyro and accel) Slide 4 of 10

5. INS Error Mechanization Background - Linearization Mon, March 21 EE 495 Modern Navigation Systems A state-space model Slide 5 of 10

6. INS Error Mechanization Background – Error terms Mon, March 21 EE 495 Modern Navigation Systems Defining the PVA error state vector as: Where (truth = estimate + error): What about attitude error? Slide 6 of 10

7. INS Error Mechanization Background – Error terms Mon, March 21 EE 495 Modern Navigation Systems Position Error Definition: Velocity Error Definition: Attitude Error Definition:  Thus, and = Truth - Estimate = Truth * Estimate T Slide 7 of 10

8. INS Error Mechanization Background – Error terms Mon, March 21 EE 495 Modern Navigation Systems Accelerometer Measurements: Gyroscope Measurements: = Truth + errors in the measurement Bias Terms Misalignment & SF G-sensitivity Noise = Truth + errors in the measurement Slide 8 of 10

9. INS Error Mechanization Background – Error terms Mon, March 21 EE 495 Modern Navigation Systems Specific Force Error Definition: = Truth - Estimate = Estimate of errors in the measurement Slide 9 of 10 - True errors in the measurement

10. INS Error Mechanization Background – Error terms Mon, March 21 EE 495 Modern Navigation Systems Angular Rate Error Definition: = Truth - Estimate = Estimate of errors in the measurement - True errors in the measurement = Estimate of errors in the measurement - True errors in the measurement Slide 10 of 10