Class Start: August 9, 2021

Mid Semester Exam: September 20-24

Mid sem break:  September 27 - October 1

Last date for quiz: Nov 12

Last day of teaching : Nov 20

End Sem Exam: Nov 22-30, 2021

 

Text Book: Brown and Hwang, mostly 4th ed (see the syllabus) and occasionally 3rd ed

Reference book: by Jay Farrell, Bar-Shalom (see  the syllabus)

 

 Instructor: Prof. Hari Hablani

       Dr. Abhirup Datta

       Dr. Saurabh Das (Course Coordinator)

 

 

Week

 

Tutorial

Wk 1: Aug. 9 - 13

 

 1.6 Continuous random variables and probability density function; 1.7 Expectation, averages, and characteristic function; 1.8 Normal or Gaussian random variables; 1.10 Joint continuous random variables; 1.11 Correlation, covariance and orthogonality; 1.12 Sum of independent random variables;

Chapter 1 Problems

Wk 2: Aug. 16 - 20

 

 1.13 Transformation of random variables;

1.14 Multivariate normal density function; 1.15 Linear transformation and general properties of normal random variables; 1.16 Limits, convergence, and unbiased estimators

2.3 Gaussian random process;

Chapter 1 and 2 problems

Wk 3: Aug. 23 - 27

 

 2.5 Autocorrelation function; 2.6 Cross-correlation function; 2.7 Power spectral density function; 2.8 white noise; 2.9 Gauss-Markov processes; 2.10 Narrow-band Gaussian process; 2.11 Random walk; 2.12 Pseudorandom signal; 2.13 Determination of autocorrelation and spectral density from experimental data; 2.14 Sampling theorem

 

Chapter 2 problems

Wk 4: Aug 30 – Sept 3

 

Bar-Shalom: 1.4.17 Chi-square distributed random variables; 1.5.1 Hypothesis testing; 1.5.2 Confidence regions and significance; 1.5.4 Tables of Chi-square and Gaussian distribution; 2.4-3.4 Least squares estimation -- Batch, Recursive, examples; nonlinear, iterated least squares, example;

Chapter 3 problems

Wk 5: Sept. 6 - 10

 

3.5 Polynomial fitting: linear (constant velocity) model, quadratic (constant acceleration) model, cubic (constant jerk) model; 3.6 Residual norm and statistical significance of parameter estimates -- least square estimation, example; 3.7 Bearing-only target motion analysis

Chapter 3 and 4 problems

Wk 6: Sept. 13 - 17

Brown and Hwang: 3.2 Steady-state analysis; 3.3 Integral tables for computing mean-square value; 3.4 Pure white noise and bandlimited systems; 3.5 Noise equivalent bandwidth; 3.6 Shaping filter; 3.7 Transient analysis; 3.8 PSD units and white noise

Chapter 4 problems

Sept. 20 - 24

Midterm Break

(no lectures)

Sept. 27 – Oct. 1

Wk 7: Oct. 4 - 8

3.9 Vector description of random processes: Continuous-time and discrete models; 3.10 Monte Carlo simulation of discrete-time processes; 4.1 A simple recursive example; 4.2 The discrete Kalman filter;

Chapter 5 problems

Wk 8: Oct. 11 – 15

4.3 Simple examples and augmenting the state vector; 4.4 Marine navigation application; 4.5 Gaussian Monte Carlo examples; 4.6 Prediction; 4.8 Updating the error covariance matrix

Chapter 6 problems

Wk 9: Oct. 18 – 22

5.3 Orthogonality principle; 5.4 Divergence problems; 5.5 Suboptimal error analysis;5.6 Reduced-order suboptimality; 5.8 Kalman filter stability; 5.10 Deterministic inputs

Chapter 7 problems

Wk 10: Oct. 25 - 29

 

6.11 (3rd ed) Real-time implementation issues;  7.4 (3rd ed) Colored measurement noise;

6.6 Correlated process and measurement noise -- Delayed state filter

Chapter 8 problems

Wk 11: Nov. 1- 5

7.2 The extended Kalman filter; (3rd ed) Ch. 10 : Integration of non-inertial measurements into INS:  10.3 Damping the Schuler oscillation with external velocity sensors; 10.4 Baro-Aided INS vertical channel; Ch. 8 Go-Free concept:

 

Wk 12: Nov. 8-12

8.2 Go-Free of GPS Clock bias -- Double-Differencing; 8.5-8.8 Complementary filter: intuitive method, error model, total model; 8.9 Go-free Monte Carlo; 8.10 INS error models; 8.11 Integrating INS/DME position measurements; Ch. 9 GNSS or NavIC-based position and velocity determination; receiver autonomous integrity monitoring, parity check (Kaplan and Hegarty)

 

Wk 13: Nov. 15-19

 

9.2 GNSS observables, carrier smoothing of code, carrier phase differential, stand-alone positioning; 9.3 GPS error models, receiver clock model; 9.4 Delta-range processing, differential carrier, carrier smoothing; relative positioning; 9.5 GPS-aided inertial error model;

Chapter 9 problems

Nov. 22-30

End Semester Examination

(no lectures)