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) |