The main objective of this project is to track a under water target using Sound Navigation and Ranging (SONAR) measurements in passive mode, in two–dimensional space making use of bearing angle measurements. An Extended Kalman filter algorithm is considered for processing noise altered measurements along with smoothers algorithms to reduce the errors in the estimates of target parameters (range, course, and speed of the target). Details of mathematical modelling for simulating and implementation of the target and observer paths and outcomes are presented in this work.

1. DADI INSTITUTE OF ENGINEERING AND TECHNOLOGY
(Approved by A.I.C.T.E., New Delhi & Permanently Affiliated to JNTU GV)
Accredited by NAAC with ‘A’ Grade and Registered u/s 2(f) & 12(B) of UGC Act
UNDER GUIDANCE OF
Dr. Kausar Jahan M.Tech, Ph.D.
Assistant Professor
Department of ECE
TEAM MEMBERS:
NAKKA VIJAYA 20U45A0414
MARTURI HARISH 20U45A0429
DANDA SWARNA 19U41A0406
K S V AJAY KIRAN 20U45A0408
Applying SmoothingTechniques to PassiveTarget
Tracking

2. ABSTRACT
• The main objective of this project is to track a under water target using
Sound Navigation and Ranging (SONAR) measurements in passive mode,
in two–dimensional space making use of bearing angle measurements. An
Extended Kalman filter algorithm is considered for processing noise altered
measurements along with smoothers algorithms to reduce the errors in the
estimates of target parameters (range, course, and speed of the target).
Details of mathematical modelling for simulating and implementation of
the target and observer paths and outcomes are presented in this work.

3. CONTENTS
⮚Problem Statement
⮚Target-Observer Scenario
⮚Course Angle
⮚Target Motion Analysis
⮚Filtering Algorithms
- Kalman Filter
- Extended Kalman Filter
Simulation and Results
Future work

4. PROBLEM STATEMENT
OBSERVE
R
TARGE
T
TARGE
T
⮚ Underwater passive target tracking from a observer platform using bearing
measurements.

5. PROBLEM STATEMENT (CONTD.)
SPEED
COURSE
TARGET
MOTION
ANALYSIS
WEAPON
GUIDANCE
BEARING
RANGE
COURSE
SPEED
OBSERVER
SENSORS
TARGET
SENSORS
BEARING

6. TARGET MOTION ANALYSIS
Simulator Filters/Smoothers
Inputs:
Target parameters
Bearing
Observer
parameters
Course and Speed
Outputs:
True Range
Measured Range
True Bearing
Measured Bearing
Observer position
Target position
Estimated:
Bearing
Range
Course
Speed

7. TARGET MOTION ANALYSIS
• TMA is a process to determine the position of a target using passive sensor
information. Sensors like SONAR provide directional information.
• TMA is done by marking from which direction the sound come at different times,
and comparing the motion with that of the observer.
• Changes in relative motion are analyzed using standard geometrical techniques
along with some assumptions about limiting cases.

8. TARGET - OBSERVER SCENARIO
X
Target
Observer
LOS
ocr
tcr
B : Bearing
LOS : Line Of Sight
ocr : Observer Course
tcr : Target Course
O
Y
Y
X
B

9. COURSE ANGLE
y y

10. MATHEMATICAL MODELLING

11. TARGET POSITION
•

12. RANGE AND BEARING MEASUREMENTS

13. FILTERING ALGORITHMS
⮚The filtering algorithms used till now are conventional methods and
modern methods like Kalman Filter, Extended Kalman Filter,
Unscented Kalman Filter, Particle filter.

14. KALMAN FILTER

15. EXTENDED KALMAN FILTER
Extended Kalman Filter (EKF) is a non-linear version of Kalman filter in estimation theory
where it estimates mean and covariance.
Kalman filter is the optimal estimator for linear system models.
In real world, most of the engineering systems are nonlinear. So attempt was made to apply
nonlinear filters like EKF.
The idea of the extended Kalman filter (EKF), is to linearize the nonlinear system around the
Kalman filter estimate, and the Kalman filter estimate is based on the linearized system.

16. EKF ALGORITHM
All EKF implementation is as follows.
(I) Initially the estimation of state and its covariance be 𝑋(0|0)
and 𝑃(0|0). (1)
(II) State vector at the next time period is predicted as
𝑋𝑠 𝑡 + 1 : 𝑋𝑠 𝑡 + 1 = ∅ 𝑡 𝑋𝑡 𝑡 + 𝑏 𝑡 + 1 +
𝜔 𝑡 (2)
(III) The predicted covariance matrix of the state vector is given as
follows.
𝑃(𝑡) = ∅(𝑡)𝑃(𝑡)∅ 𝑇(𝑡) + 𝑄(𝑡 + 1). (3)
(IV) The gain of the Kalman filter is calculated as given in eq.(4)
𝐺(𝑡 + 1) = 𝑃(𝑡)∅ 𝑇(𝑡)[𝐻(𝑡 + 1)𝑃(𝑡)𝐻𝑇(𝑡 + 1) + 𝑅] −1. (4)

17. (V) The state estimation and its error covariance:
𝑋_𝑠 (𝑡 + 1|(𝑡 + 1) = 𝑋_𝑠 (𝑡 + 1|𝑡) + 𝐺(𝑡 + 1)[𝑍(𝑡 + 1)– 𝑍 (𝑡 +1)] (5)
𝑃(𝑡 + 1) = [1 − 𝐺(𝑡 + 1)𝐻(𝑡 + 1)𝑃(𝑡)] (6)
(VI) For next iteration
𝑋𝑠 (𝑡) = 𝑋(𝑡 + 1)
𝑃(𝑡) = 𝑃(𝑡 + 1) (7)

18. Smoothing algorithm
• The discrete-time Kalman smoother, also known as the Rauch-Tung-Strieber-smoother (RTS), (Rauch et
al., 1965; Gelb, 1974; Bar-Shalom et al., 2001) can be used for computing the smoothing solution for the
model given as distribution
p(xk/yLT) = N(xK/ X_s k,ps
k)
• The mean and covariance ms
k and ps
k are calculated with the following equations:
X_s-
K+1 = Ak X_s k
p-
k+1 = Ak Pk AT
k + Qk
Ck = PkAT
k[P-
k=1] -1
X_sk = X_s k + Ck[X_s k+1 – X_s-
k+1]
Ps
k = Pk+Ck[Ps
k+1 – P-
k+1 ] CT
k

19. SIMULATION AND RESULTS
• The criteria of acceptance is explained as follows.
• Range error estimate<=2.66% of the actual range
• Course error estimate<=1o.
• Speed error estimate<=0.33m/s.
• The convergence time of the solutions for the three scenarios based on
the above mentioned acceptance criteria for 100 runs are tabulated

20. SCENARIOS

21. OBSERVER TARGET SCENARIO-1

22. SMOOTHING OUTPUTS

23. RMS ERROR AFTER SMOOTHING

24. FUTURE WORK
24
⮚ This smoothing algorithms can be extended to other filtering algorithms
like UKF, Particle filter, etc.

25. THANK YOU