1. Target Motion Analysis for the Localization of Subsurface Targets
Stephen Haptonstahl
Northern Illinois University
December 3, 1999
I will not dazzle you with an array of deep theorems. The math used to do TMA is mostly calculus and probability. But while we all say math is important, many who teach math have only the faintest understanding of how vital it is even when used by soldiers and sailors that would have a hard time passing a “chance” course.
Target Motion Analysis

2. Disclaimer or How Different Cultures Say “I don’t know”
Politician: “We have a Congressional committee investigating that issue.”
Programmer: “You can’t do that in Windows. That only works in UNIX.”
Consultant: “I can provide that information, but it will cost you more.”
Military: “I’d tell you, but it’s classified, so then I’d have to kill you.”
Math student: “We never talked about that in class.”
Math Professor: “That’s beyond the scope of the course.”
This talk is unclassified, but it is quite easy to ask questions that require classified information to answer. Please feel free to stop me and ask questions, but understand that there will be some questions I cannot or may not answer.
Target Motion Analysis

3. The Company: Your Country
US Navy
369,220 sailors in uniform (1 officer/6 enlisted)
Who joins the Navy?
316 Ships & Subs – almost half underway
Operating in every part of the world
Other branches
Total # of people
Allied forces
# of other nations
Resume <more here>
Job description: Receive, process, display, and disseminate tactical information.
Target Motion Analysis

4. Target Motion Analysis
Strategy: Prevent enemy submarines from getting close enough to destroy your ship
Tactic: Keep the sub “occupied” dodging helicopter-launched torpedoes.
Problem: Where do you send your helicopter?
The Captain wants an answer in 30 minutes!
Why not let the computer handle it? There’s plenty of “furry” data and judgment needed for a computer to give an optimal solution – people are just better at this still.
Target Motion Analysis

5. Describing Location in Maritime Warfare
Bearing and Range from ownship - polar coordinates
Bearing (BRG): Compass direction (true, not magnetic) from ownship to target in degrees (“mills” used in gunnery – 6400 mills = 360º)
Range (RNG): Distance to target in yards or nautical miles
Relative reference frame – must correct for ownship motion to get true (WRT Earth) motion
Latitude (N-S) and Longitude (E-W)
Geo-fixed reference frame
Nautical Mile (NM)
Defined to be 1/60 degree latitude (equator to pole:=5400 NM)
Equal to about 6000 feet, 2000 yards, or 1.1 statute mile
Question: A ship traveling at X knots (NM/hr) goes how many yards in 3 minutes?
Target Motion Analysis

6. Primary Sources of Information
Active sonar
Bearing, range, perhaps depth of target – course and speed
Very limited range
Counterdetection (perhaps 10X sonar range)
Amorous marine life
Passive sonar
Greater range
No counterdetection issues (other that normal)
No range information – no course and speed
Must use TMA to get range, course, speed
Target Motion Analysis

7. Other Sources of Information
Visual – periscopes leave wakes
Lookouts (ours or on other ships) (BRG & est. RNG)
Pilots (est. lat & lon)
Sonobuoys
“Yardstick” – range from buoy
“Pointer” – bearing from buoy
“Cadillac” - both
MAD – Magnetic anomaly detector
Very short range, but can’t mistake a whale for a sub
EW - Reception of their radar or radio emissions – BRG only
Intelligence
SOSUS – Sound Surveillance System
Various classified sources
Target Motion Analysis

8. Target Motion Analysis
TMA Team PC
Sharps
Composition
Evaluator
South & North Plotters
Time/Bearing Plotter
Time/Frequency Plotter
R/T talker and Sharps
Input
Sonar/EW/Intel
Priorities set by CO
Output
Location of targets
Course/speed recommendations TF N
Geo-fixed
plot
Manual
Surface
Radar TB RT S E
This team doesn’t have a lot of room to work. They don’t get much sleep, and they must not make mistakes.
Surface/
Subsurface
Warfare
Supervisor
TMA Team Layout on
an AEGIS cruiser
Target Motion Analysis

9. Line of Sound
Line of Sound (LOS): A moving reference line joining ownship and the target
STA
STI
SOI
SOA
STA
STI
SOI
SOA
STA
STI
SOI
SOA
Lag: target and ownship speed vectors on opposite sides of LOS
Lead: target and ownship speed vectors on same side of LOS,
STA > SOA
Overlead: target and ownship speed vectors on same side of LOS,
STA < SOA
The naïve method of localization would be to search for the unknown parameters in the same order that active radar does: it determines the range, then from the position information, it calculates the course and speed of the contact. It turns out that course and speed are easier to determine, and having this, we can get the range.
Note: All of these diagrams show the contact closing, as both STI and SOI are toward each other.
Opening: Range increasing Closing: Range decreasing
Target Motion Analysis

10. Line of Sound – Evaluator’s Plot
Purpose: Determine the course and speed of the target
000
180
090
270
STI
Lead
STA
Opening
Closing
Lag
Now if we know from a blade count that he’s only making 10 knots, and we can determine from our various plots that he’s opening and in an overlead geometry, then we’ve got a pretty good idea of his course and speed.
Overlead
*Expires after ~5 degrees
of bearing shift
Target Motion Analysis

11. DRT & Geo-fixed Plot Recognizing LOS Geometries
Lag
Lead
Overlead
Max
Range
Min
Range
The geo-fixed plot on the Dead-Reckoning Tracer (DRT)
Min spd = ownship spd
Input: almost everything
Speed strips – get course, speed, range
This is where all the information is compiled, where the Captain will look for a picture of what’s going on 6
kts
Target Motion Analysis

12. Time-Bearing Plot – Range Calculations
CPA at graph inflection point
convexity determines whether opening or closing
Single-leg Ekelund
Doesn’t require ownship maneuver
Requires an estimated STA
Double-leg Ekelund
Uses info before and after ownship maneuver
Yields accurate range at a time near the maneuver
Often target’s relative motion allows this technique
Spiess
Useful when target has low bearing rate (<1º/min) (not common)
Cross-fix using only one ship
Target Motion Analysis

13. Target Motion Analysis
Single-Leg Ekelund R  x
Target Motion Analysis

14. Doppler Effect – Time-Frequency Plot
Using rt = d, we can determine the perceived change in frequency caused by STI & SOI
Sw = Speed of sound in sea water,
1664 yds/sec
SI = STI + SOI
fr = received frequency
f0 = emitted frequency
fcorr = f0 affected only by target motion
Plot fr, then calculate SOI to get fcorr
Changes in fcorr are caused by
Changes in STI caused by shifting LOS geometry
Target maneuvers (best way to detect target maneuvers)
Why can’t we do TF plot with EW? The top equation shows why.
Target Motion Analysis

15. Applying the Doppler Formula
Assume ownship fixed, or correct for SOI
fcorr increases as STI does
Lag
Lead
Overlead
We have yet to see his bow (nose), so STI is increasing
Our view or him is shifting more toward his stern (tail), so STI is decreasing
Target Motion Analysis

16. Line of Sound Determination
Lines on Geo-fixed plot
Fcorr
(f0 plus STI)
LOS Geometry
Get from Geo-fixed plot
Don’t cross
Decreasing
Lead
Min speed
Cross
Lag
Min range
Increasing
Overlead
Max range
Target Motion Analysis

17. What If We Know the Target’s Speed?
Sources
Blade count + ID of class = speed
Intelligence
“We believe a Kilo is transiting from Murmansk to Cuba over x days, so expect a minimum speed of y knots.”
Geo-fixed plot (speed strips; lead geometry)
What we get
If we have max(fc) (perhaps a natural transition from overlead to lag) then we can get f0
Evaluator can improve LOS diagram to better estimate course
Geo-fixed plot can accurately fix strips to get course and range
Target Motion Analysis

18. What If We Know the Emitted Frequency (f0)?
Sources
Inflection point of fc
“Crazy Ivan” (like in Hunt for Red October): Target turns through 360º to check for contacts in his baffles (wake). We get f0 halfway between max(fcorr) and min(fcorr). Also get contact speed.
We get
Very accurate course
Warren (freq) range
Target Motion Analysis

19. Water is Thicker than Vacuum Convergence Zones
Sound moves along paths of least resistance
Salinity, temperature and pressure all change with depth and affect sound propagation
Balance struck is a set of distinct solutions, each a path
Target Motion Analysis

20. Target Motion Analysis
The Layer
The sharp temperature gradient at the layer causes most sound to be reflected
Target Motion Analysis

21. Technology on the Horizon
Expert systems – AI based TMA
Can we do it?
Is it a good idea?
Bottom bounce
Multiple instances of the same sound coming in at slightly different times from different angles
Ambient noise
We see with ambient light, why not apply this idea to sonar?
Improved active sonar has reduced counterdetection range
Target Motion Analysis

22. Advanced Techniques and Further Questions
Tactics
What are good maneuvers to recommend that will:
Maximize information on the target
Minimize counterdetection
Zigzag plans
EMCON
How do we respond to target maneuvers?
What’s the best we can do with these formulas? Can we get more from less?
Target Motion Analysis