1 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Title here Text here

2 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Movement data from relevant species  Movement data obtained for:  Squirrel monkey  Howler monkey  Mountain tapir  Lowland tapir  White-lipped peccary  Cattle  White-tailed deer  Cougar  Red-knobbed hornbill  Malay sun bear  Tiger

3 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Introduction  Two parts  Track-level discrimination of dismounts and animals  Micro-Doppler algorithms for dismount/animal discrimination & species identification

4 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Track-level Algorithms

5 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Track-level Discrimination Algorithms Techniques we developed & presented earlier –  Wavelet analysis of Euclidean distance from arbitrary starting point  Seems to be very effective  Normal vectors to path segments  Derived from Gauss-Bonnet theorem

6 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Track-level Discrimination Algorithms  Techniques we presented earlier – MethodCriterionDismountAnimal on Home Range WaveletsWavelet coefficients for different scale factors Large values of scale factor predominate = little/no retracing of path segments Small values of scale factor predominate = frequent retracing of path segments Centroids of normal vectors Temporal evolution of centroid Centroid tends to track – or parallel – animal/dismount path Centroid independent from path, approaches quasi-stable point

7 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Track-level Discrimination Algorithms  Applied both techniques to Ft. Stewart data  Dismounts moving along designated  Domestic animals moving along pentagonal path or milling about in pens

8 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Track-level Algorithms  Loops in tracks (horse/rider combination) don’t alter correspondence with Gauss-Bonnet

9 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Track-level Algorithms  Wavelet analysis reveals small-scale structure due to the loops in the path

10 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Track-level Algorithms  Horse led point-to-point along a straight path produces characteristic picture  Same result for dismount moving along designated path.

11 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Track-level Algorithms  Wavelet analysis reveals lack of any evidence of periodicity in straight path of horses being led from point-to-point

12 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Track-level Discrimination Algorithms  Drawback – discrimination based on wavelets or normal vector centroid requires relatively large number of data points.  Time required may be too long for many tactical situations.  Wanted an algorithm that takes advantage of unique properties of animals’ home range movements over very short time scales.  Central place foraging (CPF) versus non-Central place foraging (non-CPF)

13 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Non-CPF, with more-or-less complete sampling of home range

14 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY CPF, with more-or-less complete sampling

15 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY CPF, sampling different part of home range each day - note significant linearity in paths Note Levy flights!

16 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Track-level Discrimination Algorithms  We’re treading new ground here  Most field biologists doing telemetry aren’t interested in animal movements at scales of relevance to our work  Usual goal = assess home range dimensions  Data usually recorded at intervals of tens of minutes, even hours or days.  Self-similar (fractal) nature of animal movement lets us compensate for lack of extreme short time-scale data  Lévy-type movement pattern at scales of tens of minutes, or hours will be Lévy-type at shorter time scales

17 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Mean-square successive difference:Variance Ratio

18 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Mean-square successive difference:Variance Ratio

19 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Mean-square successive difference:Variance Ratio

20 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY MSD:Variance Ratio for Home Range and Simulated Dismount Paths  TTI_movie_1.avi TTI_movie_1.avi

21 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY MSD:Variance Ratio for Home Range and Simulated Dismount Paths  How do results of normal vector centroid, wavelet analysis, and MSD:Variance Ratio compare?  Used data from:  Deer (human-sized mammal)  Dismounts moving along designated paths in Honduras

22 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Deer 2, Dismount Path 5

23 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Deer 6, Dismount Path 5

24 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Deer 7 Dismount Path 5

25 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Deer 5, Dismount Path 5

26 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Micro-Doppler Results

27 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY ‘Micro-Doppler ‘ Results here  Data consist of iFFT ‘reconstituted’ raw returns from 9 range bins centered on Horse 26’s position.  Don?  Analyzed each 5-second frame ( n = 180 ) separately  Results of preliminary wavelet analysis (Daubechies 4): horse26_full_doppler_wavelet_analysis_256.avi

28 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY  The ‘complexity’ of the wavelet coefficient matrix appears to be sensitive to  the presence of a horse in a range bin, and  the speed of the horse  This makes sense…the faster the horse runs, the more the return signal will be affected by movement of head, neck, mane, appendages, and tail.  Recall from the last QPR, I showed that the micro-Doppler signal’s rolloff depended on horse speed.  More & larger micro-Doppler peaks in the signal  more complex signal   entropy  Possible species-specific features?

29 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Analysis of ‘raw’ signals  Computed wavelet entropy for each frame, using 4 different values for the maximum scale factor  Determined Doppler value ( m/s ) for each frame  Wavelet entropy results were binned by the absolute value of the Doppler m/s

30 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Wavelet Entropy vs. Absolute Doppler

31 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Wavelet Entropy vs. Absolute Doppler

32 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Wavelet Entropy vs. Absolute Doppler

33 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Wavelet Entropy vs. Absolute Doppler

34 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Analysis of ‘raw’ signals  Next, concatenated the second chips to create a single 900-second time series of return signal amplitudes  Wavelet analysis conducted using different wavelets  Wavelets differ in  Symmetry  ‘look at’ data somewhat differently  Width  differential sensitivity to fine-scale features of the data

35 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Analysis Using Haar Wavelet

36 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Analysis Using Daubechies 4 Wavelet

37 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Analysis Using Daubechies 10 Wavelet

38 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Analysis Using Ricker (Mexican Hat) Wavelet

39 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Analysis Using Symlets 2 Wavelet

40 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Analysis Using Symlets 8 Wavelet

41 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Analysis Using Coiflet 1 Wavelet

42 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Analysis Using Coiflet 5 Wavelet

43 Technology Service Corporation / California Operations FOR OFFICIAL USE ONLY Conclusion Next steps  Work out statistical properties of the Mean-square successive difference:Variance Ratio, when applied to Lévy processes  Evaluate different wavelets for their utility under different circumstances (terrain, target type, radar type)  May develop new wavelet(s) to target specific features of data  Time series analysis of raw radar returns using  Standard approaches, e.g. ARIMA  Nonlinear dynamics & chaos theory  Lyapunov exponents & correlation dimension  Various entropy measures  Implement a Naïve Bayes Classifier using output from track-level and micro-Doppler algorithms