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A Comparison of Strategies for Processing Azimuth Data from Multi-station Radio-tracking Systems


Dean E. Biggins, U.S. Geological Survey, Biological Resources Division, Midcontinent Ecological Science Center, 4512 McMurray Avenue, Fort Collins, CO 80525-3400 USA, Marc R. Matchett, U.S. Fish and Wildlife Service, Charles M. Russell National Wildlife Refuge, Lewiston, MT 59457 USA, and Jerry L. Godbey, U.S. Geological Survey, Biological Resources Division, Midcontinent Ecological Science Center, 4512 McMurray Avenue, Fort Collins, CO 80525-3400 USA

The radio-tracking system for this study consisted of 3 stations with 11-element dual-beam yagi antennas, used simultaneously to track a transmitter whose position was determined at 102 test points (averaging 2,864 m from tracking stations) using a Rockwell HNV560C Global Positioning System (GPS) receiver with advertised accuracy of ±10 m. The study was located at the Arizona black-footed ferret (Mustela nigripes) reintroduction site near Seligman; hilly terrain afforded line-of-sight bearings. Before conducting the tracking simulation, we assessed station accuracy by calculating the standard deviation (SD) of a series of differences between telemetric and transit-surveyed azimuths to a test transmitter moved around the 3 stations (SD [n] = 0.698 [103], 0.405 [58], and 0.703 [116]). We used the SD for each station separately in TRITEL and mean SD for the 3 stations (0.602) for the Maximum Likelihood (MLE) option of LOCATE, which required a single estimate of station accuracy. We "surveyed" the 3 stations and 4 beacon transmitter locations with GPS. Station operators referenced their stations with the beacon transmitters on each of 2 nights of testing. We processed the single data set with two computer programs that generated estimated locations and accuracy. LOCATE produced 3 versions of maximum-likelihood estimates using azimuths from all 3 stations, and estimated accuracy with a confidence ellipse. TRITEL used azimuths from the two stations producing the smallest error quadrangle. Error quadrangles were formed from intersecting, station specific, error arc confidence intervals. We compared GPS locations to corresponding telemetric fixes to evaluate fix accuracy and coverage of error estimators.

We detected no reflected signals, although there was 1 "outlier" azimuth likely due to a reading or recording error. Telemetry estimates were significantly south of GPS locations (Chi-square tests, P < 0.0005), regardless of processing method (Table 1). Likely explanations for this bias are referencing error for 1 or more stations, and/or GPS inconsistencies. Straight-line distances from telemetry to GPS fixes were significantly less with 3-station MLE-type estimates than with the "best" 2-station estimate (Mann-Whitney test, P = 0.0002). Increased linear error should reduce coverage, but 2-station error quadrangles more often contained the corresponding GPS fix than did MLE 3-station ellipses of the same area (Table 1). The Tukey and Huber procedures did not use the overall SD, but based station accuracy on consistency of convergence of the 3 bearings. Resulting ellipses gave about the same coverage (86-87%) as error quadrangles of 1/7 the area (Table 1).

Table 1. Comparison of 2- and 3-station azimuth processing strategies with regard to mean distance between GPS and telemetric fixes on X and Y coordinates (bias), overall separation, and attributes of error figures.

 
Telemetry to GPS Fix (m)
Ellipse or Quadrangle
Method
Confidence
X
Y
Separation
ha
% Coverage
2-Station
89.8%
13.3
-38.9
84.4
1.02
59
2-Station
95%
13.3
-38.9
84.4
1.37
72
3-Sta., MLE
95%
18.0
-25.5
63.3
1.02
50
3-Sta., TUKEY
95%
17.9
-26.1
64.3
13.30
86
3-Sta., HUBER
95%
18.1
-25.4
63.5
12.88
86
2-Station
99%
13.3
-38.9
84.4
1.84
87

This exercise was useful in pointing out potential hazards from biases due to surveying and referencing of tracking stations, but such biases reduced our ability to objectively compare the two data processing strategies. Our results suggest relative robustness of the MLE family of estimators to effects of these biases, which probably exist in all field studies using direction-finding, and some routines enable multiple-station systems to ignore outlier azimuths caused by signal reflection. All current systems result in relatively inexact location estimates, underscoring the importance of error estimates. In our tests, error quadrangles of the best 2-station strategy seemed to perform better than the ellipses of 3-station methods. No error estimator, however, provided coverage close to the predicted confidence level, and even these predictions may be optimistic considering the difference between tracking our static targets with relatively matched polarity of receiving and transmitting antennas, and the dynamics of tracking modulating transmitters carried by live animals.


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