Reflected signal bias in biotelemetry triangulation systems

Accuracy of 4 3-tower triangulation systems was quantified using surveyed reference points. All reference points within line-of-sight (LOS) of towers produced accurate and precise bearings, but 52% of points non-line-of-sight (NLOS) to towers produced inaccurate and/or imprecise bearings due to reflected radio signals. These data were used to test performance of the Andrews, Huber, and Maximum Likelihood (ML) estimators of Lenth (1981). The Andrews estimator was more likely to fail to generate a location estimate than the Huber and ML estimators, but these latter estimators frequently generated incorrect estimates. Of those estimates generated, the Andrews estimator proved superior to the Huber and ML estimators by generating a larger proportion of confidence ellipses that included the actual radio location and by having a smaller mean distance between the estimated and true radio location. However, all 3 estimators performed poorly with confidence ellipse areas >0.6 ha. J. WILDL. MANAGE. 50(4):747-752 Accuracy of location estimates with biotelemetry triangulation is a function of the number and accuracy of receiving stations, and an animal's location relative to receiving stations (White 1985). The 1st and last factors are generally controllable by the investigator. Bearing accuracy, however, is not as easily controlled due to variables such as topography, vegetation, weather, and signal quality (Slade et al. 1965, Cederlund et al. 1979, Springer 1979, Hupp and Ratti 1983, Lee et al. 1985). A problem with telemetry system accuracy common to many studies is bearing error resulting from signal reflection (bounce) (Tester 1971, Hupp and Ratti 1983, Lee et al. 1985). Reflected signals cause inaccurate location estimates that should be identified and eliminated before data analysis. Although reflected signals may be easily detected when testing a receiving system, they are often impossible to identify when the transmitter location, and hence the true bearing, is unknown. Lee et al. (1985) suggested ways to identify reflected signals when 2 bearings are used for triangulation, but these methods are subjective and only identify bearings with large errors. Using only 2 bearings and the error polygon approach for triangulation in areas where signal reflection is a problem will result in inaccurate location estimates that cannot be identified and eliminated. Problems with signal reflection can be reduced by using -3 bearings for triangulation and by generating a location estimate with a technique that is robust to outliers caused by signal reflection. Lenth (1981) provided 3 techniques to estimate the source of a signal with multiple bearings: (1) Andrews, (2) Huber, and (3) ML estimators. The 1st 2 estimators were developed to be robust to outliers by weighting each bearing, thus providing an advantage over the error polygon approach when signal reflection is a problem. In addition, the estimators provide a rigorous estimation scheme for >3 bearings. Objectives of this study were to use techniques described by Lee et al. (1985) to quantify bearing accuracy of 4 3-tower triangulation systems and to use these data to test performance of the 3 location estimators presented by Lenth (1981) when a significant proportion of signals are reflected by topography. Financial support was provided by U.S. Dep. Energy Grants W-7405-ENG-36 to Los Alamos Natl. Lab. and DE-FGO02-85ER60297 to Colo. State Univ., Exxon Co., USA, and Colo. Fed. Aid in Wildl. Restor. Proj. 45-01-502-15050. We thank J. D. Depperschmidt, J. K. Garner, and J. C. Graham for field assistance, and appreciate the cooperation of D. M. Barker and other personnel of the Colony Shale Oil Proj. C. J. Amlaner, Jr., and J. T. Ratti critically reviewed the manuscript.