# Comparison of different measures of the error in simulated radio- telemetry locations Academic Article

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### abstract

• We used computer simulations to compare 8 potential measures of linear error involved in estimating radio locations by triangulation. Linear error is defined as the shortest or Euclidean distance (ED) between the estimated triangulation point and the actual radio location. We defined a good error measure as one that is highly correlated to the 95% quantile of all possible ED's around a given location. The major axis of the confidence ellipse (as determined by Lenth's [1981] maximum likelihood estimator) performed best. Regression function parameters and correlation coefficients varied with tower positioning and the standard deviation on the bearing. We recommend using the major axis of the confidence ellipse for estimating the linear error involved in radio location studies. J. WILDL. MANAGE. 54(1):169-174 Heezen and Tester (1967) first suggested the importance of estimating the error involved in locating an animal through radiotracking. Yet, no standards have been established to estimate and report these errors. Error measures provide information about the precision (but not bias) of the data. Radio locations based on triangulation result in either areal or linear errors. Areal error measures depict an area around the estimated triangulation point that will cover the actual transmitter location with a given probability. Linear error measures estimate an error distance that with a given probability will be larger than or equal to the Euclidean distance (ED) between the estimated (x^, ) and actual (x, y) radio locations, i.e., ED = [(i x)2 + (y y)2]/. If habitat use is the primary objective, areal estimators are preferable because they provide the probability that an animal is in a specific habitat patch. Alternatively, estimating distance between relocations, movement speed, and home-range size is influenced by the linear deviation of the true location from the estimated triangulation point; thus, a linear measure would be preferable for estimating the error involved in movement parameters. The 90% error polygon (Springer 1979) and the 95% confidence ellipse (White 1985) are parameters proposed and used as areal error measures in radio location. Both employ an estimate of the sampling error inherent in bearing determination. By placing confidence limits on the bearings, a 95% error arc (Saltz and Alkon 1985) is defined (i.e., the projected bearing +2 SD). A 90% error polygon is delineated by the outer boundaries of the region of overlap of 2 such error arcs. The 95% confidence ellipse is derived by maximum likelihood estimation (Lenth 1981). A maximum likelihood estimator (MLE) is the estimate that maximizes the likelihood of the given observations. The ellipse is the confidence limit on such a parameter that is located in 2-dimensional space. The correlation between error polygons and confidence ellipses and the linear error involved in radio location has not been determined. Saltz and Alkon (1985) suggested that linear parameters are superior to areal parameters as linear error measures and recommended (but did not test) the use of the large diagonal of the error polygon. They argued that the area of an error polygon (or a confidence ellipse) may be nearly independent of its linear dimensions. Thus, a reduction in error polygon area is not necessarily accompanied by a corresponding change in the length of the large diagonal. Furthermore, because the largest diagonal always represents the maximum distance between any 2 points on the error polygon, it is the most sensitive and therefore the most reliable error polygon measure of the ED. Our purpose was to test and to compare a set of potential error measures of the ED by computer simulation. We define a good error measure as one that is a highly correlated (i.e., a high r2) to a value that is larger than the ED 95% of the time. We term this value the 95% I Present address: Nature Reserve Authority, P. O. Box 340, Mizpeh Ramon, Israel.

### publication date

• January 1, 1990