Location of radio-tagged animals by triangulation is a widely applied research technique, the accuracy of which is often a major concern. Knowledge of the approximate accuracy and detection range of various types of automatic systems is a logical prerequisite to purchase or construction of the relatively expensive equipment required. The direction-finding performances of a fixed (non rotated) switched array of six 3-element Yagi antennas and of a rotated array of two 6-element Yagis, each in computer-controlled automated mode, were compared for the same distances and transmitter power in open surroundings free of reflecting objects. The rotated system yielded 50% greater precision and 9 times more coverage area than the fixed system. Human operators, using the rotated antenna connected for a null, determined bearings about 4 and 16 times more precisely than did the rotated and fixed automatic systems, respectively. Bias of the mean error of the fixed system was a function of direction to a transmitter, varying from nil to about 3o at typical signal levels and exceeding 10o for weak signals in some directions. Biases of the manually and automatically rotated systems were << 1o for all directions and signal levels.
Key words: Direction-finding accuracy, Radio direction-finding, Yagi antenna, Antenna array, Bio-telemetry, Automated Direction-finding
In 1960 very small radio transmitters were attached to a cottontail rabbit and a mallard duck, which were then tracked by direction-finding in Allerton Park, Piatt County, and about the prairie of Champaign County, Illinois [1]. This was the genesis of radio telemetry for wildlife research and management, now a widely-practiced technique. Later, automatic direction finding was employed using now-obsolete continuously rotated antennas [2,3]. Now, automatic direction-finding equipment has been developed, involving fixed antenna arrays and microprocessor based control and recording systems. The system must be able to direction-find and record signal strength on a pulse as short as 15 ms repeating once per second. The design of this system will be described, with emphasis on the direction finding array and on the antenna arrangement on the target animal, typically a small bird. This system has been tested for proof-of-principle and for accuracy in operational contexts in forests and open country in Illinois, Georgia and Panama.
Location of radio-tagged animals by triangulation is a widely applied research technique, the accuracy of which is often a major concern. Knowledge of the expected range and accuracy of various types of automatic systems is a logical prerequisite to purchase or construction of the relatively expensive equipment required. The accuracy of locations depends on the accuracy of bearings obtained with direction finding (DF) antennas. Pointer calibration, mapping and map errors, the effects of and tactics for mitigating signal scattering, movement bias, and statistical methods for making and evaluating triangulated location estimates are well covered in the literature (see Samuel and Fuller, [4]). No references were found that dealt quantitatively with the bearing precision of different types of antennas at various signal-to-noise ratios.
In this study, we evaluate the effects of noise and detector non linearity on the angular precision of two automatic systems and one manual system. Comparisons among systems were made at a number of different signal levels (thus signal-to-noise ratios) representing various distances to radio-tagged animals. Vertical polarization and 302 MHz were used for all tests.
A "fixed" automatic system employed an array of six stationary 3-element Yagi-Uda antennas (Yagis) pointed at 60o intervals to cover 360o. A "rotated" automatic system employed two 6-element Yagis mounted at the ends of a 1.35-wavelength boom and pointed in the same direction. The antenna rotator consisted of a computer-controlled stepper motor driving a backlash-free gear train driving a support mast in 0.09o steps.
A "manual" system used the antennas of the rotated system. The Yagis used in the arrays (Lawson, [5], Table 1.4) have the directional patterns shown in Figures 1a and 1c.
All measurements were made over flat grassland with no reflection-producing obstructions in any direction within 800 m. A test transmitter 300 m from the system under test produced a field intensity similar to that of a typical animal transmitter at close distance, i.e., about 0.7 uV into a 50-ohm (-110 dBm) receiver input from a vertical half-wave dipole at the location and height used for the systems tests. Greater distances were simulated by reducing the signal with a switched attenuator. All tests were for a 16-milliscond transmitter pulse width.
The computer controlled the antenna rotation and logged the signal strength and antenna position. The receiver employed a voltage detector, i.e., the receiver functioned as a voltmeter. The detector output was digitized by an 8-bit A-D converter. Hereafter, voltage levels are referred to by their digital step (A-D) value. Over most of its range, the detector produced an average voltage proportional to the voltage delivered by the antennas at the receiver input. At low signal voltages, however, non-linearity was apparent as the curve flattened out instead of passing through zero (Fig. 2). This non linearity caused biased mean error in fixed systems. In addition, the random noise inherent in all receiver systems produced random fluctuations of detector output voltage that for any instantaneous reading added to or subtracted from the voltage due to the signal. These fluctuations accounted for an increasing proportion of the measured voltage as the signal voltage decreased, as it would with increased distance to a transmitter or for less powerful transmitters. This random noise caused errors in both automatic systems.
The manual system used two 6-element Yagis spaced 1.35 wavelengths and connected 180o out of phase for a boresight null (Fig. 1e). When provided with a manual switch to allow selection of an in-phase connection, a pair of such Yagis constitutes the "null-peak" antenna in common use for tracking wildlife (peak shown in Fig. 1d).
In the tests the operator judged the null position by ear while rotating the antennas using the arrow keys on the computer. The computer was programmed to rotate the antenna to a randomly chosen azimuth and then to display azimuths with a fixed randomly selected offset. This arrangement allowed the operator to view relative azimuth as he/she rotated the antenna but hid the true azimuth. When the operator stopped rotation at the azimuth of the perceived null, he/she pressed the spacebar to store the difference between measured and true azimuths in an error file; this was repeated until a set of 25 error samples was obtained for a particular attenuator setting. Sample sets were obtained for various attenuator settings.
The rotated system consisted of the same pair of 6-element Yagis as the manual system. Instead of the 180o out of phase (null) connection, a computer controlled switch connected the Yagis so that one was phased ± 90o different from the other. This provided a peak that was shifted approximately 10o CW or CCW from the equal-signal boresight, depending on switch position (Fig. 1f). Unlike peak-null switching, which provides no directional cue, the beam that produces the strongest signal indicates the direction in which the antennas must be rotated in order to bring the transmitter in line with the boresight, a key feature for automatic operation.
At transmitter azimuths less than 10o off-boresight, the ratio (R) of the stronger (Vs) to the weaker (Vw) of the voltages from each beam defines an offset angle (A) from the boresight direction according to the A(R) formula:
A(degrees) = 4.7 [ tan-1 (R-1) ] 0.98 (1)This empirical formula was determined from field measurements on strong signals. The pair of 6-element Yagis was rotated under computer control plus and minus 5.6o from the true direction to the transmitter in 0.09o steps and stopped after each step while 2 sets of 16 detector voltage readings at 0.5-millisecond intervals were taken by the receiver (one set for each position of the switched beam). The 16 readings for each beam were averaged and their ratio (R) sent to the computer where R was converted to an angle (A) using the formula given above. An error file (n = 124) was created from the difference between A and the true offset angle as taken from the rotator position. The above sequence was repeated for various signal levels set by the attenuator.
The fixed system used the antennas and automated receiver described and tested by Larkin et al. [6]. Two 3-element Yagi antennas were mounted with their directions of maximum response 60o apart (Fig. 1b). We refer to the direction midway between the maximum response directions of the pair as the boresight direction. For sources in the boresight direction, the two antennas provided equal voltage. For any transmitter azimuth the ratio (R) of the stronger (Vs) to the weaker (Vw) of the voltages from two the Yagis defines an offset angle (A) from their boresight direction according to the A(R) formula:
A(degrees) = 27.6 (tan-1 ( (.877 x (R-1) ) ) 0.851 , (2)determined in the same way as for the rotated system described above. This formula and the A(R) equation for the rotated system fit the relationships between R and A to an accuracy better than 0.1o. These A(R) formulas are specific to receivers with linear voltage detectors and to the particular Yagi designs, spacings, and polarization tested. Different equations would be required for other Yagi designs.
In a full fixed array, six Yagis would be used to cover 360o. Only two adjacent Yagis are needed to test performance because the pattern repeats every 60o. Moreover, because the patterns overlap symmetrically, the system could be evaluated by measurements over the CCW 30o arc from the boresight direction to the maximum of the CCW Yagi (left half of Fig. 1b).
Instead of moving the test transmitter to various azimuths, the computer rotated the Yagis through the 30o arc in 0.09o steps. At each step the receiver stored a set of 16 detector voltage readings for each Yagis at 0.5-millisecond intervals during a pulse. The 16 readings for each Yagi were averaged and their ratio (R) sent to the computer where R was converted to an angle (A) using the equation given above. An error file (n = 330) was created from the difference between A and the true azimuth to the transmitter. The above sequence was repeated for various signal levels set by the attenuator. We calculated standard deviation and mean error for the error files in 5o sectors. Analysis of 5o sectors was appropriate because the error in this type of system is dependent on azimuth, especially for weak signals.
| Field dB * (distance **) |
Null-connected 6-element Yagi, manually-operated |
Rotated, beam-switched, 6-element Yagi, computer-controlled |
Fixed switched 3-element Yagi, computer-controlled^ |
|||||||
| SD | (mean) | [n] | SD | (mean) | [n] | SD | (mean) | [n] | ||
| 0 | (300) | .41 | (+0.13) | [330] | ||||||
| -3 | (375) | .02 | (0.00) | [25] | .60 | (+0.21) | [330] | |||
| -6 | (470) | .12 | (-0.11) | [124] | .08 | (+0.19) | [330] | |||
| -9 | (590) | .02 | (0.00) | [25] | 1.12 | (+0.47) | [330] | |||
| -12 | (730) | .20 | (+0.20) | [124] | 1.43 | (+1.36) | [330] | |||
| -15 | (920) | .10 | (0.00) | [25] | .25 | (-.09) | [124] | 2.13 | (+2.49) | [330] |
| -18 | (1150) | .15 | (0.00) | [25] | .30 | (+.08) | [124] | 2.97 | (+2.88) | [220] |
| -21 | (1425) | .52 | (+06) | [124] | 3.58 | (+1.80) | [110] | |||
| -24 | (1750) | .20 | (+0.01) | [25] | .81 | (+.03) | [124] | 4.05 | (+1.77) | [55] |
| -27 | (2100) | .28 | (0.00) | [25] | 1.26 | (-0.22) | [124] | signal unreliable | ||
| -30 | (2500) | .80 | (+0.01) | [25] | 1.65 | (+.01) | [124] | signal undetectable | ||
| -33 | (3000) | 2.32 | (+0.06) | [25] | signal unreliable | |||||
| -36 | null unreliable | signal undetectable | ||||||||
| * | 0 dB = the field strength that provided 0.7 uV (-110 dBm) from a vertical half-wave dipole at the location and height of the receiving antennas used for the systems tests. | |||||||||
| ** | Approximate distance in meters to a 1-stage transmitter near the ground | |||||||||
| ^ | Data for the switched 3-element system are the average of the useful data in Table 2. | |||||||||
| Field | sector | sector | sector | sector | sector | sector | ||||||
| 0 to -5 | -5 to -10 | -10 to -15 | -15 to -20 | -20 to -25 | -25 to -30 | |||||||
| dB | S.D. | (mean) | S.D. | (mean) | S.D. | (mean) | S.D. | (mean) | S.D. | (mean) | ||
| 0 | 0.38 | (0.02) | 0.40 | (0.17) | 0.41 | (0.06) | 0.45 | (0.15) | 0.42 | (0.18) | 0.41 | (0.21) |
| -3 | 0.60 | (0.04) | 0.57 | (0.40) | 0.59 | (0.23) | 0.62 | (0.21) | 0.63 | (0.23) | 0.58 | (0.17) |
| -6 | 0.82 | (0.11) | 0.86 | (0.14) | 0.88 | (0.21) | 0.74 | (0.19) | 0.85 | (0.01) | 0.64 | (0.45) |
| -9 | 1.13 | (0.13) | 1.11 | (0.16) | 1.24 | (0.37) | 1.24 | (0.33) | 1.03 | (0.52) | 0.95 | (1.32) |
| -12 | 1.38 | (0.14) | 1.58 | (0.94) | 1.51 | (1.17) | 1.31 | (1.88) | 1.41 | (1.80) | 1.40 | (2.14) |
| -15 | 2.29 | (0.22) | 2.38 | (1.48) | 1.89 | (2.44) | 2.23 | (2.97) | 2.24 | (3.53) | 1.75 | (4.03) |
| -18 | 2.88 | (0.50) | 3.12 | (2.56) | 2.93 | (3.65) | 2.97 | (4.81) | 2.89 | (5.16)/// | 2.79 | (7.97)/// |
| -21 | 3.52 | (1.12) | 3.63 | (2.48) | 3.00 | (5.36)/// | 2.88 | (7.58)/// | 3.71 | (9.80)/// | 3.45 | (11.48)/// |
| -24 | 4.05 | (1.77) | 3.66 | (5.22)/// | 4.08 | (8.13)/// | 4.31 | (11.77)/// | 4.04 | (15.19)/// | 4.01 | (17.80)/// |
| ** | For the -24 dB field level, n varies between 39 and 49. | |||||||||||
| /// | A threshold value of 5 excludes data taken at these field levels as not useful for DF purposes. | |||||||||||
| Type system | Yagi type, (number used) | Spacing | Relative DF gain, dB ^ | Precision degrees ^^ | Largest dimensions, wavelengths | Relative weight or wind area | |||
| rotated | 2-element | (2) | 0.50* | 8 | 0.027 | 0.2 | x | 0.5 | 1.5 |
| rotated | 3-element | (2) | 0.67* | 11 | 0.035 | 0.4 | x | 0.67 | 2.4 |
| rotated | 6-element | (2) | 1.35* | 13 | 0.100 | 1.2 | x | 1.35 | 5.7 |
| fixed | 3-element | (6) | 60** | 0 | 0.012 | 1.2 | x | 1.2 | 7.3 |
| fixed | 6-element | (10) | 36** | 5 | 0.027 | 3.6 | x | 3.6 | 26.1 |
| fixed | 15-element | (15) | 24** | 11 | 0.055 | 10 | x | 10 | 143.2 |
| * | spacing, wavelengths | ||||||||
| ** | arc between adjacent antennas, degrees | ||||||||
| ^ | for full 360º coverage | ||||||||
| ^^ | Volts per degree as a measure of relative precision is proportional to 1/ SD of error | ||||||||
Standard deviations of the error distributions, summarized in Table 1, show that near the detection limit of the fixed system (-18 dB and -21 dB), SD of error is approximately 7 times that of the rotated system. Similarly, near the detection limits of the rotated system (-24 to -30 dBm), SD is approximately 4 times that for the manual system. Compared in another way, the rotated system yielded 50% better precision at 3 times the distance to a transmitter (9 times area coverage) than the fixed system, based on the following interpretation of the data. The SD of error for the fixed system at the -6 dB field level is 0.80o; that of the rotated system at the -21 dB level is 0.52o. The 15 dB difference in field levels represents a factor of about 3 in transmitter distance.
Beam-switched and human-operated peak-null systems use equal-signal azimuths symmetrical about a boresight to determine bearing and are therefore immune to receiver detector non linearity and can function without bias down to the limit of detection. Along a boresight, fixed systems are also immune to such bias, accounting for the observation by Larkin et. al. [6] (p. 66) that "DF during range tests was unexpectedly accurate: over all distances right out to the 3.8-km maximum distance of detection, each of the transmitters was localized with little bias....." Although range tests along a boresight are necessary to evaluate the maximum range of reliable detection for fixed systems, such tests are a poor choice for testing typical DF performance as we show below.
Off-boresight, fixed systems are subject to errors that increase with weaker signals and greater off-boresight angles. Ideally, measured ratio R is independent of signal level, i.e., doubling the field from the source results in doubling both Vs and Vw, thus keeping Vs/Vw (R) unchanged. Linearity of the envelope detector of the receiver degrades for levels below about 20 (Fig. 2) where Vw will be increasingly overestimated, thereby causing a bias that results in increasing mean error as the field strength decreases and off-boresight angle increases. Finally, when Vs approaches the noise level, R will tend toward 1 for any source angle and bias toward the boresight becomes very large (lower right portion of Table 2). This error is always toward the boresight and in our tests had positive sign because the sectors tested were CCW (negative angle offsets) relative to the boresight. Larkin et al. [6] (p. 67) report "angular bias away from the antenna with the stronger signal" that was probably due to the factors we described above.
The firmware used in the automatic receiver measured noise Vn (about 9, Fig. 2) for short periods prior to and after the period during which a pulse was detected. For the tests, Vw was required to exceed a threshold of 2 above Vn to be accepted as a pulse. Data likely to have large bias due to detector non-linearity can be eliminated by using a larger threshold. A value of 5 was empirically found to be practical during operation of the fixed system for monitoring animals. This value precludes full use of the system in the lower-right portions of Table 2 where, however, the detection of a valid Vs and no Vw would at least indicate the presence of a transmitter in the general direction of the peak of a particular Yagi in a 6-Yagi array, i.e., would provide direction-finding to an accuracy of ±30o.
Our accuracy and distance (coverage area) comparisons among manual, rotated, and fixed systems are for systems of similar per-unit cost, complexity, and portability and having antenna arrays of similar size, wind resistance, and support requirements. Although accuracy and per-unit coverage will never be unimportant in wildlife radio-location systems, other factors that we do not include may be important in some applications.
For instance, the fixed systems is faster at acquiring bearings, an important factor when many animals must be located frequently; for the 1-to-70 duty cycle typical for wildlife transmitters, the fixed system can be up to 5 times faster than a rotated system of similar power consumption. Thus, where a speed of more than about 3 bearings per minute is required, a compromise must be sought among number of units (cost), per-unit coverage area, accuracy, antenna support requirements, and power consumption. Also, a fixed antenna would probably require less maintenance, an important consideration where units are used in difficult to access locations such as mountain tops. Also, the accuracy advantage of a rotated system will be less in situations with multipath propagation, such as animals and equipment both under a forest canopy. In densely wooded habitat, the attenuation versus distance can become high, reducing the per-unit coverage area advantage of the rotated system.
Our comparison of the automatic systems with a manually operated antenna is biased by two factors. First, the receiver -3dB bandwidth was 2 KHz, but for detection of coherent tone pulses > c. 15 ms, the human ear-brain operates at a bandwidth of c. 100 Hz, irrespective of equipment bandwidth. This c. 13 dB human S/N advantage in our tests explains the better accuracy of the manual system down to about -27 dB (Table 1). In fact, the measured advantage was a few dB less than 13 dB because the human ear cannot compare signals as accurately as the computer algorithm. The second bias was against the human operator, reducing his accuracy advantage to a few dB for levels below -27 dB (Table 1). This result stems from the fact that the antenna had to be rotated to equal signal positions straddling the band gap (no-signal region around the null) and the maximum rotation speed (c. 30°/s) was so slow that comparisons became difficult as the band gap (time between comparisons) increased with weaker signals. Manually controlled beam switching, or provision of a handle for rapidly skewing the antenna, either of which would have improved human performance at low signal levels, were not tested.
Frequency drift of animal transmitters with temperature and posture places a limit on mimimum practical bandwidth for automatic systems, but for many wildlife transmitters and environments, a 500 to 250 Hz bandwidth could be used with a 6-to-9 dB improvement over the results we report. A frequency search and correction algorithm could handle the occasional drift encountered, with some reduction in system speed.
The relative precision of DF systems at medium to low S/N may be estimated from the patterns of the antennas they employ. The patterns for the fixed system we tested (Fig. 1b) show equal voltages at 0o and Vw = 0.13 and Vs = 0.5 at -30o. The difference between 0.13 and 0.5 is 0.37. Thus, as the azimuth goes from 0o to -30o, the voltage difference increases from zero to 0.37, a rate of 0.0123 volts per degree. A similar calculation from the patterns of the rotated system (Fig. 1f) over the 8o arc bracketing the boresight yields 0.1 volt per degree (also see Table 3). The ratio of these rates (8.1 = 0.1 / 0.0123) provides an estimate of the relative precision obtainable from the two antenna arrays. Our empirical results show differences in standard deviation of error by a factor we conservatively typify as 7 (range 6.6 to 9.9, Table 1), not much different from the 8.1 calculated above.
A comparison of the distances at which DFing can be done regardless of azimuth may be gleaned from the ratio of the relative minimum voltages (Vw) over the arcs that must be covered. In the example above, this voltage ratio (4.6 = 0.6 / 0.13) represents a 13 dB difference favoring the rotated 6-element antenna. Values for other antennas are given in Table 3; their differences may be approximated in terms of range from Table 1.
For the sake of simplicity we used volts in the above examples, but the vertical scale of a pattern need only be proportional to volts because all comparisons are of ratios. Engineers, however, customarily normalize antenna patterns to 1.0, regardless of gain, and sometimes plot signal in dB or power rather than voltage. Therefore, in estimating performance from published patterns, it will undoubtedly be necessary to convert to volts and normalize all patterns to the one taken as the benchmark for comparison. Relative precision of a number of antenna arrays (using patterns in Lawson [5], pp. 1-18 to 1-21) is given in Table 3. We emphasize that the DF comparisons relate to error as expressed by SD and not to bias of the mean error. The latter, affecting only fixed systems, depends on signal level, detector linearity, and azimuth. When comparing systems, the only simple thing we can say regarding bias of mean error is that rotated systems are essentially immune to bias and fixed systems will always be subject to it, increasingly so for weaker signals and larger off-boresight azimuths.
Burchard [7] described a Doppler DF system that employed a circular array of 8 vertical dipoles and reported (his figure 19.7) "fluctuations of readings" that go from ±0.4o degrees to ±10o as receiver input drops from -120 dBm to -130 dBm. These input levels correspond approximately to the -9 dBm to -21 dB field levels of Table 1 where performance of the fixed system is roughly the same as that of the Doppler DF system.
Accuracy and per-unit coverage area, because they impact the quality and cost of data, are important factors in choosing data collection systems that are optimal for particular biological objectives. Samuel and Fuller [4], in their design section, provide the broad perspective from which the implications of these findings may be viewed. The present results are consistent with engineering experience and with well-established theory [8].
R. M. Anderson, J. Knight, R. P. Larkin, T. Osborn, and A. Raim provided valuable comments on the manuscript. R. Lindsey built the rotator and wrote the control software. The project received support under U.S. Army CERL contract DACA 88-97-M-0245.
[1] Cochran, W.W. and R.D. Lord. 1963. A radio tracking system for wild animals. J. Wildlife Management 27(1):9-24.
[2] Cochran, W.W., D.W. Warner, J.R.Tester, and V.B. Kuechle. 1965. Automatic radio-tracking system for monitoring animal movements. BioScience 2:98-100.
[3] Deat A.R., C.Mauget, R. Maugot, D. Maurel, and A. Sempere. 1980. The automatic, continuous and fixed radio tracking system of the Chize Forest: theoretical and practical analysis. Pages 439-451 in C. J. Amlaner, Jr. and E. W. McDonald, editors. A handbook on biotelemetry and radio tracking. Pergamon Press, Oxford, U.K.
[4] Samuel, M.D. and M.R. Fuller. 1994 Wildlife radiotelemetry. Pages 370-418 in Bookhout, T.A., editor. Research and management techniques for wildlife and habitats. The Wildlife Society, Bethesda, MD.
[5] Lawson, J.L. 1986. Yagi antenna design. Publication no. 72. American Radio Relay League. Newington, CT. 198pp.
[6] Larkin, R.P, Raim, A., and R.P. Diehl. 1996. Performance of a non-rotating direction-finder for automatic radio tracking. J. Field Ornithol. 67(1):59-71.
[7] Burchard, D. 1989. Direction finding in wildlife research by Doppler effect. Pages 169-177 in C. J. Amlaner, Jr. ed. Biotelemetry X. Univ. of Arkansas Press, Fayetteville, AR.
[8] Swerling, P. 1956. Maximum angular accuracy of a pulsed search radar. Proc.IRE 44: 1146-1155.