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Satellite Telemetry: A New Tool for Wildlife
Research and Management

Location Determination


JPEG - Doppler Effect

Information taken from: Satellite Telemetry: A New Tool for Wildlife Research and Management
Location Determination

By

Steve G. Fancy, Larry F. Pank, David C. Douglas, Catherine H. Curby,
Gerald W. Garner, Steven C. Amstrup, Wayne L. Regelin


Calculations for determining locations of PTT's are conducted at the Argos Data Processing Centers in Toulouse, France, and Landover, Maryland, following each satellite pass. The location of a PTT is determined from the Doppler shift in the carrier frequency transmitted by the PTT. The Doppler effect is the perceived change in frequency resulting from the relative movement of the source and receiver. As the satellite approaches the PTT, the frequency received by the instruments on board the satellite will be higher than the transmitted frequency (401.650 MHz), whereas frequencies lower than 401.650 MHz will be received by the satellite as it moves away from the PTT (Fig. 17). At the point of inflection of the Doppler curve, that is, when the received and transmitted frequencies are equal, the position of the transmitter will be perpendicular to the satellite ground track.

Figure 17 
Fig. 17.  Doppler shift in the uplink carrier frequency as the satellite approaches and then moves away from the location of a radio-collared animal. The slope of the Doppler curve at the inflection point determines the distance from the animal to the satellite ground track.

A field of possible positions for the PTT under consideration is calculated for each message received by the satellite. This field is in the form of a half-cone (Fig. 18), with the satellite at its apex, the satellite velocity vector as its axis of symmetry, and an apex half angle determined by the equation COS A = (C ÷ V) (FR ÷ F0) where C is the speed of light (the propagation speed), V is the satellite velocity, FR is the carrier frequency received by the satellite, and F0 is the transmitted frequency (401.650 MHz). The satellite velocity is determined from orbital characteristics, as explained below. One locational half-cone is obtained for each Doppler measurement. The intersection of two or more of these cones with the altitude sphere, which in the case of a terrestrial mammal is assumed to be sea level, yields two possible positions for the PTT that are symmetrical with respect to the satellite ground track (Argentiero and Marini 1979; see right portion of Fig. 18). The second, erroneous position is called the image. The actual position of the platform is determined from previous locations, the platform velocity, and the earth's rotation. For slow-moving PTT's (i.e., less than 20 m/sec), the ambiguity can be resolved in 95% of the cases (Argos 1978). The calculations involve an iterative least-squares technique that produces the position that minimizes differences between the expected and measured Doppler history (Levanon 1984). Before April 1987, Argos provided users with both the primary location of the transmitter and its image. Data provided by the new data-processing centers that became operational on 1 April 1987 contain only the primary location for the PTT, which in some cases might be incorrect. Argos has agreed to again provide both the calculated location and its image, beginning in October 1987.

Figure 18a Figure 18b
Fig. 18.  Summary of the procedure used to calculate animal locations. Each half-cone results from a single message and intersects the earth at two points, equidistant from the satellite ground track. An iterative least-squares procedure is used to calculate the actual location of the animal and its alternate location or image (adapted from Argos 1984).

Other information used in the location calculations includes satellite orbital elements and precise timing of measurements. Orbital elements for each satellite are provided regularly by the Air Force Space Command tracking facility in Colorado. Argos also maintains 11 reference PTT's that transmit at 30-sec intervals from precisely known locations around the world. Data from these reference platforms are used to correct the satellite orbital predictions and make it possible to predict the satellite position to within 300 m along the ground track and 250 m in the across-track direction (Argos 1984). A high-precision time-coding platform based on a cesium clock transmits from Toulouse, France. This time-coding information is used to monitor the stability of the onboard oscillator and to synchronize all measurements within a mean precision of 12 ms (Argos 1984).

To calculate a location from a single overpass, Argos normally requires a minimum of five Doppler measurements for a particular PTT, with at least a 420-sec interval between the first and last measurements. If the user wants more locations, Argos will calculate less-accurate locations from only four Doppler measurements separated by 240 sec. In each case, the algorithm uses least-square analysis to calculate PTT latitude, longitude, and the exact transmit frequency. The platform velocity is assumed to be zero in the calculations. The ambiguity between the actual location and its image is resolved primarily by the previous location of the PTT.

Before April 1987, Doppler measurements for a particular PTT made during two subsequent overpasses by the same satellite or during one pass by each of the two satellites were sometimes combined to increase the accuracy of the calculated location (Fig. 19). The two-pass algorithm requires at least 12 Doppler measurements, with at least 5 measurements from each pass, and yields latitudinal and longitudinal velocity components in addition to a more accurate position (Rosso 1985).

Figure 19 Fig. 19. Example of how Doppler data from two overpasses are merged to provide a more accurate location. Data received during orbit 1 were used to calculate locations at point 1 or 1'. Data acquired during orbit 2 were used to verify point 1 as the true location and to calculate a movement vector between points 1 and 2. Letters represent the position of the satellite when Doppler measurements were made (adapted from Argos 1978).

Several quality control criteria are used by Service Argos to prevent calculating locations with unacceptable accuracy. The primary basis for rejection is distance of the PTT from the satellite ground track (Rosso 1985; Fig. 20). Service Argos has found that locational errors are highest when the PTT is within approximately 170 km of the ground track or more than 2,700 km from it (Argos 1984). If the mean transmission frequency for a PTT during two passes differs by more than 24 Hz, or the short-term frequency stability exceeds 4 x 10-5, no location is calculated (Argos 1984).

Figure 20
Fig. 20.  Locations can be calculated for transmitters within a zone of approximately 170-2,700 km on either side of the satellite ground track. Locational errors are usually unacceptably high if the transmitter is outside these zones (adapted from Argos 1984).

The altitude of the PTT and the short- and mid-term stability of the PTT's oscillator influence locational accuracy. Errors resulting from differences in the altitude of the PTT and the assumed altitude (usually sea level) are coupled to the across-track coordinate of the fix and have essentially no effect on the along-track coordinate. Because the satellite orbits are nearly polar (only 8° inclination from the polar axis), the across-track error is almost equivalent to an error in longitude (Levanon 1984). Studies have shown that these locational errors only assume major significance for high-flying balloons and birds, and the degree of error depends on the maximum elevation of the satellite during the pass. For example, French (1986) showed that for a maximum satellite elevation of approximately 26°, an altitudinal error of 500 m results in a range error of 250 m (Table 6).

Table 6. Effect of maximum satellite elevation during a pass and the difference between the assumed and actual PTTa altitude on locational accuracy (French 1986, Fig. 5).
Table 6

An important source of error for most animal PTT's is oscillator stability, which is largely influenced by temperature (Argos 1984). Argos certification requires a medium-term stability of 4 Hz over 20 min, or one part in 10-8 Hz; an oscillator stability of this magnitude should result in locational errors of less than 1,100 m in 65% of cases, according to Service Argos data (Argos 1984). Experimental data from well-insulated PTT's with a medium-term stability of 10-8 Hz resulted in a root mean square (RMS) error of 320 m for locations based on a single satellite overpass (Fig. 21) and 235 m for locations calculated from messages received during two overpasses. (The RMS error is equivalent to 1 standard deviation of the distances from a mean of zero.) Data showing the effect of PTT distance from the satellite ground track were presented for the same experiment (Rosso 1985; Fig. 22). The locational accuracy of the smaller Telonics PTT's used on animals, which are subjected to greater temperature extremes than those used by Rosso (1985), is presented later in this report.

Figure 21
Fig. 21. Locational errors reported by Rosso (1985) for a relatively large, well-insulated, Argos-compatible transmitter.
Figure 22
Fig. 22. Relation between locational errors and
distance from the transmitter to the satellite ground track (modified from Rosso 1985).

Literature Cited

Argentiero, P., and J. Marini. 1979. Ambiguity resolution for satellite Doppler 
	positioning systems. IEEE (Inst. Electr. Electron. Eng.) Trans. 
	Aerospace Electr. Syst. 15:439-447.

Argos. 1978. User's guide--satellite based data collection and location system. 
	Service Argos, Toulouse, France. 36 pp.

Argos. 1984. Location and data collection satellite system user's guide. 
	Service Argos, Toulouse, France. 36 pp.

French, J. 1986. Environmental housings for animal PTT's. Argos Newsl. 26:7-9.

Levanon, N. 1984. The theoretical bounds on random errors in satellite Doppler 
	navigations. IEEE (Inst. Electr, Electron. Eng.) Trans. Aerospace 
	Electronic Sys. 20:810-816.

Rosso, R. 1985. Location: theory and performance. Argos Newsl. 23:15-17.

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