Accurate Localization of the Points-of-Interest by Correcting Atmospheric Effects

J. Choi
Space Systems Development Department

Introduction: Geometrical bending of the RF signal path is greatly intensified in the lower atmosphere, most notably the troposphere, due to the curvature of the air layer near the Earth's surface. The Exponential Tropospheric Model (ETM) has been developed to correct or to compensate for this deviation and to locate points of interest (POI) by correcting atmospheric effects on RF wave propagation in space. The ETM model is based on real-time weather data-surface, pressure, temperature, and humidity. The objective is to reduce RF propagation range errors and ray-bending angle errors for accurate positioning or localization of POIs. The ETM model takes surface weather data and translates it into refractivity ray-tracing profile for range and angle error correction from the ground to space up to 27 km. The ETM model is readily available and applicable to many tactical and strategic operations. These operations include tracking, navigation, search and rescue (SAR), electronic warfare (EW), positioning targets of interest (TOIs), and to any anomalies, for both military and commercial applications. Analysis results over operational benchmark data show the accuracy of errors for SAR application is less than 200 m from the TOIs and POIs for the applications described above.

ETM Model and Atmospheric Errors in the Troposphere: The ETM model¹ is based on the fact that the observed refractivity distribution is more nearly an exponential rather than a linear function of height, as assumed by the effective Earth's radius model. The exponential decrease of the refractivity N with height is sufficiently regular to permit a first approximation of average N-unit structure from surface conditions alone:²

N_h = N_s^* exp (-h/H). (1)

H is a reference (or scale) height appropriate to the value of N at zero height (or surface), N_s is the surface refractivity, and h is the height above the mean sea-surface level in km. Considering a scale height H, it is simply the height at which the value of N(h) is equal to 1/e of N_s under the assumption of Eq. (1), at which the stratified layer height h is equal to the scale height H. The refractive phenomena of angle bending and propagation time delay beyond this layer (i.e., reference height) will be limited and minimal. Temperature and humidity beyond this atmospheric layer do not significantly change to affect refractive bending above 500 MHz. This coincides with the fact that most ray-bending and refractive phenomena happen within this region from the surface of the Earth. This implies that troposphere effects on ray bending can be approximated by the reference height without loss of any significant physical or atmospheric theory. The ETM model not only adopts this exponential model, Eq. (1), but also adapts to near-real-time or real-time calculation of the reference height H over the worldwide 2.5° X 2.5° grid and 1.0° X 1.0° for finer meteorology data. ² This is the primary reason for adopting this approach: compared to existing ray-bending correction algorithms, it provides the most reliable and accurate results for applications to locate POIs.

Accuracy of Localization: The accuracy of the POI's location is characterized in several different ways. Confusion about the meanings of the terms causes some of the loudest disagreements between suppliers and users having EW and signals intelligence applications. Requirements for specific applications vary widely. In angle-measuring systems (directionfinding (DF) systems and interferometers), the errors are angular, while in distance-measuring systems, the errors are linear. The distance-measuring system only is presented here. When the precise POI location is required, the time of arrival (TOA) or time-difference of arrival (TDOA) technique is the primary distancemeasuring technique. These are often the preferred choices. Both depend on the fact that signals propagate at approximately the speed of light c. A signal leaving a transmitter at some defined time will arrive at the receiver at time R/c later, where R is the range from the transmitter to the receiver. Thus the TOA defines the distance. The accuracy with which the distance is defined depends on the accuracy with which the transmission time is known and the time received is measured. Global positioning system (GPS) receivers output very accurate time references, making precision TOA measurement much easier than it was only a few years ago. One can easily derive the semi-major axis (SMA) and semi-minor axis (SMI) equations as well as an axis direction from the leastsquare estimation of inverse theory numerical approximation. With this information error ellipse can easily be plotted with 95% EEP (error ellipse probable) or CEP (circular error probable).

Test and Analysis Result: This article emphasizes time delay and angle of arrival error by using climatology and meteorology data. Figure 6 is a global contour map of time delays for the month of January and shows the data quality and performance of the ECMWF database. The average time delay in the Northern Hemisphere is about 350 ns, and peak delay (red color) is centered near the southeast Pacific Ocean and small portions of mid-Africa and South America. This kind of time delay and angle error global contour map can be delivered every 6 hours to users anywhere and at any time for host sensor calibration and tactical or strategic adjustment in operational and field exercises. Analysis results show similar performance results of 20% improvement of SMA/SMI over conventional analytical models such as the Hopfield model.³ Figure 7 illustrates a dependency of elevation angle for shape and size of the ellipse, and containment of POIs for test data of two different cases. The unit is in feet for both coordinates. The medium-level elevation angle (Fig. 7(a)) performs better in containment perspective than that of the low-elevation angle case (Fig. 7(b)). In the figure, ch stands for the ETM model (previously called the Choi model) and hp is the Hopfield model. The ETM model not only contains the desired target, but also the uncertainty of the ellipse is narrowed down or smaller for operational advantage in SAR mission.

FIGURE 6
Global contour map for time delay and range error.

Fig7a Image

FIGURE 7(a)
95% EEP ellipse of SMA/SMI for medium elevation angle [ft].

Fig7b Image

FIGURE 7(b)
95% EEP ellipse of SMA/SMI for lower elevation angle [ft].

Conclusion and Recommendation: The ETM model can readily access real-time weather and climatology data, resulting in less data storage requirements. The ETM model generally is more accurate than currently available troposphere models. It provides more than 50% miss distance accuracy in localization and 20% miss distance accuracy in SMA/ SMI with compatible processing time.

[Sponsored by SPAWAR]

References
¹ J. Choi, "Performance Comparison of Tropospheric Propagation Model: Ray Trace Analysis Results Using Worldwide Tropspheric Databases," NRL/FR/8140-97-9857, September 1977.
² B.R. Bean and E.J. Dutton, Radio Meteorology, National Bureau of Standards, Monograph 92, U.S. Govt Printing Office, Washington, D.C., March 1966.
³ H.S. Hopfield, "Two Quartic Tropospheric Reflectivity Profile for Correcting Satelite Data," J. Geosci. Res. 18, 4487-4499 (1969).