Techniques for detection and tracking airplanes using weather radar WSR-88D Svetlana Bachmann, Victor DeBrunner, Dusan Zrnic, Mark Yeary

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1 Techniques for detection and tracking airplanes using weather radar WSR-D Svetlana Bachmann, Victor DeBrunner, Dusan Zrnic, Mark Yeary Abstract For the first time, weather radar echoes from point scatterers (airplanes) in a non-stormy environment are investigated in the time and frequency domains and compared to model simulations to build a background for differentiating these echoes from weather signals and to develop procedures for data censoring. I. INTRODUCTION The National Weather Service s network of Doppler Weather Radars (WSR-D) covers the entire US. The main purpose of the network is detection of hazardous weather and quantitative precipitation measurement. These radars operate continuously and each covers a spatial volume in about five minutes. With increase awareness about security it is natural to establish if the radars could also detect and track non cooperative targets without compromising their primary mission objectives. WSR-D radars are used for weather observations [], rainfall estimation [,,], shortterm warnings and forecast services for the general public [], detection of icing, hail, and turbulence[], and observations of biological scatterers: insects and birds[]. It is not indicated in the literature if weather radars can recognize and track airplanes or missiles. Conventional detection of targets (constant false alarm CFAR) is based on evaluating power above threshold and declaring a possible hit. The thresholds of power could be used with weather radar. The capabilities for conventional tracking (e.g., conical scan antenna or monopulse antenna) are lacking in weather radar. We demonstrate herein that tracking can be done by examining rapidly obtained fields of power (i.e., reflectivity) and velocity. Further we submit that detection and classification of aircraft might be possible by analyzing Doppler spectra of returned signals. II. DATA COLLECTION/ RADAR SET UP Time series data were collected by KOUN for Homeland Defense Radar Test on March. Antenna rapidly ( sec) scanned a sector in azimuth from through, at constant elevation., with the pulse repetition time PRT µs. One radial of time series data consists of complex samples at range locations. Spectral moment were obtained and observed on plan-position indicator (PPI) displays (Fig.) in real-time. Spectral processing and analysis was done off line. III. TRACKING (a) Reflectivity PPI, Z,dB (b) Velocity PPI, v, m s Fig. : th time of data. Circles near km range ring are used to show the airplanes locations. Power, db Range gates Fig. : Return Power along one radial km km A- A- A- A- Threshold A- Airplane airplane Fig. : Trajectory of the airplanes. The radar is located above the figure. Numbers through near the data points correspond to successive scans. A-

2 Airplane A- was flying in the center of the scanned sector at ranges from to km and was detected on the display by its substantial power compared to the background echoes. An unknown aircraft A- was detected in the same scan and is chosen to contrast A- echo features. The return power along one radial (Fig.) demonstrate the possibility of airplane detection by threshold of power simultaneously with non-zero mean velocity check (for ground clutter elimination). Both airplanes were tracked by association from scan to scan. The oscillations in the paths of the airplanes in (Fig. ) are likely due to the backlash of the antenna that occurs during scanning a sector back and forth as opposed to the full scan. IV. DOPPLER SPECTRA AND VELOCITY The velocity value displayed on PPI for A- agrees with that estimated from the trajectory. The PPI velocity of A-, ms away from the radar, contradicts the estimated trajectory. The velocities are aliased due to relatively small span of unambiguous velocities ( ms to ms ). The conventional formula for a true velocity of a scatterer v = (nv max v o ), where n is an integer, v o is the observed aliased velocity of a target, gives a set of possible A- velocities: {,,,,, } ms. There are different techniques for de-aliasing velocity to ms toward radar. For the tracked airplane estimation can be done directly from the trajectory (path over time). V. CROSS SECTION The reflectivity factor Z (Fig. a) is found according to the weather radar equation for distributed scatterers. However, the airplanes are not distributed scatterers but point scatterers. Combining the radar equations for distributed and point scatterers [], and assuming location of the scatterer in the center of the resolution volume, cross section σ b (m ) can be estimated as Z e K cτπ θ r σ b =, () λ (ln ) where Z e is the equivalent reflectivity factor, K is the parameter related to the complex index of refraction ( K water =.), c is the speed of light, τ is the pulse length (. µs), θ is the angular beam-width (. π/), r is the scatterer range (m), λ is the radar wave length (. m). The cross section for each airplane s detection is slightly different due to airplane orientation, the location of the airplane within the resolution volume, and possible presence of other scatterers. The mean cross section is m. The maximum cross-section is m. The crosssection values are likely underestimated because the computations assume that the airplane is located in the center of the resolution volume. The bending of the beam at ranges to km from the radar can be ignored. The height of the beam centerline above antenna can be calculated as product of range r and a sin of elevation angle. The radar sends beams of -width with a step of about.. Overlapping of the beams causes detection of a scatterer by neighboring beams. The stronger return is detected in the beam where the scatterer is closer to beam s centerline. Knowing that the height of the beam centerline at the A- ranges varies from meters to meters (Fig. ), the altitude of the airplane was estimated to be about m, and the largest estimated A- cross section was during time (Fig.); we deduce that during time of this scan A- was located on the beam centerline in the middle of the resolution volume, and therefore, it was navigating at the altitude h a = m above the antenna. Height above antenna (km) Range (km) Fig. : Side view of the A- trajectory. Beam centerline is shown with a dashed line. Dotted lines above and under beam centerline indicate the halfpower border of the beam. Crosses on the beam centerline show the ranges of the A- echoes. Solid line indicates the altitude of the airplane. The numbered circles indicate estimated position of A-. Numbers stand for the times of the readings. The radar beam pattern is represented by a Gaussian function A exp( x /σ b ), where A is the amplitude, and σ b = θ /ln []. The echoes of A- at time are smaller then the echoes at other times because the airplane was located farther away from the center of radar beam ( above the beam). As indicated by numbers corresponding to the times, the airplane moves from right to left (times through ), and from left to right (times to ). The distance between two consecutive positions of A-

3 can be found in terms of degrees. The cross-section values, spaced with the appropriate angular distances, form a Gaussian-like distribution. The Gaussian curve corresponding to the cross-section two square meters fits data points the best. The actual crosssection of a small craft as seen by the radar is in the range to m []. The value m is an outlier caused by favorable position of the aircraft, and possibly by presence of additional scatterers in the resolution volume. A -point average of the crosssection data without outlier is in Fig. (solid line). The dashed line shows the fitted Gaussian curve. At the th time when airplanes were at the same range, the cross-section of A- is larger than that of A-. By analyzing the flight of the A-, we noticed a change of its cross-section depending on the position of the airplane. For example, the cross-section of A- is the greatest during times when A- is turned sideways to the radar. As expected and in agreement with optical cross section the EM cross section of an aircraft side is larger then its front or back looking cross section. Cross-section (m ).. Time cut Gaussian Shifted Gaussian -pt-average return power lower then its surroundings, and the range location somewhat closer to the radar then airplane range. Airplanes spectra are shown with solid lines. The clear-air spectra are shown with dashed lines. The dotted lines show spectra at the gate in front, and behind of airplanes. For each time figures similar to Fig. were generated and analyzed. For some times the spectrum at the gates in front of and behind the airplane gate shows similar shape to the airplane gate but with smaller amplitude. This is due to the spread of the skirt of the range-dependent part of the composite weighting function. The clear-air spectra in all times are ~db below the airplane spectra and show similar Gaussian-shape curve centered between and ms -, indicating the wind velocity. The peak corresponding to velocity ms - (Fig. a) indicates that A- is moving at ms toward radar. Another interesting common feature in the A- spectrum is well pronounced peaks, with one maximum. All spectra have similar signature with a slight variation of amplitudes and fluctuations of the location of maxima. The peaks could help to distinguish these spectra from other types of scatterers. The peak corresponding to velocity ms - (Fig. b) indicates that A- is moving at ms away from the radar. All spectra of A- echoes are similar to the one shown. There are several similarities in A- and A- spectra with gradually changing velocity peak (when the airplane is turning and changing direction relative to the radar). -.. Angle (degrees) Fig. : Fitting cross-section to Gaussian curve exp( x /σ b ). -point average fits very well the Gaussian curve with amplitude. At time the aircraft turns VI. SPECTRA The spectra of A- and A- (Fig. a, and b) are weighted by the Hanning window to reduce coupling of strong spectral components into adjacent weaker ones. A range location is defined as a gate. Two gates neighboring in range with the airplane gate are called in front of, and behind the airplane regardless of the flight direction. The gate in front of the airplane is defined as the gate closer to the radar, and the gate behind the airplane is the gate farther from the radar. A clear-air is defined as the gate with the Velocity (ms - ) Velocity (ms - ) (a) A-, time (b) A-, time Fig. : Spectra weighted by Hanning window. Solid line indicates spectra of the airplane-gate. Dotted lines show spectra at the gates in front of and behind the airplane-gate. Dashed line is for clear-air. In front of the gate spectrum shows clear-air. Behind the gate spectrum repeats the airplane spectrum with smaller amplitude, due to the spread of the range dependant weighting function.

4 A range dependant repetition of the spectrum is observed in both cases. The radial component of the wind speed is the same for both cases. The maximum in the airplane spectra corresponds to the radial velocity of A-, similar to what was observed in A- case. Unlike A-, the spectra of A- do not exhibit modulations. It could be that A- propellers are small compared to the dimensions of the airplane, or it is a jet airplane. The spectra from neighboring gates repeat the airplane spectrum with smaller amplitude, due to the spread of the range dependant weighting function. The peak at zero velocity in the clear-air spectra is due to the ground clutter. Animating spectra allows observing fluctuations and distinguishing between little changes in the airplane spectra from the unique features that are approximately constant. The extracted features would define the airplane signature. Thus, the categories of airplanes may be distinguished by their spectra, if they indeed have the unique signatures. VII. SIMULATIONS The modulation (Fig.a) is apparent in A- spectra. It is hypothesized that these modulations are caused by propeller rotation. maxima are spaced by to ms - interval. In the Homeland Defense Radar Test document Test Plan of Mar, it is stated that the aircraft used in the experiment is a Cessna AgWagon. Such airplanes have to rpm and -bladed propellers. We use simulations to demonstrate that similar to A- spectrum modulation can be produced. A simple model of a flying airplane with a propeller accounts for the speed of its main body and the propeller rotation speed (Fig. ). Radar beam Fig. : Simple model for detection of a signal modulated by a -bladed propeller. The airplane is moving forward (bold vector) with the rotating propeller (black curved arrows). A received signal y(k) produced by an airplane with a constant speed, and a rotating propeller can be written in the form y( k) = Aexp jkω d + Bexp jk( ωd ω) + Bexp jk( ωd + ω) where A is amplitude caused by the airplane s main body, B is amplitude of a signal reflected from the propeller, ω d is the Doppler shift due to the airplane movement, ω is the shift caused by propeller blade. The propeller causes reflections which in turn create modulations if the airplane is not flying along beam axis. Even if the plane is aligned on the average with the beam axis, instantaneous deviations due to pitch ( ) ( ) ( ) and yaw will be present. The Doppler shift from the propeller depends on the location of dominant scatterers. If the scatterers are equally strong along the propeller then the shift will have a distribution between (propeller center) and the maximum value (the end of propeller blade). The simplified model herein assumes dominant scatterers are confined at some distance from the center hence the modulation can be represented with a single sinusoid ω = Csin(α t), with an amplitude C, and α = π(rpm/), where rpm is the propeller speed in revolutions per minute. Spectral signatures are modeled using several propeller speeds, airplane speeds, and amplitude values A, B, C. It was found that observed spectra can be reproduced in simulation if a speed of ms - and a -bladed propeller rotating at rpm were used (Fig. ). - - Velocity (ms - ) Fig. : Spectra of the simulated signal from a craft moving at ms - with a -bladed propeller rotating at rpm weighted by the Hanning window. The amplitudes of the simulated airplane body and propeller returns are and. respectively (A=, B=., C=). VIII. CONCLUSIONS We have demonstrated feasibility to track aircraft in the field of spectral moments and to identify its signature in the Doppler spectrum. Further, a simple signal model for a propeller aircraft replicated spectral characteristics of Cessna Ag Wagon showing that features in Doppler spectra correspond to the physical specifications of the craft. Categories of airplanes (e.g., with or without a propeller, large or small) could be distinguished by their spectra. Tracking was done using rapid consecutive scans and the airplane was easy to detect in both spectra and PPI at close ranges. Nonetheless tracking at WSR-D volume updates rates (~ min) might be difficult and will need association from volume scan to volume scan and might confuse airplanes with large birds or moving automobiles (from side lobe). IX. REFERENCE [] Doviak, R. J. and D. S. Zrnić, : Doppler Radar and Weather Observations. Academic Press, pp.

5 [] Goff, R.C. Amodeo, F. Pace, D. Tauss, J., : Future FAA operational needs for WSR-D architecture. IEEE Proc. Aerospace and Electronics Conference,. NAECON, Vol., - pp. [] Liu, H., Chandrasekar, V., Gorgucci, E., : Detection of rain/no rain condition on the ground based on radar observations. IEEE Trans. Geosci. Remote Sens., Issue:, Vol.,, [] Saffle, R.E., Johnson, L.D., : NEXRAD product improvement overview. IEEE Proc. Aerospace and Electronics Conference,. NAECON, Vol., - pp. [] Zrnić D. S, and A. V. Ryzhkov, : Observation of Insects and Birds with Polarimetric Radar IEEE Trans. Geosci. Remote Sens., Vol., No., - pp. [] [was ] Personal communications with Zrnić D. S, September.