Detection and Velocity Estimation of Moving Vehicles in High-Resolution Spaceborne Synthetic Aperture Radar Data Stefan Hinz, Diana Weihing, Steffen Suchandt, Richard Bamler Remote Sensing Technology, TU Muenchen, Germany
[email protected] Abstract — Automatic estimation of traffic parameters has evolved to an important topic of research. Current and upcoming SAR satellite missions offer new possibilities for traffic monitoring and control from space as an alternative to conventional traffic data acquisition. In this paper a detection approach is presented which evaluates simultaneously the effects moving objects suffer from in the SAR focusing process. Information about the measured signal and the expected signal are utilized in the detection framework. Analyses of the proposed technique are done with real spaceborne SAR data.
I.
INTRODUCTION
1.1 Motivation Increasing traffic has an influence on urban and suburban planning. Usually traffic models are utilized to predict traffic and forecast transportation. To derive statistical parameters of traffic for these models, data of large areas acquired at any time is desirable. Therefore, spaceborne SAR missions can be a solution for this aim. With the new TerraSAR-X (Roth, 2003) or RADARSAT-2 mission, SAR images up to 1 m resolution are available. Additionally, the Dual Receive Antenna (DRA) mode enables the reception of two SAR images of the same scene within a small timeframe, which can be utilized for along-track interferometry. 1.2 Related work Since moving objects suffer from special effects in the SAR processing algorithm, specific methods for detecting vehicles are required. In several publications the task of detecting moving vehicles has been treated. In military research this problem is known as Ground Moving Object Indication (GMTI). If more than two channels are available the use of Space Time Adaptive Processing (STAP) is the optimal method (Ender, 1999; Klemm, 1998). In the case of twochannel systems, like TerraSAR-X or the Canadian RADARSAT-2, interferometric approaches can be used for detecting vehicles. Along-Track Interferometry (ATI) (Sikaneta and Gierull, 2005) and the so-called Displaced Phase Center Array (DPCA) method are the classical methods to do so. They can be regarded as an approximation of the limiting case of STAP. In the ATI technique an interferogram is formed from the two SAR images by complex conjugate multiplication, whereas in the DPCA processing the two calibrated SAR images are subtracted from each other. The
978-1-4244-2340-8/08/$25.00 ©2008 IEEE
interferometric phase in ATI and the magnitude of the result in DPCA are evaluated for detection (Gierull, 2002). These detections are done based on a constant false alarm rate scheme. In (Meyer et al., 2006) these approaches have been extended by integrating apriori information, GIS data of road networks. However, e.g. ATI can only be applied if the motion of the vehicle affects the interferometric phase, which is not the case if vehicles are moving in along-track direction. To estimate ground moving parameters for vehicles travelling in along-track, one method is to apply filterbanks with differently designed matched filters (Gierull and Sikaneta, 2004; Weihing et al., 2006). The presented detection approach in this paper considers simultaneously the effects in SAR images, which are caused by the vehicle’s motion in across- and along-track. It furthermore can include multi-temporal SAR data. The scheme is derived from statistical detection theory and its principle relies on comparing an expected signal with the actual measurement. Therefore, different information is combined in this detection algorithm. The expected signal, the measured signal and their variances are included to decide whether a vehicle is present or not. In the next section a short summary is given of the different effects in SAR images caused by the vehicle’s motion. The proposed detection scheme is explained in Sect. 3. Afterwards the performance of this detector is analyzed using experimental TerraSAR-X data in Sect. 4. II. MOVING OBJECTS IN SAR DATA – A SUMMARY In an air- or spaceborne SAR imaging process a Radar scans the earth in a side-looking fashion during its flight over the scene. While the sensor is moving it transmits microwave pulses at constant intervals given by the Pulse Repetition Frequency (PRF) and receives the echoes. In Fig. 1 the geometry of an image acquisition is shown. The radar is flying in a certain altitude h along the x-axis, also referred to azimuth direction or alongtrack. The y-axis, which is oriented perpendicular to the flight path, is usually refered to as ground range or across-track direction. The position of the sensor at a certain point of time is given by Psat(t) = [xsat (t), ysat (t), zsat (t)] and the location of the moving target by Ptarget = [xmover (t), ymover (t), zmover (t)]. The distance between sensor and target corresponds to:
where vx0 and vy0 are the components of target’s velocity in along- or across-track, respectively, and ax0 and ay0 the accelerations in these directions, each at the time t = 0. The imaging effects caused by the uncompensated motion parameters are explained in the following Sections. Figure 1: Imaging geometry of a spaceborne SAR
Herewith,
is the distance at t = 0 (the shortest range between SAR and target). The received echo is a replica of the transmitted signal backscattered from the ground. For a detailed representation of the echo signal see (Bamler and Schättler, 1993). Here the received echo signal is simplified without considering range cell migration and can be written as:
2.1 Motion in across-track The object is assumed to move in across-track with a constant velocity. This results in a linear change of the range history R(t), so that the shortest distance is not at time t = 0 anymore, is shifted depending on the velocity in line-of-sight vlos = vy0 · sin(θ), with θ being the local elevation angle. In Fig. 2 this is shown. The red curve stands for the range history of an object moving in across-track, whereas the blue curve is the reference range history of a stationary target.
where
is the frequency modulation rate of the azimuth chirp. To form a SAR image out of the received echoes a matched filter algorithm is applied. The filter for azimuth focusing is defined by: To circumvent an extensive convolution in time-domain, the operation is done in the frequency-domain by multiplying the spectra of signal echos and filter.
However, for this process a stationary-world matched filter is assumed. Significantly moving and even accelerating objects violate this assumption and therefore the target will not be imaged ”correctly”. The dependencies on object velocity and acceleration components can be seen when expanding the range equation R(t) into a third order Taylor series:
Figure 2: Imaging geometry of a spaceborne SAR
The shift in time-domain can be expressed in seconds or in meters:
This means the vehicle gets displaced in the image in azimuth direction depending on its line-of-sight velocity. In the Dual Receive Antenna mode, two antennas are arranged in flight direction. They are separated by the along track baseline BATI, i.e. the same scene is imaged by the two antennas within a small timeframe. The interferometric phase is given by: which is zero for stationary objects or objects moving only in along-track.
2.2 Motion in along-track Let us consider the case the vehicle is moving in azimuth direction with constant velocity, see Fig. 3. Along-track motion changes the relative velocity between sensor and scatterer (vx0 − vsat) (cf. Equ. (5)) leading to a change of the quadratic part of the range history. The red curve is the range history of a vehicle moving in along-track compared to the range history of a stationary object (blue curve). A change of the quadratic component corresponds to a change of the FM rate according to:
2.4 Acceleration in along-track Acceleration in along-track appears in the cubic term of the range history (cf. Equ. (5)), which causes an asymmetry of the focused point spread function. However, for TerraSAR-X these effects are neglible (Hinz et al., 2007). The effects caused by across-track and along-track motion as well as across-track acceleration reach significant values when plugging the TerraSAR-X instrument parameters into the above formulae. We refer the reader to (Meyer et al., 2006) for a detailed analysis of these effects regarding TerraSAR-X. III.
where vB is the velocity of the beam on the ground. With the new FM rate FMmt the echo signal results in:
Focusing hmt,along (t) with a stationary world matched filter (SWMF) does not fully compensate for the quadratic phase term leading to a spread of the received signal. Considering the stationary phase approximation the width of the focused peak can be approximated by:
Interpretating this equation shows that a target gets smeared twice the way it moved during the time of illumination TA.
STATISTICAL DETECTION SCHEME
As shown in Sec. 2 a moving object causes an interferometric phase, hence also a displacement, and it causes a blurring of its signal. However, with the knowledge of roads and their directions, it is possible to forecast a signal one expects for certain situations. To decide whether a vehicle is existent or not, these signals will be compared with the actual value in the SAR image. Assuming the existence of a vehicle, an expected signal hidden in clutter is compared with the actual measurement. The mathematical framework for this proposed approach is derived from statistical detection theory. Two hypotheses H0 and H1 are defined: H0: only clutter and noise are existent H1: signal plus clutter and noise are existent. Together with the corresponding probability density functions f (x|H0) and f (x|H1), these hypotheses allow setting up a likelihood ratio test given by:
where
and
Figure 3: Imaging geometry of a spaceborne SAR
2.3 Acceleration in across-track Like the component of along-track motion, acceleration in acrosstrack mainly affects the quadratic part of Equ. (5). Hence, the acceleration in range also causes a spreading of the energy and the target will be smeared in azimuth. The crosstalk of along-track motion and across-track acceleration hampers the interpretability of along-track smearing without having additional information available.
are circular Gaussian Random Processes with S being the expected signal, X being the measured signal, C being the covariancematrix, and (.)H being the Hermitian Matrix. See e.g. (Bamler and Hartl, 1998) for their derivation. Finally, from Eqs. 11-13 we can derive the Bayesian decision rule of log-likelihood test, which computes to:
In particular, following pieces of information are combined in this detection approach: the expected signal S, the measured signal X, as well as their covariances C, which are described in more detail below. The measured signal consists of the SAR images from the two apertures:
with the indices standing for the two channels.
For the expected signal, a priori knowledge is required. With the information of road location and road direction from Geographical databases an expected phase for each pixel depending on the pixel’s distance to the corresponding road segment can be forecasted (see (Hinz et al. 2007)). Figure 4 depicts an example for the prediction of interferometric phase values depending on a car’s velocity on a given road axis.
Fig. 4. Example for derivation of expectation values: a) road segment associated with travelling direction, b) phase map.
With the expected phase φ the expected signal can be derived:
The complex pulse responses, actual and forecasted, are characterized by X1,i and S1,i for image 1 and X2,i and S2,i for image 2. These signals are blurred in azimuth over the cells i = 1 - n. Thereby, a reasonable guess for n can be derived from Equ. 10. To optimize processing, the possible blurring effect in these adjacent pixels subject to existing along-track motion or across-track acceleration will be adjusted by variation of filters to obtain a focused object and thus an optimized peakto-sidelobe ratio for its signal, see Fig. 5a). Therefore, a stack of resulting images processed with different FM rates is evaluated for detection, see Fig. 5b). Every pixel in this stack has to be compared to the threshold α, yielding in a decision for H1 for the pixel when using the corresponding FM rate.
The threshold that decides whether the evaluated pixel is a vehicle or not, depends on the choice of statistical parameters. The cut-off value for the cumulative density function of the resulting log-likelihood test considering a desired false alarm rate is integrated.
where also the indices related to the two channels. The covariance matrix is defined as in (Bamler and Hartl, 1998):
with
However in real scenarios with roads heading in any direction not only an interferometric phase occurs, but also a blurring of the signal over several resolution cells. Thus, neighboring pixels are included into the mathematical framework to decide whether the considered pixel is a vehicle or not. Therefore, the input into the detection scheme can be assumed to look like:
Fig. 5a) blurred signal of a vehicle focused with the filter for stationary targets (red curve) and the same signal focused with the corresponding FM rate (blue curve). b) stack of images processed with different FM rates.
The performance of the detector can be further enhanced when using multi-temporal SAR images or SAR interferograms. Since satellites can capture images of a particular scene with fixed repetition cycles (typically 10 – 40 days), it is possible to acquire background images and background interferograms by stacking the SAR data and filtering them along the temporal axis. By this, the signal-to-clutter ration can be significantly enhanced. Of course, simply averaging in time domain would bias the result in case a moving object is present at the pixel under investigation. Hence, a robust estimate including outlier detection is necessary. Figure 6 shows the effect of temporal filtering for SAR amplitude data of an urban area (30 images). As can be seen, speckle noise gets suppressed significantly and the objects can be delineated more clearly. IV.
RESULTS AND DISCUSSION
The detection scheme was tested using spaceborne SAR data of the German SAR satellite TerraSAR-X (launched in June 2007). Since dual channel data was not available in the commissioning phase of the satellite, along-track interferometric data was acquired with the so-called Aperture Switching mode (Runge et al. 2006). The data were acquired
over the Autostrada del Sole, a major motorway in Italy. Figure 7 shows the output of the processor after the channel-balancing and applying the detection scheme. Detected moving objects that were assigned to the motorway are plotted at their detected (red squares) and at their estimated true positions (colourcoded velocity). During the data acquisition several ground truth measurements were made, including two video observations from motorway bridges. They exhibited dense truck traffic at the time of imaging. A reference car was floating within a line of trucks. This way their average speed was indirectly estimated by a GPS in the floating car to be 86 km/h. This value is representative for a large number of trucks and corresponds very well to the speed value with the highest incidence among detections for that direction (82 km/h). The three small images at the bottom of Fig. 7 show the SAR amplitude, the detector’s response and an optical image of the area where the car has been detected. One can nicely see the peak of the moving target as well as the clutter suppression effect in the detector response. The optical reference image proves that no strong stationary scatterer like a power line pole has been erroneously detected.
Figure 8 shows another example of a motorway near Dresden, Germany. A total of 110 vehicles were detected for the depicted section of the motorway A4.At the time of the satellite passing the scene, a flight campaign was conducted to acquire reference data based on optical image sequences. In addition video recordings from different motorway bridges helped to reconstruct the traffic situation by measuring the average car speed (assumed constant) and by propagating positions away from observation points respectively for the time of radar imaging. Trucks and smaller transport vehicles dominated the traffic situation. Although the accuracy of positions and velocities derived this way is limited, it provides a very good representation of the whole traffic flow and the velocity distribution. The reference measurement is shown in the smaller image in Figure 8. There is a good agreement between the detection results and the reference measurements for large vehicles like trucks and busses (approx. 60-80% detection rate). However, further tests have shown that the detection rate drops down for smaller cars to 30-50%. This can mainly be explained by the limited spatial resolution. Current civilian spaceborne SAR data have resolutions in the range 1m-3m so that, in almost all situations, the target’s signal is mixed with the background signal. Hence, the interferometric phase as well as the Radar backscatter is biased towards smaller values, which makes detection less robust. ACKNOWLEDGMENT We like to thank all members of DLR’s TerraSAR-X traffic data team for their great support and providing the data. REFERENCES
(a) Single SAR image (amplitude data)
(b) SAR amplitude data filtered along temporal axis (30 images) Fig. 6. Filtering of mult-temporal SAR data.
Bamler, R. and Hartl, P., 1998. Synthetic aperture radar interferometry. Inverse Problems pp. R1–R54. Bamler, R. and Sch¨attler, B., 1993. SAR geocoding. Wichmann, Karlsruhe, chapter 3, pp. 53–102. Ender, J., 1999. Space-time processing for multichannel synthetic aperture radar. Electronics & Communication Engineering Journal 11(1), pp. 29–38. Gierull, C., 2002. Moving Target Detection with Along-Track SAR Interferometry. Technical Report DRDC-OTTAWA-TR- 2002084, Defence Research & Development Canada. Gierull, C. and Sikaneta, I., 2004. Ground Moving Target Parameter Estimation for Two-Channel SAR. In: EUSAR 2004 Conference, on CD, Ulm, Germany. Hinz, S., Meyer, F., Eineder, M. and Bamler, R., 2007. Traffic Monitoring with spaceborne SAR - Theory, simulations, and experiments. In: Computer Vision and Image Understanding, 106: 231-244. Klemm, R., 1998. Space-time adaptive processing. The Institute of Electrical Engineers, London, United Kingdom. Meyer, F., Hinz, S., Laika, A.,Weihing, D. and Bamler, R., 2006. Performance analysis of the terrasar-x traffic monitoring concept. ISPRS Journal of Photogrammetry and Remote Sensing 61(3-4), pp. 225–242.
Roth A., 2003, TerraSAR-X: A new perspective for scientific use of high resolution spaceborne SAR data, 2nd GRSS/ISPRS Joint workshop on remote sensing and data fusion on urban areas, URBAN 2003. IEEE, pp. 4-7. Runge, H., Laux, C., Metzig, R., Steinbrecher,U., 2006, Performance Analysis of Virtual Multi-Channel TS-X SAR-Modes. Proc. of EUSAR’06, Germany. Sikaneta, I. and Gierull, C., 2005. Two-Channel SAR Ground Moving Target Indication for Traffic Monitoring in Urban Terrain. In: International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol. 36number 3/W24, pp. 95–101.
opt. image
response
Suchandt, S., Eineder, M., Breit, H. and Runge, H., 2006a. Analysis of ground moving objects using SRTM/ X-SAR data. ISPRS Journal of Photogrammetry & Remote Sensing 61(3-4), pp. 209– 224. Suchandt, S., Eineder, M., Müller, R., Laika, A., Hinz, S., Meyer, F. and Palubinskas, G., 2006b. Development of a GMTI processing system for the extraction of traffic information from TerraSARX data. EUSAR 2006 Conference, on CD. Weihing, D., Hinz, S., Meyer, F., Laika, A. and Bamler, R., 2006. Detection of along-track ground moving targets in high resolution spaceborne SAR images. In: International Archives of Photogrammetry, Remote Sensing, and Spatial Information Sciences, Vol. 36-7.
amplitude
Fig. 7 TerraSAR-X data and detection results for the Autostrada del Sole, Italy (detections overlaid on SAR amplitude). Sub-images show the detector response, SAR amplitude and an optical image of the area where a car was detected.
Fig. 8 TerraSAR-X data and detection results for a motorway in Germany near Dresden. The sub-image shows the reference data, which was acquired from optical airborne images during a flight campaign (at the same time of satellite pass).
