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The Influence of Target Acceleration on Velocity Estimation in Dual-Channel SAR-GMTI Jayanti J. Sharma, Christoph H. Gierull, Senior Member, IEEE, and Michael J. Collins, Senior Member, IEEE
Abstract—This paper investigates the effects of target acceleration on estimating the velocity vector of a ground moving target from single-pass dual-channel synthetic aperture radar data. Although vehicles traveling on roads and highways routinely experience acceleration, the majority of estimation algorithms assume a constant velocity scenario, which may result in erroneous estimates of target velocity. It is shown that under most conditions, acceleration has only minor effects on the estimation of across-track velocity using along-track interferometric phase. However, under the assumption of constant velocity, acceleration may significantly bias the estimate of along-track velocity. The influence of both along-track and across-track accelerations is examined through simulations of an airborne geometry and experimental data from Environment Canada’s airborne CV 580 dual-channel synthetic aperture radar system. Index Terms—Airborne radar, interferometry, matched filters, parameter estimation, synthetic aperture radar (SAR), velocity measurement.
I. INTRODUCTION
S
YNTHETIC aperture radar (SAR) systems have become an important tool for fine-resolution mapping and other remote sensing operations [1]. In many civilian and military applications of airborne and spaceborne SAR imaging, it is desirable to monitor ground traffic simultaneously [2], [3], giving rise to the field of SAR-ground moving-target indication (GMTI). The challenge of GMTI includes both the detection of targets and the estimation of their velocities. Since there is usually little a priori knowledge of target velocity, we generally start with a stationary scene assumption. The topic of moving-target detection in clutter has been extensively studied [3]–[9], and here it is assumed that moving targets have been detected using the displaced phase center antenna (DPCA) method, along-track interferometric (ATI) phase, space-time adaptive processing (STAP), or some other metric. The majority of SAR-GMTI detection algorithms make use of multiple apertures to provide an additional degree (or degrees) of freedom with which unwanted clutter may be
Manuscript received September 15, 2004; revised April 21, 2005. This work was supported in part by Defence Research and Development Canada—Ottawa, in part by the University of Calgary, in part by the National Science and Engineering Research Council, and in part by Alberta Learning. J. J. Sharma was with the Department of Geomatics Engineering, University of Calgary, Calgary, T2N 1N4 AB, Canada. She is now with the German Aerospace Center (DLR), 82234 Wessling, Germany (e-mail:
[email protected]). M. J. Collins is with the Department of Geomatics Engineering, University of Calgary, Calgary, T2N 1N4 AB, Canada (e-mail:
[email protected]). C. H. Gierull is with the Radar Systems Section, Defence R&D Canada-Ottawa (DRDC Ottawa), ON K1A 0Z4, Canada. Digital Object Identifier 10.1109/TGRS.2005.859343
suppressed (e.g., [6] and [10]). Of particular interest is the single-pass dual-antenna case, since most operational and near-future airborne and spaceborne GMTI systems are limited to two channels for financial and practical reasons [11]. Examples of such systems include Environment Canada’s Convair 580 airborne SAR, and the Canadian RADARSAT-2 spaceborne sensor (scheduled for launch in 2006 [12]). After detection of a moving target, it is often desirable to estimate its velocity in the along- and across-track directions. This information is useful for monitoring ground vehicles, repositioning them to their true azimuth broadside location on the image, and extrapolating a target’s future position. Algorithms employing ATI phase to determine across-track velocity [7], [13], [14] and the peak response among a bank of matched filters to compute along-track velocity [11], [15] are widely used in target velocity estimation. However, in the majority of GMTI literature it is assumed that targets travel with constant velocity. One potential application of GMTI is monitoring vehicle traffic on roads and highways, where target acceleration is commonplace and must be considered. There has been very little published research examining the impacts of target acceleration on GMTI directly. Although some papers include one component of acceleration in the standard range equations for completeness (e.g., [16] and [17]), there are no papers (to the authors’ knowledge) which examine the effects of target acceleration on velocity estimation either theoretically or in experimental data. This paper investigates the effects of along- and across-track acceleration on velocity estimation for point targets in dual-aperture SAR-GMTI data under a constant target velocity assumption. In Section II, the theoretical range-compressed and azimuth-compressed moving-target signals received by a dual-channel airborne SAR are derived. Section III outlines the impact of target acceleration on along-track velocity estimation when using a bank of matched filters, and Section IV describes acceleration’s influence on across-track velocity estimates from the ATI phase. Since the effects of acceleration on along- and across-track velocity estimation are very different, they are given separate treatment. Within each section, the estimation algorithm is described, followed by an analysis of the effect of each motion parameter on the resulting velocity estimate through the use of theory and simulation. Finally, the standard estimation algorithms are applied to experimental data collected by the airborne CV 580 SAR to estimate the velocity vector of controlled movers. These velocity estimates are compared to GPS velocities, and the similarities and discrepancies between the values are discussed. A summary of the findings are presented in the closing section.
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The equation for the range to an accelerating point target from the radar platform is given as
(1) where and are the along- and across-track accelerations at broadside, and the dots indicate time derivatives of the target acceleration (higher order acceleration terms are assumed to be negligible). Equation (1) may be written as a third-order Taylor series expansion about broadside time 0 Fig. 1. Top-down view of antenna and accelerating target geometry for an airborne scenario.
II. MODEL OF THE RECEIVED ECHO This section proposes a deterministic model for the echoes backscattered from a moving point target and received by a linear antenna array with two elements. This model provides the basis for determining the effects of acceleration on the received and processed signal data. The range- and azimuth-compressed signals are derived for a SAR on an airborne platform only. The spaceborne expressions are similar, but additional factors such as Earth curvature and Earth rotation must be taken into account [18].
(2) have been dropped aswhere cubic terms on the order of suming that and that for the ground vehicles under consideration. A dual-channel system is equipped with two antennae (denoted as the fore and aft antennae, respectively) whose phase centers are separated by distance . The distance from the radar platform to the target is assumed to be large enough such that the far-field approximation may apply.
A. Radar–Target Geometry B. Model of the Range-Compressed Received Echo A conventional range and azimuth coordinate system is assumed in which the azimuth direction is taken to be parallel to the motion of the radar, and range is perpendicular to the motion of the radar. The target and radar geometry for the airborne case is illustrated in Fig. 1, where the x axis represents the along-track direction and the y axis the across-track direction (on the ground). The z axis (coming out of the page) is the elevation above the Earth’s surface. The radar transmitter onboard the aircraft moves with constant velocity along the x axis, crossing the range or y axis at time 0 (broadside time). The radar is side-looking with a fixed pointing angle orthogonal to the flight path and a fixed altitude . Radar pulses are transmitted at regular intervals in time given by the pulse repetition frequency [(PRF), also given as ]. It is assumed that the sampling interval is small enough to warrant a signal representation in continuous time. A point target is assumed to be at position (0, , 0) at time 0 and to move with velocity components and at broadside and acceleration components and (which may or may not be time-varying) along the x and y axes, respectively. The target’s height is assumed to be zero over the entire observation period, and the target is assumed to be nonrotating. is the slant range at 0 and represents the range from the radar to the target at any time .
It is assumed that at each second interval, a radar pulse is transmitted from the fore antenna, backscattered from a single ground point scatterer, received by each antenna, and processed by a typical chain of radio-frequency (RF) downconversion, IF (intermediate frequency) bandpass filtering, range compression, and range migration compensation. The rangecompressed target signal for the th receiving channel can be expressed in terms of the range history through time using the following model [19]: (3) where is the magnitude of the th channel, is the direction cosine from the th antenna to the moving target on the ground, is the range from the transmitting antenna to the moving target and back to the th antenna, is the imaginary unit, is the wavenumber , and rect is a rectangular window centered at 0 of length (the synthetic aperture length in units of time). The magnitude variable includes the two-way antenna gain pattern, target reflectivity, and spherical propagation losses. It is assumed that the radar cross section (RCS) of the point target remains constant with viewing angle over the course of the synthetic aperture. Let the signal received
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at the fore antenna be denoted and the signal at the aft an. In order to process multiaperture data, tenna be denoted one must determine the relation between the fore and aft ranges to the target through time. Using trigonometry and further Taylor series expansions, the may one-way distance to the target from the aft antenna be expressed as a function of such that (4) where from (1). A derivation of (4) is provided in the Appendix. Several of the multiaperture GMTI techniques used for detection and parameter estimation (including DPCA and ATI) require channel registration prior to further processing such that the two antenna phase centers are at the same spatial location at different times. One can select a PRF in accordance with the radar platform speed and physical separation distance of the antennae such that the antenna phase centers for consecutive pulses coincide. However, such restrictions on the PRF are unnecessary, and channel registration may be performed by interpolating the aft samples at nonsampled times [10], [20]. The two-way range histories for the fore and aft antennae after this sampling operation are given in (32) and (36) of the Appendix. Assuming that the radar transmits each pulse with the fore antenna and receives on both channels, the signals returned by the fore and aft channels are given as
Fig. 2. Magnitude response (after azimuth compression) of simulated point targets focused using a stationary world matched filter versus azimuthal distance. An azimuth of 0 m is broadside. (Top) Stationary target with high 0.1 m/s peak power. (Bottom) Target with across-track acceleration a and all other motion parameters set to zero. Note the severe azimuthal smearing of the response from the accelerating target, indicating a mismatched reference filter.
=
Performing the cross-correlation in (7) and assuming that the antenna gain is removed such that the magnitude is no longer a function of time and is identical in both channels (i.e., ), then the focused stationary target image is given by
(5) (6) where
and
are given in (37) and (38), respectively.
C. Model of the Azimuth-Compressed Received Echo Azimuth compression is achieved by constructing a reference filter with a phase history matched to that of the received signal, and then cross-correlating this reference with the target signal [21]. Thus, for the th (either fore or aft) channel (7) where is the focused signal for the th channel, is the received target signal (after range compression), is the reference signal, and denotes complex conjugation. Duration is the maximum usable synthetic aperture time, often taken as the 3-dB azimuthal beamwidth. A division by is inserted into (7) such that the focused signal is unitless. If a target is stationary, then the target in both channels may be focused using a stationary world matched filter (SWMF) (8) where represents the reference signal whose range history is derived by setting all target velocities and accelerations to zero in (37), and removing the first term (which will simply shift the phase of the reference filter a constant amount).
(9) where the azimuth compression creates a focused peak at broadside time 0. This sharp peak from stationary targets contrasts with the azimuth-compressed response from a moving point target focused using a stationary world matched filter. When processed using conventional SAR-imaging techniques, the response from a moving target is highly dependent upon the target dynamics, such that the image becomes smeared in range from target range walk and shifted in azimuth due to across-track velocity, and smeared in azimuth due to along-track velocity and across-track acceleration [16]. Inserting from (5) into (7) gives an equation which cannot be solved analytically because there is no closed-form expression for the definite integral of and with respect to . However, this integration may be performed numerically to demonstrate the decrease in peak power and smearing caused by a mismatched reference filter. Fig. 2 shows the response from a stationary target, and one with motion parameters 0 0 0 0.1 0 m/s focused using a SWMF. Note the sharp response from the stationary target and the severe smearing after azimuth compression of the accelerating target. Radar parameters and an airborne geometry typical of Environment Canada’s CV 580 SAR were used, with parameters listed in Table I.
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TABLE I RADAR AND GEOMETRY PARAMETERS FOR AIRBORNE SAR SIMULATIONS TYPICAL OF THE CV 580 VALUES
(15) The sinc function in the focused aft channel data is similar to that from the fore channel (11). Despite the added term in the sinc argument, the peak response of the aft channel is shifted only a few centimeters from that of the fore channel for typical airborne scenarios. III. ESTIMATION OF ALONG-TRACK VELOCITY
If it is assumed that and are zero such that the thirdorder term of the Taylor series expansion of the range equation is neglegibly small, and if the phase history of the target and reference signals are matched, then the azimuth compression may be evaluated in closed form. Let the reference filter be represented as (10) Performing the cross-correlation from (7) and assuming that the antenna gain is removed such that the signal amplitude is no longer a function of time, then the focused moving-target image for the fore channel is given by
(11) where (12) occurs when the argument of the sinc The maximum of function is zero, and thus the peak response of the focused target appears at broadside time 0. The closed-form focused response from the aft signal data may also be computed if the reference filter from (10) is used, and it is assumed that and are zero such that the cubic term may be dropped. The reference filter is matched perfectly to the target dynamics, and upon correlation of signal with , the compressed image is obtained
(13) where (14)
One method of estimating along-track velocity applies a bank of reference filters to the target signal to determine which filter best focuses the data [11]. This technique determines which filter best fits the quadratic coefficient from the range (2) under a zero-acceleration assumption, although additional information is required to separate along- and across-track velocity contributions to this coefficient [15]. One technique velocities and implements filters initialized with various 0. The signal data are convolved with each reference filter in turn, and the output is saved to a matrix, which is then scanned to find the location of the maximum magnitude value. A two-dimensional (2-D) search over the synthetic apers and over the along-track velocity ture time range of interest (e.g., m/s) is required. The filter maximizing the magnitude of the azimuth-compressed response corresponds to the best estimate of along-track ve. Oftentimes, the DPCA signal (formed by locity, denoted as differencing the fore and registered aft channels) is compressed using the filterbank rather than only the fore or aft channel in order to avoid obtaining maxima due to clutter discretes (such as buildings). velocity (when target across-track Analytically, the true velocity and accelerations are zero) can be found by maximizing the azimuth-compressed magnitude from (7) with respect to and time . In other words, one must determine the along-track velocity and time maximizing (16) where the reference filter
for best focus is given by (17)
However, (16) cannot be evaluated in closed form, and thus one must one use a numerical solution by searching the 2-D variable space for the maximum magnitude response. The estimation of using a bank of reference filters for a target traveling with constant velocity has been examined in [11]. One problem with the proposed matched filterbank algorithm is that it assumes the quadratic coefficient in the range equation is due solely to contributions from along-track and ). However, as seen radar–target motion (i.e., from in (2), the second-order component of the range equation also contains a term which will bias the estimation of in the presence of large velocities. However, biases
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due to nonzero are not overly severe for the range of target velocities seen in ground vehicles, and one may compensate for the across-track component through an iterative solution. One using the filterbank approach, estimate can estimate using the along-track interferometric phase (see Section IV), and then revise by taking the computed across-track velocity into account. This procedure can be repeated to converge upon the true along-track velocity. To evaluate the influence of target acceleration on the estimation of along-track velocity, several simulations were conducted. Unless otherwise stated, all simulations assume an airborne geometry with parameters typical of the CV 580 system (given in Table I). In each case the filterbank and search method was applied to simulated signal data of a moving point target. Filterbank velocities varied from 30 to 30 m/s in steps of 0.03 m/s. A. Estimating
=
Fig. 3. Magnitude responses of a simulated point target with a 0.1 m/s (and all other motion parameters set to zero) after compression with a bank of reference filters initialized with various v . An azimuth of 0 m is broadside. Note that v (estimated from the location of peak power) is biased by 2.5 m/s, since the true along-track velocity is zero.
^
in the Presence of
When a target possesses an across-track acceleration component, estimation of becomes challenging. Both and determine the value of the second-order coefficient of the range equation (2), and their effects are difficult to separate. Unand both cause severe defocusing of the compensated target in the azimuth-compressed response. If it is assumed that a target has constant velocity when it is actually accelerating, this acceleration will be mistaken for along-track velocity and . there may be a sizeable bias in the estimate of The magnitude of the bias can be examined by equating the assumed quadratic coefficient [from the reference filter of (17)] with the true quadratic coefficient [from (2)] to obtain (18) where the bias is . 0 in order to isolate the effects of , and Assuming assuming an airborne geometry typical of the CV 580 system, (18) predicts a bias of 23.5 m/s for an acceleration of 1 m/s and 0. Even a very slight acceleration of 0.1 m/s introduces a bias of 2.5 m/s, as shown in the filterbank map of Fig. 3. Each row of the filterbank map corresponds to the output after compression using one reference filter. The DPCA signal was not used since it is negligible for an across-track velocity of zero, as in this scenario [14]. Across-track acceleration can thus introduce significant biif it is assumed that targets travel at a ases when estimating constant velocity. However, even if one acknowledges the possiwill be indistinguishable bility of across-track acceleration, from ; they are both contained in the quadratic coefficient of the range equation and they cannot be estimated independently in the absence of a priori data (such as from inertial systems onboard the target) or additional SAR channels. Across-track acceleration combined with nonzero across-track velocity (as is generally the case in realistic moving-target scenarios) introduces a small cubic component into the target range history according to (2). From the range (assuming equation it is theoretically possible to solve for
0
0) by implementing a three-dimensional filterbank algorithm to determine the third-order coefficient. However, for the range of target velocities and accelerations of to this component is virtually interest, the contribution of and which are dominant in determining negligible; it is the cubic component. B. Estimating
in the Presence of
In the presence of an along-track acceleration component, the target signal has a significant cubic term as predicted in the range (2). When the filterbank method is applied to the data, it is attempted to match a quadratic reference filter to a cubic signal. This results in an uncompensated third-order component whose impacts on the azimuth-compressed response include the following: • smearing of the target energy across multiple velocities in the filterbank and multiple cells in azimuth, which severely decreases peak power; • creation of two peaks (instead of one) (where, for instance, the peaks are shifted from zero in the stationary 0.5 m/s and all other mocase to 0.3 m/s for an tion parameters set to zero); • slight shift in the azimuth focused position (e.g., the two peaks focus at an azimuth 0.4 m away from broadside for 0.5 m/s and all other motion parameters set to an zero). Some of these effects may be seen in a comparison between the filterbank magnitude image of a stationary target, and a 0.5 m/s (with all other motion parameters target with set to zero) in Fig. 4. The most striking effect is the decrease in peak power of the target responses; the full target energy is never filter since none of the (second-order) refercaptured by one ence filters represents the true (cubic) phase history of the target through time. This uncompensated cubic term creates asymmetric sidelobes visible in Fig. 4 as fringes extending in the positive azimuth direction. Also apparent in Fig. 4 is the smearing of target energy across multiple filters. Although difficult
SHARMA et al.: INFLUENCE OF TARGET ACCELERATION ON VELOCITY ESTIMATION
=
Fig. 4. Magnitude responses of a simulated point target with a 0.5 m/s (and all other motion parameters set to zero) after compression with a bank of reference filters initialized with various v velocities. An azimuth of 0 m is broadside. Note the decrease in peak power and smearing of target energy across multiple v velocities in the accelerating case; although difficult to discern, there is also a small bias in estimated v on the order of 0.3 m/s.
^
to discern in the figure, two peaks are observed in the filterbank of the accelerating target. This is due to two reference filters (with parabolic range histories) giving relatively large magnitude responses compared to the other matched filters. Since these quadratic functions do not have intercepts of 0, the target is not focused exactly at broadside (i.e., at an azimuth of ). In Fig. 4 the peaks are slightly offset from broadside position by approximately 0.4 m, although this shift is negligible when compared to the shift induced by an uncompensated across-track velocity component, which can be on the order of tens to hundreds of meters. will introduce small biases into the estiUncompensated mation of velocity (on the order of 1 m/s for 1 m/s in this simulated geometry). However the most severe effect is a decrease in peak power which may make it difficult to find the location of peak power and thus to estimate , especially in the presence of residual clutter and noise. C. Estimating
in the Presence of
Since both and appear in the cubic coefficient of the range (2), the effects of time-varying across-track acceleration estimation are very similar to the impacts of along-track on acceleration . This was confirmed in simulations of the CV of 0.03 m/s (and all other 580 airborne geometry, where an motion parameters set to zero) introduces a bias of 0.3 m/s in . D. Estimating
in the Presence of Clutter
In addition to simulations of deterministic target signals, simulations were conducted to determine the influence of target acceleration on along-track velocity estimation in the presence of homogeneous clutter and additive noise. Correlated complex Gaussian clutter was simulated with a coherence of 0.95, a relatively conservative value for land clutter observed from typical
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Fig. 5.
Magnitude responses of simulated point targets with (left) and (right) a 0.5 m/s after DPCA clutter suppression and compression with a bank of reference filters. The signals were generated with an SCR of 0 dB and a CNR of 30 dB. Clutter was simulated using a complex normal distribution with a coherence of 0.95. Each target also has an 1 m/s to ensure that the DPCA signal is across-track broadside velocity v nonzero. Note the similarities to the filterbank maps of Figs. 3 and 4, although the peak power has decreased considerably and the target responses have been azimuthally shifted due to the nonzero across-track velocity.
a
= 0.1 m/s
=
=
airborne platforms [9]. The signal-to-clutter ratio (SCR) was set to 0 dB before azimuth compression and the clutter-to-noise ratio (CNR) to 30 dB. 0.1 m/s , the other Two accelerating targets (one with 0.5 m/s ) were simulated in the clutter environment with described above. Each target was also given an across-track ve1 m/s such that the DPCA magnitude locity component signal was nonzero over the course of the observation interval [22]. Signals were generated for both the fore and aft channels and subtracted to compute the DPCA clutter-suppressed response. As in previous simulations, a filterbank of 2000 matched filters with along-track velocities ranging from 30 to 30 m/s (spaced every 0.03 m/s) was used to focus the data. The filterbank maps for the two accelerating targets are shown in Fig. 5. No stationary target signal is displayed since its filterbank map contains no defined peak; for nonmoving targets the expected value of the DPCA signal is nearly zero [22]. Note the different axis scales of the two frames in Fig. 5. The responses are similar to those obtained when simulating purely deterministic signals in Figs. 3 and 4, although the peak magnitude has decreased considerably (compare color bars) and there is an azimuthal shift of approximately 50 m in the target responses due to the nonzero across-track velocity. Still, even in the presence , across-track accelof clutter, additive noise, and a nonzero eration results in a sharply focused although biased peak in the filterbank map, whereas along-track acceleration creates severe smearing of the filterbank image, making it difficult to identify a distinct peak. Such accelerations thus have a significant impact . on the estimation of along-track velocity E. Experimental Results for
Estimation
To test along-track velocity estimation in experimental data, the filterbank method was applied to 22 target tracks extracted
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TABLE II COMPARISON OF ALONG-TRACK VELOCITIES (v ) ESTIMATED USING THE FILTERBANK METHOD FROM DUAL-CHANNEL SAR DATA
Fig. 6. Delta control target from the Petawawa 2000 data collection (DRDC Ottawa).
from SAR data. The data were collected during an experiment conducted at Canadian Forces Base (CFB) Petawawa with the Environment Canada CV 580 C-Band SAR in November of 2000. The CV 580 was equipped with two antennae separated in the along-track direction, collecting dual-channel data for eight passes. The experimental setup and further results are described in [14]. Three controlled movers were involved in the data campaign attempting to maintain constant speeds at imaging time. Control targets were equipped with GPS receivers collecting carrierphase data (for precise position and velocity information) and a trihedral corner reflector was mounted to each target. Two of the controlled moving targets (denoted as “Delta” and “Juliet”) consisted of remotely controlled, engine-powered carts guided by a rail system (see Fig. 6). A four-vehicle convoy was also deployed traveling along a straight segment of gravel road. Although the entire convoy was traveling at approximately the same speed, the latter three targets were not used in the analysis because they were not equipped with GPS receivers. The pickup truck at the front of the convoy is hereafter referred to as the “Convoy” target. A detection and tracking algorithm in the range-compressed domain (see [11]) using the DPCA technique for clutter suppression was employed to extract and store the track of each target through azimuth time. A filterbank of 2000 matched filters with along-track velocities ranging from 30 to 30 m/s (spaced every 0.03 m/s) was used to focus the data. The range-compressed fore and aft target tracks were subtracted and then convolved with each matched filter to compute the azimuth-compressed DPCA filterbank map. DPCA was used to suppress clutter, thus preventing any . All targets clutter discretes from biasing the estimation of not equal to a blind had nonzero across-track velocity velocity, and thus all targets had nonzero DPCA magnitude. The location of the peak power response in the DPCA filterbank
map was used to find the filter most closely matched to the true along-track velocity. The along-track velocities estimated using the filterbank method for each target and their velocities as measured using GPS are presented in Table II. The GPS velocities are projected to have a worst case accuracy of 0.5 m/s [22]. Note that line 2, pass 6 (abbreviated l2p6) only had data for the Convoy target since the Juliet and Delta targets were stationary during imaging time due to a miscommunication with the aircraft. Taking the absolute value of the differences between the GPS velocities and the estimated target velocities, a mean error of as estimated from the SAR data with 2.9 m/s was found in a standard deviation of 2.6 m/s. A number of targets had significant biases in their along-track velocity estimates when compared to the GPS values, with a maximum bias of 9.3 m/s. These large biases may indicate the presence of possible along- and across-track acceleration components.
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Unfortunately, it is difficult to determine the target’s true acceleration components since GPS data were only collected every two seconds. Although variations in the GPS velocity over the synthetic aperture reveal that acceleration is occurring in many of the target passes, a higher sampling rate is required for precise acceleration time-histories. Extremely accurate estimates of acceleration would be needed in any case, since simulations have shown that one must be concerned with even slight accelerations on the order of 0.1 m/s or less. Future experimental trials could equip controlled movers with survey-grade GPS systems functioning at a higher sampling rate and inertial systems with gyroscopes in order to determine a target’s acceleration time-history. However, although the limited ground-truth prevents direct support of our hypotheses, the effects of target acceleration as predicted in the theoretical analysis are consistent with results from the experimental data. Fig. 7. DPCA filterbank magnitude map from one pass of the Convoy target 11.5 m/s, whereas the GPS (line 1, pass 5). The peak response occurs at v velocity is 5.7 m/s, indicating a severe bias in the v estimate which may be due to the presence of across-track acceleration a .
= ^
IV. ESTIMATION OF ACROSS-TRACK VELOCITY Across-track velocity is a fundamental parameter of interest for GMTI applications which may be estimated using the alongtrack interferometric phase. For a two-channel SAR system, the ATI signal is computed by multiplying the signal from one channel by the complex conjugate of the second (registered) channel ATI
Fig. 8. DPCA filterbank magnitude map from one pass of the Juliet target (line 2, pass 2). In addition to a bias in the v estimate, this target displays asymmetric sidelobes to the left-hand side of the peak response and smearing of the target energy characteristic of an uncompensated cubic component in the focusing operation.
^
An example of a biased estimate from one pass of the Convoy target is shown in Fig. 7. There is a clear peak response in the filterbank magnitude map at a of 11.5 m/s. However, the GPS velocity is only 5.7 m/s, pointing to a possible acceleras described in Section III-A. ation bias due to , the smearing effects and asymIn addition to biases in metric sidelobes characteristic of an uncompensated cubic term are also visible in the experimental data. Fig. 8 shows the filterbank map from one pass of the Juliet target in which along-track and/or time-varying across-track acceleration acceleration may be causing the smearing and asymmetric sidelobe effects as were observed in simulations (see Section III-B). There may also be higher-order target motion components, improper motion compensation of the platform velocity, incorrect estiand other parameters, or residual clutter, mates of , which may be having additional impact upon the filterbank map.
(19) where and are the phase angles of the first and second channels, respectively [14]. The phase of the ATI signal is related to the target motion parameters although it is domi, and may thus be used in nated by the across-track velocity its estimation. For stationary terrain, the fore and aft signals are identical and the ATI phase is zero. The ATI method is chosen to estimate across-track velocity because of its sensitivity to compared to other techniques (e.g., subaperture methods and tracking of the target range walk). However, ATI phase suffers from a number of ambiguities which must be resolved prior to velocity estimation including directional ambiguities from wraps of the ATI phase, blind velocities, and Doppler ambiguities due to sampling limitations in azimuth [23]. Along-track interferometric phase is generally computed in the azimuth-compressed domain for improved SCRs. Deriving the expressions for the azimuth-compressed signal returns from the fore and aft channels, where the reference filter has been matched to the quadratic term of the range equation only, we can determine a closed-form expression for the ATI signal. The 0) in the focused responses of a target (with fore and aft channels from a reference filter matched only to the second-order term are
(20)
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(21) and are the compressed signals from the fore where and aft channels, respectively, is given in (12), in (14), and in (15). The peak response of the fore channel occurs when the argument of the sinc function goes to zero at time , where (22)
Applying (19), the ATI signal is then ATI
quadratic range equation terms is applied during azimuth com0), pression, the target is imaged at broadside time (i.e., and (24) reduces exactly to (26). However, generally is not known a priori, and the objective is to estimate it using the ATI and , (26) will begin phase. In the presence of moderate to degrade if the target data are focused using a filter mismatched or other motion to the linear coefficient. As well, note that if components shift the target’s Doppler centroid such that there is no spectral overlap of the target signal with the reference filter, there will be no target peak and the ATI phase cannot be found. The accuracy of (26) is verified using simulations for various , , and . The SAR signals are determined using (1) to compute the fore channel range history, and (30) and (34) to compute the aft channel range history, which make use of the far-field approximation only. Additional simulations using and across-track acceleranonzero along-track acceleration are also conducted, as well as simulations of target tion rate signals in the presence of clutter and additive noise. The influence of these parameters on the ATI phase and on the estimation of across-track velocity for an airborne simulation (with radar and geometry parameters given in Table I) is described. The es. timated across-track velocity is denoted A. Variation in ATI Phase With
(23) Substituting (14) and (15) for and , respectively, and dropping the term (which is negligible), the ATI phase is given as ATI (24)
Evaluated at its focused location phase becomes
from (22), the ATI
ATI (25)
Oftentimes, the ATI phase is approximated by the following expression (e.g., [13], [14], [24], and [25]):1 ATI
(26)
can be computed directly given such that an estimate of the interferometric phase, and the estimate is not dependent nor across-track acceleration . upon along-track velocity Note that if a reference filter perfectly matched to the linear and v
1Where
(1
it is assumed that acceleration is zero, and that v =R ).
0y
v
and v
As can be seen from (25), will influence the ATI phase. The amount it will shift the ATI phase is dependent both upon the value of and the across-track velocity . Examining the theoretical expression for the ATI phase in (25), the bias caused dependence increases indefinitely with inby ignoring the and . However, this equation does not take into creasing account wrapping of the spectrum due to a finite azimuth bandwidth. The focused image location used to derive (25) can and (twice the original signal length due only fall between to the convolution operation), and thus the error in ATI phase component will not increase indefinitely. due to ignoring the Examining the differences between the simulated ATI phase and that determined from (26) for only those target signals with some spectral overlap with the reference signal, it is found that m/s and the maximum bias for m/s (scanned in steps of 1 m/s) is 21.7 or 1.2 m/s. The focused image location is determined after ATI as the point at which the ATI magnitude is maximum, since the ATI magnitude is determined by the multiplication of two relatively narrow sinc functions [see (23)]. When a reference filter perfectly matched is applied in compression, the bias in is negligible (for to any ), and is due only to use of the far-field approximation and the Taylor series expansion of the range equation. B. Variation in ATI Phase With Similar to , nonzero will effect the ATI phase [see is the denominator of the second term in (25)]. Because multiplied by , even small accelerations such as 0.1 m/s will have a noticeable impact upon the phase. For example, for 0 m/s, 10 m/s and 0.1 m/s , the ATI phase shifts 3.8 , creating an error of 0.2 m/s if an inversion of (26) is . This shift may be lessened or increased in used to compute
SHARMA et al.: INFLUENCE OF TARGET ACCELERATION ON VELOCITY ESTIMATION
=
=
Fig. 9. ATI signal for a 1 m/s , v 10 m/s (solid line) compared with the expected ATI phase when the a dependence is neglected (dotted). There is a difference of 27.7 between the two phases, corresponding to an error of 1.6 m/s in v . Phase is given in degrees as an angle measured from the positive real axis, and magnitude as a distance from the origin.
^
the presence of an along-track velocity depending the signs of and of the same sign will reduce the motion parameters; the overall shift, whereas values of opposite signs will increase the shift in ATI phase. When more severe accelerations (but still plausible) of 1 m/s are introduced, shifts of up to 36.6 (or ) are present. Combined with shifts rebiases of 2.1 m/s in velocity, neglecting the contributions of to sulting from the ATI phase can give erroneous estimates of . A polar plot of the ATI signal at time for a target with 1 m/s and 10 m/s (and all other motion parameters set to zero) is given in Fig. 9. Note the bias in the ATI phase computed using (26). C. Variation in ATI Phase With
and
Analytically, the ATI phase of a compressed target with and/or components cannot be computed in nonzero closed form. However, we may examine the errors in using in the presence of along-track acceler(26) to estimate ation and/or time-varying across-track acceleration through simulation. and , and have a relatively small Compared to impact on the ATI phase. For varied from 1 to 1 m/s (scanned in steps of 0.1 m/s ), and varied from 30 to 30 m/s (scanned in steps of 1 m/s), the maximum deviation from of 0.14 m/s. Similarly, (26) was 2.4 , translating to a bias in varying over 0.1 m/s gave a maximum deviation of 4.6 or a bias of 0.26 m/s in . Thus, for the parameter ranges exand on ATI phase are nearly an amined, the effects of order of magnitude lower than the influence of and . D. Variation in ATI Phase in the Presence of Clutter In addition to varying target dynamics, the influence of homogeneous clutter on ATI phase was investigated through simulation. Correlated complex Gaussian clutter was simulated with an SCR of 0 dB before azimuth compression and a coherence of 0.95, and additive noise was simulated with a CNR of 30 dB.
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=
Fig. 10. ATI signals at each azimuth sample for targets with a 0.5 m/s and v 10 m/s. (Left) A deterministic target and (right) a target with additive noise and complex Gaussian clutter are compared with the theoretical ATI phase when the a dependence is neglected (dotted). In this realization there is a difference of 4.2 between the phases of the peak ATI magnitudes with and without clutter, corresponding to a difference of 0.24 m/s in v . The bias due to neglecting the influence of a is approximately 17 or 1 m/s.
=
^
In 1000 realizations, the mean phase difference between the peak ATI magnitudes with and without clutter was 0.1 with a standard deviation of 5.7 , corresponding to a negligible average difference in computed across-track velocity , and a . To illustrate the differences standard deviation of 0.3 m/s in between the deterministic target and the target plus clutter scenarios, the ATI signals for one realization are plotted in Fig. 10. Note that all data points in the ATI signal (i.e., for all azimuth times) are plotted rather than only the peak ATI magnitude as in Fig. 9. In the clutter simulation there is a concentration of clutter points about the real axis. Ideally, after coregistration the two SAR channels are identical for stationary terrain (i.e., clutter) and their ATI signal should map to the real axis. However, due to inevitable channel decorrelations, the clutter possess nonzero ATI phase and display a spread from the real axis in an ATI polar plot. A keyhole filter may be used to remove interfering clutter by nulling the amplitudes of all signal components whose phases lie within a selected threshold [14], although this technique poses a problem for slow-moving vehicles with a very small ATI phase or for vehicles traveling at speeds close to blind velocities [22]. Another problem is that when target signals are superimposed upon clutter echoes, a bias is introduced in the ATI phase as a function of the SCR of the received signal (this phenomenon is further described in [7]). In Fig. 10, this bias is approximately 4 , corresponding to a difference of 0.24 m/s between the estimated across-track velocity of the deterministic target and the target plus clutter cases. However, in this instance, the bias in the estimated across-track velocity due to clutter is still overshadowed by the bias caused by neglecting the influence of accelercauses a bias of approximately ation; in Fig. 10 neglecting 1 m/s in in both simulations. Thus, even in the presence of clutter and additive noise (which result in additional biases to the ATI phase) significant across-track acceleration will bias the ATI phase and will influence estimation of the across-track velocity.
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E. Obtaining an Unbiased Across-Track Velocity The theoretical analysis and simulations outlined in Section IV reveal that if signal data are processed using a reference filter perfectly matched to the target phase history (both to linear and quadratic terms), the ATI phase reduces to a depenonly. This suggests that to converge upon the dency on correct , the ATI phase should first be computed using a bank of reference filters initialized with the quadratic coefficient giving the maximal magnitude response (for the highest velocities (to SCR) and initialized with widely spaced ensure that some spectral overlap between the target signal and reference filter is obtained). With an initial approximation , the of across-track velocity obtained by solving (26) for in the reference target is recompressed using the estimated filter and the ATI phase is recomputed. If the quality of the initial approximation is reasonable and the ambiguities have been resolved (either using the target range walk, subbeam partitioning methods, or a priori knowledge of the approximate target motion), after several iterations this process will converge . Using this method, even significant upon the correct or accelerations will not bias the estimated using the ATI phase. moAlternatively, an ATI phase dependent only upon the tion parameter can also be derived by extending the length of the reference filter past the 3-dB synthetic aperture length. If this reference filter is matched to the quadratic coefficient of the target range history, and if it is sufficiently extended in time, there will be complete spectral overlap between the target signal and the reference filter, and the ATI phase may be reduced to (26). However, in the presence of clutter, extending the reference filter introduces additional clutter contamination into the phase estimate, and thus despite the added computational cost of carrying out multiple correlations, the algorithm suggested in . the previous paragraph is preferred for estimating F. Experimental Results for
TABLE III COMPARISON OF ACROSS-TRACK VELOCITIES (v ) ESTIMATED USING ALONG-TRACK INTERFEROMETRIC PHASE FROM DUAL-CHANNEL SAR DATA AND GPS
Estimation
Across-track velocity was estimated for each control target extracted from the Petawawa 2000 data using along-track interferometric phase. A description of this dataset and the experimental setup was provided in Section III-E. An outline of the estimation algorithm is provided below, followed by a comparison of the across-track velocity estimates from ATI to GPS velocities. , first an estimate of along-track velocity is To obtain determined using the filterbank method from Section III. The in the target track is then azimuth compressed using this reference filter to obtain focused responses for the fore and aft channels. The ATI signal is computed and then smoothed using a one-dimensional moving average filter to reduce noisy peaks. The local maxima in the ATI magnitude are extracted, normalized, and then weighted by the absolute value of their phase to ), with the highest weight given to (which varies from those points furthest away from the zero-phase clutter region in order to reduce clutter contamination. The maximum after weighting gives the best estimate of the ATI phase of the target. The phase is then unwrapped to fall
between 0 and , and its phase shift is translated into acrosstrack velocity using an inversion of (26)
ATI
(27)
A second although less accurate estimate of is then determined from the target range walk in order to resolve the -wrap ambiguity in the ATI phase. This algorithm was applied to each target track in the experimental dataset to estimate . The across-track velocities for each pass determined using ATI phase and their velocities as measured using GPS are presented in Table III. Standard deviations in the GPS target heading and velocity magnitudes project worst case accuracies of 0.5 m/s in the GPS estimates.
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The mean of the absolute value of the differences between estimates was 0.9 m/s, with a standard deviaATI and GPS tion of 1.5 m/s. The mean falls well within the standard deviation, and thus no overall bias in the measurements is suspected. There are three outliers (l1p5, l1p9, and l3p3 Convoy passes) which have significantly worse accuracies than the rest of the estimates. These errors could be due to a poor estimate of target range walk resolving to an incorrect ambiguity, asymmetric target tracks (i.e., not centered about broadside time, which is examined in [11]), or contamination of the ATI phase by other moving vehicles in the convoy. The standard deviation of 1.5 m/s is slightly higher than that predicted in [26] for an airborne scenario. However, the theoretical estimation took only phase decorrelation due to additive noise into account; speckle, time decorrelation (such as internal clutter motion), and imperfect channel balancing may also conestimation. tribute to ATI phase variations affecting The results of across-track velocity estimation in experimental data are in general agreement with the conclusions from the ATI theory and simulations examined. As predicted from the theoretical analysis, the suspected presence of target acceleration does not introduce significant biases into estimated from along-track interferometric phase. The mean of the absolute errors was only 0.9 m/s, which is more than for the a threefold improvement over the mean error in same targets examined in Section III-E. A simple algorithm was used to estimate that did not extend the reference filter length or apply a bank of reference filters initialized with velocities as was suggested in Section IV-E. It is various fortunate that some amount of spectral overlap between the target and reference signals was present for each pass, and thus the filterbank method was not required for this dataset. Perhaps could be obtained using even more accurate estimates of iteration or extended reference filters.
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may determined in future experiments using a higher sampling rate of the GPS data and/or inertial sensors. , , and moThe relation between ATI phase and the tion parameters was derived for a target compressed with a reference filter matched to the quadratic term. If processed using a reference filter perfectly matched to the target phase history (both to linear and quadratic terms), the ATI phase reduces to only, and the across-track velocity may a dependency on be determined without bias. If the linear term in the reference filter is not matched however, biases of up to several meters per second for accelerations of 1 m/s and velocities of 30 m/s . Estimation algorithms in which the ATI may be observed in phase computation is iterated or the reference filter length is extended beyond one synthetic aperture were suggested as means of obtaining a more accurate estimate of across-track velocity. A. Estimating Velocity in a Spaceborne Geometry Although this paper focused on the influence of target acceleration on airborne geometries, velocity estimation from a space-based radar geometry has also been considered in [22]. While estimation of from airborne SAR is sensitive to acceleration effects, target acceleration in data collected from spaceborne systems (such as the future RADARSAT-2 sensor) is not as critical due to scale changes in geometry, a shorter synthetic aperture time, and increased noise. These factors decrease the influence of an uncompensated cubic term in the target range history. However, even in spaceborne systems, uncompensated will significantly bias the along-track velocity estimate. The relation between ATI phase and across-track velocity from a space-based radar geometry was also investigated. It was found that for the velocities and accelerations experienced by realistic ground-based vehicles, the ATI phase may be used directly to , without the need for iteration or extended matched estimate filters. APPENDIX
V. CONCLUSION The influence of acceleration on the estimation of the velocity vector has been examined using a combination of theory, simulations, and experimental data. A 2-D search for the maxima in a bank of reference filters and along-track interferometric phase were presented as possible methods of estimating the along- and across-track velocities of a moving target, respectively. Both along- and across-track acceleration components may have a severe effect on the estimation of along-track velocity. severely biases the estimate Across-track acceleration if it is assumed that targets are traveling at a constant velocity. If acceleration is acknowledged as an additional unknown, then there are insufficient degrees of freedom to solve for all paramand time-varying acrosseters. Along-track acceleration track acceleration also effect estimation by smearing the target energy across multiple cells in the filterbank map and introducing a slight bias in the location of the peak response. Biases and smearing in the filterbank maps from experimental airborne dual-channel SAR data are consistent with these theoretical and simulated results. More direct support of the hypotheses requires knowledge of target acceleration time histories, which
Beginning from the airborne radar–target geometry described in Section II-A and the range equation from (2), the range history to the fore and aft antennae are derived. Let the difference between the range from the target to the fore antenna and the range from the target to the aft antenna be . Thus, let (28) where from trigonometry (29) is the angle between the antenna–target line of sight where and the flight direction (i.e., the axis). The directional cosine may be written as a function of the range and the separation in the direction between the target and fore antenna of the radar platform . Thus, the range difference becomes
(30)
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where higher order acceleration terms are assumed to be negligible. about 0 to the Performing a Taylor expansion of first order simplifies the expression to the following:
and
(31) is the range to the target at broadside time 0 and where 0 0 . Plugging (31) into (28) gives (4) of Section II-B. The majority of GMTI detection and estimation algorithms require a resampling of the data such that the antenna phase centers are coincident for consecutive sampling times. The effective antenna phase center is determined by the two-way range to the target. Since the fore antenna both transmits and receives, the is simply twice the range equation two-way range previously derived
(38)
ACKNOWLEDGMENT The authors would like to thank the GMTI group at Defence Research Development Canada (DRDC) Ottawa, particularly to I. Sikaneta and C. Livingstone for their guidance and advice.
(32) However, the aft aperture, which is receive-only, receives radar pulses transmitted from the fore aperture, such that the two-way range is (33) For any sampled time available in the fore channel, the range must be determined for the to the target at time aft data in order to line up the channels. Thus, the registered aft channel can be expressed as (34) (2) and the Using the third-order Taylor expansion for (31) this may be rewritten as Taylor expansion for
(35) Rearranging (35), we can express , with leftover terms represented by
as a function of (36)
where
(37)
REFERENCES [1] P. Rosen, S. Hensley, I. Joughin, F. Li, S. Madsen, E. Rodrigueza, and R. Goldstein, “Synthetic aperture radar interferometry,” Proc. IEEE, vol. 88, no. 3, pp. 333–382, Mar. 2000. [2] C. H. Gierull and I. C. Sikaneta, “Raw data based two-aperture SAR ground moving target indication,” in Proc. IGARSS, vol. 2, Jul. 21–25, 2003, pp. 1032–1034. [3] I. Sikaneta and C. H. Gierull, “Ground moving target detection for alongtrack interferometric SAR data,” presented at the IEEE Aerospace Conf., vol. 4, Big Sky, MT, Mar. 6–13, 2004, pp. 2227–2235. [4] S. Barbarossa, “Detection and imaging of moving objects with synthetic aperture radar. Part 1. Optimal detection and parameter estimation theory,” Proc. Inst. Elect. Eng. F, Radar Signal Process., vol. 139, no. 1, pp. 79–88, Feb. 1992. [5] M. Soumekh and B. Himed, “Moving target detection and imaging using an X-band along-track monopulse SAR,” IEEE Trans. Aerosp. Electron. Syst., vol. 38, no. 1, pp. 315–333, Jan. 2002. [6] J. Ender, “Detection and estimation of moving target signals by multichannel SAR,” AEÜ Int. J. Electron. Commun., vol. 50, no. 2, pp. 150–156, 1996. [7] C. H. Gierull, “Moving target detection with along-track SAR interferometry—A theoretical analysis,” Defence Research and Development, Ottawa, ON, Canada, Tech. Rep. TR 2002-084, Aug. 2002. [8] M. Kirscht, “Detection and imaging or arbitrarily moving targets with single-channel SAR,” Proc. Inst. Elect. Eng., Radar, Sonar Navigat., vol. 150, no. 1, pp. 7–11, Feb. 1996. [9] V. Chen, “Detection of ground moving targets in clutter with rotational Wigner-Radon transforms,” in Proc. Eur. Synthetic Aperture Radar Conf. (EUSAR), Cologne, Germany, Jun. 4–6, 2002, pp. 229–232. [10] D. J. Coe and R. G. White, “Experimental moving target detection results from a three-beam airborne SAR,” AEÜ Int. J. Electron. Commun., vol. 50, no. 2, pp. 157–164, 1996. [11] C. H. Gierull and I. Sikaneta, “Ground moving target parameter estimation for two-channel SAR,” presented at the Proc. Eur. Synthetic Aperture Radar Conf., Ulm, Germany, May 25–27, 2004. [12] MDA, “RADARSAT-2: A new era in remote sensing,” MacDonald Dettwiler and Associates Ltd., Richmond, BC, Canada, 2004. [Online]. Available: Available: http://www.mda.ca/radarsat-2. [13] V. Pascazio, G. Schirinzi, and A. Farina, “Moving target detection by along-track interferometry,” in Proc. IGARSS, vol. 7, Sydney, Australia, Jul. 9–13, 2001, pp. 3024–3026. [14] C. Livingstone, I. Sikaneta, C. Gierull, S. Chiu, A. Beaudoin, J. Campbell, J. Beaudoin, S. Gong, and T. Knight, “An airborne synthetic aperture radar (SAR) experiment to support RADARSAT-2 ground moving target indication (GMTI),” Can. J. Remote Sens., vol. 28, no. 6, pp. 794–813, 2002. [15] M. Soumekh, “Moving target detection in foliage using along track monopulse synthetic aperture radar imaging,” IEEE Trans. Image Process., vol. 6, no. 8, pp. 1148–1163, Aug. 1997. [16] R. K. Raney, “Synthetic aperture imaging radar and moving targets,” IEEE Trans. Aerosp. Electron. Syst., vol. AES-7, no. 3, pp. 499–505, May 1971.
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[17] W. Rieck, “Zeit-frequenz-signal-analyze für radaranwendungen mit synthetischer apertur (SAR),” Ph.D. dissertation, Rheinisch-Westfälische Technische Hochschule Aachen, Shaker Verlag, Aachen, Germany, 1998. [18] R. K. Raney, “Considerations for SAR image quantification unique to orbital systems,” IEEE Trans. Geosci. Remote Sens., vol. 29, no. 5, pp. 754–760, May 1991. [19] C. H. Gierull and C. Livingstone, “SAR-GMTI concept for RADARSAT-2,” in The Applications of Space-Time Processing, R. Klemm, Ed. Stevenage, U.K.: IEE Press, 2004. [20] M. Pettersson, “Extraction of moving ground targets by a bistatic ultrawideband SAR,” in Proc. Inst. Elect. Eng., Radar, Sonar Navigat., vol. 148, Feb. 2001, pp. 35–49. [21] G. Franceschetti and R. Lanari, Synthetic Aperture Radar Processing. Boca Raton, FL: CRC, 1999. [22] J. J. Sharma, “The influence of target acceleration on dual-channel SARGMTI (synthetic aperture radar ground moving target indication) data,” M.S. thesis, Univ. Calgary, Calgary, AB, Canada, Oct. 2004. [23] C. Livingstone and I. Sikaneta, “Focusing moving targets/terrain imaged with moving-target matched filters: A tutorial,” Defence Research and Development, Ottawa, ON, Canada, Tech. Rep. TM-2004-160, Sep. 2004. [24] A. Moccia and G. Rufino, “Spaceborne along-track SAR interferometry: Performance analysis and mission scenarios,” IEEE Trans. Aerosp. Electron. Syst., vol. 37, no. 1, pp. 199–213, Jan. 2001. [25] H. Breit, M. Eineder, J. Holzner, H. Runge, and R. Bamler, “Synthetic aperture imaging radar and moving targets,” in Proc. IGARSS, vol. 2, Toulouse, France, Jul. 2003, pp. 1187–1189. [26] A. Thompson and C. Livingstone, “Moving target performance for RADARSAT-2,” in Proc. IGARSS, vol. 6, Honolulu, HI, Jul. 24–28, 2000, pp. 2599–2601.
Jayanti J. Sharma received the B.Sc. and M.Sc. degrees in geomatics engineering from the University of Calgary, Calgary, AB, Canada, in 2002 and 2005, respectively. She is currently pursuing the Ph.D. degree in electrical engineering at the University of Karlsruhe, Karlsruhe, Germany, and the Institute of Radio Frequency Technology at the German Aerospace Center (DLR), Oberpfaffenhofen, under the supervision of Dr. A. Moreira. Her research was part of a joint project between the University of Calgary and Defence Research and Development Canada–Ottawa. Her research interests include radar signal processing, ground moving-target detection, and estimation, and polarimetric interferometric synthetic aperture radar.
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Christoph H. Gierull (S’94–M’95–SM’02) received the Dipl.-Ing. and the Dr.-Ing. degrees in electrical engineering from the Ruhr-University Bochum, Bochum, Germany, in 1990 and 1995, respectively. From 1991 to 1994, he was a Scientist with the Electronics Department, German Defence Research Establishment (FGAN), Wachtberg, Germany. From 1994 to 1999, he was the Head of the SAR simulation group at the Institute of Radio Frequency Technology, German Aerospace Center (DLR), Oberpfaffenhofen, Germany. In 2000, he joined the Radar Systems Section, Defence R&D Canada-Ottawa (DRDC Ottawa), Ottawa, ON, Canada, as a Defence Scientist. In February 2000, he was an X-SAR Performance Engineer on the Shuttle Radar Topography Mission’s operations team at the Johnson Space Center, Houston, TX. His work concentrates on various aspects of radar (array) signal processing, including adaptive jammer suppression, space-time adaptive processing, superresolution, and airborne and spaceborne SAR in combination with MTI as well as bistatic SAR. Dr. Gierull received the Paper Prize Award of the Information Technology Society (ITG) of the Association of German Electrical Engineers (VDE) in 1998.
Michael J. Collins (S’87–M’93–SM’00) received the B.Sc.Eng. degree in survey engineering from the University of New Brunswick, Fredericton, NB, Canada, the M.Sc. degree in physical oceanography from the University of British Columbia, Vancouver, BC, Canada, and the Ph.D. in earth and space science from York University, Toronto, ON, Canada, in 1981, 1987, and 1993, respectively. His Ph.D. research was a theoretical and experimental analysis of the response of a synthetic aperture radar to sea ice. He is currently a Faculty Member in the Department of Geomatics Engineering, University of Calgary, Calgary, AB, Canada. He has also been a Faculty Member with the Department of Survey Engineering, University of Maine and in the Department of Geodesy and Geomatics Engineering, University of New Brunswick; a Project Scientist with the Institute for Space and Terrestrial Science in Toronto, Canada, and an Engineer with the McElhanney Group in Vancouver and Calgary. He has also served as a consultant to government and industry on various aspects of remote sensing. He has research interests in several aspects of radar remote sensing, including simulation of signal data, texture analysis, segmentation and classification, estimation of forest and sea-ice characteristics, and the fusion of radar with electro-optical and other geospatial data.
