Real-time tracking of maneuvering targets is the prerequisite for continuous imaging of moving targets in inverse synthetic aperture radar (ISAR). In this paper, the range and azimuth tracking (RAT) method with wideband radar echoes is first presented for a mechanical scanning monopulse ISAR, which is regarded as the simplest phased array unit due to the two antenna feeds. To relieve the estimation fluctuation and poor robustness of the RAT method with a single snapshot, a modified range and azimuth tracking approach based on centroid algorithm (RATCA) with forgotten factor and multiple echoes is then proposed. The performances of different forgotten factors are investigated. Both theoretical analysis and experimental results demonstrate that RATCA is superior to RAT method. Particularly, when target echo is missing occasionally, RAT method fails while RATCA still keeps good performance. The potential of continuous imaging with shipborne ISAR is verified by experimental results. With minor modification, the method proposed in this paper can be potentially applied in the phased array radar.
Inverse synthetic aperture radar (ISAR) has been widely employed to obtain the high-resolution image of the target for coastal surveillance and target recognition [
In conventional ISAR, the imaging processing consists of two successive stages: (1) detect and estimate the position of target by narrow bandwidth echoes and (2) use the wideband echo to obtain the ISAR image of the prelocated target. In this kind of system, to redetect the target after imaging is necessary because of the range shift and angular change in the imaging duration, which is typically several seconds for marine target. Due to the redetection procedure, the time difference between two consecutive imaging processes is almost the same as the antenna scan period, which is too long for coastal ISAR system, and the ability of surveillance is seriously limited. Therefore, in this paper, we propose a wideband target tracking technique which allows ISAR system continuous imaging without the redetection procedure. Thus, the ISAR images of the same threatening target from different views could be continuously obtained. This is of great importance for target recognition. Because the redetection is canceled, range and azimuth tracking simultaneously is required to capture the target by adjusting the radar line of sight (LOS) and receiver sampling gate adaptively.
Range tracking is to record only the effective target data in each echo according to the estimated time delay of the target. This decreases the quantity of recorded data largely and is beneficial to the subsequent digital signal processing. A conventional method is to track the prominent scatterers on the target [
In this paper, a novel instantaneous range and azimuth tracking (RAT) algorithm based on a single wideband echo is proposed for continuous imaging of marine target. To improve the tracking performance and robustness of RAT method under some extreme conditions such as target echo missing, a modified range and azimuth tracking approach based on centroid algorithm (RATCA) is further proposed. Both RAT and RATCA are real-time tracking methods; however, RATCA extends the RAT method by using multiple wideband echoes and employing forgotten factors. These proposed methods are verified by the experiments of shipborne ISAR system. Note that the methods proposed in this paper can be easily extended to the case of phase array systems with numerous transmit/receive (T/R) modules.
The rest of this paper is organized as follows. The RAT algorithm for a single snapshot is presented in Section
Modern radar system needs not only to estimate the target tracks but also to obtain ISAR images of targets for data fusion and recognition. As mentioned before, to detect and to obtain the image of the target, respectively, by short time division multiplexing is a conventional process in traditional radar system. Detecting and imaging are two main operation modes of the practical ISAR. In detecting mode, radar transmits short linear frequency modulation (LFM) pulse with narrow bandwidth to sense the presence of targets and estimate their ranges and azimuths as a priori knowledge for imaging. When radar is operated in imaging mode, the bandwidth of the transmitted LFM pulse is typically several hundreds of megahertz to achieve the high range resolution.
The ISAR image contains many details of targets and now plays an important role in marine surveillance. From the high range resolution image, more information about the target of interest, such as attitude, size, and type, can be inferred. To monitor and obtain the images of an unknown marine target continuously is of great significance in coastal surveillance. However, the redetection procedure is required in conventional radar system and the continuous imaging is unable to be implemented. By considering radar scan period, redetection may take a long time in searching the target of interest between successive imaging processes; hence, the ability to monitor some threatening target is limited. Therefore, target continuous imaging based on wideband echoes without any redetection is preferred for some threatening targets.
The most challenging part in continuous imaging is target tracking during the imaging processing. In high range resolution radar, only the effective target data is recorded for range tracking by a setup sampling gate after stretch processing, which is widely employed to reduce the effective baseband signal bandwidth substantially and is an advantage of data sampling and following digital signal processing. On the other hand, imaging target needs to be illuminated by the antenna to obtain the target returns. Ideally, target should be located in the center of imaging range scene and the main beam of antenna as shown in Figure
Different positions of the target. (a) Different positions of the target in the imaging range scene. (b) Different positions of the target in the radar antenna beam.
For tracking and imaging simultaneously, the RAT method is proposed in this section. RAT method is a signal processing method based on high range resolution profile (HRRP) of the target consisting of numerous scatterers, which are uniformly distributed in range, with different amplitudes and phases. RAT method consists of range tracking and azimuth tracking, as shown in Figure
Principles of RAT method. (a) Basic block diagram of imaging processing with range and azimuth tracking. (b) Tracking of marine target in ISAR imaging.
The main task of range tracking is to estimate the range deviation from the center of the imaging scene. The first local oscillator (LO) delay is then modified according to the estimated range deviation, also called range-error, to record only the effective target data for further processing.
In high-resolution radar, the major scattering features could be projected into a range profile, which consists of numerous scatterers in each position with different amplitudes and phases. Stretch processing is a technique for wideband LFM pulse compression, allowing the range of the target in time-domain to be represented by a corresponding frequency. A stretch processor allows the effective baseband signal of the target to be significantly reduced. The range profile digital sequence, which contains details of target such as amplitude, phase, and location in range, could be obtained via fast Fourier transform (FFT) of the baseband data after stretch processing. A slide window with given length smoothens the random fluctuation of the range profile to obtain the contour of the target, as illustrated in Figure
Basic block diagram of range and azimuth tracking. (a) Basic block diagram of range tracking. (b) Basic block diagram of azimuth tracking.
Assume that there are
The range-error, which is the key quantity for adjusting the first LO delay in data sampling, can be obtained by
Therefore, the range of imaging target in the current HRRP is
Angle-error is sensed by azimuth tracking for adjusting the LOS of antenna to keep the moving target illuminated permanently. The scatterer with maximum amplitude in the range profile in sum channel is selected for azimuth estimation.
The well-known sum-difference amplitude-comparison monopulse method, as shown in Figure
Block diagram of the sum-difference amplitude-comparison monopulse in azimuth coordinate.
The monopulse ratio, proportional to the angle-error
In practice, the experimental sum-difference amplitude-comparison monopulse ratios are prestored in the signal processing system. The angle-error will be estimated by searching the look-up table when needed, as shown in Figure
Owing to the instability of receiver and transient interference, the problem of target echo loss may occur occasionally. In this case, the target may be excluded from the imaging range scene or not be illuminated by antenna due to the erroneous estimations of range and azimuth by RAT method, both of which result in the failure of continuous imaging.
In this section, a modified RATCA method is proposed based on centroid algorithm by using multiple echoes with forgotten factor to improve the performance and robustness of range and azimuth tracking.
The centroid of an object in physics, namely, the center of mass, is the unique point where the weighted relative position of the distributed mass sums to zero. The HRRP of the target can be considered as a single object which consists of several major scatterers with different amplitudes (as shown in Figure
Ship and high range resolution profile.
The RAT method generally works well in normal situation. However, some potential risks are involved when sudden jamming and random interference are taken into consideration. The scatterers used for range and azimuth tracking in RAT method are only selected by the corresponding amplitudes, which may be interrupted by sudden outlier. Both range and azimuth tracking will be affected seriously especially for the latter one, which only utilizes one prominent scatterer for angle-error estimation without determining whether the chosen maximum amplitude response is a return from real target or a spurious interference in the same range bin. A modified algorithm named RATCA is proposed here to decrease these impacts of amplitude weighting.
The RATCA method consists of inner-pulse processing and pulse-to-pulse processing. The inner-pulse processing first employs
Similar to the RAT method, assume that
The range-error, angle-error, and amplitude in sum channel of each selected scatterer are
According to the experimental results, the ratio of the maximum amplitude of the range profile in sum channel with target to that without target is about 30 to 40 dB, as shown in Figure
Comparison of range profiles in sum channel (top) and difference channel (bottom) for target missing and existing. (a) Range profiles without targets. (b) Range profiles of the target.
As mentioned above, the significant advantage of pulse-to-pulse processing is to improve the tracking performance by decreasing the unexpected interference. Because the motion of the marine target is complicated, the significance of historic results should be considered in pulse-to-pulse processing. Therefore, the forgotten factors are used to represent the influence of historic result on the present one, which can be regarded as processing through weighted summation. This principle is illustrated in Figure
Basic principle of the forgotten factor.
In the pulse-to-pulse processing with a given length
Basic block diagram of RATCA algorithms.
The weight of historic estimation in each of the target echoes is determined by forgotten factor, which is usually constant, linear, or exponential sequence. Target tracking with RATCA method consists of range tracking and azimuth tracking. For convenience, selection of forgotten factors in range tracking is discussed as a representative. Assume that the radial motion of marine target can be modeled as
Note that the true value of the range-error in the
The true range-error in the above is utilized as the reference value for the following analysis with different types of forgotten factors.
Under this condition, the forgotten factors can be expressed as
This is the simplest type and the estimate after pulse-to-pulse processing is simplified to the form in (
The above satisfies the real position ideally while suffering the same level of noise background. The estimation error is given as
In this type, the forgotten factors turn to be
The estimation error is
Under this condition, the style of forgotten factors is a linear function with the form
Similarly, the estimation error is
“General” means that the selection of forgotten factors is undetermined. The estimate of range-error,
In fact, the three types of forgotten factors are special cases of “General” type. The IPI
The range tracking RMSEs with different forgotten factors versus velocity in various SNRs with
Range-error root-mean-square errors (RMSEs) of different forgotten factors versus velocity with
When the target velocity is approximately smaller than 5 m/s, the “Constant” and “Linear” types outperform the other two kinds of forgotten factors. When target velocity increases, the RMSEs of “Constant” and “Linear” types go up rapidly while the “Exponential” one is still stable. Although the radar line of sight and the first LO time delay are modified in a fixed interval longer than the PRI in practice, the radial and rotational motion can be ignored for low-speed marine target. The noise could be averaged via constant- or linear-weighting while the high range resolution profile of the target keeps steady. However, motion of the target at high speed cannot be neglected because the movement may spread through adjacent range cells or azimuth cells. The latest range-error and angle-error may be seriously affected by the historical estimations, which can be relieved properly by exponential weighting. As shown in Figure
The range tracking RMSEs with different accelerations with velocity fixed at
Range-error RMSEs of different forgotten factors versus acceleration with
Since azimuth tracking uses the same processing method as used in range tracking, similar performances could be predictable in the azimuth tracking and thus are omitted here to save space.
To investigate the range-error RMSEs estimated of the aforementioned forgotten factors with different SNR, the tracking RMSEs of a typical marine target, which is similar to the cooperative vessel in the experiment referred to in this paper, are shown in Figure
Range-error RMSEs in typical marine target parameters. (a) RMSE versus SNR with
In this section, tracking error analysis and simulation results with different kinds of forgotten factors are given versus different target velocities, accelerations, and SNRs. Experimental results from an ISAR marine imaging experiment are provided to verify the proposed method. The system parameters are as follows: radar carrier frequency Successive radar echoes of a cooperative moving ship were recorded without range or azimuth tracking by an onshore radar to verify the performances of RAT and RATCA methods. The results are presented in Sections Locate the radar on a moving vessel platform. The same cooperative moving target was imaged continuously with simultaneous range and azimuth tracking. The ISAR images are given in Section
If the radar works normally, the wideband echoes of the target could be received correctly. Under this condition, the performance of tracking is mainly related to the interior noise. The estimations of range and azimuth with a unique echo fluctuate slightly, assuming that the SNR of the target in sum pattern is coequal to the null depth in difference pattern, though the target and seawater keep a standstill [
Comparisons of tracking performances between RAT and RATCA when radar is performing normally. (a) Range-error. (b) Azimuth-error.
The length of the cooperative ship is 30 meters and the antenna beam width is 3.3 degrees. As shown in Figure
In this subsection, the performances of RAT and RATCA in the extreme situation are studied. Two conditions are taken into consideration: echo loss and jamming existence. The former one is analyzed with experimental data and the latter one is investigated with computer simulations.
The target is generally located in the middle of imaging scene and the center of the antenna beam in normal situation. Once the echo is missing, the maximum erroneous range-error may deviate from the real one for about 105 m. The value of the deviation depends on the practical radar parameters and affects the first LO time delay. Once the range-error estimation exceeds the upper or nether threshold, the range tracking will fail. As shown in Figure
Tracking performances of the RAT and RATCA method in extreme condition. (a) Range estimations in RAT and RATCA methods with echo loss. (b) Azimuth estimations in RAT and RATCA methods with echo loss. (c) Range estimations in RAT and RATCA methods with jamming. (d) Azimuth estimations in RAT and RATCA methods with jamming.
In azimuth tracking with the RAT method, if only the estimated angle-error exceeds 1.65 degrees, which is a half of the practical antenna 3 dB beam width (only 3.3 degrees in the practical ISAR) and is presented as upper and nether thresholds in Figure
Figures
The range and azimuth tracking results show that both of the range-error and angle-error exceed the threshold obviously with RAT method while RATCA method still works robustly.
According to the experimental results above, it is obvious that if echoes from imaging target are correctly received, the target will be tracked accurately and located in the middle of the imaging scene and antenna beam. The RATCA algorithm still works well though the random noise is dominated when the target echo is missing and the RAT algorithm fails. In this part, the robustness of RATCA algorithm is theoretically analyzed. Considering the influence induced by the weighted historical estimations with different forgotten factors, the bias of RATCA estimator is also investigated.
The adjustment of the first LO time delay and rotation of antenna will be slight when echoes are received correctly because the real values of range-error
Due to the erroneous estimations of range and azimuth induced by echo missing, the first LO time delay and LOS of antenna will be modified by mistake. Assume that
The performances of range-error and angle-error estimations with “Constant” and “Linear” forgotten factors are similar when target SNR is higher than 30 dB as shown in Figure
Substituting (
Recalling that the value of
Similar to (
From (
In this subsection, the biases of estimations with four types of forgotten factors are investigated with typical parameters of a marine target. Assume that the estimator operates in Gaussian white noise with zero mean.
The value of (
Considering the fact that IPI is fixed and typically about 0.1 seconds in the practical ISAR, we are interested in the maximum number of
Assuming that the parameters of the targets are identical to those of Section
Similarly, the bias is tolerable if
The accepted range of
Though the maximum value of
When a target moves along the tangential direction of radar antenna LOS, its azimuth changes most rapidly, which means that azimuth tracking is more difficult. If (
The marine experiment was conducted in January 2014 at the Yellow Sea, China. As shown in Figure
Routes of radar platform and cooperative target.
During the experiment, a priori knowledge of cooperative target, such as range and azimuth relative to the antenna line of sight, is estimated first in detecting mode. Then, the imaging mode turns to work and the ISAR images of the target could be obtained continuously. There is no requirement of any redetection because the latest target range and azimuth, which is curial to data record and target capture, are obtained successively and simultaneously by range and azimuth tracking.
As investigated in Section
Some representative ISAR images from 11:55 to 12:33 are given in Figure
ISAR images of cooperative target. (a) Side-looking image at 11:55, (b) oblique-looking image at 11:58, (c) oblique-looking image at 12:01, (d) oblique-looking image at 12:04, (e) front-looking image at 12:06, (f) oblique-looking image at 12:08, (g) oblique-looking image at 12:11, (h) oblique-looking image at 12:14, (i) oblique-looking image at 12:17, (j) side-looking image at 12:20, (k) side-looking image at 12:22, (l) oblique-looking image at 12:23, (m) front-looking image at 12:26, (n) oblique-looking image at 12:27, (o) oblique-looking image at 12:29, and (p) side-looking image at 12:33.
The route of cooperative ship during the aforementioned time period consists of three parts in Figure
For convenience, we define several types of ISAR image attitude:
Figure
In this paper, range and azimuth tracking in ISAR with wideband radar echoes is investigated. For the purpose of continuous imaging of threatening marine targets, the range and azimuth tracking (RAT) method is first presented for monopulse ISAR, which consists of two antenna feeds and could be regarded as the simplest phased array unit. However, the theoretical analysis and experimental results show that the RAT method is inappropriate for imaging in some extreme cases such as echo missing and jamming existence.
On the basis of centroid algorithm with forgotten factors, a modified approach for tracking range and azimuth simultaneously, namely, RATCA, is proposed to improve the tracking performance. The tracking performances with different forgotten factors are discussed versus velocity, acceleration, and SNR. Normally, the fluctuations of range and azimuth estimations with RATCA would be smoothed. More significantly, the modified method performs effectively when the target echo is missing occasionally. The range and azimuth are accurately estimated and the impacts of the erroneous estimations on the radar system are relieved. Compared with the RAT method, the RATCA method can be utilized to track a threatening marine target continuously for imaging, which is verified by the experimental results and numerous continuous ISAR images. The robustness and bias of the RATCA method are also theoretically analyzed. The method proposed in this paper is also applicable for phased array radar system, which could track multiple targets simultaneously.
The authors declare that there are no competing interests regarding the publication of this paper.
This work was supported by a CASC-HIT United Technology Center key project (CASC-HIT11-1A01).