Motion Compensation Algorithm Research Articles

Motion Compensation for an Unmanned Aerial Vehicle Remote Radar Life Sensor

Unmanned aerial vehicle platforms are ideal for remote life sensing applications including military, humanitarian, and post-disaster search and rescue operations. Doppler radar sensors can remotely detect human respiration vital signs to assess triage but any sensor motion will corrupt the signal. The respiration signal can be recovered by measuring the platform motion with a secondary radar and removing the motion induced phase modulation from the primary radar signal that contains both the platform motion and the desired vital signs signal. We simulated and tested a motion compensation algorithm using the dual radar approach and successfully recovered the respiration signal from the radar sensor using a laboratory testbed and on an airborne quadcopter. We measured a signal to motion interference ratio improvement of 15 dB to 41 dB on the benchtop motion testbed and an improvement of 26 dB for the radar sensor on an airborne quadcopter.

Efficient Space-Variant Motion Compensation Approach for Ultra-High-Resolution SAR Based on Subswath Processing

Motion compensation (MOCO) is essential to obtain high-quality images for airborne synthetic aperture radar (SAR). In the case of ultrahigh resolution, how to compensate the space-variant motion errors accurately and efficiently is still a great challenge. An improved space-variant MOCO scheme is presented in this paper, taking into account both precision and efficiency. By subswath processing, an approximate range envelope compensation without interpolation can be implemented efficiently. Meanwhile, to correct the range-variant component of motion errors effectively, the conventional MOCO processing flow should be modified, guaranteeing that the phase compensation of the one-step MOCO algorithm is not affected by the approximate range envelope compensation. Moreover, based on subswath processing, the range variance of residual azimuth-variant errors can also be degraded, as well as the influence of that on azimuthal time–frequency relationship. Thus, the focusing effect in the case of wide beam is improved significantly, and the computational burden of the precise topography- and aperture-dependent (PTA) algorithm is also reduced. The proposed approach is useful in practice, and the resolution of image corrected by this approach attains 0.1 m. Simulations with point targets and processing of real data have validated the proposed approach.

Optimal Coherent Processing Interval Selection for Aerial Maneuvering Target Imaging Using Tracking Information

When a target is in complex three-dimensional (3-D) motions, inverse synthetic aperture radar (ISAR) images cannot be obtained with any motion compensation algorithms. In this case, selecting optimal coherent processing interval (CPI) (or frame) of the fixed rotational axis is the only way to obtain focused ISAR images. In this article, we focus on selecting optimal CPI for ISAR imaging of maneuvering targets, and a novel method using tracking information is proposed. Without complex computational procedures, the proposed method provides robust performance. The method includes three steps. First, target’s orientation (roll, pitch, and yaw) is estimated by using an extended Kalman filter. Second, the least-square method is adopted to find the best fitted lines of roll, pitch, and yaw angles in different time intervals, and the linearity degrees of the three rotation angles are measured over the imaging intervals. Third, the thresholds of the linearity degrees are set, according to which, optimal CPIs can be selected. The performance of proposed method is demonstrated using both simulated data and measured data. In both cases, optimal CPIs can be selected and well-focused ISAR images can be achieved.

Improved Frame-Selection Scheme for ISAR Imaging of Targets in Complex 3-D Motion

When a target is in complex three-dimensional (3-D) motions, inverse synthetic aperture radar (ISAR) images cannot be obtained with any motion compensation algorithms. To address this problem, phase nonlinearity can be used to select imaging frames where target 2-D motion is dominant enough to obtain focused ISAR images. Conventionally, adaptive joint time frequency (AJTF) and particle swarm optimization (PSO) algorithms are performed to estimate the phase signals of prominent scatterers. These estimates are used to determine phase nonlinearity. However, such estimation algorithms undergo multi-dimensional optimizations, which yield significant increases in computational complexity for ISAR frame-selections. For more practical use of AJTF- and PSO-based frame-selections, we introduce a method to improve the computational efficiencies of the conventional methods. To this end, in the proposed method, a simple phase unwrapping-and-least square fitting method is used as an alternative to the AJTF and PSO methods. Because PU-LSM can provide reliable phase estimates quickly without complex optimization procedures, the proposed method is an improvement over AJTF- and PSO-based methods, especially in terms of computational efficiency. In simulations using ideal point scatterers, our proposed method performs well, in terms of frame-selection ability and computational efficiency. Furthermore, experimental results using real radar echoes validated the robustness and efficacy our proposed frame-selection method.

Generalized Image Navigation & Registration Algorithms for Ground and Space Segments

Ground segment image navigation and registration algorithms and space segment image motion compensation algorithm are presented. The fundamental ground algorithm is based on Kalman filter instead of least squares and does not require ranging or accurate orbit to be provided by flight dynamics. Kalman filter is used to estimate attitude correction angles, orbit position and velocity relative to ideal geostationary orbit, and internal misalignments of imagers with single mirror or two mirrors. Kalman filter measurements consist of landmarks extracted from the imaging instrument level 1A data blocks, maneuver delta V or coarse orbit from flight dynamics, and spacecraft attitude telemetry inserted in the imager wideband data. The ground algorithm is then shown how to be applied to systems with star and landmark measurements, systems with star only measurements with accurate orbit provided by flight dynamics or by the global positioning system, and systems with spacecraft inertial angular rate. Pixel location transformation from imager line of sight reference frame to GOES and CGMS fixed grid frames is also provided for on-ground image registration using resampling.

Head motion correction based on filtered backprojection for x-ray CT imaging.

For head x-ray CT imaging, the head needs to remain motionless during the scan. In clinical practice, however, head motion is sometimes unavoidable depending on the patient. The motion can occur abruptly during the scan and can be unpredictable. It thereby causes motion artifacts such as tissue blurring or doubled edges around the skull area. To mitigate this problem, we propose a 3D head motion estimation (ME) and compensation algorithm based on filtered backprojection. If a patient moves his or her head during the scan, a motion-corrupted sinogram is obtained. Modeling the head motion as a 3D rigid transformation, we develop a motion-compensated (MC) reconstruction algorithm based on the FDK algorithm. To determine the head motion of a rigid transformation, we propose two optimization-based ME schemes depending on the degree of head motion, both of which are performed by updating motion parameters and the corresponding MC reconstructed image alternatively until the proposed cost function is minimized for the MC reconstructed image. In particular, to improve the robustness in the case of large motion, we propose attaching a fiducial marker to the head so that more reliable motion parameters can be initialized by determining the marker position, before the optimization. To evaluate the proposed algorithm, a numerical phantom with realistic, continuous, and smoothly varying motion, and a moving physical phantom are used with a gantry rotation time of 1s. In the simulation using a numerical phantom and in the experiment using a physical phantom, the proposed algorithm provides well-restored 3D motion-compensated images in both cases of small and large motion. In particular, in the case of large motion of the physical phantom, using a fiducial marker, we obtain remarkable improvement of image quality in cerebral arteries and a lesion as well as the skull. Quantitative evaluations using the image sharpness and root-mean-square error also show noticeable improvement of image quality in both simulations and experiments. We propose a framework for head motion correction in an axial CT scan, which consists of motion estimation and compensation steps. Two image-based ME algorithms for rigid motion tracking are developed according to the degree of head motion. The estimated motion information is then used for MC image reconstruction. Both motion estimation and compensation algorithms are based on computationally efficient filtered backprojection. Excellent performance of the proposed framework is illustrated by means of simulations using a numerical phantom and experiments using a physical phantom.

Effective multi-stage error control algorithms for robust 3D video transmission over wireless networks

The Three-Dimensional Video (3DV) contains diverse video streams taken by different cameras around an object. Thence, it is an imperative assignment to fulfill efficient compression to match the future resource limitations, whilst preserving a decisive reception 3DV quality. The efficient 3DV communication over wireless networks has become a recent considerable hot issue due to the restricted resources and the presence of severe channel errors. The high-rate 3DV encoding and transmission over mobile or Internet are vulnerable to packet losses due to the existence of heavy channel losses and limited bandwidth. Therefore, this paper presents efficient multi-stage error control algorithms for reliable 3DV transmission over error-prone wireless channels. At the encoder, the error resilience schemes of context adaptive variable length coding, slice structured coding, and explicit flexible macro-block ordering are utilized. At the decoder, a joint approach of a directional interpolation error concealment algorithm and a directional textural motion coherence algorithm is proposed to conceal the corrupted color frames. For the concealment of the lost depth frames, an encoder independent decoder dependent depth-assisted error concealment algorithm is suggested. Moreover, the weighted overlapping block motion and disparity compensation algorithm is exploited to choose the candidate concealment Motion Vectors (MVs) and Disparity Vectors (DVs). Furthermore, an improved recursive Bayesian filtering algorithm is utilized as a refinement stage to smooth the remaining errors in the previously selected candidate MVs and DVs for achieving better 3DV quality. Simulation results on several 3DV sequences show that the proposed algorithms achieve adequate objective and subjective 3DV quality performance at severe packet loss rates compared to the state-of-the-art algorithms.

Free-breathing whole-heart 3D cine magnetic resonance imaging with prospective respiratory motion compensation.

To develop and validate a new prospective respiratory motion compensation algorithm for free-breathing whole-heart 3D cine steady-state free precession (SSFP) imaging. In a 3D cine SSFP sequence, 4 excitations per cardiac cycle are re-purposed to prospectively track heart position. Specifically, their 1D image is reconstructed and routed into the scanner's standard diaphragmatic navigator processing system. If all 4 signals are in end-expiration, cine image data from the entire cardiac cycle is accepted for image reconstruction. Prospective validation was carried out in patients (N = 17) by comparing in each a conventional breath-hold 2D cine ventricular short-axis stack and a free-breathing whole-heart 3D cine data set. All 3D cine SSFP acquisitions were successful and the mean scan time was 5.9 ± 2.7 min. Left and right ventricular end-diastolic, end-systolic, and stroke volumes by 3D cine SSFP were all larger than those from 2D cine SSFP. This bias was < 6% except for right ventricular end-systolic volume that was 12%. The 3D cine images had a lower ventricular blood-to-myocardium contrast ratio, contrast-to-noise ratio, mass, and subjective quality score. The novel prospective respiratory motion compensation method for 3D cine SSFP imaging was robust and efficient and yielded slightly larger ventricular volumes and lower mass compared to breath-hold 2D cine imaging. Magn Reson Med 80:181-189, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Video Superresolution via Motion Compensation and Deep Residual Learning

Video superresolution (SR) techniques are of essential usages for high-resolution display devices due to the current lack of high-resolution videos. Although many algorithms have been proposed, video SR still remains a very challenging inverse problem under different conditions. In this paper, we propose a new method for video SR named motion compensation and residual net (MCResNet). We use optical flow algorithm for motion estimation and motion compensation as a preprocessing step. Then, we employ a novel deep residual convolutional neural network (CNN) to predict a high-resolution image using multiple motion compensated observations. The new residual CNN model preserves the low-frequency contents and facilitates the restoration of high-frequency details. Our method is able to handle large and complex motions adaptively. Extensive experimental results validate that our proposed method outperforms state-of-the-art single-image-based and multi-frame-based algorithms for video SR quantitatively and qualitatively.

Precise Aperture-Dependent Motion Compensation with Frequency Domain Fast Back-Projection Algorithm.

Precise azimuth-variant motion compensation (MOCO) is an essential and difficult task for high-resolution synthetic aperture radar (SAR) imagery. In conventional post-filtering approaches, residual azimuth-variant motion errors are generally compensated through a set of spatial post-filters, where the coarse-focused image is segmented into overlapped blocks concerning the azimuth-dependent residual errors. However, image domain post-filtering approaches, such as precise topography- and aperture-dependent motion compensation algorithm (PTA), have difficulty of robustness in declining, when strong motion errors are involved in the coarse-focused image. In this case, in order to capture the complete motion blurring function within each image block, both the block size and the overlapped part need necessary extension leading to degeneration of efficiency and robustness inevitably. Herein, a frequency domain fast back-projection algorithm (FDFBPA) is introduced to deal with strong azimuth-variant motion errors. FDFBPA disposes of the azimuth-variant motion errors based on a precise azimuth spectrum expression in the azimuth wavenumber domain. First, a wavenumber domain sub-aperture processing strategy is introduced to accelerate computation. After that, the azimuth wavenumber spectrum is partitioned into a set of wavenumber blocks, and each block is formed into a sub-aperture coarse resolution image via the back-projection integral. Then, the sub-aperture images are straightforwardly fused together in azimuth wavenumber domain to obtain a full resolution image. Moreover, chirp-Z transform (CZT) is also introduced to implement the sub-aperture back-projection integral, increasing the efficiency of the algorithm. By disusing the image domain post-filtering strategy, robustness of the proposed algorithm is improved. Both simulation and real-measured data experiments demonstrate the effectiveness and superiority of the proposal.

Performance evaluation of enhanced error correction algorithms for efficient wireless 3D video communication systems

SummaryIn the Three‐Dimensional Multi‐View Video (3D MVV) coding prediction structure, the coded bit‐streams may be dropped down due to error transmissions. So, it is compulsory to recover the corrupted Macro‐Blocks (MBs) at the decoder utilizing efficient Error Concealment (EC) post‐processing techniques. The EC methods exploit the temporal, inter‐view, and spatial matching among 3D MVV views and frames without any alterations in the encoder software or hardware or in the transmission rate. They retrieve the Disparity Vectors (DVs) and Motion Vectors (MVs) of the erroneous MBs. To enhance the received 3D MVV quality, we suggest several optimized schemes to reconstruct the lost and erroneous MBs of inter‐encoded and intra‐encoded frames. A hybrid method combining the Circular Scan Order Interpolation Algorithm (CSOIA) and Partitioning Motion Compensation Algorithm (PMCA) is proposed for intra‐frame EC. For inter‐corrupted MBs, a hybrid method comprising Directional Textural Motion Coherence Algorithm (DTMCA) and Directional Interpolation Error Concealment Algorithm (DIECA) is suggested. Experimental outcomes on several 3D MVV frames demonstrate that the suggested EC algorithms have more robustness to both heavily random and slice losses. They objectively and subjectively work better than the state‐of‐the‐art EC techniques. The proposed work achieves high 3D MVV quality with an improved average Peak Signal‐to‐Noise Ratio (PSNR) gain up to 2.45 to 4.55 dB compared with traditional EC algorithms at Packet Loss Rates (PLRs) of 40%.

Real-time registration of 3D to 2D ultrasound images for image-guided prostate biopsy.

During image-guided prostate biopsy, needles are targeted at tissues that are suspicious of cancer to obtain specimen for histological examination. Unfortunately, patient motion causes targeting errors when using an MR-transrectal ultrasound (TRUS) fusion approach to augment the conventional biopsy procedure. This study aims to develop an automatic motion correction algorithm approaching the frame rate of an ultrasound system to be used in fusion-based prostate biopsy systems. Two modes of operation have been investigated for the clinical implementation of the algorithm: motion compensation using a single user initiated correction performed prior to biopsy, and real-time continuous motion compensation performed automatically as a background process. Retrospective 2D and 3D TRUS patient images acquired prior to biopsy gun firing were registered using an intensity-based algorithm utilizing normalized cross-correlation and Powell's method for optimization. 2D and 3D images were downsampled and cropped to estimate the optimal amount of image information that would perform registrations quickly and accurately. The optimal search order during optimization was also analyzed to avoid local optima in the search space. Error in the algorithm was computed using target registration errors (TREs) from manually identified homologous fiducials in a clinical patient dataset. The algorithm was evaluated for real-time performance using the two different modes of clinical implementations by way of user initiated and continuous motion compensation methods on a tissue mimicking prostate phantom. After implementation in a TRUS-guided system with an image downsampling factor of 4, the proposed approach resulted in a mean ± std TRE and computation time of 1.6 ± 0.6 mm and 57 ± 20 ms respectively. The user initiated mode performed registrations with in-plane, out-of-plane, and roll motions computation times of 108 ± 38 ms, 60 ± 23 ms, and 89 ± 27 ms, respectively, and corresponding registration errors of 0.4 ± 0.3 mm, 0.2 ± 0.4 mm, and 0.8 ± 0.5°. The continuous method performed registration significantly faster (P < 0.05) than the user initiated method, with observed computation times of 35 ± 8 ms, 43 ± 16 ms, and 27 ± 5 ms for in-plane, out-of-plane, and roll motions, respectively, and corresponding registration errors of 0.2 ± 0.3 mm, 0.7 ± 0.4 mm, and 0.8 ± 1.0°. The presented method encourages real-time implementation of motion compensation algorithms in prostate biopsy with clinically acceptable registration errors. Continuous motion compensation demonstrated registration accuracy with submillimeter and subdegree error, while performing < 50 ms computation times. Image registration technique approaching the frame rate of an ultrasound system offers a key advantage to be smoothly integrated to the clinical workflow. In addition, this technique could be used further for a variety of image-guided interventional procedures to treat and diagnose patients by improving targeting accuracy.

Interview Motion Compensated Joint Decoding for Compressively Sampled Multiview Video Streams

In this paper, we design a novel multiview video encoding/decoding architecture for wirelessly multiview video streaming applications, e.g., 360 degrees video, Internet of Things (IoT) multimedia sensing, among others, based on distributed video coding and compressed sensing principles. Specifically, we focus on joint decoding of independently encoded compressively sampled multiview video streams. We first propose a novel side-information (SI) generation method based on a new interview motion compensation algorithm for multiview video joint reconstruction at the decoder end. Then, we propose a technique to fuse the received measurements with resampled measurements from the generated SI to perform the final recovery. Based on the proposed joint reconstruction method, we also derive a blind video quality estimation technique that can be used to adapt online the video encoding rate at the sensors to guarantee desired quality levels in multiview video streaming. Extensive simulation results of real multiview video traces show the effectiveness of the proposed fusion reconstruction method with the assistance of SI generated by an interview motion compensation method. Moreover, they also illustrate that the blind quality estimation algorithm can accurately estimate the reconstruction quality.

INS/GPS Integrated Smoothing Algorithm for Synthetic Aperture Radar Motion Compensation Using an Extended Kalman Filter with a Position Damping Loop

In this study, we propose a real time inertial navigation system/global positioning system (INS/GPS) integrated smoothing algorithm based on an extended Kalman filter (EKF) and a position damping loop (PDL) for synthetic aperture radar (SAR). Integrated navigation algorithms usually induce discontinuities due to error correction update by the Kalman filter, which are as detrimental to the performance of SAR as the relative position error. The proposed smoothing algorithm suppresses these discontinuities and also reduces the relative position error in real time. An EKF estimates the navigation errors and sensor biases, and all the errors except for the position error are corrected directly and instantly. A PDL activated during SAR operation period imposes damping effects on the position error estimates, where the estimated position error is corrected smoothly and gradually, which contributes to the real time smoothing and small relative position errors. The residual errors are re-estimated by the EKF to maintain the estimation performance and the stability of the overall loop. The performance improvements were confirmed by Monte Carlo simulations. The simulation results showed that the discontinuities were reduced by 99.8% and the relative position error by 48% compared with a conventional EKF without a smoothing loop, thereby satisfying the basic performance requirements for SAR operation. The proposed algorithm may be applicable to low cost SAR systems which use a conventional INS/GPS without changing their hardware configurations.

Respiratory motion compensation for the robot-guided laser osteotome.

The use of a robot-guided laser osteotome for median sternotomy is impeded by prohibiting cutting inaccuracies due to respiration-induced motions of the thorax. With this paper, we advance today's methodologies in sternotomy procedures by introducing the concept of novel 3D functional cuts and a respiratory motion compensation algorithm for the computer-assisted and robot-guided laser osteotome, CARLO®. We present a trajectory planning algorithm for performing 3D functional cuts at a constant cutting velocity. In addition, we propose the use of Gaussian process (GP) prediction in order to anticipate the sternum's pose providing enough time for the CARLO® device to adjust the position of the laser source. We analysed the performance of the proposed algorithms on a computer-based simulation framework of the CARLO® device. The median position error of the laser focal point has shown to be reduced from 0.22mm without GP prediction to 0.19mm with GP prediction. The encouraging simulation results support the proposed respiratory motion compensation algorithm for robot-guided laser osteotomy on the thorax. Successful compensation of the respiration-induced motion of the thorax opens doors for robot-guided laser sternotomy and the related novel cutting patterns. These functional cuts hold great potential to significantly improve postoperative sternal stability and therefore reduce pain and recovery time for the patient. By enabling functional cuts, we approach an important threshold moment in the history of osteotomy, creating innovative opportunities which reach far beyond the classic linear cutting patterns.

Motion compensation algorithm in narrowband imaging for mid-course targets

Imaging precession targets based on the narrowband radar to distinguish the real warhead from mid-course targets is a new technique in missile defense systems. Aiming at the typical mid-course flying scene, this paper describes the principle of the narrowband imaging method, and analyzes the influence on the narrowband imaging by the target translational motion. Then the precision qualification is deduced for both the distance compensation and the velocity compensation, and the conclusion that the velocity compensation is more appropriate for the motion compensation in the narrowband imaging is given. Furthermore, this paper proposes a motion compensation algorithm for the narrowband radar which reduces the interference of the signal phase chaos caused by the rebuilt real signal phase, thus realizing the precise translational motion compensation of the narrowband signal. Finally, the effectiveness of this method is proved by both theoretic analysis and experiment results.

Motion Estimation and Compensation Strategies in Dynamic Computerized Tomography

A main challenge in computerized tomography consists in imaging moving objects. Temporal changes during the measuring process lead to inconsistent data sets, and applying standard reconstruction techniques causes motion artefacts which can severely impose a reliable diagnostics. Therefore, novel reconstruction techniques are required which compensate for the dynamic behavior. This article builds on recent results from a microlocal analysis of the dynamic setting, which enable us to formulate efficient analytic motion compensation algorithms for contour extraction. Since these methods require information about the dynamic behavior, we further introduce a motion estimation approach which determines parameters of affine and certain non-affine deformations directly from measured motion-corrupted Radon-data. Our methods are illustrated with numerical examples for both types of motion.

Assessing State-of-the-Art Capabilities for Probing the Atmospheric Boundary Layer: The XPIA Field Campaign

Abstract To assess current capabilities for measuring flow within the atmospheric boundary layer, including within wind farms, the U.S. Department of Energy sponsored the eXperimental Planetary boundary layer Instrumentation Assessment (XPIA) campaign at the Boulder Atmospheric Observatory (BAO) in spring 2015. Herein, we summarize the XPIA field experiment, highlight novel measurement approaches, and quantify uncertainties associated with these measurement methods. Line-of-sight velocities measured by scanning lidars and radars exhibit close agreement with tower measurements, despite differences in measurement volumes. Virtual towers of wind measurements, from multiple lidars or radars, also agree well with tower and profiling lidar measurements. Estimates of winds over volumes from scanning lidars and radars are in close agreement, enabling the assessment of spatial variability. Strengths of the radar systems used here include high scan rates, large domain coverage, and availability during most precipitation events, but they struggle at times to provide data during periods with limited atmospheric scatterers. In contrast, for the deployment geometry tested here, the lidars have slower scan rates and less range but provide more data during nonprecipitating atmospheric conditions. Microwave radiometers provide temperature profiles with approximately the same uncertainty as radio acoustic sounding systems (RASS). Using a motion platform, we assess motion-compensation algorithms for lidars to be mounted on offshore platforms. Finally, we highlight cases for validation of mesoscale or large-eddy simulations, providing information on accessing the archived dataset. We conclude that modern remote sensing systems provide a generational improvement in observational capabilities, enabling the resolution of finescale processes critical to understanding inhomogeneous boundary layer flows.

Azimuth Motion Compensation With Improved Subaperture Algorithm for Airborne SAR Imaging

Conventional motion compensation (MOCO) under beam-center approximation is usually insufficient to correct severe track deviations for high-resolution synthetic aperture radar imaging. In this paper, a novel MOCO approach is developed for correction of the azimuth-variant motion errors by exploiting a precise angle-to-Doppler relationship within subapertures. The corruption from the residual motion errors to the angle-to-Doppler mapping is investigated and overcome by a compensation scheme of the scaled Fourier transform. Inheriting the high efficiency, the proposed azimuth MOCO approach has dramatically improved precision over the conventional subaperture MOCO method by reducing high side-lobe peaks of the point spread function. Extensive comparisons with other MOCO algorithms are given to show the superiority of the proposed algorithm. Moreover, real-data experiments are provided for a clear demonstration of our proposed approach.

Precise aperture‐dependent motion compensation for high‐resolution synthetic aperture radar imaging

Aperture-dependent motion compensation (MOCO) is crucial for high-resolution airborne synthetic aperture radar (SAR) imaging, which can suppress image degradation especially for SAR systems working at a high-frequency waveband, such as millimetre-wave (MMW) SAR. The current precise topography and aperture (PTA) dependent MOCO algorithm aims to compensate the azimuth-dependent motion error by using a modified azimuth matched filtering. However, the matched filter is deduced with the principle of stationary phase without considering the effects from the azimuth-dependent motion errors, which limits its precision in focusing MMW SAR data involving severe motion errors. This study proposes a refined PTA algorithm with a precise post matched filter established by the method of series reversion. The range-variant characteristic of residual motion errors is also investigated for an improved precision. Simulated and real MMW SAR data sets are used to validate the effectiveness of the proposal.