Andon Lazarov

Isar Signal Modeling and Image Reconstruction with Entropy Minimization Autofocussing

In this work a model of deterministic components of ISAR trajectory signal with stepped frequency modulation based on 3D ISAR geometry is suggested. The object space, moving rectilinearly, is presented as a 3D regular grid of isotropic point scatterers. The analytical expressions for computing distances to each point scatterer of the object space are derived. The image reconstruction procedure includes both range and azimuth compression. Cross correlation technique and fast Fourier transform (FFT) to 2D ISAR signal map to realize range compression and azimuth compression, respectively are applied. An autofocusing technique based on entropy minimization is implemented to each ISAR return signal. In order to illustrate the capability of the ISAR signal model and verify the phase correction technique performed by entropy minimization numerical experiment is worked out

SAR Imaging of a Moving Target

In the proposed work new synthetic aperture radar geometry named generalized inverse synthetic aperture radar (GISAR) geometry is addressed. A new three-dimensional (3D) model of deterministic components of GISAR trajectory signals with stepped frequency modulation is suggested. 3D GISAR geometry is described by means of the analytical geometry. The geometry and kinematics of the object and GISAR observation system are described in separate 3-D Cartesian coordinate system. The stationary objects are presented in 3-D regular grid of isotropic point scatterers, relatively moving with respect to GISAR system at the velocity of the SAR carrier. The SAR carrier is considered unmoving placed in the origin of the coordinate system of observation. The stationary targets are moving at the complex velocity equal to the geometrical sum of the target velocity and SAR carrier velocity. The analytical expressions to compute the range distance to point scatterers of the stationary scene and moving targets are derived. The image reconstruction procedure includes both range and azimuth compression: cross correlation technique to GISAR signal to realize range compression and short time frequency transform to realize azimuth compression. A range alignment and an autofocusing technique are applied to GISAR signal. To illustrate the capability of the 3D ISAR signal model numerical experiment is implemented.

SAR triangle CW LFM signal formation and imaging

Synthetic Aperture Radar (SAR) with triangle Linear Frequency Modulated (LFM) Continuous Wave (CW) is considered. Algorithms for signal formation and image reconstruction of a moving target are suggested. Three-dimensional (3-D) SAR geometry of the target presented as an assembly of point scatterers is analytically described. Mathematical expressions for distance vector determination defined from SAR to each point scatterer are derived. SAR signal model based on a triangle linear frequency modulated continuous wave emitted signal, 3-D geometry and reflectivity function of the target is derived. Image reconstruction procedure based on Fourier transform for range compression and azimuth compression is applied. SAR imaging algorithm of a moving target is suggested. Numerical experiment is carried out.

Three dimensional Barker’s ISAR signal and image reconstruction

In the present paper an analytical description of three-dimensional (3-D) inverse synthetic aperture radar (ISAR) geometry is performed. A model of 3-D ISAR signal with Barkerpsilas phase code modulation (BPCM) is created. Image reconstruction procedure including range compression by cross correlation over fast time record data and azimuth compression by fast Fourier transform over slow time row data, is developed. Numerical experiment over the simulated ISAR data with Barkerpsilas phase code modulation is accomplished to demonstrate the validity of the proposed ISAR signal model and image reconstruction procedure and the quality of the reconstructed ISAR image.

Bistatic SAR system with GPS transmitter

Bistatic Synthetic Aperture Radar (BSAR) with GPS transmitter is in a focus of consideration. Bistatic topology, satellite transmitter of opportunity and stationary receiver, combined with inverse synthetic aperture radar (ISAR) technology with GPS P code modulated waveform for imaging of a moving are presented. Kinematical equations and mathematical model of the deterministic BSAR signal are created. It is proven that the signal formation and image reconstruction can be regarded as direct and inverse space transforms. Stages of image reconstruction, including phase correction, cross-correlation range compression and Fourier transform azimuth compression are defined. The effectiveness of models and algorithms are illustrated with results of numerical experiments.

ISAR autofocusing image reconstruction of sea target

This work deals with the implementation of ISAR method to extract an image of a sea target with high resolution. Three dimensional ISAR scenario, including radar and a target of interest, is depicted in one and the same 3-D Cartesian coordinate system and duly considered. The sea target is presented as an assembly of discrete point scatteres which intensities are interpreted as an image function of the object observed. Analytical geometrical expressions to define a range distance from the radar to each point scatterer from the object space are derived. In order to realize high range resolution on the line of sight an informative linear frequency modulated waveform is applied. An ISAR signal model as a superposition of signals reflected from targets point scatterers is described and graphicaly illustrated. Image extraction from ISAR signal returns is performed by implementation of Fourier transformation on both range and cross-range coordinates. Image enhancement is accomplished by iterative polynomial focusing procedure and entropy as a cost function. In order to verify the supposed algorithm a numerical experiment is performed.

ISAR image reconstruction and autofocusing procedure over phase modulated signals

A model of inverse synthetic aperture radar (ISAR) signal with Barkers code phase modulation (PCM) is developed. To cope with the image blurring due to the range migration of objects point scatterers an autofocusing technique for ISAR signal processing is performed. The correlation algorithm for range compression and spectral fast Fourier transform (FFT) for azimuth compression are exploited. The presented image reconstruction procedures are invariant to the objects trajectory parameters. Numerical experiment over the simulated ISAR data is accomplished.

Complex SAR signal modeling and image reconstruction

The work addresses the Synthetic Aperture Radar (SAR) geometry, signal model and imaging process. Mathematical description of the observed surface is presented. A waveform with linear frequency modulation (LFM) reflected by the surface is used to produce a two-dimensional (2-D) SAR signal model presented as a sum of Hadamard products of two-and four-dimensional matrices (arrays) with a specially defined rectangular function. It is proven that the SAR signal formation and image reconstruction can be interpreted as direct and inverse projection operations. Based on linearization of the inverse projection, two-dimensional inverse Fourier transform is applied to obtain a complex image known as a Single Look Complex (SLC) image, which can be used for interferogram generation. To verify the proposed SAR kinematics and geometry, surface geometry, signal models and image reconstruction algorithms a numerical experiment is carried out.

Kalman tracking filter in 3-D space

In this work a Kalman filter for tracking Unmanned Aerial Vehicle (UAV) moving near the base lane of a bistatic radar system and illuminated by GPS signals in three-dimensional (3-D) space is suggested. Continuous-time and discrete-time state equations are derived to define a linear time-invariant model. Model matrices describing the behavior of the object, state vectors, measurement vectors and vector noise process with its statistical characteristic are defined. Structures of the discrete state transition matrix of the dynamic model and covariance noise matrix are given. Linear time-invariant model matrices are derived. State model matrices with constant entries, measurement model matrix, state transition matrix of the dynamic model, covariance noise state matrix and covariance matrix of the measurements, are defined. Recurrent Kalman equations are described. To verify a 3-D Kalman tracking a numerical experiment is performed.

Ultrasonic Positioning System Implementation and Dynamic 3D Visualization

Abstract The paper contributes to the design and implementation of the ultrasonic positioning system based on new multifunctional hardware components, newly released. A moving object coordinates’ determination is described analytically and a matrix equation in respect to unknown coordinates with coefficients, measurement distances, is derived. Stages of data packet processing are formulated, and a pseudo pyramid of measurement distances is built. HX7TR multifunctional ultrasonic devises, transceivers, are used to implement the positioning system. A C# program source code for coordinate determination and 3D visualization is created. The algorithm for moving object coordinate computation, and its program realization as well as HX7TR ultrasonic devises can be used in development of indoor ultrasonic positioning systems embedded in IoT and robotics applications.