Dimitar Minchev

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.

Multi-Satellite Interferometric SAR System

In the present work a multi-satellite SAR system is considered. Between every pair of SAR satellites an interferometric concept is implemented. It allows the height of each pixel on the surface to be evaluated with high precision and a three dimensional map to be created. InSAR geometry is analytically described. Mathematical expressions for determination of current distances between SAR’s and detached pixels on the ground, and principal InSAR parameters are derived. A model of linear frequency modulated (LFM) SAR signal with InSAR applications, reflected from the surface is developed. Correlation and spectral SAR image reconstruction algorithms and co-registration procedure are described. To verify the correctness of the signal model and image reconstruction and co-registration algorithm numerical experiment is carried out.

Ultrasonic sensor explorer

Ultrasonic Sensor Explorer (USE) is a cheap mobile robot for mapping. Instead of expensive laser sensor, it uses cheap ultrasonic sensor HC-SR04 with range up to 4 meters. The chassis of the robot is made of ABS plastic material and it is 3D printed from a model called Mini-Me on RepRap Prusa Iteration 3 3D printer. The hardware is based on ROMEO BLE mainboard. The Software consists of two parts: firmware and application. The firmware part is an Arduino source code project, written in C++ programming language, which is deployed on the robot. The application part is Windows IoT source code, written in C# programming language, which can be run on PC, tablet, phone or ARM device. The suggested robot has been tested in the university lab environment. The presented concept proves it has a potential for SLAM.

GISAR image reconstruction based 2-D smoothed l0 norm minimization in sparse decomposition

General Inverse Synthetic Aperture Radar (GISAR) imaging algorithm based on two-dimensional (2-D) l0 norm minimization in signal sparse decomposition is discussed. GISAR geometry and kinematics are analytically described. GISAR signal model based on Linear Frequency Modulated (LFM) waveform is derived. The GISAR signal formation process is presented as a sparse decomposition in redundant Fourier basis. Image reconstruction procedure is presented as minimization of smooth norm of the image matrix. The algorithm of minimization of the number of non-zero point scatterers is thoroughly described. The results are illustrated by a numerical experiment.

Two-Dimensional l1-Norm Minimization in SAR Image Reconstriction

Abstract A nonconventional image algorithm, based on compressed sensing and l1-norm minimization in Synthetic Aperture Radar (SAR) application is discussed. A discrete model of the earth surface relief and mathematical modeling of SAR signal formation are analytically described. Sparse decomposition in Fourier basis to solve the SAR image reconstruction problem is discussed. In contrast to the classical one-dimensional definition of l1-norm minimization in SAR image reconstruction, applied to an image vector, the present work proposes a two-dimensional definition of l1-norm minimization to the image. To verify the correctness of the algorithm, results of numerical experiments are presented.

BISATIC SAR SLC IMAGE MODELLING AND INTERFEROMERIC GENERATION

This work addresses the model of Bistatic Interferometric Synthetic Aperture Radar BInSAR imaging process. BInSAR geometry with multiple satellite receivers is thoroughly mathematical described. A linear frequency modulated (LFM) SAR signal model and single look complex (SLC) image are derived. To verify proposed models an implementation of the processing chain, implemented in MATLAB environment is performed.