Space-time Processing Research Articles

Efficiency Estimation of Discrete Algorithms for Adaptation of Weight Coefficients in Space-Time Processing of Radar Signals

A comparative analysis of the efficiency of adaptive spatial filters with different methods of classified training sample formation under conditions of simultaneous exposure to active noise and passive interference is carried out. Based on the proposed methodology, analytical calculations of the changes in interchannel phase shifts for discrete algorithms for the adaptation of the weight coefficients of the spatial filter in various modes of operation of the 36D6 radar are carried out. It is shown that interchannel phase desynchronization/error arise at pause intervals in the adaptation of weight coefficients during antenna system scanning. The magnitude of these desynchronizations depends on the angular velocity of the antenna system rotation and on the repetition period of the radar pulses. An estimation of the suppression coefficient realized at the end of the pause in the adaptation of the weight coefficients taking into account the interchannel phase desynchronization is carried out. The recommendations on the choice of the formation method of the classified training sample under the conditions of the combined interferences are considered taking into account the losses that arise in case of discrete adaptation of the weight coefficients of the spatial filter.

Continuity Pattern Structure of Target Scene in Support of Multiple-Channel ISAR Imagery

This paper presents a multiple-channel ISAR system for multiple air-targets imaging by illuminating a sequence of N narrow and high-gain signal beams over a wide area. Echoes are received by M channels and synthesized into N independent sub-channels using space-time processing technique. The ISAR imaging for each sub-channel is based on the continuity pattern structure technique. Comparing to the conventional ISAR imaging methods, the proposed method can reduce the computational complexity. The numerical results obtained from simulation and experiments demonstrate that the proposed multiple-channel ISAR system has the advantage in detecting multiple air-targets over a wide area and preserving the weak scatterer points comparing to conventional ISAR system.

Analysis of efficiency of space-time signal processing methods in mobile communication systems

Analysis of efficiency of space-time signal processing methods in mobile communication systems

Analysis of the efficiency of space­time access in the mobile communication systems based on an antenna array

We performed analysis of effectiveness of various methods and criteria of space-time processing of the signals by an adaptive antenna array with a view to identifying the algorithm suitable for using in arrangement of space-time access to mobile communication systems. It was shown that all methods are based on the assessment of an integrated vector of weight coefficients, included in the reception tract of every antenna element and controlled by certain algorithms. It was shown that recursive procedures that make it possible to correct the vector of weight coefficients in the dynamic situation, including non-stationary signal-interference situation, are more constructive for using in problems of space-time access. This is especially important for communications with mobile subscriber stations and allows reducing the time for processing calling signals due to the rapid convergence of recursive procedures. A comparative analysis of Widrow-Hoff and Kalman-Bucy algorithms was conducted. It was shown that the Kalman-Bucy procedure, in addition to optimality, in complicated signal-interference situation is characterized by maximally short time of convergence to the sustainable state. The convergence of the procedure is ensured on the time interval, allocated for the action of calling signals of subscriber stations in a mobile network. We proposed the model for studying the influence of initial conditions on the effectiveness of space-time access by the parameter of the convergence rate of the algorithm for adaptive space-time signal processing in an antenna array. It is possible to approximate the vector value to the optimal due to configuration of the integrated vector of weight coefficient based on the use of the information about directions of arrival of calling signals of subscriber stations in a mobile network. The results of the calculations of the indicator of the signal/(interference + noise) ratio on the convergence pitch for different algorithms of an adaptive antenna array were obtained. It was shown that it was possible to improve essentially the transitive characteristics of the algorithms for a linear four-element adaptive antenna array due to the successful initial choice of the value of the integrated vector of weight coefficients. This made it possible to increase the value of the signal/ (interference + noise) ratio at the outlet of an antenna up to 4 dB

CORRELATION METHOD FOR FORMING THE TRAINING SAMPLE FOR ADAPTATION OF THE SPATIAL FILTER

Contex. To ensure noise immunity of modern radar stations, two-stage space-time signal processing is used. However, with simultaneous exposure to active and passive interference, the latter decorrelates the active interference. This significantly limits the noise immunity of coherent-impulse radar stations. Therefore, the formation of a classified training sample, generated only by active noise interference, is quite important task. Objective. The aim of the work is to investigate the correlation method for the formation of a classified learning sample in real time by the current analysis of the interchannel correlation coefficient module over distance in each period of repeating the radar signal. The method is realized by forming an interval synchronous evaluation of both the interchannel correlation coefficient modulus and the spatial filter weight coefficients. In this case, the interval with the maximum value of the interchannel correlation coefficient modulus is defined as the classified training sample, and the weight coefficient formed on this interval is used to adapt the spatial filter weight factor when the active noise interference is compensated in the next period of repeating the signals of the radar. Results. The theoretical and practical aspects of the formation of the classified training sample are considered. It was developed a block diagram of the spatial filter with a correlation analysis of the current passive interference distribution over distance by estimating the interchannel correlation coefficient modulus of the signals acting in the channels of the spatial filter. A mathematical model of the adaptive spatial filter was developed and tested. The possibility of working a spatial filter with the formation of a classified training sample in real time has been confirmed. Conclusions. The scientific novelty of the study is to further develop a new method for the formation of a classified training sample for the adaptation of a spatial filter. It is shown that the current analysis of the module of the interchannel correlation coefficient allows in real time to determine the interval on which there is no passive interference and to form a training sample for adaptation of the weight coefficients of the spatial filter.

Non-homogeneous space-time fractional Poisson processes

The space-time fractional Poisson process (STFPP), defined by Orsingher and Poilto (2012), is a generalization of the time fractional Poisson process (TFPP) and the space fractional Poisson process (SFPP). We study the fractional generalization of the non-homogeneous Poisson process and call it the non-homogeneous space-time fractional Poisson process (NHSTFPP). We compute their pmf and generating function and investigate the associated differential equation. The limit theorems for the NHSTFPP process are studied. We study the distributional properties, the asymptotic expansion of the correlation function of the non-homogeneous time fractional Poisson process (NHTFPP) and subsequently investigate the long-range dependence (LRD) property of a special NHTFPP. We investigate the limit theorem for the fractional non-homogeneous Poisson process (FNHPP) studied by Leonenko et al. (2014). Finally, we present some simulated sample paths of the NHSTFPP process.

A Unified Framework for the Tractable Analysis of Multi-Antenna Wireless Networks

Densifying networks and deploying more antennas at each access point are two principal ways to boost the capacity of wireless networks. However, the complicated distributions of the signal power and the accumulated interference power, largely induced by various space-time processing techniques, make it highly challenging to quantitatively characterize the performance of multi-antenna networks. In this paper, using tools from stochastic geometry, a unified framework is developed for the analysis of such networks. The major results are two innovative representations of the coverage probability, which make the analysis of multi-antenna networks almost as tractable as the single-antenna case. One is expressed as an $\ell_1$-induced norm of a Toeplitz matrix, and the other is given in a finite sum form. With a compact representation, the former incorporates many existing analytical results on single- and multi-antenna networks as special cases, and leads to tractable expressions for evaluating the coverage probability in both ad hoc and cellular networks. While the latter is more complicated for numerical evaluation, it helps analytically gain key design insights. In particular, it helps prove that the coverage probability of ad hoc networks is a monotonically decreasing convex function of the transmitter density and that there exists a peak value of the coverage improvement when increasing the number of transmit antennas. On the other hand, in multi-antenna cellular networks, it is shown that the coverage probability is independent of the transmitter density and that the outage probability decreases exponentially as the number of transmit antennas increases.

METHODS OF JAMMING INTERFERENCE

The article investigates the problem of providing high noise immunity radar under the influence of passive and intentional interference. The purpose of radio operation of the radar is to create conditions that would impede the operation of systems and minimize its effectiveness. The main method of radio transmission is still creating (staging) interference. Modern radar systems must solve the tasks in terms of electronic suppression using, including intentional interference and under severe time constraints. It is shown that the most effective way to improve the noise immunity of radar systems designed to operate in multipoint space, including non-stationary, interference is adaptive space-time processing of the received signals, based on the angular selection of targets, due to the formation of zeros in the directional diagram in the direction of interference sources. This problem is solved by determining the accuracy of the direction finding of interference sources and is achieved by the joint operation of the antenna array and multi-channel signal processing devices, namely the separation of interference signals on different receiving channels.

Adaptive Lattice Filters for Systems of Space-Time Processing of Non-Stationary Gaussian Processes

Adaptive systems protecting pulse radars from non-stationary in time (range) clutter echoes are usually tuned using training vectors composed of complex amplitudes of input signals and comprising a finite-length “sliding window” of data. From any current range gate to a subsequent one, a training sample is partially updated (or modified) by means of excluding the “old” training vectors (correspond to the current range gate) and including the “new” ones (correspond to the next range gate). As a consequence, respective estimates of adaptive system parameters are corrected according to a modified sample correlation matrix (CM), which is typically a sum of an initialCMand a modifying matrix of rank K ≥ 1. In this case it is possible to avoid re-computing these parameters based on a new training sample of full size and, instead of this, we correct them in an “economical” way employing K-rank modification of a matrix inverse to the CM estimate. This paper is devoted to comparative analysis of various (K ≥ 1)-rank modification algorithms that correct the parameters of adaptive lattice filters (ALF). Main attention is paid to synthesis as well as theoretical and experimental study of algorithms of direct (K > 1)-rank modification of the ALF parameters. These algorithms attain the said objective omitting the K-fold application of known rank-one (K = 1) modification algorithms. We also synthesize a combined algorithm (CA) of (K ≥ 1)-rank modification of the ALF parameters that is more computationally simple and more numerically robust compared to known algorithms. The ALF employing the CA can serve as an effective tool for solving various tasks of space-time adaptive signal processing in pulse radars of different purpose.

Space-Time Processing of Object Images in Passive Radio Imaging Systems

This paper describes the concept and methods of space-time processing of radio images of small objects in a multiposition radiometer system, which make it possible to increase the performance of this system. The spatial processing is carried out in each overlook cycle of scanning radiometers in order to determine the spatial coordinates of objects and mutual orientation of coordinate systems. The time processing is carried out in a sequence of overlook cycles of radiometers for determining the trajectory of the objects that change mutual positions.

Measurements of noise energy angular distribution at the building envelope using microphone arrays

This paper presents an experimental procedure for determining the probability density function of incident noise energy angular distribution at the building envelope using a microphone array as a measuring device. The motivation for this analysis is the development of a methodology which would provide an insight into the actual structure of the sound field impeding the façades in urban environments. The procedure is based on spatial source localization using a microphone array mounted on the building façade. The results are presented for one characteristic situation in an urban area using different algorithms for space-time signal processing. It is assumed that measurements in different types of façade surroundings, such as canyon and non-canyon streets, would point to the specificities of energy distributions which can be expected in the given situations.

Drone delivery systems: job assignment and dimensioning

This article studies how to dimension and control at the system level a fleet of autonomous aerial vehicles delivering goods from depots to customers. Customer requests (jobs) arrive according to a space-time stochastic process. We compute a lower bound for the infrastructure expenditure required to achieve a certain expected delivery time. It is shown that job assignment policies can exhibit a tipping point behavior: One vehicle makes the difference between almost optimal delivery time and instability. This phenomenon calls for careful dimensioning of the system. We thus demonstrate the trade-off between financial costs and service quality. We propose a policy that assigns each incoming job to the vehicle that will do the job faster than other ones, seeking to minimize the overall workload in the system in the long term. This policy is scalable with the number of depots and vehicles, performs optimal in low load, and works well up to high loads. Simulations suggest that it stabilizes the system for any load if the number of vehicles per depot is sufficient.

Modeling Temporally Evolving and Spatially Globally Dependent Data

SummaryThe last decades have seen an unprecedented increase in the availability of data sets that are inherently global and temporally evolving, from remotely sensed networks to climate model ensembles. This paper provides an overview of statistical modeling techniques for space–time processes, where space is the sphere representing our planet. In particular, we make a distintion between (a) second order‐based approaches and (b) practical approaches to modeling temporally evolving global processes. The former approaches are based on the specification of a class of space–time covariance functions, with space being the two‐dimensional sphere. The latter are based on explicit description of the dynamics of the space–time process, that is, by specifying its evolution as a function of its past history with added spatially dependent noise.We focus primarily on approach (a), for which the literature has been sparse. We provide new models of space–time covariance functions for random fields defined on spheres cross time. Practical approaches (b) are also discussed, with special emphasis on models built directly on the sphere, without projecting spherical coordinates onto the plane.We present a case study focused on the analysis of air pollution from the 2015 wildfires in Equatorial Asia, an event that was classified as the year's worst environmental disaster. The paper finishes with a list of the main theoretical and applied research problems in the area, where we expect the statistical community to engage over the next decade.

Питання забезпечення сумісної обробки інформації від різнорідних засобів спостереження та розвідки в АСУ військового призначення

Analysis of the conduct of local wars and armed conflicts at the end of the ХХ-th century and the beginning of the XXI century shows that the fighting has become very dynamic, and the use of precision weapons makes it possible to achieve the goal in the shortest possible time. Under these conditions, the struggle for gaining time for planning and fire damage to the enemy (VPU) is extremely acute for both belligerents. Success will accompany someone who will be able to collect and process the necessary information in a short time, make a decision, set tasks and organize the actions of the troops, prepare and strike for certain goals, pull up and introduce reserves in time. We emphasize that the volumes of information that need to be collected, processed and transmitted, are continuously increasing. And this trend will continue in the future.In order to improve the efficiency and quality of command and control of troops and forces in many countries around the world, work is underway to introduce information systems (automated control systems) into management processes. One of the main advantages of their use is the automation of information support processes, that is, the automation of the processes of collecting, accounting, classifying and systematizing data, analyzing and distributing prepared information. In this regard, the issue of ensuring the joint processing of information from diverse means of surveillance and reconnaissance in automated military command and control systems is of particular relevance.In work the principles of processing of complex intelligence information from heterogeneous sources of reconnaissance systems are considered.The task of integrating intelligence and joint processing of intelligence information should be to provide a continuous cycle of automated (automatic) processing of information from the sensor input (space-time processing of primary parameters) to its detailed integrated processing (operational-information processing).The presence of a large number of technical reconnaissance means provides for their integrated application and, accordingly, the complex processing of reconnaissance data (information).Complex processing of intelligence data (information) helps to increase the reliability and accuracy of determining the coordinates of the target. The reconnaissance means have different accuracy in determining the coordinates of the target, and therefore the obtained coordinates will be characterized by unequal middle errors in their determination.In the article it is proved that conducting reconnaissance of one object in three ways simultaneously practically guarantees reliability of determination of its coordinates.

Sequential mean shift algorithms for space–time point data

Principal component mean shift (PCMS) algorithms are well-established methods for denoising and smoothing manifold data. Main fields of application are feature detection and recognition in point data produced by laser scanning, seismic catalogs and remote sensing. Till now, they have been applied to pure spatial processes in 2D or 3D forms, obtaining good estimates of principal curves and surfaces. However, in space–time processes a specific treatment must be devoted to their temporal component. Earthquakes data, in particular, are characterized by the occurrence time which requires a dynamic approach to their smoothing for tectonic fault identification. In this paper, we treat this aspect by developing sequential PCMS algorithms, both in normal and in blurring form, and by dealing with the selection of their smoothing coefficients. Using both real and simulated data, we show that the sequential approach does improve the detection performance of classical PCMS in the presence of complex point clouds. In particular, it turns out to be effective in tracking multiple overlapping curves and nonsmooth corners.

Kerr-de Sitter spacetime, Penrose process, and the generalized area theorem

We investigate various aspects of energy extraction via the Penrose process in the Kerr-de Sitter spacetime. We show that the increase in the value of a positive cosmological constant, $\mathrm{\ensuremath{\Lambda}}$, always reduces the efficiency of this process. The Kerr-de Sitter spacetime has two ergospheres associated with the black hole and the cosmological event horizons. We prove by analyzing turning points of the trajectory that the Penrose process in the cosmological ergoregion is never possible. We next show that in this process both the black hole and cosmological event horizons' areas increase, and the latter becomes possible when the particle coming from the black hole ergoregion escapes through the cosmological event horizon. We identify a new, local mass function instead of the mass parameter, to prove this generalized area theorem. This mass function takes care of the local spacetime energy due to the cosmological constant as well, including that which arises due to the frame-dragging effect due to spacetime rotation. While the current observed value of $\mathrm{\ensuremath{\Lambda}}$ is quite small, its effect in this process could be considerable in the early Universe scenario where its value is much larger, where the two horizons could have comparable sizes. In particular, the various results we obtain here are also evaluated in a triply degenerate limit of the Kerr-de Sitter spacetime we find, in which radial values of the inner, the black hole and the cosmological event horizons are nearly coincident.

Method of Cumulative Estimation of the Parameters of Information Flows in the Radio Channels of Information Telecommunication Systems

The method of cumulative estimation of the parameters of information flows in the radio channels of information telecommunication systems is considered. Estimation is performed under the conditions of a complex information target situation based on a comparison of the indicated parameters with a simulated reference measure. It is proposed that the simulated directional pattern of an adaptive antenna system that implements a space-time processing algorithm be used as the measure. It is shown that the use of phase and correlation methods of simulation of a measure assures a high degree of precision of estimation of the parameters. Estimators may be obtained on a time scale close to real time through the use of the present highly efficient procedure.

A Statistical Model of Equivalent Grinding Heat Source Based on Random Distributed Grains

Accurate information about the evolution of the temperature field is a theoretical prerequisite for investigating grinding burn and optimizing the process parameters of grinding process. This paper proposed a new statistical model of equivalent grinding heat source with consideration of the random distribution of grains. Based on the definition of the Riemann integral, the summation limit of the discrete point heat sources was transformed into the integral of a continuous function. A finite element method (FEM) simulation was conducted to predict the grinding temperature field with the embedded net heat flux equation. The grinding temperature was measured with a specially designed in situ infrared system and was formulated by time–space processing. The reliability and correctness of the statistical heat source model were validated by both experimental temperature–time curves and the maximum grinding temperature, with a relative error of less than 20%. Finally, through the FEM-based inversed calculation, an empirical equation was proposed to describe the heat transfer coefficient (HTC) changes in the grinding contact zone for both conventional grinding and creep feed grinding.

The Root solution to the multi-marginal embedding problem: an optimal stopping and time-reversal approach

We provide a complete characterisation of the Root solution to the Skorokhod embedding problem (SEP) by means of an optimal stopping formulation. Our methods are purely probabilistic and the analysis relies on a tailored time-reversal argument. This approach allows us to address the long-standing question of a multiple marginals extension of the Root solution of the SEP. Our main result establishes a complete solution to the n-marginal SEP using first hitting times of barrier sets by the time–space process. The barriers are characterised by means of a recursive sequence of optimal stopping problems. Moreover, we prove that our solution enjoys a global optimality property extending the one-marginal Root case. Our results hold for general, one-dimensional, martingale diffusions.

Characterizing Diffusion Dynamics of Disease Clustering: A Modified Space–Time DBSCAN (MST-DBSCAN) Algorithm

Epidemic diffusion is a space–time process, and showing time-series disease maps is a common way to demonstrate an epidemic progression in time and space. Previous studies used time-series maps to demonstrate the animation of diffusion process. Epidemic diffusion patterns were determined subjectively by visual inspection, however. There currently are still methodological concerns in developing effective analytical approaches for profiling diffusion dynamics of disease clustering and epidemic propagation. The objective of this study is to develop a geocomputational algorithm, the modified space–time density-based spatial clustering of application with noise (MST-DBSCAN), for detecting, identifying, and visualizing disease cluster evolution, which takes the effect of the incubation period into account. We also map the MST-DBSCAN algorithm output to visualize the diffusion process. Dengue fever case data from 2014 were used as an illustrative case study. Our results show that compared to kernel-smoothed mapping, the MST-DBSCAN algorithm can better identify the evolution type of any cluster at any epoch. Furthermore, using only one two-dimensional map (and graphs), our approach can demonstrate the same diffusion process that time-series maps or three-dimensional space–time kernel plotting displays but in an easy-to-read manner. We conclude that our MST-DBSCAN algorithm can profile the spatial pattern of epidemic diffusion in detail by identifying disease cluster evolution.