Disturbance Covariance Matrix Research Articles

Wald Test for Adaptive Array Detection With General Configuration

Assume that a modern radar system has a general antenna array configuration consisting of primary channels with high-gain beams and reference channels with low-gain beams. We consider the target detection problem for such array radar systems in Gaussian disturbance with unknown covariance matrix. An adaptive detector is proposed according to the criterion of Wald test. The statistical properties of the proposed detector are provided in the mismatched case, where the nominal target steering vector may not be aligned with the true target steering vector. An analytical expression for the probability of false alarm is derived, which reveals that the proposed detector has a constant false alarm rate property with respect to the disturbance covariance matrix. Moreover, a closed-form expression for the detection probability is obtained in the mismatched case. Simulation results demonstrate that the proposed detector exhibits strong robustness against the target steering vector mismatch.

Improved Model-Based Rao and Wald Test for Adaptive Range-Spread Target Detection

This article addresses the problem of the detection of range-spread targets in the presence of Gaussian disturbance which are in possession of unidentified covariance matrices. The detectors have been derived by resorting to a design composed of two steps. Based on the Rao test and Wald test, the corresponding strategies of detection were respectively derived, assuming the expression of disturbance covariance matrix has been obtained. Afterwards, the unknown parameters in the detectors were estimated on the basis of both the primary and the training data, utilizing the autoregressive property of the disturbance. A remarkable characteristic of the Rao and Wald detectors is they both asymptotically attain constant false-alarm rate (CFAR) in respect of the disturbance covariance matrix. Finally, we completed a performance assessment by utilizing the simulated data, and the result demonstrated the effectiveness of the existing proposals compared with the detectors previously proposed.

Performance Analysis of the Generalized Likelihood Ratio Test in General Phased Array Radar Configuration

We consider a modern radar system which has a general antenna array configuration consisting of primary channels with high-gain beams and reference channels with low-gain beams. A generalized likelihood ratio test (GLRT) was proposed in this context for target detection and direction of arrival estimation. However, the analytical performance of the GLRT has not been provided yet. In this paper, we derive finite-sum expressions for the probabilities of false alarm and detection. It is proven that the GLRT exhibits a constant false alarm rate against the overall interference disturbance covariance matrix. Numerical examples show that the detection performance of the GLRT may not necessarily improve when the number of sensors increases

A Novel Post-Doppler Parametric Adaptive Matched Filter for Airborne Multichannel Radar

The post-Doppler adaptive matched filter (PD-AMF) with constant false alarm rate (CFAR) property was developed for adaptive detection of moving targets, which is a standardized version of the post-Doppler space–time adaptive processing (PD-STAP) in practical applications. However, its detection performance is severely constrained by the training data, especially in a dense signal environment. Improper training data and contamination of moving target signals remarkably degrade the performance of disturbance suppression and result in target cancellation by self-whitening. To address these issues, a novel post-Doppler parametric adaptive matched filter (PD-PAMF) detector is proposed in the range-Doppler domain. Specifically, the detector is introduced via the post-Doppler matched filter (PD-MF) and the lower-diagonal-upper (LDU) decomposition of the disturbance covariance matrix, and the disturbance signals of the spatial sequence are modelled as an auto-regressive (AR) process for filtering. The purpose of detecting ground moving targets as well as for estimating their geographical positions and line-of-sight velocities is achieved when the disturbance is suppressed. The PD-PAMF is able to reach higher performances by using only a smaller training data size. More importantly, it is tolerant to moving target signals contained in the training data. The PD-PAMF also has a lower computational complexity. Numerical results are presented to demonstrate the effectiveness of the proposed detector.

An Information Elasticity Framework for the Adaptive Matched Filter

The adaptive matched filter (AMF) uses a number of training samples observed by the radar to estimate the unknown disturbance covariance matrix of a cell under test. In general, as the number of homogeneous training samples increases, the detection performance of the AMF improves up to a theoretical limit (defined by the performance of a matched filter detector where the disturbance covariance is known). However, radar data are nonhomogeneous in practice. Consequently, a high number of training samples is typically undesirable, since nonhomogeneous training data cause detection performance to suffer. Thus, a decision maker (DM) must consider these tradeoffs when selecting this number of training samples, along with other decision parameters for the AMF. Using the concept of information elasticity, this tradeoff behavior is characterized for decisions that are relevant to a DM. A simple user defined constraint function is proposed, characterizing the relative cost of selecting different decisions. Using a multi-objective optimization (MOO) technique known as compromise programming, information overload is observed, in that increasing the cost of decisions improves performance up to a point, beyond which increasing the cost no longer provides meaningful benefit. Using this framework, a cost-efficient solution is selected.

Tunable Adaptive Target Detection With Kernels in Colocated MIMO Radar

We introduce a framework for exploring adaptive target detection in colocated MIMO radar in non-linear feature space by exploiting the theory of kernel. The kernel theory inspires us to replace the inner products of test statistics with that of nonlinear mapped data in the feature space or that of their kernel tricks to achieve better detection performance. We apply this framework to the problem of tunable adaptive target detection in colocated MIMO radar, according to the principle of the generalized likelihood ratio (GLR), Rao and Wald (RaW) tests, and propose several new detectors under two new tunable detector forms, namely kernel tunable GLR-based and kernel tunable Raw-based detectors. The proposed tunable detectors include most of the prior detectors in colocated MIMO radar as special cases. One capability of the proposed detectors is that their robustness or selectivity (RoS) to steering vector mismatch (SVM) can be tuned flexibility through an RoS tuning parameter. In addition, we are able to incorporate the prior distribution (PD) of the disturbance covariance matrix, if available, through a PD tuning parameter. Therefore, the proposed detectors can be tuned based on the tuning RoS parameter to achieve robust or selective performance in the presence of SVM as well as to switch between the Bayesian or non-Bayesian based detectors through the PD parameter. For practical situations, we show that the proposed detectors possess CFAR property against disturbance covariance matrix by resorting to the invariance principle. Extensive Monte Carlo simulation results are provided to indicate that the proposed detectors have better detection performance than their counterparts in both single-target and multi-target scenarios.

Model-Based Wald Test for Adaptive Range-Spread Target Detection

For the problem of range-spread target detection, many adaptive detectors commonly estimate the covariance matrix of the disturbance by utilizing the training data without target information. However, in the limited-training case, the conventional detectors suffer significant performance degradation. This paper devises and assesses a model-based Wald detector by modeling the disturbance as an autoregressive (AR) process with unknown parameters, which is able to overcome the detection degradation caused by insufficient training data. Meanwhile, the Wald test reduces the computational complexity because the unknown parameters are only estimated by maximum likelihood criterion under hypothesis that the target exists. Remarkably the asymptotic expression for the probability of detection and false alarm shows the detector is asymptotically constant false alarm rate (CFAR) with respect to the disturbance covariance matrix. The performance evaluation, conducted by resorting to simulation data, has confirmed the effectiveness of the current proposal in comparison with the previously proposed detectors.

Investigating Factors Affecting Import Demand of Meat and Livestock Inputs in Iran

Introduction Despite the relative advantage of producing some agricultural products, Iran is one of the largest importers of agricultural sector, so the total agricultural imports in 2016 were about 8.78 billion dollars. One of the most imported products is red meat and livestock inputs. Animal corn is the first imported product of Iran and is one of the most important livestock feed. Due to the low level of domestic production of animal corn, large quantity of it is imported every year. Soybean meal is also the fourth-largest imported agricultural product and the seventh product of the country's import. High dependence on the import of red meat and livestock inputs and the lack of domestic production of these products in Iran have caused any change in import policy of these products will affect the welfare of many producers and consumers. Due to the close relationship between import of these products and food security and the welfare of the society, recognizing the factors affecting the import demand of these products is important to proper policy making in livestock sector. In fact, the import demand function in developing economies should be investigated because it has significant effects on the international trade policy in general and the exchange rate policy in particular. Materials and Methods In this study, contrary to previous studies which considered only a few factors, it was investigated the effects of tariff rate, GDP, real effective exchange rate, domestic production and relative price of imported products on the import demand of veal, lamb, chicken, animal corn and soybean meal. Due to correlation between the disturbance term in different equations, it was used the simultaneous equations method and also it was used imperfect substitution approach to derive import demand function. For this purpose, monthly data from April 2010 to March of 2016 has been used. To determine the appropriate estimator, Hegy test and diagonal disturbance covariance matrix test was used. In order to investigate co-integration, the Johansen-Juselius test was used for each import demand equation. Additionally, it was used Engle ARCH LM heteroscedasticity test and Harvey LM autocorrelation test for all equations. Results showed that there is no heteroscedasticity and autocorrelation in the system. Results and Discussion Based on results there was a long run relationship between variables in veal, lamb, chicken, animal corn and soybean meal equation. Results showed that all the variables in the import demand equations including veal, lamb, animal corn and soybean meal has been expected signs. Also results showed that in the equation of veal import demand, the coefficients of tariff rate and relative price was negative and significant. In the equation of lamb import demand, the coefficient of domestic production of veal was negative and significant. Moreover, in the equation of animal corn import demand, the coefficients of tariff rate and real effective exchange rate were negative and significant. Eventually in the equation of soybean meal import demand, the coefficients of tariff rate, real effective exchange rate and relative price were negative and significant. Therefore, it can be noted that due to high dependence on imports of livestock inputs, especially animal corn and soybean meal, it is decided every year to import these inputs only basis of factors such as tariff rate, real effective exchange rate and relative price. Suggestion Based on results which showed that tariff rate has significant effect on the import demand of veal, animal corn and soybean meal, it is helpful to use this tool to control the import quantity of veal, animal corn and soybean meal, whereas changing tariff rate to control the import quantity of lamb do not have much effect. Also, it was found that the import demand for livestock inputs was highly elastic to change in real effective exchange rate. So, it is necessary to prevent unreasonable increase in exchange rate and its fluctuations. Since, it was found that the lamb import demand was highly elastic to domestic production, it is recommended to adopt policies to increase production of lamb through the provision of livestock inputs required by producers. JEL Classification: F12, F31, F41

Detection of subspace distributed target in partial observation scenario with Rao test

This paper deals with the problem of detecting a subspace distributed target obscured by disturbance consisting of clutter plus white noise. We focus on the partial observation scenario where some of the radar observations are missing, a phenomenon that usually caused by interference, spectrum sharing, compressed sampling, and so on. Detection strategies are established based on the Rao test. Specifically, we first derive the Rao test with the assumption that the disturbance covariance matrix under the null hypothesis is known. Then, the unknown covariance matrix in the test statistic is replaced with a suitable estimate to make the detector adaptive. At the estimation stage, two cases are considered, involving with and without disturbance only secondary data. The estimate of the disturbance covariance matrix is obtained by solving an optimization problem in the respective case that considers both the likelihood maximization and low-rank property of the clutter covariance matrix. Simulation results are presented to verify the effectiveness of the proposed method.

Persymmetric Rao test for MIMO radar in Gaussian disturbance

This paper considers the target detection problem in multiple-input multiple-output radar where the disturbance covariance matrix is unknown. Based on the Rao criterion, a persymmetric Rao test is designed by exploiting the persymmetric structure of the disturbance covariance matrix. Particularly, the proposed detector does not require training data, and exhibits strong selectivity to mismatched signals. Another contribution in this paper is to propose a two-stage detector whose second stage coincides with the proposed persymmetric Rao test. The selectivity or robustness of the two-stage detector can be tuned by selecting different threshold pairs.

A class of periodic trend models for seasonal time series

AbstractTrend and seasonality are the most prominent features of economic time series that are observed at the subannual frequency. Modeling these components serves a variety of analytical purposes, including seasonal adjustment and forecasting. In this paper we introduce unobserved components models for which both the trend and seasonal components arise from systematically sampling a multivariate transition equation, according to which each season evolves as a random walk with a drift. By modeling the disturbance covariance matrix we can encompass traditional models for seasonal time series, like the basic structural model, and can formulate more elaborate ones, dealing with season specific features, such as seasonal heterogeneity and correlation, along with the different role of the nonstationary cycles defined at the fundamental and the harmonic frequencies in determining the shape of the seasonal pattern.

Persymmetric GLRT Detection in MIMO Radar

The problem of target detection in colocated multiple-input multiple-output radar with unknown disturbance covariance matrix is considered. According to the generalized likelihood ratio test, we design an adaptive detector by exploiting the persymmetric structure of the covariance matrix. In particular, training data are not required in the proposed adaptive detector. Analytical expressions for the probability of false alarm and detection probability are derived, which are confirmed by Monte Carlo simulations. The expression for the probability of false alarm shows that the proposed detector exhibits a constant false alarm rate property against the disturbance covariance matrix. Numerical examples based on both simulated and experimental data confirm that the proposed detector has better detection performance than its counterparts.

Target detection exploiting covariance matrix structures in MIMO radar

Abstract We aim to address the problem of target detection in collocated multiple-input multiple-output (MIMO) radar where the disturbance covariance matrix is unknown. In practice, the disturbance covariance matrix has a persymmetric or Toeplitz structure, when the MIMO radar receiver is equipped with a symmetrically or uniformly spaced linear array. We exploit the persymmetric or Toeplitz structure of the disturbance covariance matrix to design two adaptive detectors that do not require training data. Analytical expressions for the probability of false alarm and detection probability are derived for the proposed detector that takes the persymmetry into account. Numerical examples are provided to show that the proposed detectors outperform the conventional counterparts.

China's increasing global influence: Changes in international growth linkages

Changes in linkages between growth in the USA, Euro area and China are investigated utilising an iterative procedure for detecting structural breaks in VAR coefficients and disturbance covariance matrix. We find dynamics to be unchanged and, accounting for volatility changes, cross-country correlations are constant until the end of 2007. Although largely isolated from the other large economies until 2007, growth in China is subsequently strongly related to that of the US and the Euro area. The effects are illustrated using generalised impulse responses and forecast error variance decompositions. The increased international synchronisation found may be associated with the effects of the Great Recession on the US and Euro area together with China's extraordinary export growth since joining the World Trade Organisation in 2001.

Distributed Target Detection With Partial Observation

This paper considers the detection of a distributed target in a partial observation scenario. A distributed target model is usually adopted when the target size is larger than the range bin, for example, in some high-resolution radars. Based on the distributed target model, joint processing of several consecutive range bins can be adopted to achieve performance improvement with respect to processing just one range bin. In applications in complex electromagnetic environments, the radars may miss some of their observations, a phenomenon that usually caused by interference, spectrum sharing, and so on. This partial observation problem leads to degradation of the estimation accuracy for the disturbance (clutter plus noise) covariance matrix and target amplitude vector, which results in decline of the target detection performance. In this paper, a scheme is proposed by using the low-rank priori knowledge of clutter covariance matrix to estimate the detector's unknown parameters. Specifically, the target amplitude vector is obtained by maximizing the likelihood function, and the disturbance covariance matrix is reconstructed by solving an optimization that considers both the likelihood maximization and low-rank property of the clutter covariance matrix. The simulation results indicate that this algorithm improves the estimation accuracy, and achieves a better detection performance in the partial observation scenarios.

Tunable Adaptive Detection in Colocated MIMO Radar

We consider the adaptive target detection problem in colocated MIMO radar where disturbance covariance matrix is unknown, and no training data are available. A tunable detector is proposed, which includes the Rao and Wald tests as special cases. The selectivity or robustness of the proposed detector to mismatched signals can be flexibly tuned by adjusting the tuning parameter. An equivalent form of the proposed detector is obtained to provide a deeper insight into how the selectivity or robustness is adjusted by selecting the tuning parameter. We derive analytical expressions for the probability of false alarm and the detection probability to evaluate its detection performance in both matched and mismatched steering vector cases. It is shown that the proposed detector bears a constant false alarm rate property with respect to the disturbance covariance matrix. Numerical results reveal that the selectivity of the proposed detector can be enhanced by increasing the value of the tuning parameter.

Model-based Rao test for adaptive range-spread target detection

This paper deals with the problem of detecting range-spread target in Gaussian disturbance with unknown covariance matrix. A model-based Rao detector is derived by modeling the disturbance as an autoregressive (AR) process with unknown parameters. Meanwhile, the asymptotic expressions for the probabilities of false alarm and detection are derived in closed form, which show that the newly proposed detector is asymptotically constant false alarm rate with respect to the disturbance covariance matrix. The performance assessment conducted by resorting to the simulated data, also in comparison to the previously proposed detectors, has confirmed the effectiveness of the newly proposed detectors.

Suboptimal Anisotropy-based Control for Linear Discrete Time Varying Systems with Noncentered Disturbances

This paper is concerned with a γ-optimal control for linear discrete time varying systems on bounded time intervals driven by statistically uncertain random disturbances with nonzero mean values. The uncertainty is described in information theoretic terms using a previously introduced anisotropy functional. It is shown that, under additional constraints on the mean value and the covariance matrix of the input disturbance, the γ-optimal anisotropy-based controller design problem can be reduced to a multiobjective control problem. In comparison with the original anisotropy-based control setting, which uses the anisotropic norm of a system as a performance criterion, the suboptimal control approach, considered in the present paper, employs a modified version of the norm. The modified anisotropic norm is related to the original norm at a reduced anisotropy level and the H∞-norm of the system. Using this connection, we obtain sufficient conditions for γ-optimal anisotropy-based control. The resulting controller involves the solution of a certain convex optimization problem. A numerical example is presented in order to demonstrate the method proposed.

ADMISSIBLE SIGNIFICANCE TESTS IN SIMULTANEOUS EQUATION MODELS

Consider testing the null hypothesis that a single structural equation has specified coefficients. The alternative hypothesis is that the relevant part of the reduced form matrix has proper rank, that is, that the equation is identified. The usual linear model with normal disturbances is invariant with respect to linear transformations of the endogenous and of the exogenous variables. When the disturbance covariance matrix is known, it can be set to the identity, and the invariance of the endogenous variables is with respect to orthogonal transformations. The likelihood ratio test is invariant with respect to these transformations and is the best invariant test. Furthermore it is admissible in the class of all tests. Any other test has lower power and/or higher significance level. In particular, this likelihood ratio test dominates a test based on the Two-Stage Least Squares estimator.

A Geometric Approach to Covariance Matrix Estimation and its Applications to Radar Problems

A new class of disturbance covariance matrix estimators for radar signal processing applications is introduced following a geometric paradigm. Each estimator is associated with a given unitary invariant norm and performs the sample covariance matrix projection into a specific set of structured covariance matrices. Regardless of the considered norm, an efficient solution technique to handle the resulting constrained optimization problem is developed. Specifically, it is shown that the new family of distribution-free estimators shares a shrinkagetype form; besides, the eigenvalues estimate just requires the solution of a one-dimensional convex problem whose objective function depends on the considered unitary norm. For the two most common norm instances, i.e., Frobenius and spectral, very efficient algorithms are developed to solve the aforementioned one-dimensional optimization leading to almost closed form covariance estimates. At the analysis stage, the performance of the new estimators is assessed in terms of achievable Signal to Interference plus Noise Ratio (SINR) both for a spatial and a Doppler processing assuming different data statistical characterizations. The results show that interesting SINR improvements with respect to some counterparts available in the open literature can be achieved especially in training starved regimes.