On the testing hypothesis in uniform family of distributions with nuisance parameter

The problem of finding optimal tests in the family of uniform distributions is investigated. The general forms of the uniformly most powerful and generalized likelihood ratio tests are derived. Moreover, the problem of finding the uniformly most powerful unbiased test for testing two-sided hypothesis in the presence of nuisance parameter is investigated, and it is shown that such a test is equivalent to the generalized likelihood ratio test for the same problem. The simulation study is performed to evaluate the performance of power function of the tests.

Radar-Based, Simultaneous Human Presence Detection and Breathing Rate Estimation

Human presence detection is an application that has a growing need in many industries. Hotel room occupancy is critical for electricity and energy conservation. Industrial factories and plants have the same need to know the occupancy status to regulate electricity, lighting, and energy expenditures. In home security there is an obvious necessity to detect human presence inside the residence. For elderly care and healthcare, the system would like to know if the person is sleeping in the room, sitting on a sofa or conversely, is not present. This paper focuses on the problem of detecting presence using only the minute movements of breathing while at the same time estimating the breathing rate, which is the secondary aim of the paper. We extract the suspected breathing signal, and construct its Fourier series (FS) equivalent. Then we employ a generalized likelihood ratio test (GLRT) on the FS signal to determine if it is a breathing pattern or noise. We will show that calculating the GLRT also yields the maximum likelihood (ML) estimator for the breathing rate. We tested this algorithm on sleeping babies as well as conducted experiments on humans aged 12 to 44 sitting on a chair in front of the radar. The results are reported in the sequel.

Using extended Kalman filter for failure detection and prognostic of degradation process in feedback control system

In this article, we study a new approach to predict failures in feedback control system and particularly in actuators. However, we use two-tank control system with a proportional–integral–derivative controller for controlling a process variable. In practice, the actuator is a dynamic operating component in a random environment. Moreover, its capacity decreases over time and becomes valuable information for reliability analysis. The loss of capacity which is related to degradation, either normally or in an accelerated manner, depends on different operational conditions of the feedback control system and environmental factors. For this reason, to improve its working condition, a service life time analysis is necessary. Obviously, one has to predict the trend of future system characteristics, such as the reliability, which is measured by the estimate value of remaining useful life. In this situation, we use the stochastic gamma process model to describe the degradation behavior of the actuator. Generally, the algorithm of extended Kalman filter is a widely used method to overcome the difficulties of estimating the state vector in a nonlinear model of two-tank control system. This algorithm gives an innovation vector or prediction residual which contains fault information, when the system is failed. The prediction residuals can be recursively computed for diagnosis by the generalized likelihood ratio test. However, we use the generalized likelihood ratio test algorithm to estimate the moment at which the prognostic started. Finally, a practical case study is given to show the effectiveness of the proposed approaches for failure detection. Obviously, the simulation results show that the degradation path of the actuator capacity is estimated and the reliability based on remaining useful life predicted is analyzed.

Adaptive Waveform Design with Multipath Exploitation Radar in Heterogeneous Environments

The problem of detecting point like targets over a glistening surface is investigated in this manuscript, and the design of an optimal waveform through a two-step process for a multipath exploitation radar is proposed. In the first step, a non-adaptive waveform is transmitted anda constrained Generalized Likelihood Ratio Test (GLRT) detector is deduced at reception which exploits multipath returns in the range cell under test by modelling the target echo as a superposition of the direct plus the multipath returns. Under the hypothesis of heterogeneous environments, thus by assuming a compound-Gaussian distribution for the clutter return, this latter is estimated in the range cell under test through the secondary data, which are collected from the out-of-bin cells. The Fixed Point Estimate (FPE) algorithm is applied in the clutter estimation, then used to design the adaptive waveform for transmission in the second step of the algorithm, in order to suppress the clutter coming from the adjacent cells. The proposed GLRT is also used at the end of the second transmission for the final decision. Extensive performance evaluation of the proposed detector and adaptive waveform for various multipath scenarios is presented. The performance analysis prove that the proposed method improves the Signal-to-Clutter Ratio (SCR) of the received signal, and the detection performance with multipath exploitation.

Robust Spectrum Sensing Detector Based on MIMO Cognitive Radios with Non-Perfect Channel Gain

The spectrum has increasingly become occupied by various wireless technologies. For this reason, the spectrum has become a scarce resource. In prior work, the authors have addressed the spectrum sensing problem by using multi-input and multi-output (MIMO) in cognitive radio systems. We considered the detection and estimation framework for MIMO cognitive network where the noise covariance matrix is unknown with perfect channel state information. In this study, we propose a generalized likelihood ratio test (GLRT) for the spectrum sensing problem in cognitive radio where the noise covariance matrix is unknown with non-perfect channel state information. Two scenarios are examined in this study: (i) in the first scenario, the sub-optimal solution of the worst case of the system’s performance is considered; (ii) in the second scenario, we present a robust detector for the MIMO spectrum sensing problem. For both scenarios, the Bayesian approach with a generalized likelihood ratio test based on the binary hypothesis problem is used. From the results, it can be seen that our approach provides the best performance in the spectrum sensing problem under specified assumptions. The simulation results also demonstrate that our approach significantly outperforms other state-of-the-art spectrum sensing detectors when the channel uncertainty is addressed.