Auto-regressive model based polarimetric adaptive detection scheme part I: Theoretical derivation and performance analysis

This paper deals with the problem of target detection in coherent radar systems exploiting polarimetric diversity. We resort to a parametric approach and we model the disturbance affecting the data as a multi-channel autoregressive (AR) process. Following this model, a new polarimetric adaptive detector is derived, which aims at improving the target detection capability while relaxing the requirements on the training data size and the computational burden with respect to existing solutions. A complete theoretical characterization of the asymptotic performance of the derived detector is provided, using two different target fluctuation models. The effectiveness of the proposed approach is shown against simulated data, in comparison with alternative existing solutions

Multitarget Joint Delay and Doppler Shift Estimation in Bistatic Passive Radar

Bistatic passive radar (BPR) system does not transmit any electromagnetic signal unlike the active radar, but employs an existing Illuminator of opportunity (IO) in the environment, for instance, a broadcast station, to detect and track the targets of interest. Therefore, a BPR system is comprised of two channels. One is the reference channel that collects only the IO signal, and the other is the surveillance channel which is used to capture the targets\u27 reflected signals. When the IO signal reflected from multiple targets is captured in the surveillance channel (SC) then estimating the delays and Doppler shifts of all the observed targets is a challenging problem. For BPR system, the signal processing algorithms developed so far models the IO waveform as a deterministic process and discretizes the delays and Doppler shifts parameters. In this thesis, we deal with the problem of jointly estimating the delays and Doppler shifts of multiple targets in a BPR system (i.e., a two channel system) when the unknown IO signal is modeled as a correlated stochastic process. Unlike the previous work, we take all the delays and Doppler shifts as continuous-valued parameters to avoid straddle loss due to discretization and propose a computationally efficient Expectation-Maximization (EM) based algorithm that breaks up the complex multidimensional maximum likelihood optimization problem into multiple separate optimization problems. The EM algorithm jointly provides the estimates of all the delays and Doppler shifts of the targets along with the estimate of each target\u27s component signal in the SC and the estimate of the unknown IO signal. We also derive the Cramer-Rao lower bound for the considered multitarget estimation problem with stochastic IO signal. Numerical simulations are presented where we compare our proposed EM-based multi-target estimator with the widely used conventional cross correlation estimator under different multitarget environments

Fault Detection for Systems with Multiple Unknown Modes and Similar Units

This dissertation considers fault detection for large-scale practical systems with many nearly identical units operating in a shared environment. A special class of hybrid system model is introduced to describe such multi-unit systems, and a general approach for estimation and change detection is proposed. A novel fault detection algorithm is developed based on estimating a common Gaussian-mixture distribution for unit parameters whereby observations are mapped into a common parameter-space and clusters are then identified corresponding to different modes of operation via the Expectation- Maximization algorithm. The estimated common distribution incorporates and generalizes information from all units and is utilized for fault detection in each individual unit. The proposed algorithm takes into account unit mode switching, parameter drift, and can handle sudden, incipient, and preexisting faults. It can be applied to fault detection in various industrial, chemical, or manufacturing processes, sensor networks, and others. Several illustrative examples are presented, and a discussion on the pros and cons of the proposed methodology is provided. The proposed algorithm is applied specifically to fault detection in Heating Ventilation and Air Conditioning (HVAC) systems. Reliable and timely fault detection is a significant (and still open) practical problem in the HVAC industry { commercial buildings waste an estimated 15% to 30% ($20.8B -$41.61B annually) of their energy due to degraded, improperly controlled, or poorly maintained equipment. Results are presented from an extensive performance study based on both Monte Carlo simulations as well as real data collected from three operational large HVAC systems. The results demonstrate the capabilities of the new methodology in a more realistic setting and provide insights that can facilitate the design and implementation of practical fault detection for systems of similar type in other industrial applications

Radio Channel Prediction Based on Parametric Modeling

Long range channel prediction is a crucial technology for future wireless communications. The prediction of Rayleigh fading channels is studied in the frame of parametric modeling in this thesis. Suggested by the Jakes model for Rayleigh fading channels, deterministic sinusoidal models were adopted for long range channel prediction in early works. In this thesis, a number of new channel predictors based on stochastic sinusoidal modeling are proposed. They are termed conditional and unconditional LMMSE predictors respectively. Given frequency estimates, the amplitudes of the sinusoids are modeled as Gaussian random variables in the conditional LMMSE predictors, and both the amplitudes and frequency estimates are modeled as Gaussian random variables in the unconditional LMMSE predictors. It was observed that a part of the channels cannot be described by the periodic sinusoidal bases, both in simulations and measured channels. To pick up this un-modeled residual signal, an adjusted conditional LMMSE predictor and a Joint LS predictor are proposed. Motivated by the analysis of measured channels and recently published physics based scattering SISO and MIMO channel models, a new approach for channel prediction based on non-stationary Multi-Component Polynomial Phase Signal (MC-PPS) is further proposed. The so-called LS MC-PPS predictor models the amplitudes of the PPS components as constants. In the case of MC-PPS with time-varying amplitudes, an adaptive channel predictor using the Kalman filter is suggested, where the time-varying amplitudes are modeled as auto-regressive processes. An iterative detection and estimation method of the number of PPS components and the orders of polynomial phases is also proposed. The parameter estimation is based on the Nonlinear LS (NLLS) and the Nonlinear Instantaneous LS (NILS) criteria, corresponding to the cases of constant and time-varying amplitudes, respectively. The performance of the proposed channel predictors is evaluated using both synthetic signals and measured channels. High order polynomial phase parameters are observed in both urban and suburban environments. It is observed that the channel predictors based on the non-stationary MC-PPS models outperform the other predictors in Monte Carlo simulations and examples of measured urban and suburban channels

A frequency domain test for propriety of complex-valued vector time series

This paper proposes a frequency domain approach to test the hypothesis that a stationary complexvalued vector time series is proper, i.e., for testing whether the vector time series is uncorrelated with its complex conjugate. If the hypothesis is rejected, frequency bands causing the rejection will be identified and might usefully be related to known properties of the physical processes. The test needs the associated spectral matrix which can be estimated by multitaper methods using, say, K tapers. Standard asymptotic distributions for the test statistic are of no use since they would require K → ∞, but, as K increases so does resolution bandwidth which causes spectral blurring. In many analyses K is necessarily kept small, and hence our efforts are directed at practical and accurate methodology for hypothesis testing for small K. Our generalized likelihood ratio statistic combined with exact cumulant matching gives very accurate rejection percentages. We also prove that the statistic on which the test is based is comprised of canonical coherencies arising from our complex-valued vector time series. Frequency specific tests are combined using multiple hypothesis testing to give an overall test. Our methodology is demonstrated on ocean current data collected at different depths in the Labrador Sea. Overall this work extends results on propriety testing for complex-valued vectors to the complex-valued vector time series setting