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The problems of stationary robust L ∞ -induced filtering and deconvolution are addressed for discrete-time linear systems with deterministic and stochastic uncertainties in the state–space model. Stochastic uncertainties are in the form of state- and input-dependent multiplicative white noises which appear in both state and the measurement equations. The deterministic part of the system matrices and covariance matrices of the stochastic parameters is unknown and resides in a given polytopic-type domain. For this system a new lemma is derived which characterizes the induced L ∞ norm disturbance attenuation performance by linear matrix inequalities (LMIs). According to this lemma, the problem of estimator design is solved for stochastic uncertain systems based on the notion of quadratic stability. To further reduce the overdesign in the quadratic framework, this paper also proposes a parameter-dependent design procedure, which is much less conservative than the quadratic approach. The proposed estimators guarantee the mean-square exponential stability of estimation error dynamics and satisfy the prescribed induced L ∞ performance index. Two examples are used to demonstrate the proposed methods and their effectiveness. [ABSTRACT FROM AUTHOR]

Azimuthal angles and Doppler frequencies of radar targets usually suffer from estimation uncertainty in practice, which poses a big challenge in target detection. In this work, we consider the problem of target detection in the presence of uncertainty in the azimuthal angle and Doppler frequency. This uncertainty is characterized by a subspace model. Precisely, the spatial and temporal steering vectors of the target are assumed to lie in certain known subspaces but with unknown coordinates. Two detectors are devised in the framework of generalized likelihood ratio test. Moreover, the properties of the proposed detectors are derived for the case of sufficiently large training data. It is shown by numerical examples that the detector derived according to the one-step design procedure has higher probability of detection than its counterparts in the absence of signal mismatch, while the detector devised according to the two-step design procedure is most robust to the signal mismatch. [ABSTRACT FROM AUTHOR]

Abstract: This paper addresses the design of robust weighted fusion Kalman filters for multisensor time-varying systems with uncertainties of noise variances. Using the minimax robust estimation principle and the unbiased linear minimum variance (ULMV) optimal estimation rule, the five robust weighted fusion time-varying Kalman filters are presented based on the worst-case conservative systems with the conservative upper bounds of noise variances. The actual filtering error variances or their traces of each fuser are guaranteed to have a minimal upper bound for all the admissible uncertainties of noise variances. A Lyapunov equation approach is presented to prove the robustness of the robust Kalman filters. The concept of robust accuracy is presented and the robust accuracy relations among the local and fused robust Kalman filters are proved. Specially, the corresponding steady-state robust local and fused Kalman filters are also presented for multisensor time-invariant systems, and the convergence in a realization of the local and fused time-varying and steady-state Kalman filters is proved by the dynamic error system analysis (DESA) method and dynamic variance error system analysis (DVESA) method. A simulation example is given to verify the robustness and robust accuracy relations. [Copyright &y& Elsevier]

Abstract: We consider a broadcast channel in which the base station is equipped with multiple antennas and each user has a single antenna, and we study the design of transceivers based on Tomlinson–Harashima precoders with probabilistic quality of service (QoS) requirements for each user, in scenarios with uncertain channel state information (CSI) at the transmitter. Each user's QoS requirement is specified as a constraint on the maximum allowed outage probability of the receiver's mean square error (MSE) with respect to a specified target MSE, and we demonstrate that these outage constraints are associated with constraints on the outage of the received signal-to-interference-plus-noise-ratio (SINR). We consider four different stochastic models for the channel uncertainty, and we design the downlink transceiver so as to minimize the total transmitted power subject to the satisfaction of the probabilistic QoS constraints. We present three conservative approaches to solving the resulting chance constrained optimization problems. These approaches are based on efficiently solvable deterministic convex design formulations that guarantee the satisfaction of the probabilistic QoS constraints. We also demonstrate how to apply these approaches in order to obtain computationally efficient solutions to some related design problems. Our simulations indicate that the proposed methods can significantly expand the range of QoS requirements that can be satisfied in the presence of uncertainty in the CSI. [Copyright &y& Elsevier]

Abstract: In this paper, 1 [1] Part of the algorithm in this paper has been presented in IEEE ISIT’2008 [1]. we examine the problem of robust power control in a downlink beamforming environment under uncertain channel state information (CSI). We suggest that the method of power control using the lower bounds of signal-to-interference-and-noise ratio (SINR) is too pessimistic and will require significantly higher power in transmission than is necessary in practice. Here, a new robust downlink power control solution based on worst-case performance optimization is developed. Our approach employs the explicit modeling of uncertainties in the downlink channel correlation (DCC) matrices and optimizes the amount of transmission power while guaranteeing the worst-case performance to satisfy the quality of service (QoS) constraints for all users. This optimization problem is non-convex and intractable. In order to arrive at an optimal solution to the problem, we propose an iterative algorithm to find the optimum power allocation and worst-case uncertainty matrices. The iterative algorithm is based on the efficient solving of the worst-case uncertainty matrices once the transmission power is given. This can be done by finding the solutions for two cases: (a) when the uncertainty on the DCC matrices is small, for which a closed-form optimum solution can be obtained and (b) when the uncertainty is substantial, for which the intractable problem is transformed into a convex optimization problem readily solvable by an interior point method. Simulation results show that the proposed robust downlink power control using the approach of worst-case performance optimization converges in a few iterations and reduces the transmission power effectively under imperfect knowledge of the channel condition. [Copyright &y& Elsevier]

Abstract: A new approach to the design of robust adaptive beamforming is introduced. In the proposed approach, the mismatch vector of the desired steering vector is estimated by solving a quadratically constrained quadratic programming problem using an interference-plus-noise subspace projection matrix. The presumed look direction of desired signal is the only prior information of the proposed approach, and the parameters of uncertainty set or the angular sectors of the desired signal are not needed. In the presence of large DOA mismatch, the proposed beamformer performs well. Moreover, the proposed approach can deal with arbitrary steering vector mismatch in theory while many existing advanced robust beamformers cannot. Hence, it is very suitable for many practical applications. [Copyright &y& Elsevier]

Abstract: This paper investigates the problem of energy-to-peak filtering for both discrete-time and continuous-time systems with polyhedral uncertainties in the state-space equations. By increasing the flexible dimensions in the solution space for the energy-to-peak optimization, less conservative results on the robust energy-to-peak filtering are obtained. The filter parameters can be readily designed by solving a set of parameter-dependent linear matrix inequalities (LMIs). In comparison with the existing methods, the improvement of the proposed method over the existing results is shown via two numerical examples. [Copyright &y& Elsevier]

Abstract: The optimal guaranteed cost control problem via static-state feedback controller is addressed in this paper for a class of two-dimensional (2-D) discrete systems described by the Roesser model with norm-bounded uncertainties and a given quadratic cost function. A novel linear matrix inequality (LMI) based criterion for the existence of guaranteed cost controller is established. Furthermore, a convex optimization problem with LMI constraints is formulated to select the optimal guaranteed cost controller which minimizes the guaranteed cost of the closed-loop uncertain system. [Copyright &y& Elsevier]