Enbin Song

Brief paper: Optimal Kalman filtering fusion with cross-correlated sensor noises

When there is no feedback from the fusion center to local sensors, we present a distributed Kalman filtering fusion formula for linear dynamic systems with sensor noises cross-correlated, and prove that under a mild condition the fused state estimate is equivalent to the centralized Kalman filtering using all sensor measurements, therefore, it achieves the best performance. Then, for the same dynamic system, when there is feedback, a modified Kalman filtering fusion with feedback for distributed recursive state estimators is proposed, and prove that the fusion formula with feedback is, as the fusion without feedback, still exactly equivalent to the corresponding centralized Kalman filtering fusion formula; the various P matrices in the feedback Kalman filtering at both local filters and the fusion center are still the covariance matrices of tracking errors; the feedback does reduce the covariance of each local tracking error.

Secure Beamforming for MIMO Broadcasting With Wireless Information and Power Transfer

This paper considers a basic MIMO information-energy broadcast system, where a multi-antenna transmitter transmits information and energy simultaneously to a multi-antenna information receiver and a dual-functional multi-antenna energy receiver which is also capable of decoding information. Due to the open nature of wireless medium and the dual purpose of information and energy transmission, secure information transmission while ensuring efficient energy harvesting is a critical issue for such a broadcast system. Providing that physical layer security techniques are adopted for secure transmission, we study beamforming design to maximize the achievable secrecy rate subject to a total power constraint and an energy harvesting constraint. First, based on semidefinite relaxation, we propose global optimal solutions to the secrecy rate maximization (SRM) problem in the single-stream case and a specific full-stream case. Then, we propose inexact block coordinate descent (IBCD) algorithm to tackle the SRM problem of general case with arbitrary number of streams. We prove that the IBCD algorithm can monotonically converge to a Karush-Kuhn-Tucker (KKT) solution to the SRM problem. Furthermore, we extend the IBCD algorithm to the joint beamforming and artificial noise design problem. Finally, simulations are performed to validate the effectiveness of the proposed beamforming algorithms.

Globally Optimal Multisensor Distributed Random Parameter Matrices Kalman Filtering Fusion with Applications

This paper proposes a new distributed Kalman filtering fusion with random state transition and measurement matrices, i.e., random parameter matrices Kalman filtering. It is proved that under a mild condition the fused state estimate is equivalent to the centralized Kalman filtering using all sensor measurements; therefore, it achieves the best performance. More importantly, this result can be applied to Kalman filtering with uncertain observations including the measurement with a false alarm probability as a special case, as well as, randomly variant dynamic systems with multiple models. Numerical examples are given which support our analysis and show significant performance loss of ignoring the randomness of the parameter matrices.

Robust SINR-constrained MISO downlink beamforming: when is semidefinite programming relaxation tight?

We consider the multiuser beamforming problem for a multi-input single-output downlink channel that takes into account the errors in the channel state information at the transmitter side (CSIT). By modeling the CSIT errors as elliptically bounded uncertainty regions, this problem can be formulated as minimizing the transmission power subject to the worst-case signal-to-interference-plus-noise ratio constraints. Several methods have been proposed to solve this nonconvex optimization problem, but none can guarantee a global optimal solution. In this article, we consider a semidefinite relaxation (SDR) for this multiuser beamforming problem, and prove that the SDR method actually solves the robust beamforming problem to global optimality as long as the channel uncertainty bound is sufficiently small or when the transmitter is equipped with at most two antennas. Numerical examples show that the proposed SDR approach significantly outperforms the existing methods in terms of the average required power consumption at the transmitter.

Minimax Robust Optimal Estimation Fusion in Distributed Multisensor Systems With Uncertainties

In this paper, the robust estimation fusion problem in multisensor systems with norm-bounded uncertainties concerning the error covariance matrix between local estimates is addressed. A robust fusion method by minimizing the worst-case fused mean-squared error (MSE) for all feasible error covariance matrices of local estimates is proposed. The minimax robust fusion weighting matrices can be explicitly formulated as a function of solution of a semidefinite programming (SDP). Some numerical examples demonstrate that when the error covariance matrix suffers disturbance, the proposed fusion method is more robust than the nominal fusion method which ignores the uncertainties, and can improve the performance when the disturbance is considerably large.

Globally Optimal Distributed Kalman Fusion With Local Out-of-Sequence-Measurement Updates

In a distributed multisensor fusion systems, observations produced by sensors can arrive at local processors out of sequence. The resulting problem at the central processor/fusion center-how to update current estimate using multiple local out-of-sequence-measurement (OOSM) updates - is a nonstandard distributed estimation problem. In this note, based on the centralized update algorithm with multiple asynchronous (1-step-lag) OOSMs see we firstly deduce the optimal distributed fusion update algorithm with multiple local asynchronous (1-step-lag) OOSM updates, which is proved, under some regularity conditions, to be equivalent to the corresponding optimal centralized update algorithm with all-sensor 1-step-lag OOSMs. Then, we propose an optimal distributed fusion update algorithm with multiple local arbitrary-step-lag OOSM updates.

Optimal Distributed Kalman Filtering Fusion With Singular Covariances of Filtering Errors and Measurement Noises

In this paper, we present the globally optimal distributed Kalman filtering fusion with singular covariances of filtering errors and measurement noises. The following facts motivate us to consider the problem. First, the invertibility of estimation error covariance matrices is a necessary condition for most of the existing distributed fusion algorithms. However, it can not be guaranteed to exist in practice. For example, when state estimation for a given dynamic system is subject to state equality constraints, the estimation error covariance matrices must be singular. Second, the proposed fused state estimate is still exactly the same as the centralized Kalman filtering using all sensor raw measurements. Moreover, the existing performance analysis results on the distributed Kalman filtering fusion for the multisensor system with feedback are also extended to the singular covariance matrices of filtering error. The final numerical examples support the theoretical results and show an advantage of less computational burden.

Optimal Distributed Kalman Filtering Fusion Algorithm Without Invertibility of Estimation Error and Sensor Noise Covariances

Although the globally optimal distributed Kalman filtering fusion has been proposed and studied for more than twenty years, the invertibility of estimation error and measurement noise covariances has been always a restrictive assumption to derive a globally optimal distributed Kalman filtering fusion equivalent to the centralized Kalman filtering fusion. This letter proposes an optimal distributed Kalman filtering fusion algorithm for general dynamic systems without invertibility of estimation error and measurement noise covariances. The new algorithm uses the convex combination fusion, whose fusion weights are recursively given. Computer experiments show that the performance of this fusion algorithm is very likely to be equivalent to that of the centralized Kalman filtering fusion. In practice, the new fusion algorithm can be applied to any distributed Kalman filtering fusion, such as the equality constrained distributed Kalman filtering fusion.

Robust SINR-constrained MISO downlink beamforming: When is semidefinite programming relaxation tight?

We consider the robust beamforming problem under imperfect channel state information (CSI) subject to SINR constraints in a downlink multiuser MISO system. One popular approach to solve this nonconvex optimization problem is via semidefinite relaxation (SDR). In this paper, we prove that the SDR method is tight when the channel uncertainty bound is small or when the base station is equipped with two antennas.

The Kalman type recursive state estimator with a finite-step correlated process noises

This paper consider the Kalman type recursive filter with finite-step correlated process noises. We propose a modified Kalman type filtering for such dynamic system. More importantly, unlike the previous result on the Kalman filtering with color noises, no process noise correlation model is required. What we need is only the correlation of process noises of two different time instants. We analyze its local optimality and demonstrate via several examples that the proposed recursive filter can significantly increase the performance over the standard Kalman filter when dynamic system with finite-step correlated process noises.