Zhisheng You

Technical Communique: The optimality for the distributed Kalman filtering fusion with feedback

A rigorous performance analysis is dedicated to the distributed Kalman filtering fusion with feedback for distributed recursive state estimators of dynamic systems. It is shown that the Kalman filtering track fusion formula with feedback is, like the track fusion without feedback, exactly equivalent to the corresponding centralized Kalman filtering formula. Moreover, the so-called P matrices in the feedback Kalman filtering at both local trackers and fusion center are still the covariance matrices of tracking errors. Although the feedback here cannot improve the performance at the fusion center, the feedback does reduce the covariance of each local tracking error. The above results can be extended to a hybrid track fusion with feedback received by a part of the local trackers.

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.

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.

Brief paper: An efficient sensor quantization algorithm for decentralized estimation fusion

In this paper, we consider the design problem of optimal sensor quantization rules (quantizers) and an optimal linear estimation fusion rule in bandwidth-constrained decentralized random signal estimation fusion systems. First, we derive a fixed-point-type necessary condition for both optimal sensor quantization rules and an optimal linear estimation fusion rule: a fixed point of an integral operation. Then, we can motivate an iterative Gauss-Seidel algorithm to simultaneously search for both optimal sensor quantization rules and an optimal linear estimation fusion rule without Gaussian assumptions on the joint probability density function (pdf) of the estimated parameter and observations. Moreover, we prove that the algorithm converges to a person-by-person optimal solution in the discretized scheme after a finite number of iterations. It is worth noting that the new method can be applied to vector quantization without any modification. Finally, several numerical examples demonstrate the efficiency of our method, and provide some reasonable and meaningful observations how the estimation performance is influenced by the observation noise power and numbers of sensors or quantization levels.

Optimal centralized update with multiple local out-of-sequence measurements

In multisensor target tracking systems, observations produced by sensors typically arrive at a central processor out of sequence. There have been some update algorithms for single out-of-sequence measurement (OOSM). In this paper, we consider optimal centralized update algorithms with multiple asynchronous (different lag time) OOSMs. Firstly, we generalize the optimal update algorithm with single 1-step-lag OOSM in [2] to optimal centralized update algorithm with multiple 1-step-lag OOSMs. Then, based on best linear unbiased estimation, we present an optimal centralized update algorithm with multiple arbitrary-step-lag OOSMs.

A Near-Optimal Iterative Algorithm via Alternately Optimizing Sensor and Fusion Rules in Distributed Decision Systems

For parallel distributed sensor systems with statistically independent sensor decision rules, Chair and Varshney in [2] has obtained the optimal fusion rule. On the other hand, under a given fusion rule, the optimal sensor compression rules have been proposed by Zhu et al. in [21], [23] for generally distributed and dependent sensor observations. An open problem is how to simultaneously obtain an optimal fusion rule and optimal sensor compression rules for general parallel distributed sensor decision systems. Obviously, the exhaustive method for searching for the optimal fusion rule is computationally intractable. For general parallel distributed sensor decision systems, we provide necessary conditions of an optimal fusion rule and optimal sensor compression rules and propose a computationally efficient iterative algorithm to simultaneously/alternately search for a fusion rule and sensor compression rules by combining both Zhus and Chair and Varshneys methods. Moreover, the algorithm is extended to multiple bit compression and Network decision systems. Numerical examples show that the fusion rule obtained by the algorithm is in most cases the same as the optimal fusion rule obtained by the exhaustive method, therefore, it is effective and near optimal.

Performance Analysis of Communication Direction for Two-Sensor Tandem Binary Decision System

In this paper, the communication direction problem of a two-sensor tandem binary decision system is considered. Rigorous analysis shows that the performance of communication from the sensor with higher noise power to the sensor with lower noise power is not always better than the performance of the reverse communication direction when the signal and sensor noises are both Gaussian. This result can be extended to a more general two-sensor tandem binary decision system without the assumption of a specific data distribution. This seems somewhat counterintuitive but has significance for optimization design of sensor communication direction. Computer experiments support our analytic results and illustrate interesting information which requires need further study.

Performance analysis for distributed track fusion with feedback

A rigorous performance analysis is dedicated to track fusion with feedback for distributed recursive state estimators of dynamic systems. It is shown that the track fusion formula with feedback is, same as the track fusion without feedback, exactly equivalent to the corresponding centralized track fusion formula. Moreover, the so called P matrices in the feedback Kalman filtering at both local trackers and fusion center are still the covariance matrices of tracking errors. Although the feedback here cannot improve the performance at the fusion center, the feedback does reduce the covariance of each local tracking error. The above results can be extended to a hybrid track fusion with feedback received by partial local trackers.

Globally optimal flight path update with adding or removing out-of-sequence measurements

In a multisensor target tracking system, observations produced by sensors can arrive at a central processor out of sequence. There have been some state estimate update algorithms for out-of-sequence measurements (OOSMs). In this paper, we propose a flight path update algorithm for a sequence with arbitrary delayed OOSMs. The new algorithm has three advantages: 1) it is a globally optimal recursive algorithm; 2) it is an algorithm for arbitrary delayed OOSMs including the case of interlaced OOSMs with less storages, compared with the optimal state update algorithm in [19]; 3) it can update the current whole flight path other than only the current single state with less computation, i.e., the dimension of the matrices which need to be inverted is not more than that of the state in process of updating the past ℓ (lag steps) estimates and corresponding error covariances. Besides, this algorithm can be easily modified to derive a globally optimal flight path update with removing an earlier (incorrectly associated) measurement.

Minimum Variance in Biased Estimation With Singular Fisher Information Matrix

This paper extends the work of Y. C. Eldar, ldquoMinimum variance in biased estimation: Bounds and asymptotically optimal estimators,rdquo in IEEE Trans. Signal Process., vol. 52, pp. 1915-1929, Jul. 2004, which deals with only nonsingular Fisher information matrix. In order to guarantee the uniform Cramer-Rao bound to be a finite lower bound and also to have a feasible solution to the optimization problem in the work of Y. C. Eldar, it is proved that the norms of bias gradient matrices of all biased estimators must have a nonzero exact lower bound, which mainly depends on the rank of the singular Fisher information matrix. The smaller the rank of the singular Fisher information matrix is, the larger the lower bound of norms of bias gradient matrices of all biased estimators is. For a specific Frobenius norm, the exact lower bound is simply the difference between the parameter dimension and the rank of the singular Fisher information matrix.