Yunmin Zhu

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.

Optimal update with out-of-sequence measurements

This paper is concerned with optimal filtering in a distributed multiple sensor system with the so-called out-of-sequence measurements (OOSM). Based on best linear unbiased estimation (BLUE) fusion, we present two algorithms for updating with OOSM that are optimal for the information available at the time of update. Different minimum storages of information concerning the occurrence time of OOSMs are given for both algorithms. It is shown by analysis and simulation results that the two proposed algorithms are flexible and simple.

An efficient algorithm for optimal linear estimation fusion in distributed multisensor systems

Under the assumption of independent observation noises across sensors, Bar-Shalom and Campo proposed a distributed fusion formula for two-sensor systems, whose main calculation is the inverse of submatrices of the error covariance of two local estimates instead of the inverse of the error covariance itself. However, the corresponding simple estimation fusion formula is absent in a general distributed multisensor system. In this paper, an efficient iterative algorithm for distributed multisensor estimation fusion without any restrictive assumption on the noise covariance (i.e., the assumption of independent observation noises across sensors and the two-sensor system, and the direct computation of the Moore-Penrose generalized inverse of the joint error covariance of local estimates are not necessary) is presented. At each iteration, only the inverse or generalized inverse of a matrix having the same dimension as the error covariance of a single-sensor estimate is required. In fact, the proposed algorithm is a generalization of Bar-Shalom and Campos fusion formula and reduces the computational complexity significantly since the number of iterative steps is less than the number of sensors. An example of a three-sensor system shows how to implement the specific iterative steps and reduce the computational complexities

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.

Optimal linear estimation fusion. Part V. Relationships

For pt.IV see proc. 2001 International Conf on Information Fusion. .In this paper, we continue our study of optimal linear estimation fusion in. a unified, general, and systematic setting. We clarify relationships among various BLUE and WLS fusion rules with complete, incomplete, and no prior information presented in Part I before; and we quantify the effect of prior information and data on fusion performance, including conditions under which prior information or data are redundant.

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.

Globally optimal Kalman filtering with finite-time correlated noises

In this paper, an extension of the standard Kalman filtering for the dynamical systems with white noises to finite-time correlated noises is addressed. Although one can augment the state vector with white noises in a time-variant moving average process which models the finite-time correlated noise, and then use standard Kalman filtering to obtain the optimal state estimate in the mean square error sense, a direct recursion for the optimal estimate of original state in general cases was pursued owing to the lower computational complexity. By decomposing the original Kalman gain to two recursively represented factors and increasing some recursive terms (for more than one-step correlated noises), we directly provide recursive algorithms for the globally optimal estimate of original state for stochastic linear dynamic systems with (i) multi-step correlated process noises; (ii) multi-step correlated observation noises; and (iii) multi-step correlated process and observation noises. There is no any limitation on all involved matrices in the model and algorithms. The new development for Kalman filtering is expected to further promote practical applications of dynamic system theory and methods.

Integrative analyses of transcriptome sequencing identify novel functional lncRNAs in esophageal squamous cell carcinoma

Long non-coding RNAs (lncRNAs) have a critical role in cancer initiation and progression, and thus may mediate oncogenic or tumor suppressing effects, as well as be a new class of cancer therapeutic targets. We performed high-throughput sequencing of RNA (RNA-seq) to investigate the expression level of lncRNAs and protein-coding genes in 30 esophageal samples, comprised of 15 esophageal squamous cell carcinoma (ESCC) samples and their 15 paired non-tumor tissues. We further developed an integrative bioinformatics method, denoted URW-LPE, to identify key functional lncRNAs that regulate expression of downstream protein-coding genes in ESCC. A number of known onco-lncRNA and many putative novel ones were effectively identified by URW-LPE. Importantly, we identified lncRNA625 as a novel regulator of ESCC cell proliferation, invasion and migration. ESCC patients with high lncRNA625 expression had significantly shorter survival time than those with low expression. LncRNA625 also showed specific prognostic value for patients with metastatic ESCC. Finally, we identified E1A-binding protein p300 (EP300) as a downstream executor of lncRNA625-induced transcriptional responses. These findings establish a catalog of novel cancer-associated functional lncRNAs, which will promote our understanding of lncRNA-mediated regulation in this malignancy.

Optimal interval estimation fusion based on sensor interval estimates with confidence degrees

The interval estimation fusion method based on sensor interval estimates and their confidence degrees is developed. When sensor estimates are independent of each other, a combination rule to merge sensor estimates and their confidence degrees is proposed. Moreover, two optimization criteria: minimizing interval length with an allowable minimum confidence degree, or maximizing confidence degree with an allowable maximum interval length are suggested. In terms of the two criteria, an optimal interval estimation fusion can be obtained based on the combined intervals and their confidence degrees. Then we can extend the results on the combined interval outputs and their confidence degrees to obtain a conditional combination rule and the corresponding optimal fault-tolerant interval estimation fusion in terms of the two criteria. It is easy to see that Marzullos fault-tolerant interval estimation fusion [Marzullo, (1990). Tolerating failures of continuous-valued sensors. ACM Transactions on Computer System, 8(4), 284-304] is a special case of our method.