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Department of Defence, Australia, 7 p. Hall and J. Llinas - An Introduction to Multisensor Fusion. Jan Goodman, R. Mahler and H. Paradis, B. Chalmers, R. Carling, P. Strategies in data fusion - sorting through the tool box. Proceedings of European Conference on Data Fusion, From to direct marketing into the millennium, Marketing Intelligence and Planning, 16 1 , pp. Some terms of reference in data fusion. Steinberg, C.
https://sergysasea.tk Bowman and F. Revisions to the JDL data fusion model. Ton and D. Internationan Conference on Information Fusion. In this paper, we consider the generalization of [ 16 ] for arbitrary, nonequal horizon lengths. Design of distributed filters for sensor measurements with nonequal horizon lengths is generally more complicated than for equal lengths due to a lack of common time intervals that contain all sensor data, making it impossible to design a centralized filtering algorithm.
We propose using a distributed receding horizon filter for a set of local sensors with nonequal horizon lengths.
YUNMIN ZHU In the past two decades, multi sensor or multi-source information fusion tech niques have attracted more and more attention in practice, where. Networked Multisensor Decision and Estimation Fusion: Based on Advanced Mathematical Methods - CRC Press Book.
Also, we derive the key differential equations for error cross-covariances between LRHKFs using different horizon lengths. The remainder of this paper is organized as follows. The problem setting is described in Section 2. In Section 3, we present the main results pertaining to the distributed receding horizon filtering for a multisensor environment. Here, the key equations for cross-covariances between the local receding horizon filtering errors are derived.
In Section 4, two examples for continuous-time dynamic systems within a multisensor environment illustrate the main results, and concluding remarks are then given in Section 5. Consider the linear continuous-time dynamic system with sensors:. Also, the superscript denotes the th sensor, and is the total number of sensors. The initial state , , is assumed to be Gaussian and uncorrelated with and ,. Our purpose, then, is to find the distributed fusion estimate of the state based on the overall horizon sensor measurements with different horizon time intervals , such that.
Now, we will show that the fusion formula FF [ 10 , 17 ] is able to serve as the basis for designing a distributed fusion filter.
According to 1 and 2 , we have local dynamic subsystems with the state vector and local individual sensor measurement :. Next, let us denote the local receding horizon estimate of the state based on the individual sensor measurements by. To determine we can apply the optimal receding horizon Kalman filter to subsystem 4 [ 12 — 15 ] to obtain the following differential equations:. In this case,. Theorem 1 see [ 10 , 17 ]. The optimal weights satisfy the following linear algebraic equations:.
The fusion error covariance , is given by. Therefore, 9 — 11 , defining the unknown weights and fusion error covariance , depend on the local covariances , determined by 5 , and the local cross-covariances. Without losing generality, let one assume that or. The covariance in 14 represents the nondiagonal element of the block covariance-matrix :. In the particular case of equal horizon lengths , , the local cross-covariances 12 satisfy the following differential equations:. In other words, each local estimate can be found independently of the other estimates. Note, however, that the local error covariances , and the weights may be precomputed, since they do not depend on the sensor measurements 3 , but rather on the noise statistics and and the system matrices , , and , which are the part of the system model 1 , 2.
In this section, two examples of continuous-time dynamic system with parametric model uncertainty are presented.
The corresponding dynamic model is written as. Then the reliability of local tracks is calculated, and the local tracks with high reliability are chosen for the state estimation fusion. Sichuan University P. Consider a water tank system that accepts two different water temperatures, while simultaneously throws off the mixed water [ 18 ]. My library Help Advanced Book Search. In many practical decision problems, statistical decision theory and methods may not be usable since the available information on the problems cannot provide the required statistical knowledge for statistical decision, or the problems themselves must be presented via other mathematical frames concerning uncertain decision theory and methods, such as Dempster-Shafer evidence theory, fuzzy set theory, and random set theory.
In both cases, the local and final fusion estimates are biased. Nevertheless, these examples demonstrate the robustness of the proposed filter in terms of mean square error MSE. The first example demonstrates the effectiveness of the distributed fusion receding horizon filter for different values of horizon lengths, and the second provides a comparison of the proposed filter with its nonreceding horizon version [ 17 ]. The corresponding dynamic model is written as.
The initial values are , and The system noise intensity is and the uncertainty is for the interval.
The second coordinate , related to the aircraft engine turbine temperature, is observable through a measurement model having three identical local sensors, one of which is the main sensor, while the others are reserve sensors. We have. Specifically, we focused on comparing the MSEs for the turbine temperature of the aircraft engine that directly contain the uncertainty in 19 , such that.
Our point of interest is the behavior of the aforementioned filters, both inside and outside of the uncertainty interval.
Since the uncertainty has little effect on the behavior of the filters estimates after the extremity of interval , for convenience of the MSE analysis, we introduce the extended time-interval , referred to as the Extended Uncertainty Interval EUI. According to the simulation results, and. The reason for such a robust property 22 is to compensate for the given uncertainty , as the common horizon length for all local sensors common memory of LRHKFs should be minimal.
In this case, it is equal, as.
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