Asynchronous Triggered Distributed Moving Horizon Estimation for Sensor Networks With Unknown External Inputs
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摘要: 考虑未知外部输入无线传感器网络的约束分布式状态估计问题, 提出一种新型异步触发分布式滚动时域估计方法. 首先针对传感器网络节点的有限观测能力与资源约束, 设计基于异步事件触发机制的数据交互策略. 同时为抑制异步事件触发可能引入的最坏影响, 构建基于min-max优化的分布式滚动时域状态估计器. 其次, 通过松弛输入矩阵条件, 建立保证估计误差满足输入−状态稳定性的充分条件, 并利用该条件离线确定估计器参数. 进一步, 将状态估计器等价转化为基于线性矩阵不等式的凸规划问题, 减轻估计器在线计算负担. 最后, 通过对比实验验证了本文方法的优越性.Abstract: This paper considers the constrained distributed state estimation problem for wireless sensor networks with unknown external inputs, and a novel asynchronous triggered distributed moving horizon estimation method is proposed. For the limited observation capability and resources constraint of nodes in the sensor network, a data interaction strategy is firstly designed based on an asynchronous event trigger mechanism. Then to suppress the potential worst impacts induced by the asynchronous event trigger, a distributed moving horizon state estimator is built based on min-max optimization. Secondly, sufficient conditions are established by relaxing the conditions of input matrices, thereby ensuring the input-to-state stability of estimation errors. These conditions can be used to compute the parameters of the estimator offline. Moreover, to reduce the online computational burden, the state estimator is reformulated as an equivalent convex programming problem in the form of linear matrix inequality. Finally, some comparative experiments demonstrate the advantages of the proposed method.
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图 4 理想网络环境下不同方法的估计误差对比
Fig. 4 Comparison of estimation errors of different methods in ideal network environment
表 1 理想网络环境下不同方法的MSE
Table 1 MSE of different methods in ideal network environment
误差分量 所提方法 OE CMHE $ \text{MSE}_{z_{rs,k}}\,\big(\left(\text{mm}\right)^2 \big) $ 0.0436 0.1391 0.1598 $ \text{MSE}_{v_{rs,k}}\,\big(\left(\text{mm}/\text{s}\right)^2\big) $ 1.3523 2.8916 1.9939 $ \text{MSE}_{z_{ru,k}}\,\big(\left(\text{mm}\right)^2 \big)$ 0.0394 0.1369 0.0404 $ \text{MSE}_{v_{ru,k}}\,\big(\left(\text{mm}/\text{s}\right)^2 \big) $ 2.8290 3.0533 3.0505 
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表 2 不同触发阈值下节点1和节点2的对比结果
Table 2 Comparison results of node 1 and node 2 under different triggering thresholds
$ \delta^{1,m} $, $ \delta^{1,s} $ 节点1的状态
估计触发频率节点1的测量
值触发频率节点2的
ACT (s)节点2的
MSE$ \delta^{1,m}=0 $,
$ \delta^{1,s}=0 $1.0000 1.0000 0.0865 1.4086 $ \delta^{1,m}=0 $,
$ \delta^{1,s}=5 $0.9301 1.0000 0.0909 2.6117 $ \delta^{1,m}=0 $,
$ \delta^{1,s}=10\sqrt2 $0.6088 1.0000 0.1036 54.2147 $ \delta^{1,m}=2 $,
$ \delta^{1,s}=0 $1.0000 0.8782 0.1076 1.4308 $ \delta^{1,m}=8 $,
$ \delta^{1,s}=0 $1.0000 0.5250 0.1173 1.3927 $ \delta^{1,m}=10\sqrt2 $,
$ \delta^{1,s}=0 $1.0000 0.3533 0.1266 1.4379
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