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Detection Paradigms for Radar
Published in Alexander D. Poularikas, Stergios Stergiopoulos, Advanced Signal Processing, 2017
Bhashyam Balaji, Michael K. McDonald, Anthony Damini
The filtering problem is as follows. The time evolution of the state, or signal of interest, is assumed to be well-described by a discrete-time (continuous-time) stochastic process. However, the state process is not directly observable, i.e., the state process is a hidden continuous-time (or discrete-time) Markov process. Instead, what is measured is a related discrete-time (or continuous-time) stochastic process termed the measurement process. The filtering problem is to estimate the state of the system given the measurements.
Structure of finite dimensional exact estimation algebra on state dimension 3 and linear rank 2*
Published in International Journal of Control, 2023
Xiaopei Jiao, Stephen S.-T. Yau
The goal of filtering problems is to estimate the state of a stochastic system under noisy observations. After Kalman and Bucy first proposed filtering algorithm for linear systems with Gaussian initial condition in the 1960s (Kalman, 1960; Kalman & Bucy, 1961), a large number of research activities are motivated in nonlinear filtering problems (NFPs). In the late 1970s, Brockett and Clark (1980), Brockett (1981), and Mitter (1980) proposed the idea of using estimation algebras to construct finite dimensional filters (FDFs) independently. The motivation came from Wei-Norman method (Wei & Norman, 1964) to solve time-varying linear partial differential equations (PDEs). The advantage of the estimation algebra approach is that if estimation algebra is finite dimensional and one can find a set of basis, finite dimensional recursive filters can be constructed. Estimation algebra method can be widely applied in any filtering systems such as engineering and physical models which include navigation on aircraft and submarines, radar tracking problem, trajectory detection, guidance, positioning, orbit determination, etc.
Resource-efficient and secure distributed state estimation over wireless sensor networks: a survey
Published in International Journal of Systems Science, 2021
As one of the fundamental issues in the field of control theory and control engineering, state estimation allows system designers to acquire accurate and full knowledge of the true system state, which further empowers them to make informed control decisions. However, state estimation is challenging because the complete state of a dynamical system is not always measurable and accessible in many practical scenarios, especially in the presence of unknown disturbance and noise. Emphasising the effects of disturbance and noise on system performance, a problem of state estimation is also referred to as a filtering problem. In this paper, the terms ‘state estimation’ and ‘filtering’ are used interchangeably throughout the paper, whenever without causing confusion. WSN-based distributed estimation has also been widely explored for estimating some unknown parameter of interest, which results in distributed parameter estimation in a WSN setting (Kar & Moura, 2011; Kar et al., 2012; Zhang & Zhang, 2012). However, ‘distributed parameter estimation’ and ‘distributed state estimation’ lead to distinct problem formulations, and thus require different analysis and design methods. The term ‘distributed state estimation’ is preferred throughout this paper as an emphasis will be laid on the existing results in a state–space description of dynamical systems.
Asynchronous H∞ filtering for networked switched systems under effective DoS attacks
Published in International Journal of Systems Science, 2022
Lijie You, Xiaowu Mu, Zhe Yang
For dynamic systems with noise, the purpose of the filtering problem is to estimate state of the systems (or a linear combination of them) by using noisy output measurements. Kalman filtering and filtering are currently two important types of filtering. Different from Kalman filtering, filtering uses unknown disturbance with limited energy instead of white noise process to drive the state space system, while ensuring that the energy gain from interference to estimation error is less than a certain positive number. The literatures (Iqbal et al., 2013; Wang et al., 2015; Zhang et al., 2011; Zheng & Zhang, 2017) studied the related issues of filtering for SS. However, all the above research results for SS filtering were based on time-triggered communication, which leads to that limited computing and network resources are not fully utilised in the network environment. In order to overcome this shortcoming, the ETCM was proposed in the late 1990s (Åström & Bernhardsson, 1999; Hendricks et al., 2010). The sampling points can only be transmitted when meeting the predefined event triggering conditions. The ETCM can not only effectively save the limited communication resources and reduce the unnecessary data transmission, but also maintain good performance. ETCM was widely used in network filtering (Duan & Zong, 2020; Ren & Zong, 2017; Xiao et al., 2018, 2017; Zong et al., 2021), network control (Gao et al., 2021; Liu et al., 2020; Ma et al., 2020; Wang et al., 2020; Wang, Jia et al., 2020) and network synchron tion (Liu & Zhou, 2016; Zhang & Peng, 2016), etc. Due to the introduction of ETCM, the switching signal of filter is updated only when an event is triggered. In this case, there may exist an asynchronous phenomenon, in other words, the filter mode may be not match the system mode.