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This note presents new results on the design of the process noise covariance matrix in Kalman filtering. The proposed design belongs to the realm of worst case methods: the optimal covariance is sought such as to maximize an upper bound on the estimation error matrix under a total budget constraint. Optimality conditions are derived along with a numerical algorithm for iterative approximation of the optimal solution. The optimal solution features a few time points and the associated covariances. Broadly speaking, the process noise is only “active” at the time points that enhance its controllability. The importance of the method is that it bounds from above the performance of any Kalman filter with a different design. Monte Carlo simulations on a double harmonic system numerical example illustrate the good convergence, performance, and low sensitivity to initial guesses of the proposed method. Moreover, in terms of estimation accuracy, the Kalman filter with the optimal design outperforms a robust $H_2$ filter designed to cope with an equivalent uncertainty. [ABSTRACT FROM AUTHOR]

In this paper, we consider the properties for Kalman filtering in a multi-hop network. A time-homogeneous Markov chain is used to characterize the stochastic packet delay and loss phenomenon of each relay. Since, after several relays, the average expected estimation error covariance at the terminal is difficult to calculate, we derive lower and upper bounds for the average value. Using these bounds, it is found that the stability is related to one special entry in the channel's transition probability matrix, from which we obtain a necessary and sufficient condition for the stability of the single-hop case and extend the result to the multihop one. [ABSTRACT FROM AUTHOR]

Descent algorithms based on the gradient, conjugate gradient, and Newton methods are investigated to perform optimization in moving horizon state estimation for discrete-time linear and nonlinear systems. Conditions that ensure the stability of the estimation error are established for single and multi iteration schemes with a least-squares cost function that takes into account only a batch of most recent information. Simulation results show the effectiveness of the proposed approaches also in comparison with techniques based on the Kalman filter. [ABSTRACT FROM AUTHOR]

State estimation is of great importance in various applications based on wireless networked control systems. Wireless sensor node usually forwards its data to a remote receiver through a series of relay nodes in order to save its limited energy. In this technical note, we investigate the data forwarding strategy design for accurate remote state estimation in multi-hop wireless networks. Based on different computational capability of relay nodes, we first propose two relay strategies, namely, Direct Forwarding Strategy (DFS) and Local Processing and Forwarding Strategy (LFS). Stability condition, estimation performance and energy efficiency of both the two strategies are theoretically analyzed. We further propose an Event-triggered Forwarding Strategy (EFS) which is able to balance the estimation accuracy and relay energy consumption. Numerical examples are employed to demonstrate the effectiveness of our design. [ABSTRACT FROM AUTHOR]

This note addresses Distributed State Estimation (DSE) over sensor networks. Two existing consensus approaches for DSE, i.e., consensus on information (CI) and consensus on measurements (CM), are combined to provide a novel class of hybrid consensus filters (named Hybrid CMCI) which enjoy the complementary benefits of CM and CI. Novel theoretical results, limitedly to linear systems, on the guaranteed stability of the Hybrid CMCI filters under collective observability and network connectivity are proved. Finally, the effectiveness of the proposed class of consensus filters is evaluated on a target tracking case study with both linear and nonlinear sensors. [ABSTRACT FROM AUTHOR]

This paper addresses the stability of a Kalman filter when measurements are intermittently available due to constraints in the communication channel between the sensor and the estimator. We give a necessary condition and a sufficient condition, with a trivial gap between them, for the boundedness of the expected value of the estimation error covariance. These conditions are more general than the existing ones in the sense that they only require the state matrix of the system to be diagonalizable and the sequence of packet losses to be a stationary finite order Markov process. Hence, we extend the class of systems for which these conditions are known in two directions, namely, by including degenerate systems, and by considering network models more general than i.i.d. and Gilbert-Elliott. We show that these conditions recover known results from the literature when evaluated for non-degenerate systems under the assumption of i.i.d. or Gilbert-Elliott packet loss models. [ABSTRACT FROM PUBLISHER]

We consider sensor transmission power scheduling for remote state estimation with limited communication energy. A sensor needs to decide when to switch between different transmission energy levels in order to minimize the average expected estimation error covariance subject to the available energy budget. In the existing work the sensor only exploits the prior knowledge of the system parameters, the noise covariance and the channel characteristics but neglects the realtime information the estimator can provide. Thanks to the power asymmetry between the sensor and the estimator, we propose an online scheduling scheme which makes a choice based on the acknowledgement sequence at the remote estimator side and show that the scheme outperforms the optimal offline schedule under the same energy constraint. [ABSTRACT FROM AUTHOR]

This technical note is concerned with the distributed Kalman filtering problem for a class of networked multi-sensor fusion systems (NMFSs) with missing sensor measurements, random transmission delays and packet dropouts. A novel stochastic model is proposed to describe the transmission delays and packet dropouts, and an optimal distributed fusion Kalman filter (DFKF) is designed based on the optimal fusion criterion weighted by matrices. Some sufficient conditions are derived such that the MSE of the designed DFKF is bounded or convergent. Moreover, steady-state DFKF is also presented for the NMFSs. An illustrative example is given to demonstrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

In this paper, we present the globally optimal distributed Kalman filtering fusion with singular covariances of filtering errors and measurement noises. The following facts motivate us to consider the problem. First, the invertibility of estimation error covariance matrices is a necessary condition for most of the existing distributed fusion algorithms. However, it can not be guaranteed to exist in practice. For example, when state estimation for a given dynamic system is subject to state equality constraints, the estimation error covariance matrices must be singular. Second, the proposed fused state estimate is still exactly the same as the centralized Kalman filtering using all sensor raw measurements. [ABSTRACT FROM AUTHOR]

We consider sensor data scheduling for remote state estimation. Due to constrained communication energy and bandwidth, a sensor needs to decide whether it should send the measurement to a remote estimator for further processing. We propose an event-based sensor data scheduler for linear systems and derive the corresponding minimum squared error estimator. By selecting an appropriate event-triggering threshold, we illustrate how to achieve a desired balance between the sensor-to-estimator communication rate and the estimation quality. Simulation examples are provided to demonstrate the theory. [ABSTRACT FROM AUTHOR]

Optimal filters for nonlinear systems are in general difficult to derive or implement. The common approach is to use approximate solutions such as extended Kalman filters, ensemble filters or particle filters. However, no optimality properties can be guaranteed by these approximations, and even the stability of the estimation error cannot often be ensured. Another relevant issue is that, in most practical situations, the system whose variables have to be estimated is not known, and a two-step procedure is adopted, based on model identification from data and filter design from the identified model. However, the designed filter may display large performance deteriorations in the case of modeling errors. In this paper, a new approach overcoming these issues is proposed, allowing the design of optimal filters for nonlinear systems in both the cases of known and unknown system. The approach is based on the direct filter design from a set of data generated by the system. Either experimental or simulated data can be used for design. A bound on the number of data necessary to ensure a given filter accuracy is also provided, showing that the proposed approach is not affected by the curse of dimensionality. [ABSTRACT FROM AUTHOR]

This technical note studies some of the challenging issues on moving horizon state estimation for networked control systems in the presence of multiple packet dropouts in both sensor-to-controller and controller-to-actuator channels, which both situations are modeled by two mutually independent stochastic variables satisfying the Bernoulli binary distribution. Compared with standard Kalman filter, this study proposes a novel moving horizon estimator to deal with the uncertainties induced from the multiple packet dropouts, which has a larger degree of freedom to obtain better behavior by tuning the weight parameters. A sufficient condition for the convergence of the norm of the average estimation error is also presented to guarantee the performance of the estimator. Finally, a real-time simulation experiment is presented to demonstrate the feasibility and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]