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Register a new userA Distributed Implementation of Steady-State Kalman Filter
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This paper studies the distributed state estimation in sensor network, where $m$ sensors are deployed to infer the $n$-dimensional state of a linear time-invariant (LTI) Gaussian system. By a lossless decomposition of optimal steady-state Kalman filter, we show that the problem of distributed estimation can be reformulated as synchronization of homogeneous linear systems. Based on such decomposition, a distributed estimator is proposed, where each sensor node runs a local filter using only its own measurement and fuses the local estimate of each node with a consensus algorithm. We show that the average of the estimate from all sensors coincides with the optimal Kalman estimate. Numerical examples are provided in the end to illustrate the performance of the proposed scheme.
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In this paper, we propose an approach to address the problems with ambiguity in tuning the process and observation noises for a discrete-time linear Kalman filter. Conventional approaches to tuning (e.g. using normalized estimation error squared and covariance minimization) compute empirical measures of filter performance and the parameter are selected manually or selected using some kind of optimization algorithm to maximize these measures of performance. However, there are two challenges with this approach. First, in theory, many of these measures do not guarantee a unique solution due to observability issues. Second, in practice, empirically computed statistical quantities can be very noisy due to a finite number of samples. We propose a method to overcome these limitations. Our method has two main parts to it. The first is to ensure that the tuning problem has a single unique solution. We achieve this by simultaneously tuning the filter over multiple different prediction intervals. Although this yields a unique solution, practical issues (such as sampling noise) mean that it cannot be directly applied. Therefore, we use Bayesian Optimization. This technique handles noisy data and the local minima that it introduces.
Many state estimation algorithms must be tuned given the state space process and observation models, the process and observation noise parameters must be chosen. Conventional tuning approaches rely on heuristic hand-tuning or gradient-based optimization techniques to minimize a performance cost function. However, the relationship between tuned noise values and estimator performance is highly nonlinear and stochastic. Therefore, the tuning solutions can easily get trapped in local minima, which can lead to poor choices of noise parameters and suboptimal estimator performance. This paper describes how Bayesian Optimization (BO) can overcome these issues. BO poses optimization as a Bayesian search problem for a stochastic ``black box cost function, where the goal is to search the solution space to maximize the probability of improving the current best solution. As such, BO offers a principled approach to optimization-based estimator tuning in the presence of local minima and performance stochasticity. While extended Kalman filters (EKFs) are the main focus of this work, BO can be similarly used to tune other related state space filters. The method presented here uses performance metrics derived from normalized innovation squared (NIS) filter residuals obtained via sensor data, which renders knowledge of ground-truth states unnecessary. The robustness, accuracy, and reliability of BO-based tuning is illustrated on practical nonlinear state estimation problems,losed-loop aero-robotic control.
This paper proposes a novel approach to estimate the steady-state angle stability limit (SSASL) by using the nonlinear power system dynamic model in the modal space. Through two linear changes of coordinates and a simplification introduced by the steady-state condition, the nonlinear power system dynamic model is transformed into a number of single-machine-like power systems whose power-angle curves can be derived and used for estimating the SSASL. The proposed approach estimates the SSASL of angles at all machines and all buses without the need for manually specifying the scenario, i.e. setting sink and source areas, and also without the need for solving multiple nonlinear power flows. Case studies on 9-bus and 39-bus power systems demonstrate that the proposed approach is always able to capture the aperiodic instability in an online environment, showing promising performance in the online monitoring of the steady-state angle stability over the traditional power flow-based analysis.
Distributed linear control design is crucial for large-scale cyber-physical systems. It is generally desirable to both impose information exchange (communication) constraints on the distributed controller, and to limit the propagation of disturbances to a local region without cascading to the global network (localization). Recently proposed System Level Synthesis (SLS) theory provides a framework where such communication and localization requirements can be tractably incorporated in controller design and implementation. In this work, we derive a solution to the localized and distributed H2 state feedback control problem without resorting to Finite Impulse Response (FIR) approximation. Our proposed synthesis algorithm allows a column-wise decomposition of the resulting convex program, and is therefore scalable to arbitrary large-scale networks. We demonstrate superior cost performance and computation time of the proposed procedure over previous methods via numerical simulation.
This paper investigates the state estimation problem for a class of complex networks, in which the dynamics of each node is subject to Gaussian noise, system uncertainties and nonlinearities. Based on a regularized least-squares approach, the estimation problem is reformulated as an optimization problem, solving for a solution in a distributed way by utilizing a decoupling technique. Then, based on this solution, a class of estimators is designed to handle the system dynamics and constraints. A novel feature of this design lies in the unified modeling of uncertainties and nonlinearities, the decoupling of nodes, and the construction of recursive approximate covariance matrices for the optimization problem. Furthermore, the feasibility of the proposed estimators and the boundedness of the mean-square errors are ensured under a developed criterion, which is easier to check than some typical estimation strategies including the linear matrix inequalities-based and the variance-constrained ones. Finally, the effectiveness of the theoretical results is verified by a numerical simulation.
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