State estimation with two-level fusion structure

Identification and distributed fusion filter for multi-sensor networked systems with stochastic deception attacks

In this article, we consider a state estimation problem for large‐scale nonlinear processes in the absence of first‐principles process models. By exploiting process operation data, both process modeling and state estimation design are addressed within a distributed framework. By leveraging the Koopman operator concept, a parallel subsystem modeling approach is proposed to establish interactive linear subsystem process models in higher‐dimensional subspaces, each of which correlates with the original nonlinear subspace of the corresponding process subsystem via a nonlinear mapping. The data‐driven linear subsystem models can be used to collaboratively characterize and predict the dynamical behaviors of the entire nonlinear process. Based on the established subsystem models, local state estimators that can explicitly handle process operation constraints are designed using moving horizon estimation. The local estimators are integrated via information exchange to form a distributed estimation scheme, which provides estimates of the unmeasured/unmeasurable state variables of the original nonlinear process in a linear manner. The proposed framework is applied to a chemical process and an agro‐hydrological process to illustrate its effectiveness and applicability. Good open‐loop predictability of the linear subsystem models is confirmed, and accurate estimates of the process states are obtained without requiring a first‐principles process model.

This dissertation presents new approaches for cognitive radio networks that combat fading effects and improve detection accuracy. We propose an advance framework for performance analysis of cooperative spectrum sensing over non-identical Nakagami- A detect-amplify-and-forward strategy is proposed to mitigate bandwidth requirements of relaying local observations to a fusion center. The end-to-end performance of a relay-based cooperative spectrum sensing over independent identically distributed Rayleigh fading channels is also investigated in this dissertation. Specifically, we aim to incorporate sensing time, end-to-end SNR, and end-to-end channel statistic into the performance analysis of cooperative CR networks. We also propose a cluster-based cooperative spectrum sensing approach to overcome the bandwidth limitations of the reporting links. The approach reduces the number of reporting terminals to a minimal reporting set and replaces the global fusion center by a local fusion center to mitigate the destructive channel conditions of global relaying channels. A new approach is proposed to select the location of the local fusion center using the general center scheme in graph theory. We aim to show that multipath fading on relaying channels yields similar performance degradations as multipath fading on sensing channels. With the detect-amplify-and forward strategy, refraining the heavily faded relays improves the detection accuracy. A gain of 3 dB is achieved by switching from amplify-and-forward strategy to detect-amplify-and-forward strategy with 3 cooperative users. Compared to the non-cooperative spectrum sensing, a gain of up to 8 dB is achieved with 4 cooperative users and equal gain combining receiver. Similar experimental set up but with selection combining receiver, a gain of 5 dB is achieved.

A cross-layer approach to contour nodes inference of monitored physical phenomena with data fusion in wireless sensor networks is investigated in this work. The authors first analyze three sources of signal distortion: sensing noise, data quantization error and data communication noise. The sensing noise is often negligible. We need to choose the proper data quantization levels to balance the communication cost and the desired signal quality. Besides, data fusion at a local fusion center can be used to mitigate the communication noise due to the poor wireless channel. Instead of making a hard binary decision, the probability for a sensor node to be a contour node is calculated at the local fusion center. An adaptive data fusion scheme is proposed to avoid excessive packet retransmissions. Simulation results are given to show the effects of different system parameters on the overall system performance.

Structural control can enhance occupant comfort within structures during earthquakes and high-wind events. In traditional structural control systems, a central processor acquires data through extensive wiring from an array of sensors, calculates control forces, and commands a network of actuators to reduce undesired vibrations in the structure. To reduce costs associated with cable installation, multiple wireless units can perform the same calculations emulating a central computing station by communicating data throughout a large wireless sensor network. In such a system, it is common that a single sensor may be the only measurement source for an important section of a structure. As the number of sensors in a control network grows, it becomes increasingly difficult to transmit all sensor data during a single control step over the fixed wireless bandwidth, necessitating the use of staggered data communication. Control force calculations rely on accurate state measurements or estimates. In this paper, an approach to select and evaluate different communication group sizes and wireless unit combinations that still provide accurate state estimates is presented. With respect to a single wireless unit, multiple estimator gains are derived and stored on-board to perform state-estimation calculations using staggered data received from different combinations of units. It is found that state estimation and control performance are affected by the network topology used at each timestep with different sensors and sensor combinations providing more useful information than others. Sensor placement theory is used to form sensor groups that provide consistently high-quality output information to the network but still utilize all sensors.

Data-driven power control for state estimation: A Bayesian inference approach

In this paper, we apply belief propagation algorithm for consensus building in distributed wireless sensor networks (WSN). The objective is to achieve convergence to a global consensus value at all sensor nodes in the network. In order to implement the proposed belief propagation algorithm in a WSN, we introduce virtual fusion center nodes, which serve as sensors as well as local fusion centers in the sensor network. This paper also investigates the structure of WSNs that achieves convergence asymptotically, and guarantees achieving global consensus at all sensor nodes. Our results suggest that introducing certain range of irregularity in the network structure results in an improvement in the rate of convergence.

Robust event-triggered distributed fusion for multi-sensor systems with unknown failure rates

In order to solve the problem of larger single-point GPS positioning errors, a GPS positioning algorithm based on distributed Kalman filter data fusion with feedback (DKFDFWF) is proposed. Firstly, the data of the GPS receiver are filtered locally to obtain the local optimal state estimation and corresponding estimation error covariance. Secondly, the outputs of all local filters are fused in the fusion center to obtain the global fused state estimation and corresponding estimation error covariance. Finally, the output of the fusion center is fed back to each local filter to correct the larger estimation error of the abnormal local filter. We use three Unicore Communications UM220 receivers to locate and collect data in the same place, and continuously collect data for 24 hours. The experimental results show that the average maximum positioning error of distributed Kalman filter with feedback is reduced by 22.96% and 48.59% compared with single-point GPS Kalman filter and the averaging method of the position data of three GPS receivers, respectively. In other words, the proposed GPS positioning algorithm based on DKFDFWF has better positioning accuracy in the sense of weighted fusion than single-point GPS Kalman filter and the averaging method of the position data of three GPS receivers. The validity and feasibility of the proposed algorithm are verified.

Maintaining reliability during power system operation relies heavily on the operator’s knowledge of the system and its current state. With the increasing complexity of power systems, full system monitoring is needed. Due to the costs to install and maintain measurement devices, a cost-effective optimal placement is normally employed, and as such, state estimation is used to complete the picture. However, in order to provide accurate state estimates in the current power system climate, the models must be fully expanded to include probabilistic uncertainties and non-linear assets. Recognizing its analogous relationship with state estimation, machine learning and its ability to summarily model unseen and complex relationships between input data is used. Thus, a power system state estimator was developed using modified long short-term (LSTM) neural networks to provide quicker and more accurate state estimates over the conventional weighted least squares-based state estimator (WLS-SE). The networks are then subject to standard polynomial scheduled weight pruning to further optimize the size and memory consumption of the neural networks. The state estimators were tested on a hybrid AC/DC distribution system composed of the IEEE 34-bus AC test system and a 9-bus DC microgrid. The conventional WLS-SE has achieved a root mean square error (RMSE) of 0.0151 p.u. for voltage magnitude estimates, while the LSTM’s were able to achieve RMSE’s between 0.0019 p.u. and 0.0087 p.u., with the latter having 75% weight sparsity, estimates about ten times faster, and half of its full memory requirement occupied.

In this paper, the problem of fusion estimation for networked multi-sensor systems with multiplicative noise and correlated noise is studied. First, the state space model is transformed into a new system with fictitious noises and local Kalman filter are obtained. Then the sequential inverse covariance intersection (SICI) fusion algorithm is applied and the SICI fusion estimator is proposed to avoid the computation burden of local estimators. Compared with the Sequential Covariance Intersection (SCI) fusion algorithm, SICI fusion algorithm is less conservative, and its estimation accuracy is higher than that of local filter and SCI fusion estimator. The validity and consistency of the proposed fusion estimator are verified by a simulation example.

The task of simultaneous localization and mapping (SLAM) is to build environmental map and locate the position of mobile robot at the same time. FastSLAM 2.0 is one of powerful techniques to solve the SLAM problem. However, there are two obvious limitations in FastSLAM 2.0, one is the linear approximations of nonlinear functions which would cause the filter inconsistent and the other is the “particle depletion” phenomenon. A kind of PSO & H∞-based FastSLAM 2.0 algorithm is proposed. For maintaining the estimation accuracy, H∞ filter is used instead of EKF for overcoming the inaccuracy caused by the linear approximations of nonlinear functions. The unreasonable proposal distribution of particle greatly influences the pose state estimation of robot. A new sampling strategy based on PSO (particle swarm optimization) is presented to solve the “particle depletion” phenomenon and improve the accuracy of pose state estimation. The proposed approach overcomes the obvious drawbacks of standard FastSLAM 2.0 algorithm and enhances the robustness and efficiency in the parts of consistency of filter and accuracy of state estimation in SLAM. Simulation results demonstrate the superiority of the proposed approach.

The cubature Kalman filter (CKF) is well-known for a decade as a derivative-free nonlinear Kalman filter that is well-suited for high-dimensional nonlinear estimation problems. This paper further develops this classical CKF in order to cope with time-varying noise statistics as well as inequality constraints on the estimated states. The resulting adaptive filter is suggested to provide more accurate state estimates and to be more robust against filter divergence. Moreover, this contribution proposes an automated filter design based on numerical optimization which uses the normalized estimation error squared (NEES) and the normalized innovation squared (NIS) as part of the objective function. The novel adaptive CKF is applied to wind turbines in order to assess the potential improvement for state and parameter estimation. The simulation results for an illustrative acid test scenario with time-varying measurement noise show the superiority of the novel adaptive CKF since it compensates the noise robustly and thereby outperforms the classical filter.

For nonlinear discrete systems with dual unknown inputs, there are many limitations regarding previous nonlinear filters. This paper proposes two new, improved square-root cubature Kalman filtering (ISRCKF) algorithms to estimate system states and dual unknown inputs. Improved square-root cubature Kalman filtering 1 (ISRCKF1) introduces an innovation that first obtains the unknown input estimates from the measurement equation, then updates the innovation to derive the unknown input estimates from the state equation, then uses the already obtained estimates of the dual unknown inputs to correct the one-step estimate of the state, and finally the minimum variance unbiased estimate of the state is obtained. Improved square-root cubature Kalman filtering 2 (ISRCKF2) builds a unified innovation feedback model, then applies the minimum variance unbiased estimation (MVUE) criterion to obtain the estimates of system states and dual unknown inputs, refining a more concise recursive filter but requiring stronger assumptions. Finally, simulation results demonstrate that the above two algorithms can achieve the optimal estimates of system states and dual unknown inputs simultaneously, and ISRCKF2 further enhances the accuracy of both state and dual unknown inputs estimation, which verifies the validity of the proposed algorithms.

In this paper, the robust distributed fault estimation problem is considered for a network of dynamical systems with external disturbances. Based on local output measurements and state estimates from neighbors, a distributed intermediate estimator is constructed for each node. By spectral decomposition of the Laplacian and proper scalings of the faults and the disturbances, a specially structured global error system can be created. It is proved that the states of the global error system are uniformly ultimately bounded with an explicit error bound. Compared with the existing results, the proposed fault estimation strategy has no requirements of the observer-matching condition and the preliminary knowledge of the upper bounds of the faults; moreover, the robustness of the global error system can be ensured by directly adjusting the design parameters of the intermediate estimators, without introducing any performance specifications. Simulation examples verify the effectiveness of the proposed method.