The Uncertainty Aware Salted Kalman Filter: State Estimation for Hybrid Systems with Uncertain Guards

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.

State estimation of hybrid systems is a significant problem for the design of feedback control and model-based diagnosis algorithms. In this paper, a methodology for state estimation of hybrid systems with discrete sensors based on particle filtering is presented. The quality of the algorithm is evaluated by comparing its performance with Cramer-Rao bounds computed for the discrete-time hybrid filtering problem. The approach is illustrated using simulation results of a tank system example.

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Many technologies need to be established to realize autonomous ships. In particular, accurate state estimation in real time is one of the most important technologies. In the ship and ocean engineering fields, there have been many studies on state estimation using nonlinear Kalman filters. Several methods have been proposed for nonlinear Kalman filters. However, there is insufficient verification on the selection of which filter should be applied among them. Therefore, this study aims to validate the filter selection to provide a guideline for filter selection. The effects of modeling error, observation noise, and type of maneuvers on the estimation accuracy of the unscented Kalman filter (UKF) and ensemble Kalman filter (EnKF) used in this study were investigated. In addition, it was verified whether filtering could be performed in real time. The results show that modeling error significantly impacts the estimation accuracy of the UKF and EnKF. However, the observation noise and types of maneuvers did not have an impact like the modeling error. Thus, we obtained the guideline that UKF and EnKF should be used differently depending on the required computation time. We also obtained that keeping the modeling error sufficiently small is essential to improving the estimation accuracy.

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.

A novel approach combining agile beam switching with deep learning to enhance the speed and accuracy of Direction of Arrival (DOA) estimation for millimeter-wave (mmWave) phased array systems with low-complexity hardware implementations is proposed and evaluated. Traditional DOA methods requiring direct access to individual antenna elements are impractical for analog or hybrid beamforming systems prevalent in modern mmWave implementations. Recent agile beam switching techniques have demonstrated rapid DOA estimation, but their accuracy and robustness can be further improved via deep learning. BeamSeek addresses these limitations by employing a Multi-Layer Perceptron (MLP) and specialized data augmentation that emulates real-world propagation conditions. The proposed approach was experimentally validated at 60 GHz using the NSF PAWR COSMOS testbed, demonstrating significant improvements over a correlation-based method across various Signal-to-Noise Ratio (SNR) levels. Results show that BeamSeek achieves up to an 8° reduction in average estimation error compared to this baseline, with particular advantages in noisy channels. This makes it especially suitable for practical mmWave deployments in environments characterized by multipath interference and hardware constraints.

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.

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.

—Fast and accurate state estimation has a crucial role in practical implementation of state feedback-based controllers. But most of the states are not accessible or economically feasible to measure and must be estimated. Although such controllers are normally designed offline, their dynamic performance is evaluated online. Hence, having high speed with acceptable accuracy is an essential feature for estimators. In this article, a state estimator based on an artificial neural network incorporated into a linear optimal regulator is introduced. First, an extended Kalman filter is designed, then an estimator based on a proposed feed-forward neural network structure is elaborated after much effort on promising neural network structures. Different neural networks are trained using the data collected from the extended Kalman filter, and a qualified and shapeable alternative for the extended Kalman filter in reducing its drawbacks is obtained. The optimum structure is identified when minimum state estimation error is achieved. Significant speed and sufficient accuracy are the main advantages of the proposed structure to be used online for state estimation. Dynamic performance of the system equipped with the linear optimal regulator plus different estimators is examined and compared to a single-machine/infinite-bus power system in MATLAB (The MathWorks, Natick, Massachusetts, USA).

We present the novel iterated cubature Kalman filter (ICKF) in which the measurement update of square root of cubature Kalman filter (SR-CKF) is refined to iterate process for fully exploiting the latest measurement so as to achieve the high accuracy of state estimation. The ICKF is implemented easily and inherits the virtues of SR-CKF. We apply ICKF to state estimation for reentry ballistic target with unknown ballistic coefficient. Simulation results indicate ICKF outperforms over the unscented Kalman filter (UKF) and SR-CKF in state estimation accuracy.

In order to obtain more accurate state estimation from multisensor system, the state estimation with two-level fusion structure is presented. By means of measurement fusion algorithm, the local first-level fusion centers can obtain the globally optimal fused measurement information, and then the local state estimation can be got by classical Kalman filtering. At the second-level fusion center, the fused estimation can be received by applying the covariance intersection fusion algorithm, which avoids the calculation of the correlation among local first-level fusion centers. The simulation example shows the effectiveness and higher accuracy of the presented fusion structure.

The accuracy of state estimators using the Kalman Filter (KF) is largely influenced by the measurement and the process noise covariance matrices. The former can be directly inferred from the available measurement devices whilst the latter needs to be assessed, as a function of the process model, in order to maximize the KF performances. In this paper we present different approaches that allow assessing the optimal values of the elements composing the process noise covariance matrix within the context of the State Estimation (SE) of Active Distribution Networks (ADNs). In particular, the paper considers a linear SE process based on the availability of synchrophasors measurements. The assessment of the process noise covariance matrix, related to a process model represented by the ARIMA [0,1,0] one, is based either on the knowledge of the probabilistic behavior of nodal network injections/absorptions or on the a-posteriori knowledge of the estimated states and their accuracies. Numerical simulations demonstrating the improvements of the KF-SE accuracy achieved by using the calculated matrix Q are included in the paper. A comparison with the Weighted Least Squares (WLS) method is also given for validation purposes.

Various Kalman filter approaches have been presented for performance estimation of aircraft engines provided that sensor measurement numbers are sufficient and all of them are available. However, it is difficult to collect all physical parameters along the gas path since the complex structure limits sensor installation, especially around the high-pressure turbine. The contribution of this article is to create a virtual sensor in the hot-section based on the component physical characteristics and aerothermodynamic theory and develop a dual hypothesis test strategy combined with a state estimator to track abrupt degradation of the engine component. A novel couple algorithm of the unscented Kalman filter using a virtual sensor is developed that has three primary advantages: (i) The performance degradation of four rotatory components can be estimated without sensor P43. (ii) The accuracy of state estimation using the virtual sensor is equivalent to that of sensor P43, and it adapts to the abrupt change of engine operating condition in the whole flight envelope. (iii) If the sensor can be installed in the future, it can be engaged to its analytical redundancy. Simulations are carried out on typical abrupt degradation datasets of aircraft engines, which demonstrate the superiority of anomaly detection of gas path component performance using virtual sensor measurements, especially hot-section components.

Estimation of internal states in a Li-ion battery using BiLSTM with Bayesian hyperparameter optimization

Accurate and reliable vehicle state estimation results are very significant to the active safety, energy optimization, and the intelligent control of vehicles. In this paper, to improve the accuracy and adaptability of vehicle running state estimation, the vehicle running states fused estimation strategy is presented for in-wheel motor drive electric vehicle using the Kalman filters and tire force compensation method. The concept of electric drive wheel model (EDWM) is developed and deduced, and then, considering that the EDWM is a nonlinear model with an unknown input, the design concept of high-order sliding mode observer is used to construct the state space equation of longitudinal force. To improve the accuracy and the reliability of vehicle state estimation, an overall estimation strategy with information fusion and tire force compensation is designed, in which a weighted square-root cubature Kalman filter with an adaptive covariance matrix of measurement noise is developed for observer design. Finally, the simulations in CarSim-Simulink co-simulation model and experiments are carried out, and the effectiveness of the designed estimation strategy is validated.