An iterative augmented unscented Kalman filter for simultaneous state-parameter-input estimation for systems with/without direct feedthrough

Simultaneous estimations of the states, parameters and unknown inputs of nonlinear structural systems subjected to non-Gaussian noise are essential, because the inputs are not always available and the system noise is not always Gaussian. However, filters developed for this task require the inter-story drift measurements to be “fused” with the acceleration measurements to avoid the “drift phenomenon”. Because inter-story drifts may be inconvenient to obtain in practice, it is more desirable to use acceleration measurements only. To this end, this study develops a novel iterative augmented unscented Kalman particle filter (IAUKPF) for the simultaneous state-parameter-input estimation for systems subjected to non-Gaussian noise. The iterative strategy proposed in this study effectively corrects the “drift phenomenon” when only acceleration measurements are incorporated, so that the accuracies of the estimated unknown inputs are promoted. The importance density of the particle filter at each time step is provided by the augmented unscented Kalman filter so that the filter takes the best known information into consideration. Numerical examples of nonlinear structural systems affected by non-Gaussian noise are adopted to examine the effectiveness of the proposed IAUKPF.

State of Charge (SOC) estimation plays a crucial role in managing the performance and longevity of electric vehicle (EV) batteries. Various estimation techniques, including various Kalman Filters (KF), have been employed for this purpose. The mathematical process and limits of different KF family algorithms are analysed. In this study, an impact of nonlinear KF parameters on SOC estimation accuracy for EV batteries is analyzed. Specifically, the performance of Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Particle Filter (PF) is examined. EKF is most preferred for SOC estimation whereas introducing sigma points in UKF is the basic difference between EKF and UKF. In comparison to EKF and UKF, PF is more flexible since it applies to nonlinear systems with non-Gaussian distributions. Utilising a sequence of noisy measurements, KF is a recursive method that approximates the state of a dynamic system. It requires accurate parameters such as process noise covariance (Q) and measurement noise covariance (R) to work effectively. In this work, the effect of these parameters on state of charge estimation using nonlinear KFs has been analysed under different settings of noise covariance matrices. Tuning these parameters is essential for optimizing the performance of the KF and ensuring accurate and reliable state estimation in real-world applications. To find parameter values that provide the best balance between accuracy, robustness, and computational efficiency, the tuning process involves experimentation, simulation, and validation using real-world data. According to the results observed, the filter parameters such as three diagonal elements of Q are selected as 2e-8, 0.005, 0.003 and R as 2e-6. By evaluating the state estimation accuracy under different driving scenarios, robustness and sensitivity of filtering technique in estimating SOC for EV batteries has been studied. This analysis contributes to the optimization of SOC estimation algorithms, enhancing the reliability and efficiency of EV battery management systems.

PurposeAutonomous orbit determination using geomagnetic measurements is an important backup technique for safe spacecraft navigation with a mere magnetometer. The geomagnetic model is used for the state estimation of orbit elements, but this model is highly nonlinear. Therefore, many efforts have been paid to developing nonlinear filters based on extended Kalman filter (EKF) and unscented Kalman filter (UKF). This paper aims to analyze whether to use UKF or EKF in solving the geomagnetic orbit determination problem and try to give a general conclusion.Design/methodology/approachThis paper revisits the problem and from both the theoretical and engineering results, the authors show that the EKF and UKF show identical estimation performances in the presence of nonlinearity in the geomagnetic model.FindingsWhile EKF consumes less computational time, the UKF is computationally inefficient but owns better accuracy for most nonlinear models. It is also noted that some other navigation techniques are also very similar with the geomagnetic orbit determination.Practical implicationsThe intrinsic reason of such equivalence is because of the orthogonality of the spherical harmonics which has not been discovered in previous studies. Thus, the applicability of the presented findings are not limited only to the major problem in this paper but can be extended to all those schemes with spherical harmonic models.Originality/valueThe results of this paper provide a fact that there is no need to choose UKF as a preferred candidate in orbit determination. As UKF achieves almost the same accuracy as that of EKF, its loss in computational efficiency will be a significant obstacle in real-time implementation.

This paper presents the efficient Unscented Kalman filter (UKF) based estimation and control of a 3-DOF Omni bundle robot. The angular trajectory tracking becomes more difficult under highly non-linear measurement noise and process noise. A rapidly converging Unscented Kalman Filter (UKF) is presented in the paper. The extended Kalman filter (EKF) provides less accurate results in the highly non-linear system and sometime may become unstable because of convergence related issues, whereas in UKF the results in the non-linear system are better than EKF. UKF is more accurate in state and noise estimation. The computed torque technique is taken as a model to apply UKF. After, estimation the noise is removed. The experiment is conducted on Omni bundle with process and measurement noise. The results prove the superiority of presented UKF over conventional UKF and EKF.

For the direct feedthrough system where unknown input affects both process equation and measurement equation, an unscented recursive three-step filter based unbiased minimum-variance (URTSF-UMV) estimation algorithm is proposed. The algorithm is based on the unbiased minimum-variance (UMV) method and uses statistical linearisation technology to approximate the nonlinear system and the nonlinear measurement function to linear regression form. The estimation of unknown input is obtained from innovation through weighted least-squares (WLS) estimation. The approximate linear regression form allows us to process the nonlinear system with unknown input direct feedthrough by using the UMV state estimation framework, and derive the filter by minimising the trace of the state error covariance of the measurement update under the unbiased condition. The URTSF-UMV requires that the unknown input distribution matrix is full column rank. We use the full rank decomposition method to deal with the nonlinear system containing the unknown input rank-deficient distribution matrix. The effectiveness of the URTSF-UMV algorithm is demonstrated through an illustrative simulation example.

Unscented Kalman Filter (UKF) has been proved to be a superior alternative to the extended Kalman filter (EKF) when solving the nonlinear system in recent years. In order to improve the real-time of the UKF, A new kind of UKF called Sequence UKF is proposed in this paper. Like Rao-Blackwellised Unscented Kalman Filter (RBUKF) [4], it also deals with nonlinear stochastic discrete-time system with linear measurement equation, however it can decrease the computational complexity with the same filtering accuracy. This algorithm reduces the measurement vector to scalars in measurement-update of UKF by sequence method, so it can avoid inversing the covariance of measurement and reduce a great mount of computation bound. Special algorithm is deduced in this paper. The high performance of sequence UKF is verified by using Monte Carlo simulations.

A simultaneous input and state interval observer is presented for Lipschitz continuous nonlinear systems with unknown inputs and bounded noise signals for the case when the direct feedthrough matrix has full column rank. The observer leverages the existence of bounding decomposition functions for mixed monotone mappings to recursively compute the maximal and minimal elements of the estimate intervals that are compatible with output/measurement signals, and are proven to contain the true state and unknown input. Furthermore, we derive a Lipschitz-like property for decomposition functions, which provides several sufficient conditions for stability of the designed observer and uniform boundedness of the sequence of estimate interval widths. Finally, the effectiveness of our approach is demonstrated using an illustrative example.

Nowadays, experimental techniques allow scientists to have access to large amounts of data. In order to obtain reliable information from the complex systems that produce these data, appropriate analysis tools are needed. The Kalman filter is a frequently used technique to infer, assuming a model of the system, the parameters of the model from uncertain observations. A well-known implementation of the Kalman filter, the unscented Kalman filter (UKF), was recently shown to be able to infer the connectivity of a set of coupled chaotic oscillators. In this work, we test whether the UKF can also reconstruct the connectivity of small groups of coupled neurons when their links are either electrical or chemical synapses. In particular, we consider Izhikevich neurons and aim to infer which neurons influence each other, considering simulated spike trains as the experimental observations used by the UKF. First, we verify that the UKF can recover the parameters of a single neuron, even when the parameters vary in time. Second, we analyze small neural ensembles and demonstrate that the UKF allows inferring the connectivity between the neurons, even for heterogeneous, directed, and temporally evolving networks. Our results show that time-dependent parameter and coupling estimation is possible in this nonlinearly coupled system.

Estimating unknown inputs in indoor heating, ventilation, and air conditioning (HVAC) systems, particularly under the influence of diverse environmental constraints and time-varying relative humidity, presents a significant challenge. A viable solution is to employ a weighted least squares approach for estimating unknown inputs, which utilizes an unbiased minimum variance (UMV) estimator in conjunction with an unscented Kalman filter (UKF)-based nonlinear filtering technique. This allows for the simultaneous estimation of the system’s state and the unknown inputs. To accurately represent the real-life nonlinear thermal profile influenced by these uncertain inputs, it is essential to adopt an RC network-based mathematical modeling approach that captures the system’s dynamic behavior over time. The integration of the UMV-based optimal estimator with the UKF culminates in the proposed unscented Kalman filter with unbiased minimum variance for unknown inputs (UKF-UMV-UI) estimation algorithm. Extensive experimentation with the proposed UKF-UMV-UI algorithm has been conducted in a laboratory-scale realistic environment, dealing with uncertain and challenging unknown inputs. The results of the investigation indicate that the proposed method outperform the unscented Kalman filter with unknown input (UKF-UI) by 41.64% and 35.85% in Cumulative Mean Squared Error (CuMSE) for two distinct measurement conditions, respectively.

Structural health assessment procedures using extended and unscented Kalman filter concepts are presented and compared. The extended Kalman filter (EKF)-based algorithm proposed earlier for nonlinear system identification comes with limitations. The linearisation process used in EKF may lead to non-convergence for higher level of nonlinearity. To address the deficiency, the authors proposed a new algorithm known as unscented Kalman filter with unknown input and weighted global iteration (UKF-UI-WGI). In this study, a weighted global iteration technique with objective function is incorporated with the UKF algorithm in order to improve its efficiency. To generate the information required to implement the algorithm, it is integrated with least-squares-based algorithm. The stability, convergence, and robustness of the UKF-UI-WGI over EKF-based algorithm are compared in terms of several parameters including the sampling interval, duration of responses, and the dimension of the frames. With the help of examples, the overall superiority of UKF-UI-WGI over EKF-based algorithm is established.

Over the last 20-30 years, the extended Kalman filter (EKF) has become the algorithm of choice in numerous nonlinear estimation and machine learning applications. These include estimating the state of a nonlinear dynamic system as well estimating parameters for nonlinear system identification (eg, learning the weights of a neural network). The EKF applies the standard linear Kalman filter methodology to a linearization of the true nonlinear system. This approach is sub-optimal, and can easily lead to divergence. Julier et al. (1997), proposed the unscented Kalman filter (UKF) as a derivative-free alternative to the extended Kalman filter in the framework of state estimation. This was extended to parameter estimation by Wan and Van der Merwe et al., (2000). The UKF consistently outperforms the EKF in terms of prediction and estimation error, at an equal computational complexity of (OL/sup 3/)/sup l/ for general state-space problems. When the EKF is applied to parameter estimation, the special form of the state-space equations allows for an O(L/sup 2/) implementation. This paper introduces the square-root unscented Kalman filter (SR-UKF) which is also O(L/sup 3/) for general state estimation and O(L/sup 2/) for parameter estimation (note the original formulation of the UKF for parameter-estimation was O(L/sup 3/)). In addition, the square-root forms have the added benefit of numerical stability and guaranteed positive semi-definiteness of the state covariances.

In this paper, vision-based relative navigation of two spacecraft is addressed using the sparse Gauss-Hermite quadrature filter. The relative navigation provides the estimation of the relative attitude and relative orbit between spacecraft, which is a challenging filtering problem since it is a highly nonlinear and high dimensional estimation problem. Many filters have been used to solve this problem, such as, the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). However, these filters are not accurate enough when the initial uncertainty is large or the nonlinearity is significant. Moreover, although the conventional Gauss-Hermite quadrature filter is more accurate than the UKF, it cannot be used since a huge number of points is required. It is shown in this paper that the sparse Gauss-Hermite quadrature filter can achieve better estimation accuracy than the EKF, the UKF, and the cubature Kalman filter without excessive computation load.

A solution to the state estimation problem of systems with unmeasurable non-zero mean inputs/disturbances, which do not satisfy the disturbance decoupling conditions, is given using the Kalman filtering and Bayesian estimation theory. The proposed estimation algorithm, named Supervisory Kalman Filter (SKF), consists of a Kalman filter with an extra update step which is inspired by the particle filtering technique. The extra step, called supervisory layer, numerically solves the measurement equations for the portion of the state vector that cannot be estimated by the Kalman filter. First, it produces N randomly generated state vectors, the particles, which are distributed based on the Kalman filter’s last updated estimate. Then, the estimated measurement vector associated with each particle is compared to the actual measurement vector to identify the particle’s probability to be a solution. Finally, a so-called resampling stage is implemented to refine the particles with higher likelihoods. The effectiveness of the SKF is demonstrated by comparing its estimation performance with that of the standard Kalman Filter and the particle filter for a vehicle state estimation problem. The estimation results confirm that the SKF precisely estimates those states of the vehicle that cannot be estimated by either the Kalman filter or the particle filter, regardless of the unknown disturbances from the road. The filtering methodology offered in the article has a potential to improve performance of the systems presented in the patents WO2011115960, WO2010024751, US8073528, and US20110299730. Keywords: Bayesian state estimation, disturbance decoupling conditions, inputs/disturbances, particle filtering, state estimation, systems with unknown kalman filtering, unscented kalman filtering

Constrained nonlinear state estimation based on the UKF approach

Traffic state estimation problems must deal with imperfect information. Imperfect information may occur as a result of misalignments between reality and the assumptions or simplifications made when developing the models as well as incomplete or corrupted data. One of the well-known methods of handling imperfect information is the Kalman filter algorithm and its variations, such as the extended Kalman filter and the unscented Kalman filter. While the standard Kalman filter and the extended Kalman filter have been widely applied to the state estimation of linear systems, the unscented Kalman filter has been reported the better choice in the multiclass traffic state estimation. In many applications of Kalman filters to traffic estimation problems, the model and measurement noise covariance matrices are normally estimated. When there is a mismatch between the true and the assumed noise distribution, however, the filter often suffers from performance degradation and even divergence in certain situations. To this end, this paper presents a more efficient and accurate algorithm embedded in the unscented Kalman filter to simultaneously estimate the traffic state and the model noise distribution statistics. The proposed method is facilitated through a simultaneous update of the model noise covariance matrix in the predicted covariance equations of the unscented Kalman filter algorithm. It is found through simulation that the proposed algorithm may improve the model performance over the standard algorithm.