Pose estimation by extended Kalman filter using noise covariance matrices based on sensor output

The process and measurement noise covariance matrices significantly impact the Extended Kalman Filter (EKF) performance and are often hand-tuned in practice, which usually entails a tedious task. Q-learning, a well-known method in reinforcement learning, has been applied recently to better adapt the noise covariance matrices for the EKF, thanks to its simplicity and capability in handling uncertain environments. Typically, some heuristics are involved in designing the Q-learning-based EKF (QLEKF), such as tuning grid size and covariance matrices values of each state, which inevitably degrades the estimation performance when the heuristics are not suitable. We propose a dynamic grid-based Q-learning EKF (DG-QLEKF) to overcome that drawback, which brings two novelties, an updated ϵ-greedy algorithm and a dynamic grid strategy. The proposed algorithm and strategy can thoroughly exploit arbitrary search scope and find appropriate values of noise covariance matrices. The effectiveness of DGQLEKF, applied in navigation for attitude and bias estimation, is validated through the Monte Carlo method and real flight data from an unmanned aerial vehicle. The DG-QLEKF leads to much more improved state estimation than the QLEKF and traditional EKF.

The electrification of the transport sector increases the demand for a battery management system that allows the Li-ion battery to work in a sophisticated way to reach its maximum. The main focus of the battery management system is the estimation of the battery’s state of charge (SOC) which is an indicator to determine the driving range of an electric vehicle. However, battery modeling has a direct influence on SOC estimation. In this article, the equivalent circuit model (ECM) and extended Kalman filter (EKF) algorithm are combined for SOC estimation of the Li-ion battery. Since the performance of Kalman filter algorithms strictly depends on noise covariance matrices, incorrect values reduce the accuracy and make divergence in state estimation. Therefore, it is motivated to analyze the impact of process noise and measurement noise covariance matrix values on SOC estimation using Kalman filter algorithms. Ten different combinations of noise covariance matrices are employed to analyze the effect of these matrices on SOC estimation. As a result, the tuning of the filter is critical for improvement in state estimation regardless of the type of the battery model and filtering technique. The matrix values are chosen to take into account the convergence rate and estimation error. To validate the effectiveness of the chosen noise covariance matrices, the simulation results of the ECM based EKF estimation method is superimposed with the discharge curves available in the data sheet. The simulation results show minimal estimation error and a good convergence rate for tuned EKF.

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.

The paper proposes a new Kalman filtering (KF) algorithm called VBI-MCKF that combines the variational Bayesian inference (VBI)-based KF algorithm and the maximum correntropy KF (MCKF) for visual tracking problem. The VBI-based KF algorithm works to estimate the unknown measurement noise covariance matrix (MNCM) and process noise covariance matrix (PNCM), and the MCKF works to deal with non-Gaussian process noise and measurement noise. In order to cater for the visual tracking target scenario, where the MNCM and PNCM are unknown and non-Gaussian, we modify the VBI-based KF algorithm to work for suddenly occurring outliers and modify the MCKF work for small bandwidth. Simulations show that the proposed VBI-MCKF algorithm performs well when both covariance matrices of Gaussian process noise and non-Gaussian measurement noise are unknown or inaccurate.

High precision is a very important index in target tracking. In order to improve the prediction accuracy of target tracking, an optimized Kalman filter approach based on improved Gray Wolf algorithm (IGWO-OKF) is proposed in this paper. Since the convergence speed of traditional Gray Wolf algorithm is slow, meanwhile, the number of gray wolves and the choice of the maximum number of iterations has a great influence on the algorithm, a nonlinear control parameter combination adjustment strategy is proposed. An improved Grey Wolf Optimization algorithm (IGWO) is formed by determining the best combination of adjustment parameters through the fastest iteration speed of the algorithm. The improved Grey Wolf Optimization algorithm (IGWO) is formed, and the process noise covariance matrix and observation noise covariance matrix in Kalman filter are optimized by IGWO. The proposed approach is applied into. The experiment results show that the proposed IGWO-OKF approach has low error, high accuracy and good prediction effect.

Real-time state of charge estimation for electric vehicle power batteries using optimized filter

The satellite clock plays a key role in the global navigation satellite system (GNSS). The accuracy of GNSS and its applications depend on the quality of the satellite clock. Therefore, precisely estimating and predicting the satellite clock is an important issue in the fields of GNSS and its application. As an optimal estimation algorithm, Kalman filter has been used to estimate and predict the satellite clock. However, in a conventional Kalman filter algorithm, the noise covariance matrices of satellite clock need to be predetermined, which restricts its further applications since the noise covariance matrices, especially the process noise covariance matrix, are usually unknown in the real cases. With inappropriate noise covariance matrices, the state estimation of conventional Kalman filter is suboptimal. To cope with this problem, a new noise covariance matrix estimation method of Kalman filter is proposed, and then we apply it to the problem of satellite clock estimation and prediction. Considering the fact that the process noise covariance matrix depends on the unknown noise parameters, the problem of estimating process noise covariance matrix can be solved by estimating the unknown noise parameters. First, the correlation between the Kalman innovations is used to establish a linear relationship with the unknown noise parameters. Then the unknown parameters can be estimated by least-squares estimation. Finally, the satellite clock can be estimated and predicted with the estimated noise parameters. In the new method, no prior information about the noise parameters is needed. Even with some extreme prior noise parameters, the new method can also work very well and has good convergence properties. For comparison, we conduct two experiments using the new method and the adaptively robust Kalman filter with classified adaptive factors based on opening windows separately, both results are consistent with each other very well, which verifies the correctness and effectiveness of this new method.

This study represents a method for estimating the state of charge (SOC) of lithium‐ion batteries using radial basis function (RBF) networks and square‐root unscented Kalman filter (KF). The RBF network is trained offline by sampled data from the battery in the charging process. This type of neural network finds the non‐linear relation which is required in the state‐space equations. The state variables include the battery terminal voltage and the SOC, at the previous sample and the present sample, respectively. The proposed method is tested experimentally on a lithium‐ion battery with 1.2 Ah capacity to estimate the actual SOC of the battery. The experimental results of the proposed method show some advantages, which include: (i) it is not very sensitive to determine, precisely, the measurement and process noise covariance matrices such as Kalman filter and (ii). It contains lower noise on the output, in comparison with Adaptive extended Kalman filter (EKF).

ABSTRACTIn complex indoor environments, the ultrawide band (UWB) positioning systems enhanced by Kalman filters (KFs) often struggle with large variations in accuracy and reliability due to outlier observations in the state system. This paper presents a cumulative adaptive extended KF (CA‐EKF) to mitigate this issue by optimizing state estimation accuracy. The proposed technique adaptively adjusts process and measurement noise covariance matrices based on residual and innovation vectors, effectively suppressing filtering divergence and significantly enhancing positioning precision. Performance evaluation demonstrates the superiority of CA‐EKF over traditional extended KF (EKF), innovation adaptive KF (IAKF), and Sage–Husa adaptive KF (SHAKF). Monte Carlo simulations under multiple outlier scenarios and nonlinear motion trajectories confirm CA‐EKF's robustness, achieving lower positioning errors, smoother error evolution, and improved resilience against multiple simultaneous outliers. Quantitative results highlight that CA‐EKF consistently outperforms other filters in terms of running‐average root mean square error (RA‐RMSE), mean squared error (MSE), and standard deviation (STD), reducing error accumulation over time and enhancing tracking accuracy. Notably, cumulative distribution function (CDF) analysis confirms that 99% of positioning errors with CA‐EKF remain below 7.65 cm significantly outperforming competing methods. These results establish CA‐EKF as a highly effective solution for high‐precision UWB tracking applications in dynamic environments.

Robust unscented Kalman filter with adaptation of process and measurement noise covariances

Tracking a ballistic target in its reentry mode by considering the radar measurements is a highly complex problem in nonlinear filtering. Kalman Filter (KF) is used to estimate the position of target when the measurements are corrupted with noise. If the measurements are nonlinear (radar measurements) then Extended kalman filter (EKF) is used. For obtaining reliable estimate of the target state, filter has to be tuned before the operation which is offline. Tuning an EKF is the process of estimating the process noise covariance matrix (Q) and measurement noise covariance matrix (R). This paper presents a new method of tuning the EKF using different evolutionary algorithms.

Most existing localization schemes necessitate a priori statistical characteristic of measurement noise, which may be unrealistic in practical applications. This paper investigates the variational Bayesian adaptive unscented Kalman filtering (VBAUKF) for received signal strength indication (RSSI) based indoor localization under inaccurate process and measurement noise covariance matrices. First, an inaccurate and slowly varying measurement noise covariance matrix can be estimated by choosing appropriate conjugate prior distribution for an indoor localization model with inaccurate process and measurement noise covariance matrices. By choosing inverse Wishart priors distribution, the state, predicted error and measurement noise covariance matrices are inferred on each time separately. Second, a parameter optimization algorithm is designed to minimize the localization error of VBAUKF until it less than the threshold set in advance. Finally, experimental validation is presented to demonstrate the accuracy and effectiveness of the proposed filtering method for indoor localization.

The detection of fouling in exhaust gas recirculation (EGR) coolers of diesel engines should be fast and accurate. This would facilitate deciding an effective strategy to combat fouling and to prolong the lifetime of EGR coolers. In the present study, the propensity of soot deposition in a rectangular EGR cooler is modeled using Kalman filters. Noises, coherent feature of many deposition processes which can be resulted from measurement sensors such as thermocouples or incidental deposit flake-off, are also considered in the model. The Kalman filter minimizes the estimation error covariance by considering the measurement and process noise covariance matrices while it can simultaneously handle the noisy data. The results are characterized with measurement process noise covariance. The relation between these two defines the smoothness and shape of the estimated trend of fouling resistance. Comparisons of the experimental data and the resultant model confirmed the usefulness of the applied method for various operating conditions of an EGR cooler prone to particulate deposition of soot particles. The paper proceeds with the impact of such models in monitoring fouling and taking an appropriate mitigation approach in diesel engines.

Real-time water demand pattern estimation using an optimized extended Kalman filter

<p>Inspection of large space structures is imperative for long term mission success. One solution is to utilize a second free flying spacecraft capable of performing inspection in orbit. An Extended Kalman Filter (EKF) is used to perform estimations on the relative position, velocity, angular velocity, and attitude through the use of navigation markers. Simulation takes place using MATLAB to compare the true values with the estimated values using the EKF. The initial covariance (P), process noise covariance (Q), and measurement noise covariance (R) matrices were tuned for a space structure with three navigation points. The largest recorded errors over 100 iterations occurred during the initial estimation yielding 26.78 centimeters in relative position, 1.80 centimeters per second in relative velocity, 0.0444 radians per second in relative angular velocity, and a difference of 0.0172 in the unit vector of relative attitude. After allowing 20 seconds of settling time the maximum errors were reduced to 5.0 centimeters in relative position, 0.40 centimeters per second in relative velocity, 0.0046 radians per second in relative angular velocity, and a difference of 0.0020 in the unit vector of relative attitude. The paper also discusses the application of training algorithms to tune the EKF parameters for future consideration.</p>