Time and covariance threshold triggered optimal uncooperative rendezvous using angles only navigation

Underwater target tracking system can be kept covert using the bearing-only or the bearing-Doppler measurements (passive measurements), which will reduce the risk of been detected. According to the characteristics of underwater target tracking, the square root unscented Kalman filter (SRUKF) algorithm, which is based on the Bayesian theory, was applied to the underwater bearing-only and bearing-Doppler non-maneuverable target tracking problem. Aiming at the shortcomings of the unscented Kalman filter (UKF), the SRUKF uses the QR decomposition and the Cholesky factor updating, in order to avoid that the process noise covariance matrix loses its positive definiteness during the target tracking period. The SRUKF uses sigma sampling to avoid the linearization of the nonlinear bearing-only and the bearing-Doppler measurements. To ensure the target state observability in underwater target tracking, the paper uses single maneuvering observer to track the single non-maneuverable target. The simulation results show that the SRUKF has better tracking performance than the extended Kalman filter (EKF) and the UKF in tracking accuracy and stability, and the computational complexity of the SRUKF algorithm is low.

This paper investigates the application, design, and implementation of the Square Root Unscented Kalman Filter (SRUKF) for induction motor (IM) sensorless drives. The UKF uses nonlinear unscented transforms (UT) in the prediction step in order to preserve the stochastic characteristics of a nonlinear system. The advantage of using the UT is its ability to capture the nonlinear behavior of the system, unlike the extended Kalman filter (EKF) that uses linearized models. The SRUKF implements the UKF using square root filtering and has the potential of reducing the errors in numerical computation. We discuss the theoretical aspects and implementation details of the SRUKF for IM drives. Experimental results for a direct torque controlled drive are presented for a wide speed range of operation, with focus on low speed performance. A comparison with the conventional EKF is included. It is concluded that the SRUKF is a viable and powerful tool for IM state estimation.

As environmental regulations become stricter, the advantages of pure electric vehicles over fuel vehicles are becoming more and more significant. Due to the uncertainty of the actual operating conditions of the vehicle, accurate estimation of the state-of-charge (SOC) of the power battery under multi-temperature scenarios plays an important role in guaranteeing the safety, economy, and reliability of electric vehicles. In this paper, a SOC estimation method based on the fusion of convolutional neural network-transformer (CNN-Transformer) and square root unscented Kalman filter (SRUKF) for lithium-ion batteries in low-temperature scenarios is proposed. First, the CNN-Transformer base model is established. Then, the SRUKF algorithm is used to update the state of the Coulomb counting method results based on the base model results. Finally, ensemble learning theory is applied to estimate SOC in multi-temperature scenarios. Data is obtained from laboratory conditions at −20 °C, −7 °C, and 0 °C. The experimental results show that the SOC estimation method proposed in this study is stable in terms of the root mean square error (RMSE) being between 2.69% and 4.22%. The proposed base model is also compared with the long short-term memory (LSTM) network and gated recurrent unit (GRU) network to demonstrate its relative advantages.

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 the atomic gravimeter, the interference fringe is obtained by scanning the chirp rate of the Raman lasers to compensate for the gravity induced Doppler frequency shift and then the gravitational acceleration can be obtained by extracting the phase of the atomic interference fringe. The phase of the interference fringe is proportional to the chirp rate, therefore the accurate estimation of the chirp rate is the key issue to obtain accurate gravitational acceleration. In practice, the model for estimating the chirp rate is not perfect, and there is system state error. In this paper, we propose a square root unscented Kalman filter (SR-UKF) approach for estimating gravitational acceleration, which can take the system state error into account. The experiments on simulated and real data are performed to demonstrate the feasibility and effectiveness of the SR-UKF method, which can provide an alternative approach for the gravity estimation. In addition, it can be combined with the tidal model for gravity estimation, and can also be used for real-time gravity measurement.

The Internet of Things (IoT), which is usually established over architectures of wireless sensor networks, provides an actual platform for various applications of personal and ubiquitous computing. Recently, moving target localization and tracking in an IoT environment have been paid more and more attention. This paper proposes a square-root unscented Kalman filtering (SR-UKF)-based algorithm to discover real-time location of a moving target in an IoT environment where there exist quantities of sensors. The data generated from wireless sensor nodes of the IoT make contributions to localization and tracking of the moving target. First, a least-square (LS) criterion-based mathematical model is proposed for localization initialization in an IoT scenario. Next, we employ an SR-UKF idea for the further localization and tracking. By using the data coming from sensor nodes near the target, real-time location of the moving target can be estimated by implementation of SR-UKF in an iterative fashion so as to achieve target status tracking. Simulation results show that the proposed algorithm achieves good performance in estimation of both position and velocity of the target with either uniform linear motion or variable-speed curve motion. Compared with some existing conventional extended Kalman filtering (EKF) or UKF-based methods, the proposed algorithm shows lower location/velocity estimation error under the same computational complexity, which demonstrates its potential significance in ubiquitous computing applications for an IoT environment.

X-ray pulsars navigation is a newly developed celestial navigation method, but the filter cycle time is long, and it cannot provide continuous navigation information. COMPASS can provide all-weather and continuous navigation information, but it has poor dynamic performance, and is susceptible to electromagnetic interference and the satellite signal is easy to be blocked. A X-ray pulsars/COMPASS integrated navigation method was proposed in order to improve the autonomous navigation capability of spacecraft. In this case, an autonomous orbit determination method of spacecraft is proposed through federal filtering that combines COMPASS navigation with X-ray pulsar navigation system. The extended Kalman filter (EKF), unscented Kalman filter (UKF) and the square root unscented Kalman filter (SR_UKF) algorithm are applied as the sub-filter. Simulation shows that the integration of the two systems can provide a higher accuracy of orbit determination, and SR_UKF performs better than EKF and UKF in filtering precision and stability.

Dynamic state estimation of a power system provides essential information about its inherent dynamic change. Nonlinear Kalman filters (NKFs) have been identified as potential versatile tools in performing state estimations. One key challenge of using NKFs lies in the fact that the available observations are inaccurate due to the presence of non-Gaussian noise that degrades the filtering precision and robustness. Some robust NKFs are developed to correct the state estimation via using robust optimality criteria or approximating the posterior density. Considering that the essence in these robust NKFs is to weight the error covariance and noise variance, we propose a novel method that can directly act on measurement to weight error covariance and noise variance. The novel method is based on a square root unscented Kalman filter that can enhance the numerical stability. Then, a weighting factor is applied to the measurement model for alleviating the effect of abnormal measurement errors. The weighting factor is derived from consideration of an anisotropy covariance function and an upper envelope of the traditional “sinc” function for suppressing large measurement errors and retaining the information of very large errors. We call the new filter the square root unscented Kalman filter with modified measurement (SRUKF-MM). The proposed SRUKF-MM is applied to state estimation of the Western System Coordinating Council (WSCC) 3-machine system and the Northeastern Power Coordinating Council (NPCC) 48-machine system in a non-Gaussian noise environment. Simulation results show that the proposed method achieves significantly improved filtering performance compared to other related NKFs.

Aiming at the problem of low positioning accuracy caused by unknown or inaccurate noise statistics when the underwater robot inspects submarine pipelines, the marine pipeline nodes' position are used to improve the navigation and positioning accuracy of the underwater INS/DVL integrated navigation system in the harsh underwater environment. The underwater integrated navigation system adopts an Adaptive Square-Root Unsented Kalman Filtering approach (ASUKF) approach based on the Square Root Unscented Kalman Filtering (SRUKF) and the improved Sage-Husa algorithm to resist errors caused by inaccurate noise such as ocean flow. Simulation experiments show that this method can improve the reliability and accuracy of the integrated navigation system compared with the traditional Square Root Unscented Kalman Filter algorithm.

Aiming at solving the problem that the accuracy and stability of Square-root Unscented Kalman Filter(SRUKF) will be affected if there are outliers in the observation values, this paper proposes an improved SRUKF restraining outliers based on orthogonality of innovation in the filtering processing. This modified filter at first detects whether there are outliers in the observation values by judging if the orthogonality of innovation is lost or not, and then assigns an activation function as the weight to each observation value, which can keep the orthogonal properties of the innovation sequence and the outliers can be detected and corrected. The Matlab simulation results about the GPS/DR integrated navigation system show that this modified filter is effectively resistant to outliers in the observation values and improves the filtering accuracy and stability.

In recent years, the wireless sensor network (WSN) has been widely applied to a variety of applications. Localization and tracking of a mobile node in a mixed line-of-sight (LOS) and non-line-of-sight (NLOS) environment is one of the most main application fields of WSN technology. In this paper, we unite a square-root unscented Kalman filter (SRUKF) and a particle filter (PF). We develop a PF-SRUKF-PF multistage filter with a variable constraint. First, we use PF to preprocess the measured data. Then SRUKF is used to operate on the processed data, and after the operation, the feasible domain is adjusted according to the number of sigma points outside the feasible domain, and then the results are projected into the feasible domain. The projected results are passed to the PF for secondary filtering. Through simulations, we show that the proposed algorithm can achieve higher localization accuracy compared with other methods.

Acquiring accurate space object orbits is crucial for many applications such as satellite tracking, space debris detection, and collision avoidance. The widely used two-line element (TLE) method estimates the position and velocity of objects in space, but its accuracy can be limited by various factors. A combination of multiple TLEs and advanced modeling techniques such as batch least squares differential correction and high-precision numerical propagators can significantly improve TLE accuracy and reliability, ensuring better space object surveillance. Previous studies analyzed additional factors that may influence TLE accuracy and evaluated the accuracy of Starlink TLE using precise ephemeris data from SpaceX. The results indicate that utilizing multiple TLEs for precise orbit determination can significantly enhance the performance of orbit prediction methods, particularly when compared to SGP4. By leveraging 10-day Starlink TLEs, the accuracy of 5-day predictions can be improved by approximately twofold. Additionally, producing two pseudo-observations within an orbital period near the TLE epoch yields the greatest effect on prediction accuracy, with this distribution of pseudo-observations increasing accuracy by approximately 10% compared to a uniform distribution. Further research can explore more data fusion and machine learning approaches to optimize operations in space.

The stochastic nature of noise signals affects the vehicle’s internal states and the outputs, resulting in the difficulty in estimation. The unknown or time-varying nature of noise signals if not taken into account for estimation, the results will diverge and be highly deteriorated. In this paper, a maximum likelihood principle (MLP) based adaptive robust extended kalman filter for estimating the states of the adopted non-linear vehicle model is proposed. An observability test is done for the purpose of estimation. A covariance matching (CM) based robust adaptive high forgetting factor based fault tolerant technique is also employed on the robust adaptive extended and unscented kalman filters for comparison purpose. The Robustness of the filter is analyzed by varying the parameter of the vehicle through a local sensitivity analysis. The results show that the MLP based approach to the extended kalman filter performs well in three simulations for sinusoidal steering, Double Lance Change, J-Turn, Fishhook, Slalom maneuver in comparison to robust adaptive unscented kalman filter. Friction coefficient of 0.8 (dry road) and 0.4 (wet road) is chosen for the simulation. The sideslip angle RMSE value for MLP based estimation is obtained as 2.62e-05, 4.545e-06 for Sine and DLC maneuver.

This study focuses on real-time model predictive control (MPC) implementation for a point-absorber-type wave energy converter (WEC) to achieve maximum wave power extraction. To address the MPC dependence on current and future wave excitation force knowledge, the control framework includes a square-root unscented Kalman filter (SR-UKF) to estimate the wave excitation force, whereas an autoregressive (AR) model forecasts the excitation force over the prediction horizon. The MPC utilizes a linear model of the point absorber, and its cost function is formulated as a quadratic programming (QP) problem with the objective of maximizing the wave energy extraction subject to physical limitations and constraints. A set of Laguerre functions was used to reduce the MPC computational complexity by decreasing the number of decision variables in the QP problem. The MATLAB/Simulink simulation results showed that the embodiment of point absorber nonlinearities by the SR-UKF enhanced the estimation accuracy compared with that of linear Kalman filters in terms of maximum error, root mean square error, and goodness of fit. Moreover, an AR model of order 100 provided satisfactory prediction performance for a 4 s prediction. The MPC strategy was simulated to evaluate its efficiency with respect to the absorbed wave power and generated electrical power under different sea-state conditions and disturbance uncertainties. Depending on sea state, it was found that the proposed MPC strategy generated 27.8% to 80% more electrical power than resistive loading control. Finally, a hardware-in-the-loop experimental setup was used to validate the computational viability of the proposed control framework in real-time WEC applications.

Object-Oriented Environment for Assessing Tracking Algorithms