Comparative Statistical Analysis of New Adaptive Filtering Techniques for Precise Indoor Local Positioning

A computationally efficient algorithm for selecting the most informative subset of terrestrial signals of opportunity (SOPs) is proposed. The following problem is considered. An aerial vehicle navigates in an environment where global navigation satellite system (GNSS) signals are unavailable. The aerial vehicle is equipped with an on-board receiver that extracts pseudorange observations from an abundant number of M terrestrial SOPs with known locations but unknown dynamic, stochastic clock error states (bias and drift). An extended Kalman filter (EKF) is employed to fuse these pseudorange observations to estimate the aerial vehicle’s states (position and velocity) and the difference between the aerial vehicle-mounted receiver’s clock error states and the clock errors of all SOPs. Due to size, weight, power, and cost (SWaP-C) constraints, the aerial vehicle should select a subset K < M of the available SOPs with which it navigates. Since solving the optimal selection problem is rather involved, a sub-optimal, yet computationally efficient algorithm, termed opportunistic greedy selection (OGS), is proposed. The OGS is formulated by exploiting the additive, iterative properties of the Fisher Information Matrix (FIM), to minimize the aerial vehicle’s average position error variance (i.e., A-optimality criterion). Numerical simulations are presented showing that the proposed OGS algorithm performs comparably with the optimal M choose K selection algorithm, but executes in a small fraction of the time. Furthermore, experimental results are presented for a U.S. Air Force high-altitude aircraft navigating without GNSS signals in an environment comprising M = 57 cellular terrestrial SOPs for 9.39 km in 105 s. It is shown that upon choosing K = 15 SOPs according to the proposed OGS algorithm, the position and velocity root mean square errors (RMSEs) were 11.45 m and 0.80 m/s, respectively. Monte Carlo results are presented arguing that the results achieved from the proposed OGS algorithm are very close to what the global optimal selection algorithm would yield.

A better carbon-water flux simulation in multiple vegetation types by data assimilation

The focus of this work is the extension of nonlinear state estimation methods to gas-lifted systems. The extended Kalman filter (EKF), unscented Kalman filter (UKF) and particle filter (PF) were used to estimate the nonlinear states. Brief descriptions of the filters were first presented starting from the linear Kalman filter. Hypothesis tests on the expectation of the residuals were performed to show how close to optimal the estimation methods are and it showed the UKF estimates to be slightly better than EKF while PF performs the worst. The PF has poor accuracy using residual visualisation, hypothesis test and the root mean squared error (RMSE) values of the residuals. The gas-lifted system exhibits casing heading instability where the states show oscillatory behaviour depending on the value of the input but the results here do not change in a known way for each filter as the input is changed from the non-oscillatory region to the oscillatory region. Therefore, for this noise distribution and model assumption, either the EKF or UKF can be used for nonlinear state estimation with UKF better preferred if computational cost is not considered when control solutions are used in gas-lifted system.

Combined Kalman and sliding innovation filtering: An adaptive estimation strategy

This article examines an economic growth model that expresses the interaction between production, technology stock, and research and development (R&amp;D) investments. The goal of this study is to maximize production. Considering the presence of Gaussian white noises, this model is reformulated as a stochastic optimal control problem, where the R&amp;D investment rate is defined as the control input. We aim to explore the efficiency of Kalman filtering approaches for solving this problem. Here, the extended Kalman filter (EKF) and unscented Kalman filter (UKF) are applied for state estimation. The state equation linearization is made in the EKF, while the unscented transform is taken in the UKF for generating a set of sigma points. These approaches aim to estimate the state dynamics from different perspectives. With these state estimates, two different computational algorithms are proposed, the EKF for state-control (EKF4SC) and UKF for state-control (UKF4SC) algorithms. The optimal control policy is designed to minimize the cost function. For illustration, the model's parameters are considered in the simulation experiment. The simulation results showed that the UKF has higher accuracy in the state estimation with the smallest mean squares of error compared with the EKF. Moreover, the optimal control policy based on the state estimate generated from the UKF could optimize the cost function of the problem. Hence, the results show the efficiency of the algorithms proposed. In conclusion, the application of the Kalman filtering algorithms to the economic growth model is presented. The significance of this study is to provide a stochastic optimal control model for the economic growth problem and to suggest an efficient computational approach for solving this stochastic optimal control problem.

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.

The unscented Kalman filter (UKF) has become a popular alternative to the extended Kalman filter (EKF) during the last decade. UKF propagates the so called sigma points by function evaluations using the unscented transformation (UT), and this is at first glance very different from the standard EKF algorithm which is based on a linearized model. The claimed advantages with UKF are that it propagates the first two moments of the posterior distribution and that it does not require gradients of the system model. We point out several less known links between EKF and UKF in terms of two conceptually different implementations of the Kalman filter: the standard one based on the discrete Riccati equation, and one based on a formula on conditional expectations that does not involve an explicit Riccati equation. First, it is shown that the sigma point function evaluations can be used in the classical EKF rather than an explicitly linearized model. Second, a less cited version of the EKF based on a second-order Taylor expansion is shown to be quite closely related to UKF. The different algorithms and results are illustrated with examples inspired by core observation models in target tracking and sensor network applications.

Fast non-intrusive estimation of liquid-phase interface and boundary heat flux in participating media by the Kalman filtering methods

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.

Requirements of highly precise pointing performance have been imposed on recently developed spacecrafts for a variety of missions. The stringent requirements have called on on-orbit estimation of spacecraft dynamics parameters and calibration of on-board sensors as indispensible practices. Consequently, on-orbit estimation of the mass moment of inertia of spacecraft has been a major issue mostly due to the changes by solar panel deployment and a large portion of fuel consumption (Creamer et al., 1996; Ahmed et al., 1998; Bordany et al., 2000; VanDyke et al., 2004; Myung et al., 2007; Myung & Bang, 2008; Sekhavat et al., 2009). As for measurement sensors, on-board calibration of alignment and bias errors of attitude and rate sensors is one of the main concerns of attitude sensor calibration researches (Pittelkau, 2001 & 2002, Lai et al., 2003). Pittelkau (2002) proposed an attitude estimator based on the Kalman filter (Kalman, 1960), in which spacecraft attitude quaternion, rate sensor misalignment and bias, and star tracker misalignments are taken into consideration as states, whereas the body rate is dealt as a synthesized signal by the estimates. Lai at al. (2003) derived a method for alignment estimation of attitude and rate sensors based on the unscented Kalman filter (UKF) (Julier and Uhlmann, 1997). Ma and Jiang (2005) presented spacecraft attitude estimation and calibration based only magnetometer measurements using an UKF. An interesting point is that we need predesigned 3-axis excitation manoeuvres of spacecraft for both dynamics parameter estimation and sensor calibration. Therefore, this study is motivated to merge above estimation and calibration processes into a single filtering problem. It is noteworthy that poor information of moments of inertia is to be treated as a system uncertainty while the rate sensor model errors are to be incorporated into the measurement process. As a filtering algorithm, this study employs a UKF. Extended Kalman filters (EKFs) have been successfully applied to the nonlinear attitude estimation problem (Crassidis et al., 2007). Hybrid estimation using the EKF has been reported by Myung at al. (2007). However, the EKF estimates using the first order linearization, which may lead to instability of the filter (ValDyke et al., 2004). The UKF approximates the nonlinear model to the second order by spreading points 1 sigma apart from the a priori mean. Performing nonlinear

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.

The data obtained by sensor is strong randomness and deviates from Gaussian distribution. The Extended Kalman Filter (EKF) is cost-effective and easy to cause large errors while processing data. At the same time, the accuracy of the data prediction is not high enough. Therefore, an improved filter based on the original EKF is proposed to improve the prediction accuracy and noise reduction effect in this paper, which combines the predicted value and the measured value of the EKF twice to find the root mean square to obtain a more accurate predicted value. The noise reduction effect of EKF and TWEKF is compared by using MATLAB. And the root means square error (RMSE), signal-to-noise ratio (SNR), smoothness (S) and other quantitative judgment indexes prove that TWEKF has better noise reduction effect than EKF.

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.

The extended Kalman filter (EKF) has been used widely in Global Position System (GPS) and Strapdown Inertial Navigation Systems (SINS) integrated navigation systems,which simply linearizes all nonlinear models.However, careful treatment of the nonlinearity of the system models is particularly critical when the integrated systems use low cost micro-electro-mechanical (MEMS) inertial sensors. Hence application of the EKF in MEMS inertial sensor-based integrated navigation systems will likely lead to inaccurate results. To overcome the shortcomings of the EKF, the unscented Kalman filter (UKF) has been proposed.The UKF does not require the linearization of the system models. Alternatively it uses a set of deterministically selected "sigma-points",which completely capture the true mean and covariance of the original random vector. Then these sigma-points are propagated through the nonlinear models.This captures the mean and covariance to second order accuracy for arbitrary nonlinear functions. In this paper the EKF and UKF are applied in GPS/SINS integrated systems respectively. Simulation result demonstrates that the performance of the UKF is better than the EKF in MEMS inertial sensor-based SINS/GPS integrated systems.