Square Root Unscented Kalman Filter Research Articles

Study on SRUKF Applied in Initial Alignment with Large Misalignment Angle on Stationary Base of SINS

The initial alignment error model of SINS (Strap-down Inertial Navigation System) with large misalignment angle is nonlinear. The traditional EKF (Extended Kalman Filter) was used to linearization a nonlinear system, but its performance is limited. In this paper we use the SRUKF (Square Root Unscented Kalman Filter) to process this nonlinear system and the results indicate that SRUKF is better than EKF in convergence speed and estimation accuracy.

Model‐based measurement of particle size distributions in layering granulation processes

AbstractIn this work, we present a method for the online estimation of particle size distributions in layering granulation processes using a methodology known as model‐based measurement or state estimation. After presenting the necessary model equations for two practically relevant processes it is investigated which quantities of the processes have to be measured to estimate the size distribution. For the different processes square‐root unscented Kalman filters (SR‐UKF) are designed and tested in simulations to demonstrate the feasibility of this approach. © 2010 American Institute of Chemical Engineers AIChE J, 2011

Evaluation of Matrix Square Root Operations for UKF within a UAV GPS/INS Sensor Fusion Application

Using an Unscented Kalman Filter (UKF) as the nonlinear estimator within a Global Positioning System/Inertial Navigation System (GPS/INS) sensor fusion algorithm for attitude estimation, various methods of calculating the matrix square root were discussed and compared. Specifically, the diagonalization method, Schur method, Cholesky method, and five different iterative methods were compared. Additionally, a different method of handling the matrix square root requirement, the square-root UKF (SR-UKF), was evaluated. The different matrix square root calculations were compared based on computational requirements and the sensor fusion attitude estimation performance, which was evaluated using flight data from an Unmanned Aerial Vehicle (UAV). The roll and pitch angle estimates were compared with independently measured values from a high quality mechanical vertical gyroscope. This manuscript represents the first comprehensive analysis of the matrix square root calculations in the context of UKF. From this analysis, it was determined that the best overall matrix square root calculation for UKF applications in terms of performance and execution time is the Cholesky method.

SUKF-based Modeling for General Behavior of the Environment and Its Application in Long-range AUV Propulsion System

Due to the poor adaptive capacity of long-range autonomous underwater vehicles(AUV) for general behavior of the environment,a square-root unscented kalman filter(SUKF) based modeling is proposed.In the offline model of general behavior of the environment,some parameters are time-varying,or not possible to be predicted,these parameters must be estimated and predicted through the information detected by the sensors.According to the sensor's information online and model offline,SUKF is used to estimate the state and parameter about the general behavior of the environment in real time.Modeling for behavior environment of AUV is the main work,taking propulsion system as an example,a model structure of fault used actuator effectiveness factors(AEFs) is constructed,then the SUKF is used for on-line joint estimation of both the states and AEFs parameters of AUV.Simulators are conducted by using the model of long-range AUV,and the results show the validity of the algorithm.Finally,the factors that affect the performance for estimation of SUKF are analyzed.

Improvement in the accuracy of estimating the time-of-flight in an ultrasonic ranging system using multiple square-root unscented Kalman filters

The square-root unscented Kalman filter (SRUKF) is applied to identify the shape parameters of an ultrasonic echo envelope. The SRUKF has better stability than the normal unscented Kalman filter (UKF) because the square-root of the error covariance matrix used in the SRUKF guarantees positive semidefiniteness. Considering the effect of the initial state on the convergence speed of filters, the multi-SRUKF is used to estimate the time-of-flight (TOF). Each SRUKF has a different initial state. The result estimated in a limited time with minimum mean square error is finally adopted. Simulation experiments for various couples of shape parameters and signal-to-noise ratios validate the improvement in the TOF accuracy. Real experiments using the echo signals of a SensComp 600 ultrasonic transducer show that the relative means and standard deviations of the TOF error obtained using the multi-SRUKF method are less than 0.2% and 0.15%, respectively.

TRACKING ALGORITHM FOR MMW/IR MULTI-SENSORS FUSION

Millimeter wave(MMW)/infrared (IR) sensor is a key technology for composite guidance system of missiles. Aimming to solve the problems that there were linear errors in the algorithm of square-root unscented Kalman filter (SR-UKF) and it was difficult to obtain the importance density function for the algorithm of particle filter(PF), a square-root unscented Kalman particle filter (SR-UK-PF) algorithm with the sequential fusion was presented by combining SR-UKF with PF. The main idea of this algorithm was to calculate the state transition matrix and the error covariance matrix by SR-UKF, and to construct the importance density function by the sequential fusion of particle filter. Thus, the importance density function could integrate the latest observation into system state transition density, and the proposal distribution could be more in line with the distribution of real states. To demonstrate the effectiveness of this model, simulations were carried out based on tracking algorithm for the surface-to-air missile with MMW/IR sensor.The results show that this technique can overcome the flaw that it is hard to get the optimization importance density function in the particle filter, and it can significantly improve the accuracy of state estimation for the system with multi-sensors.

Estimating parameters of synchronous generators using square-root unscented Kalman filter

A new method to estimate the parameters of a synchronous generator using the square-root unscented Kalman filter (SRUKF) is presented in the paper. A third-order model for the parameter estimation of both round rotor and salient generators is developed first and then the SRUKF method is applied to the third-order model to perform the joint estimation of state variables and unknown generator parameters. The simulation results on a test system demonstrated the effectiveness of the proposed method in parameter recognition of a synchronous generator. The estimation processes of generator parameters steadily converge to the estimated values whereas the estimation processes of state variables are consistent with the dynamic responses in the numerical simulations.

Square-root sigma-point Kalman filtering for spacecraft relative navigation

Abstract A variant of sigma-point Kalman filters family called square-root unscented Kalman filter is derived to estimate the relative attitude and position of two spacecrafts referred to as the leader and follower. The square-root forms of unscented Kalman filter have a consistently increased numerical stability because all resulting covariance matrices are guaranteed to stay semi-positive definite. The general six degrees of freedom relative equations of motion are developed based upon the tensors. All leader states are assumed known, whereas the relative states are estimated using available line-of-sight observations between the vehicles along with acceleration and angular velocity measurements of the follower. The quaternion is used to describe the spacecraft relative attitude kinematics, while a three-dimensional generalized Rodrigues parameter is used to maintain the quaternion normalization constraint in the filter formulation. The simulation results indicate that the proposed filter can provide lower relative attitude and position estimation errors with faster convergence rates than the standard extended Kalman filter.

State estimation of a solid‐state polymerization reactor for PET based on improved SR‐UKF

AbstractA state estimator for the continuous solid‐state polymerization (SSP) reactor of polyethylene terephthalate (PET) is designed in this study. Because of its invalidity in the application to some of the practical examples such as SSP processes, the square‐root unscented Kalman filter (SR‐UKF) algorithm is improved for the state estimation of arbitrary nonlinear systems with linear measurements. Discussions are given on how to avoid the filter invalidation and accumulating additional error. Orthogonal collocation method has been used to spatially discretize the reactor model described by nonlinear partial differential equations. The reactant concentrations on chosen collocation points are reconstructed from the outlet measurements corrupted with a large noise. Furthermore, the error performance of the developed ISR‐UKF is investigated under the influence of various initial parameters, inaccurate measurement noise parameters and model mismatch. Simulation results show that this technique can produce fast convergence and good approximations for the state estimation of SSP reactor. Copyright © 2009 Curtin University of Technology and John Wiley & Sons, Ltd.

An O(N²) Square Root Unscented Kalman Filter for Visual Simultaneous Localization and Mapping

This paper develops a Square Root Unscented Kalman Filter (SRUKF) for performing video-rate visual simultaneous localization and mapping (SLAM) using a single camera. The conventional UKF has been proposed previously for SLAM, improving the handling of nonlinearities compared with the more widely used Extended Kalman Filter (EKF). However, no account was taken of the comparative complexity of the algorithms: In SLAM, the UKF scales as O(N;{3}) in the state length, compared to the EKF's O(N;{2}), making it unsuitable for video-rate applications with other than unrealistically few scene points. Here, it is shown that the SRUKF provides the same results as the UKF to within machine accuracy and that it can be reposed with complexity O(N;{2}) for state estimation in visual SLAM. This paper presents results from video-rate experiments on live imagery. Trials using synthesized data show that the consistency of the SRUKF is routinely better than that of the EKF, but that its overall cost settles at an order of magnitude greater than the EKF for large scenes.

Reduced-rank unscented Kalman filtering using Cholesky-based decomposition

We consider a reduced-rank square-root unscented Kalman filter based on the Cholesky decomposition of the state-error covariance. The performance of this filter is compared with an analogous filter based on the singular value decomposition. We evaluate the performance of these filters for illustrative linear and non-linear systems.