Spherical Simplex Unscented Kalman Filter Research Articles

An experimental comparative study of adaptive sigma-point Kalman filters: Case study of a rigid–flexible four-bar linkage mechanism and a servo-hydraulic actuator

This paper investigates the application, design, and implementation of different adaptive sigma-point Kalman filters for nonlinear dynamic systems. It is a well-known fact that the performance of nonlinear Kalman filters depends on a prior knowledge of system noise statistics. In real-time applications, this knowledge is difficult and in some cases impossible to predefine. Therefore, an adaptation mechanism based on the random weighting method is proposed in this work to estimate, simultaneously, noise covariance and the state of the system. On the other hand, for real time execution, the computational efficiency of such filters should also be considered to minimize the burden on computational resources. Based on these two factors, in this paper, four different variants of the adaptive sigma-point Kalman filter are studied in detail: (I) an Adaptive Unscented Kalman filter (AUKF), (II) an Adaptive Square-root Unscented Kalman filter (ASr-UKF) with an Unscented Transformation sigma-point selection strategy, (III) an Adaptive Scaled Spherical Simplex Unscented Kalman filter (AS3UKF), and (IV) an Adaptive Square-root Scaled Spherical Simplex Unscented Kalman filter (ASr-S3UKF) with scaled spherical simplex sigma-point selection strategy. The performance of these adaptive sigma-point Kalman filters is analyzed here in depth and discussed for application to a simulated rigid–flexible four-bar linkage mechanism and a practical servo-hydraulic actuator setup under different scenarios. The simulation and the experimental results indicated that, for the cases studied in this article, the filters are competitive and present advantages and disadvantages that should be dealt with according to the requirements of the problem.

Adaptive particle filter for state estimation with application to non‐linear system

Particle filtering (PF) has certain application value, but the disadvantage is that there is a phenomenon of particle degradation. In order to reduce the impact of this problem, this paper presents a new adaptive PF approach to improve the estimate accuracy. From the perspective of selecting an appropriate important density functions, in this filter, the particles are first updated using the Spherical Simplex Unscented Kalman Filter algorithm, and then the particles are updated using the Adaptive Extended Kalman filter algorithm. Simultaneously, from the perspective of improving the resampling method, a new resampling technique based on the random resampling method has been designed and fused to this filter. The comparison and analysis of two simulation schemes have been conducted to assess the performance of the designed filtering algorithm. The simulation results show the effectiveness of the proposed approach.

Angle-Only Target Tracking Method for Optical Imaging Micro-/Nanosatellite Based on APSO-SSUKF

To ensure the safety of the space station and improve the accuracy of the estimated trajectory tracking of noncooperative target, an optical imaging micro-/nanosatellite based on APSO-SSUKF (adaptive particle swarm optimization-spherical simplex unscented Kalman filter) is proposed to track low-orbit target using angle-only measurement. First, the algorithm considers the effect of J2 perturbation, uses the angle-only data as the observation vector, and uses spherical simplex unscented Kalman filter (SSUKF) to reduce the cost of calculation of the UKF in space noncooperative target tracking. Secondly, it is proposed to use the actual and theoretical covariance of the innovation sequence for real-time estimation of measurement noise, designing the adaptive particle swarm optimization (APSO) algorithm for real-time tracking of the process noise in the SSUKF that improves the accuracy of the filter in angle-only tracking. Finally, the tracking simulation of low-orbit satellite is carried out by using optical imaging micro-/nanosatellite, and the result shows that, compared with UKF, SSUKF, and PSO-SSUKF, APSO-SSUKF reduces the root mean square of the error in predicting the position in space target tracking by 45.44%, 35.26%, and 20.94%, and APSO-SSUKF reduces the root mean square of the error in velocity by 45.58%, 33.53%, and 16.33%, respectively; in the angle-tracking target, APSO-SSUKF improves the convergence and estimated accuracy of the algorithm in tracking.

A Comparison of Two Sigma Point Kalman Filters for Adaptive Cross-phase Cavity Pressure Control in Injection Molding

Injection molding is a discontinuous manufacturing process used for the automated production of plastic parts. An adaptive model-based predictive controller (MPC) for cross-phase cavity pressure control has been proposed in prior work showing good reference tracking capabilities for different processing conditions. The adaptive control topology is complemented by an Unscented Kalman Filter (UKF) estimating the system states along with a lumped model parameter mapping the system's time-variant dynamics. Previous experiments with a deterministic MPC have shown that the closed-loop performance is significantly improved when reducing the sample time. Thereby, a lower bound is given by the limited computing capacity of the controller hardware. Additionally, the closed-loop control performance correlates with the convergence rate of the parameter estimate. Both convergence behavior and computational effort are influenced by the sigma points (SP) selected within the UKF algorithm. Therefore, two different SP selection procedures, namely the standard UKF as well as the spherical simplex UKF (ssUKF) are evaluated for accuracy, computational effort and closed-loop performance. Both variations of the UKF are implemented in context of the adaptive control scheme and experimentally validated. It is shown that for both UKF designs the adaptive controller ensures good tracking of a given cross-phase cavity pressure reference. Similar closed-loop control performance is obtained if an individual tuning for each filter is performed. However, the averaged computation time of the ssUKF is approximately 34.2 (%) less compared to the UKF, which enables a significant reduction of the sampling time.

A Quaternion-Based Robust Adaptive Spherical Simplex Unscented Particle Filter for MINS/VNS/GNS Integrated Navigation System

An improved filtering algorithm-robust adaptive spherical simplex unscented particle filter (RASSUPF) is proposed to achieve high accuracy, induce the amount of computation, and resist the influence of abnormal interference for the MINS/VNS/GNS integrated navigation system. This algorithm adopts spherical simplex unscented transformation (SSUT) to approximate the probability distribution, employs the spherical simplex unscented Kalman filter (SSUKF) to generate the importance sampling density of particle filter, and applies robust and adaptive estimation to control the influence of the abnormal information on the state model and the observation model. Simulation results demonstrate the proposed algorithm can effectively reduce the navigation error, improve the navigation positioning precision, and decrease the computation cost.

Celestial navigation in deep space exploration using spherical simplex unscented particle filter

Deep space exploration has significant meaning both in science and economy; however, it is very hard to obtain the relevant information due to its complexity. In this study, the autonomous celestial navigation method is utilised. To achieve high accuracy of the celestial navigation in a deep space environment, the improved filtering algorithm–spherical simplex unscented particle filter (SSUPF) is implemented, which adopts the spherical simplex unscented Kalman filter (SSUKF) algorithm to generate the important sampling density of particle filter (PF). According to simulation results, the authors derive that the SSUPF method can greatly increase the performance of the navigation system compared with unscented Kalman filter (UKF), SSUKF and unscented PF (UPF), and the computational burden of SSUPF is reduced by 24% in comparison with UPF.

Spherical Simplex Unscented Kalman Filter-Based Jumping and Static Interacting Multiple Model

A modified interacting multiple model (IMM) method called spherical simplex unscented Kalman filter-based jumping and static IMM (SSUKF-JSIMM) is proposed to solve the problem of nonlinear filtering with unknown continuous system parameter. SSUKF-JSIMM regards the continuous system parameter space as a union of disjoint regions, and each region is assigned to a model. For each model, under the assumption that the parameter belongs to the corresponding region, one sub-filter is used to estimate the parameter and the state when the parameter is presumed to be jumping, and another sub-filter is used to estimate the parameter and the state when the parameter is presumed to be static. Considering that spherical simplex unscented Kalman filter (SSUKF) is more suitable for a real-time system than the unscented Kalman filter (UKF), SSUKFs are adopted as the sub-filters of SSUKF-JSIMM. Results of the two SSUKFs are fused as the estimation output of the model. Experimental results show that SSUKF-JSIMM achieves higher performance than IMM, SIR, and UKF in bearings-only tracking problem.

Kinematic state estimation for rigid-link multibody systems by means of nonlinear constraint equations

In the multibody field the design of state observers proves useful for several tasks, ranging from the synthesis of control schemes and fault detection strategies, to the identification of uncertain parameters. State observers are designed to obtain accurate estimates of unmeasurable or unmeasured variables. Their accuracy and performance depend on both the models used and the measurement sets. In multibody systems, if it is reasonable to neglect joint clearance and to assume that links are rigid, the estimates of kinematic variables (i.e. position, velocity and acceleration) can be carried out very effectively using kinematic models, i.e. models based on kinematic constraint nonlinear equations, which provide much less uncertain models than dynamic equations. Under the aforementioned assumptions, this paper proposes a general theory, valid for both open-chain and closed-chain multibody systems, to design observers based on nonlinear kinematic models. The concurrent use of kinematic models and nonlinear estimators is original in the multibody field and represents the chief contribution of the paper. The soundness of the proposed theory is proved through numerical and experimental tests on both open-chain and closed-chain multibody systems. Finally, a comparison is given between the kinematic estimations computed through two nonlinear observers (the extended Kalman filter, EKF, and the spherical simplex unscented Kalman filter, SS-UKF), in order to demonstrate the benefits of the SS-UKF in nonlinear estimation.

Angular velocity estimation based on adaptive simplified spherical simplex unscented Kalman filter in GFSINS

In this paper, the adaptive simplified spherical simplex unscented Kalman filter was proposed to calculate angular velocity in gyro-free strapdown inertial navigation system. Firstly, a general angular velocity calculation modeling method with time-varying process noise was proposed, which was not limited to a certain kind of accelerometer configuration. Then aiming at the issues of large amount of calculation of unscented Kalman filter and the time variation of the process noise, and based on the characteristics of additive noise and linear state equation, the adaptive simplified spherical simplex unscented Kalman filter was proposed to estimate the angular velocity. The sampling points were decreased in this method through adopting the spherical simplex sampling strategy and not augmenting the state, thus improving the calculation efficiency. Meanwhile, Sage–Husa suboptimal maximum a posteriori noise estimator was brought in to estimate the process noise in real time in order to settle the problem of filter divergence induced by the time variation. Lastly, the proposed algorithm was simulated and also contrasted with the integration method, the evolution method and the conventional adaptive UKF algorithm. The simulation results indicated that the adaptive simplified spherical simplex unscented Kalman filter algorithm has higher precision than the integration method and evolution method and has higher efficiency than the AUKF, which could effectively improve the calculation precision and meanwhile guarantee the calculation efficiency.

One new onboard calibration scheme for gimbaled IMU

In most cases, a gimbaled inertial measurement unit (IMU) can provide more accurate navigation information than a strap-down IMU when there is no navigation aiding of global positioning system (GPS) or other equipments. The gimbaled IMU is still used in self-contained precision navigation systems such as launch vehicles, missiles and vessels.To guarantee precision navigation, it is necessary to carry out in-field calibration for the gimbaled IMU before a mission. It is not fit to adopt multi-position calibration method to calibrate the gimbaled IMU mounted on a carrier on the sea because the signal to noise ratio (SNR) of gyro and accelerometer is low when the gimbals are locked. Traditional continuous calibration methods which use measured acceleration to calibrate gyros and accelerometers are not fit either because of the lever-arm errors caused by the vessel’s attitude motion.Focusing on the problem above, this paper proposes a new calibration scheme. The gyro parameters are calibrated separately through measured gimbal angles and the accelerometer parameters are calibrated by a “shape-from-motion” method without attitude information.Keeping the gimbals unlocked and rotating the gimbals continuously, the measured gimbal angles can be used to calibrate gyro parameters and case misalignments as the IMU is mounted on a gyro-stabilized platform. Because the gyro errors and case misalignments propagate nonlinearly in gimbal angles error model, a nonlinear estimation filer, spherical simplex unscented Kalman filter (SSUKF), is adopted to deal with this problem. Besides, the parameters’ observability is analyzed by the singular value analysis of the observability matrix and the theory of relative output sensitivity and a continuous calibration scheme is established. Simulation for the proposed calibration scheme is conducted and the sensitivity to environment disturbances is analyzed. It is shown that the proposed method can calibrate onboard gimbaled IMU with high precision and proves practical in dealing with environment disturbances.

Contingency Estimation of States for Unmanned Aerial Vehicle using a Spherical Simplex Unscented Filter

Aiming at survival from contingency situations for unmanned aerial vehicles, a square root spherical simplex unscented Kalman filter is applied for state and parameter estimation and a rough model is used for state prediction when essential measurements are lost. Processing real flight data, received by telemetry at quite low sampling rate, the paper shows that filter performance of reasonable quality can be achieved despite the low sampling rate and the result is a low order model that can be useful during contingency operation. It is shown that the filter-estimator approach can cope with the low rate measurements requiring very little system knowledge and very limited tuning efforts. A generic aircraft model is utilised as process model where the non dimensional coefficients are identified online with joint estimation of states. Numerical stability is guaranteed by mathematically efficient square root implementation of the filter algorithm. A case of loss of GPS signal demonstrates the use of the state estimates to obtain return of the UAV to close to it's home base where safe recovery is possible.