Hybrid Kalman Filter Research Articles

Research on Intelligent Navigation System Based on Aerospace Big Data Traffic System

This paper studies the navigation technology of the On-Orbit Servicing Spacecraft (OSS) and proposes an overall solution for the OSS navigation system. The composition of the OSS satellite navigation simulation system and simulation supporting environment are studied. Then a new SSUKF navigation filter is proposed based on the hyper spherical distributed feature sampling point transform algorithm (SSUT) and the non-scanning Kalman filter (UKF). The numerical simulation of the OSS system is studied based on MATLAB/RTW. Finally, the SSUKF algorithm and the conventional UKF algorithm are simulated digitally. The effectiveness and advanced nature of the hybrid Kalman filter applied to spacecraft autonomous navigation are verified.

A Novel Adaptive Indoor Positioning Using Mobile Devices with Wireless Local Area Networks

In this paper, mobile devices were used to estimate the received signal strength indicator (RSSI) of wireless channels with three wireless access points (APs). Using the RSSI, the path loss exponent (PLE) was adapted to calculate the estimated distance among the test points (TPs) and the APs, through the root mean square error (RMSE). Moreover, in this paper, the proposed adaptive PLE (APLE) of the TPs was obtained by minimizing the positioning errors of the PLEs. The training samples of RSSI were measured by TPs for 6 days, and different surge processing methods were used to obtain APLE and to improve the positioning accuracy. The surge signals of RSSI were reduced by the cumulated distribution function (CDF), hybrid Kalman filter (KF), and threshold filtering methods, integrating training samples and APLE. The experimental results show that with the proposed APLE, the position accuracy can be improved by 50% compared to the free space model for six TPs. Finally, dynamic real-time indoor positioning was performed and measured for the performance evaluation of the proposed APLE models. The experimental results show that, the minimum dynamic real-time positioning error can be improved to 0.88 m in a straight-line case with the hybrid method. Moreover, the average positioning error of dynamic real-time indoor positioning can be reduced to 1.15 m using the four methods with the proposed APLE.

Intelligent Navigation System based on Big Data Traffic System

This paper studies the navigation technology of the On-Orbit Servicing Spacecraft (OSS) and proposes an overall solution for the OSS navigation system. The composition of the OSS satellite navigation simulation system and simulation supporting environment are studied. Then a new SSUKF navigation filter is proposed based on the hyper spherical distributed feature sampling point transform algorithm (SSUT) and the non-scanning Kalman filter (UKF). The numerical simulation of the OSS system is studied based on MATLAB/RTW. Finally, the SSUKF algorithm and the conventional UKF algorithm are simulated digitally. The effectiveness and advanced nature of the hybrid Kalman filter applied to spacecraft autonomous navigation are verified.

A Study of Data-Driven Optimization of Personalized Instructional Strategies for Physical Education Training

Abstract As a new type of sports training, the application of sports information technology can effectively improve the athletes’ sports level and sports performance. In this paper, based on the way and effect of sports information technology application, a system for sports teaching and training assistance is designed. Through sports training intensity monitoring, the training intensity of the athletes is obtained, and a high load alarm is triggered. At the same time, the improved hybrid Kalman filter is used to solve the posture of training movements, and the DTW algorithm is used to recognize the training movements and compare them with the standard movements to obtain the training scores. Coaches can be assisted in formulating personalized teaching strategies by using the system’s obtained sports training data. This paper’s sports teaching and training assistance system has a significantly shorter response time than the two comparative systems, which suggests it has better response performance and practicality. The RMSE values of the improved hybrid Kalman filter are 0.92, 0.84 and 1.47 for the roll, pitch and yaw angles, respectively, which are better than that of the extended Kalman filter, indicating that it is closer to the original data and has better data fusion performance. Compared with the control class using traditional teaching strategies, the students in the experimental class using the personalized teaching strategies of this paper have higher skill improvement, indicating that the strategies of this paper have an important guiding role for personalized physical education teaching.

Time‐varying reliability analysis based on hybrid Kalman filtering and probability density evolution

AbstractThe study introduces a novel approach for time‐varying reliability analysis of structures called “hybrid UKF‐PDEM” by integrating the unscented Kalman filter (UKF) and the probability density evolution method (PDEM). The UKF estimates the displacement, velocity, stiffness, and damping parameters of a structure at each time step subjected to dynamic loading for structural damage quantification. The estimated parameters at each time step are then input into the PDEM to calculate the time‐varying probability density function (PDF) of the estimated states. The estimated PDF is used to update the uncertainty matrix of the estimated states in each iteration and to determine the time‐varying reliability curves of the structure. To demonstrate the effectiveness of the proposed method, we applied it to a numerical model of a three‐degree‐of‐freedom system and a full‐scale seven‐story building with different damage scenarios. The method is used to estimate the level of damage and calculate the corresponding reliability curve of the system over time for each damage scenario, utilizing the estimated structural responses and stiffness values. The extracted reliability values for each damage scenario follow the level of damage over time. This study shows that the newly developed method is computationally efficient for building a digital twin and enables real‐time damage identification and reliability analysis in various structural systems. The method's applicability to different types of structures highlights its versatility and potential for widespread use in assessing the integrity of buildings and infrastructure.

Adaptive hybrid Kalman filter for attitude motion parameters estimation of space non-cooperative tumbling target

Attitude motion parameters estimation of the space non-cooperative tumbling target is the premise of the on-orbit target capture task. However, existing methods cannot balance the estimation accuracy and efficiency. In this paper, an adaptive hybrid Kalman filter is presented to estimate the attitude, angular velocity and inertia motion parameters of the space non-cooperative tumbling target. First, the dynamic model of the non-cooperative tumbling target is derived, and the nonlinear discrete state-space equation is obtained. Then, a hybrid Kalman filter is designed by combining the extended Kalman filter and the unscented Kalman filter. The adaptive technique is introduced to track time-varying uncertain measurement noise caused by complex space disturbances. After that, based on the first-order linearization technique, the sufficient condition for the local convergence of the proposed method is proved. Finally, the numerical simulation experiment was conducted to compare the proposed method with the adaptive extended Kalman filter and the adaptive unscented Kalman filter. The experimental results show that the estimation accuracy of the proposed method is much higher than that of the adaptive extended Kalman filter and slightly lower than that of the adaptive unscented Kalman filter, and the iteration-average Central-Processing-Unit time is 64.2% smaller than that of the adaptive unscented Kalman filter and slightly longer than that of the adaptive extended Kalman filter. The proposed method achieves a much higher accuracy with a slight loss of iteration-average Central-Processing-Unit time.

Research on Identification and Suppression of Vibration Error for MEMS Inertial Sensor in Near-Bit Inclinometer

The measurement information of the traditional conventional measurement while drilling (MWD) method lags seriously because the installation position is far from the bit. However, the near-bit inclinometer will generate a large number of vibration interference signals when the bit breaks the rock in the drilling process, resulting in the continuous increase in errors measured by the microelectromechanical system (MEMS) inertial sensor. Aiming at the problems of low accuracy and poor stability of near-bit inclinometer under the interference of long-term complex vibration signals, a vibration error identification and suppression method of MEMS inertial sensor of near-bit inclinometer is proposed in this article. Firstly, the characteristics of the vibration signal of near-bit inclinometer are analyzed. The near-bit vibration errors of first-order linear vibration and high-order nonlinear vibration are identified, and the vibration characteristics are analyzed, the error model of gyroscope and accelerometer under complex vibration interference is established, and then the vibration error suppression model of inclinometer gyroscope and accelerometer is established based on the hybrid Kalman filter (KF) and unscented KF (UKF) algorithm. Finally, the hardware and software experimental platform of near-bit inclinometer is built. The experimental results show that the dynamic measurement errors of inclination, toolface, and azimuth are kept within ±0.6°, and the vibration errors of gyroscope and accelerometer are effectively suppressed.

Observer design for hybrid dynamical systems with approximately known jump times

This paper proposes a general framework for state estimation of systems modeled as hybrid dynamical systems with jumps occurring at (approximately) known times. A candidate observer is a hybrid dynamical system with jumps triggered when the system jumps. With some information about the time elapsed between successive jumps, a Lyapunov-based analysis allows us to derive sufficient conditions for observer design. In particular, a high-gain flow-based observer, with innovation during flow only, can be designed for systems with an average dwell-time when the flow dynamics are strongly differentially observable. On the other hand, when the jumps are persistent, a jump-based observer, with innovation at jumps only, should be designed based on an equivalent discrete-time system corresponding to the hybrid system discretized at jump times. In the context of linear maps, this reasoning leads us to a hybrid Kalman filter. These designs apply to a large class of hybrid systems, including cases where the time between successive jumps is unbounded or tends to zero – namely, Zeno behavior–, and cases where detectability only holds during flows, at jumps, or neither. We also study the robustness of this approach when the jumps of the observer are delayed with respect to those of the system. Under some regularity and dwell-time conditions, we show that the estimation error is semiglobally practically asymptotically stable over time intervals after such delays. The results are illustrated in examples and applications, including mechanical systems with impacts, spiking neurons, and switched systems.

Input-to-state Stability for Hybrid Kalman Filters

In this article, we propose a Lyapunov-based characterization of exponential input-to-state stability (ISS) for hybrid systems. We propose a new formulation of the continuous-discrete Kalman filter algorithm Särkkä (2006) using the hybrid systems framework Goebel et al. (2012) where we consider continuous-time system dynamics and discrete-time observations. We prove exponential input-to-state stability on the estimation error of the hybrid Kalman filter under mild assumptions on the system's model.

Observation of Stage Position in a 2-Axis Nano-positioner Using Hybrid Kalman Filter

This paper presents a novel method for observation of the stage position in a 2D Nano-positioning system based on a hybrid Kalman filter. In the proposed method, there is no need to measure the stage position directly using complex and costly capacity sensors. Instead, by using traditional piezo actuators equipped with strain gauge sensors, the deflection of the magnification system at the position of actuators is measured. Then, by employing a powerful estimation algorithm named as Kalman filter, the displacements of the stage are observed. The designed hybrid Kalman filter uses dynamical equations of motion in the prediction step. The piezo actuators deflections are measured and exploited to correct the predicted values for the system state variables. In order to simulate realistic conditions, a relatively exact COMSOL model has been developed for the nano-positioner where noise has been added to the piezo displacements obtained by simulating this model and these noisy data are used as measurements in the Kalman filter algorithm. The designed hybrid Kalman filter is examined for three different updating time steps. The results show that the designed Kalman filter appropriately estimates the stage displacements, and its accuracy is improved when the filter time step reduces.

Estimation of Angular Velocity and Position of a Permanent Magnet Synchronous Motor Using Discrete-Time Extended Kalman Filter and Hybrid Extended Kalman Filter

In this paper we analyze the permanent magnet synchronous motor. The state equations governing the permanent magnet synchronous motor are nonlinear, so the angular position and velocity of its rotor are estimated using nonlinear filters. Since the current passing through the armature is measurable, this measurement is used to estimate system states (i.e. angular position and angular velocity). Discrete extended Kalman filter and hybrid extended Kalman filter algorithms are presented. The comparison between simulation results of rotor’s position and velocity estimation using discrete extended Kalman filter and hybrid Kalman filter shows that hybrid Kalman filter estimator has better performance.

Particle Swarm Optimization Based on Hybrid Kalman Filter and Particle Filter

The combination of particle swarm and filters is a hot topic in the research of particle swarm optimization (PSO). The Kalman filter based PSO (K-PSO) algorithm is efficient, but it is prone to premature convergence. In this paper, a particle filter based PSO (P-PSO) algorithm is proposed, which is fine search with fewer premature problems. Unfortunately, the P-PSO algorithm is of higher computational complexity. In order to avoid the premature problem and reduce the computational burden, a hybrid Kalman filter and particle filter based particle swarm optimization (HKP-PSO) algorithm is proposed. The HKP-PSO algorithm combines the fast convergence feature of K-PSO and the consistent convergence performance of P-PSO to avoid premature convergence as well as high computational complexity. The simulation results demonstrate that the proposed HKP-PSO algorithm can achieve better optimal solution than other six PSO related algorithms.

Comparison of SOC Estimation between the Integer-Order Model and Fractional-Order Model Under Different Operating Conditions

Accurate estimation of the state of charge (SOC) is an important criterion to prevent the batteries from being over-charged or over-discharged, and this assures an electric vehicle’s safety and reliability. To investigate the effect of different operating conditions on the SOC estimation results, a dual-polarization model (DPM) and a fractional-order model (FOM) are established in this study, taking into account the prediction accuracy and structural complexity of a battery model. Based on these two battery equivalent circuit models (ECMs), a hybrid Kalman filter (HKF) algorithm is adopted to estimate the SOC of the battery; the algorithm comprehensively utilizes the ampere-hour (Ah) integration method, the Kalman filter (KF) algorithm, and the extended Kalman filter (EKF) algorithm. The SOC estimation results of the DPM and FOM, under the dynamic stress test (DST), federal urban driving schedule (FUDS), and hybrid pulse power characteristic (HPPC) cycle conditions, are compared and analyzed through six sets of experiments. Simulation results show that the SOC estimation accuracy of both the models is high and that the errors are within the range of ±0.06. Under any operating conditions, the SOC estimation error, based on the FOM, is always lower than the SOC estimation error of the DPM, but the adaptability of the FOM is not as high as that of the DPM.

Remaining useful life prediction of lithium-ion battery based on improved cuckoo search particle filter and a novel state of charge estimation method

For battery management system, accurate estimation of state of charge (SOC) and state of health (SOH), as well as prediction of remaining useful life (RUL) are of great significance. Herein, backward smoothing square root cubature Kalman filter (BS-SRCKF) is proposed to improve accuracy and convergence speed of SOC estimation. Then the multiscale hybrid Kalman filter (MHKF), which consists of BS-SRCKF and extended Kalman filter (EKF), is employed for the joint estimation of SOC and SOH. Furthermore, improved cuckoo search (ICS) algorithm is embedded in the standard particle filter (PF) to improve its performance, by transferring the particles in the prior distribution region to the maximum likelihood region. Eventually, RUL prediction is achieved based on the SOH information estimated by the joint estimation of SOC and SOH and the improved cuckoo search particle filter (ICS-PF). The simulation results demonstrate that the method for RUL prediction present in this paper has improved accuracy, confidence level and resampling rate compared with two existing methods based on PF and unscented particle filter (UPF).

Set-Membership Based Hybrid Kalman Filter for Nonlinear State Estimation under Systematic Uncertainty.

This paper presents a new set-membership based hybrid Kalman filter (SM-HKF) by combining the Kalman filtering (KF) framework with the set-membership concept for nonlinear state estimation under systematic uncertainty consisted of both stochastic error and unknown but bounded (UBB) error. Upon the linearization of the nonlinear system model via a Taylor series expansion, this method introduces a new UBB error term by combining the linearization error with systematic UBB error through the Minkowski sum. Subsequently, an optimal Kalman gain is derived to minimize the mean squared error of the state estimate in the KF framework by taking both stochastic and UBB errors into account. The proposed SM-HKF handles the systematic UBB error, stochastic error as well as the linearization error simultaneously, thus overcoming the limitations of the extended Kalman filter (EKF). The effectiveness and superiority of the proposed SM-HKF have been verified through simulations and comparison analysis with EKF. It is shown that the SM-HKF outperforms EKF for nonlinear state estimation with systematic UBB error and stochastic error.

Design and implementation of hybrid Kalman filter for state estimation of power system under unbalanced loads

State estimation technique plays a vital role in predicting the stability of the power system and is done by estimating the primary variables (states) of the system. Voltage magnitudes (V) and angles (δ) at network buses define the state of a power system. Supervisory control and data acquisition is used to monitor and control the power system state variables where in accurate state variable estimation is quite complex due to the presence of noise in the measured data. State estimation (SE) using conventional techniques such as weighted least square, regularised least square, Kalman filter predict the state vectors with still random error due to its parametric limitations. This study proposes hybrid Kalman filter based SE where the limitation in efficient handling of more number of variables using Kalman filter is addressed by regularising the state variables with constrains and the results are validated for 62-bus Indian utility system. The simulation results explain the operational efficiency of the hybrid Kalman filtering method under various load variation conditions and the results are compared with SE using conventional Kalman filtering method.

Dual-arm coordinated capturing of an unknown tumbling target based on efficient parameters estimation

A malfunctioned satellite or other space debris is generally non-cooperative and tumbling, bringing great challenge to capture and remove it. In this paper, we propose a dual-arm coordinated capturing method based on efficient parameters estimation. Firstly, the dynamics model of a tumbling target is deduced in details. Its motion characteristics are then analyzed. Secondly, we design an efficient Hybrid Kalman Filter (HKF) by combining Extended Kalman Filter (EKF) with Unscented Kalman Filter (UKF). It effectively overcomes the shortcoming of low accuracy of EKF and long iteration time of UKF, and improves the speed and accuracy of the Kalman Filter iteration algorithm. Two movement cases of an uncontrolled target are considered: one is rotation around the principal axes of inertia; the other is rotation around arbitrary axes. Thirdly, the estimated motion and inertia parameters are used to plan the trajectories of a dual-arm space robot to capture the tumbling target. Finally, the simulation environment is created and the proposed method is verified. The simulation results show that the proposed HKF algorithm can estimate the attitude quaternion, angular velocity, and the inertia tensor (including Ixx, Iyy, Izz, Ixy, Ixz and Iyz) with higher accuracy (compared to EKF) and lower computation cost (compared to UKF); the planned trajectories of the dual-arm space robot are effectively for tumbling target capturing.

Double hybrid Kalman filtering for state estimation of dynamical systems

In this paper authors present a new approaches to the hybrid Kalman filtering and modified hybrid Kalman filtering, with the changed order of methods inside (Unscented Kalman Filter and Extended Kalman Filter). For these algorithms, the modification based on double use of Hybrid Kalman Filters (Excented and Unscented) has been proposed. This new modification has been checked for Hybrid Kalman Particle Filters too, for the variable number of particles. Based on the obtained results, one can see that duplication of hybrid filters can improve the estimation quality.

Hybrid Kalman Filtering Algorithm With Stochastic Nonlinearities and Multiple Missing Measurements

In this paper, the hybrid Kalman filter is designed for a class of special nonlinear systems where the state equation is nonlinear and the measurement equation is linear. The stochastic nonlinearities, which are described by statistical means, are considered in the system model to reflect the multiplicative stochastic disturbances. The phenomenon of multiple missing measurements is depicted by a set of the Bernoulli distributed random variables with known conditional probabilities and the missing rates of every sensor are different. We need to compute the parameters to reduce the effects of the stochastic nonlinearities and the phenomenon of multiple missing measurements. In addition then, based on the recursive projection formula and the unscented transformation approach, a new hybrid Kalman filtering algorithm is proposed such that, for the stochastic nonlinearities and multiple missing measurements, the filtering error is minimized. By solving the recursive matrix equation, the filter gain matrices and the error covariance matrices can be obtained and the proposed results can be easily verified by using the standard numerical software. We finally provide a numerical example to show the performance of the proposed approach.

Biased Constrained Hybrid Kalman Filter for Range-Based Indoor Localization

The range-based localization method is widely used in wireless sensor localization systems. Many existing localization algorithms are unbiased estimators. However, the estimation performance presents biased features in the real localization systems. On the other hand, many biased location estimators show some essential advantages over unbiased estimators, e.g., robust to the noise, more accurate estimation, and low complexity. In this paper, we deeply investigate the performance of biased estimator, min-max, to achieve a new accuracy limit, and propose a hybrid Kalman filtering algorithm, which recursively locates the target based on biased feature. The first contribution is that we formulate the biased Cramer-Rao lower bound of the min-max algorithm to indicate that the biased localization algorithm can outperform the unbiased algorithms, e.g., maximum likelihood, as if the estimation bias were attained. The second contribution is that we propose a hybrid Kalman filtering algorithm while employing the min-max to construct a constrain region and using the dynamic Gaussian model for calculation in non-Gaussian environments. Our algorithm is robust to complicated environments with high accuracy. And, we implement it in an IoT target tracking platform. Both theoretical analysis and experimental evaluation indicate that the proposed algorithm outperform the unbiased optimal estimation methods. And our algorithm can control the estimation error in only 1 m.