室内行人航迹推算/超声波组合定位融合算法

为提高室内定位系统精度和跟踪性能以及适应复杂环境,将行人航迹推算与超声波定位组合,提出基于平方根无迹卡曼滤波的噪声权因子辅助协方差加权融合算法,并将全局最优融合状态作为反馈量引入算法。针对超声波对行人航向角测量困难,采用一种简单有效的几何方法。仿真结果表明:在模拟的室内动态环境中,包括在多路径效应和惯性累积误差的影响下,融合算法始终比单模型定位精度高,并有很好的收敛性、稳定性与适应性,对室内定位技术研究与应用具有重要意义。

Robust UKF algorithm in SINS initial alignment

In the traditional unscented Kalman filter（UKF）,accuracy and robustness decline when uncertain disturbances exist in the practical system.To deal with the problem,a robust UKF algorithm based on an H-infinity norm is proposed.In Krein space,a robust element is added in the simplified UKF so as to improve the algorithm.The filtering gain is adjusted by the robust element and in this way the performance of the robustness of the filtering algorithm is promoted.In the initial alignment process of the large heading misalignment angle of the strapdown inertial navigation system（SINS）,comparative studies are conducted on the robust UKF and the simplified UKF.The simulation results illustrate that compared with the simplified UKF,the robust UKF is more accurate,and the estimation error of heading misalignment decreases from 16.9＇ to 4.3＇.In short,the robust UKF can reduce the sensitivity to the system disturbances resulting in better performance.

Application of unscented Kalman filter to novel terrain passive integrated navigation system

To improve the navigation accuracy of an autonomous underwater vehicle （AUV）, a novel terrain passive integrated navigation system （TPINS） is presented. According to the characteristics of the underwater environment and AUV navigation requirements of low cost and high accuracy, a novel TPINS is designed with a configuration of the strapdown inertial navigation system （SINS）, the terrain reference navigation system （TRNS）, the Doppler velocity sonar （DVS）, the magnetic compass and the navigation computer utilizing the unscented Kalman filter （UKF） to fuse the navigation information from various navigation sensors. Linear filter equations for the extended Kalman filter （EKF）, nonlinear filter equations for the UKF and measurement equations of navigation sensors are addressed. It is indicated from the comparable simulation experiments of the EKF and the UKF that AUV navigation precision is improved substantially with the proposed sensors and the UKF when compared to the EKF. The TPINS designed with the proposed sensors and the UKF is effective in reducing AUV navigation position errors and improving the stability and precision of the AUV underwater integrated navigation.

Federated UKF algorithm for mobile location estimation with TDOA/Doppler measurements

In order to enhance the location estimation performance of mobile station（MS）tracking and positioning, a new method of mobile location optimal estimation based on the federated filtering structure and the simplified unscented Kalman filter （UKF） is presented. The proposed algorithm uses the Singer mobile statement model as the reference system, and the simplified UKF as the subfilters. The subfilters receive the two groups of independently detected time difference of arrival （TDOA） measurement inputs and Doppler measurement inputs, and produce local estimation outputs to the main estimator. Then the main estimator performs the optimal fusion of the local estimation outputs according to the scalar weighted rule, and a global optimal or suboptimal estimation result is achieved. Finally the main estimator gives feedback and reset information to the subfilters and the reference system for next step estimation. In the simulations, the estimation performance of the proposed algorithm is evaluated and compared with the simplified UKF method with TDOA or Doppler measurement alone. The simulation results demonstrate that the proposed algorithm can effectively reduce the location estimation error and variance of the MS, and has favorable performance in both root mean square error（RMSE） and mean error cumulative distribution function（CDF）.

基于遥感无人机的多移动目标协同跟踪算法

针对地面移动目标的跟踪问题,提出基于无人机协作的多移动目标跟踪算法(MTCU)。MTCU算法配备悬挂遥感器的无人机(UAV)跟踪目标,先通过无迹卡曼滤波(UKF)描述目标的移动状态,再通过采样变换技术对观测值进行转换,降低目标位置的不确定性。同时,MTCU算法采用二进制一致性算法协调UAVs间跟踪目标的方案,使多个UAVs跟踪目标的方案达成一致,均衡UAVs跟踪目标的任务。仿真结果表明,通过多个UAVs协同,MTCU算法能够有效跟踪目标。

Navigation system of a class of underwater vehicle based on adaptive unscented Kalman fiter algorithm

Inherent flaws in the extended Kalman filter(EKF) algorithm were pointed out and unscented Kalman filter(UKF) was put forward as an alternative.Furthermore,a novel adaptive unscented Kalman filter(AUKF) based on innovation was developed.The three data-fusing approaches were analyzed and evaluated in a mathematically rigorous way.Field experiments conducted in lake further demonstrate that AUKF reduces the position error approximately by 65% compared with EKF and by 35% UKF and improves the robust performance.

On-line Estimation in Fed-batch Fermentation Process Using State Space Model and Unscented Kalman Filter

On-line estimation of unmeasurable biological variables is important in fermentation processes,directly influencing the optimal control performance of the fermentation system as well as the quality and yield of the targeted product.In this study,a novel strategy for state estimation of fed-batch fermentation process is proposed.By combining a simple and reliable mechanistic dynamic model with the sample-based regressive measurement model,a state space model is developed.An improved algorithm,swarm energy conservation particle swarm optimization(SECPSO) ,is presented for the parameter identification in the mechanistic model,and the support vector machines(SVM) method is adopted to establish the nonlinear measurement model.The unscented Kalman filter(UKF) is designed for the state space model to reduce the disturbances of the noises in the fermentation process.The proposed on-line estimation method is demonstrated by the simulation experiments of a penicillin fed-batch fermentation process.

New sigma point filtering algorithms for nonlinear stochastic systems with correlated noises

New sigma point filtering algorithms, including the unscented Kalman filter （UKF） and the divided difference filter （DDF）, are designed to solve the nonlinear filtering problem under the condition of correlated noises. Based on the minimum mean square error estimation theory, the nonlinear optimal predictive and correction recursive formulas under the hypothesis that the input noise is correlated with the measurement noise are derived and can be described in a unified framework. Then, UKF and DDF with correlated noises are proposed on the basis of approximation of the posterior mean and covariance in the unified framework by using unscented transformation and second order Stirling＇s interpolation. The proposed UKF and DDF with correlated noises break through the limitation that input noise and measurement noise must be assumed to be uneorrelated in standard UKF and DDF. Two simulation examples show the effectiveness and feasibility of new algorithms for dealing with nonlinear filtering issue with correlated noises.

Geomagnetic Orbit Determination Using Fuzzy Regulating Unscented Kalman Filter

Geomagnetic orbit determination fits for nanosatellites which pursue low cost and high-density ratio,but one of its disadvantages is the poor position accuracy introduced by magnetic bias.Here,a new method,named the fuzzy regulating unscented Kalman filter(FRUKF),is proposed.The magnetic bias is regarded as a random walk model,and a fuzzy regulator is designed to estimate the magnetic bias more accurately.The input of the regulator is the derivative of magnetic bias estimated from unscented Kalman filter(UKF).According to the fuzzy rule,the process noise covariance is adaptively determined.The FRUKF is evaluated using the real-flight data of the SWARMA.The experimental results show that the root-mean-square(RMS)position error is 3.1 km and the convergence time is shorter than the traditional way.

Hybrid Kalman and unscented Kalman filters for INS/GPS integrated system considering constant lever arm effect

In inertial navigation system(INS) and global positioning system(GPS) integrated system, GPS antennas are usually not located at the same location as the inertial measurement unit(IMU) of the INS, so the lever arm effect exists, which makes the observation equation highly nonlinear. The INS/GPS integration with constant lever arm effect is studied. The position relation of IMU and GPS's antenna is represented in the earth centered earth fixed frame, while the velocity relation of these two systems is represented in local horizontal frame. Due to the small integration time interval of INS, i.e. 0.1 s in this work, the nonlinearity in the INS error equation is trivial, so the linear INS error model is constructed and addressed by Kalman filter's prediction step. On the other hand, the high nonlinearity in the observation equation due to lever arm effect is addressed by unscented Kalman filter's update step to attain higher accuracy and better applicability. Simulation is designed and the performance of the hybrid filter is validated.

Noise estimation and filtering method of MEMS gyroscope based on EMMAP

Aiming at the problems of low measurement accuracy,uncertainty and nonlinearity of random noise of the micro electro mechanical system(MEMS)gyroscope,a gyroscope noise estimation and filtering method is proposed,which combines expectation maximum(EM)with maximum a posterior(MAP)to form an adpative unscented Kalman filter(UKF),called EMMAP-UKF.According to the MAP estimation principle,a suboptimal unbiased MAP noise statistical estimation model is constructed.Then,EM algorithm is introduced to transform the noise estimation problem into the mathematical expectation maximization problem,which can dynamically adjust the variance of the observed noise.Finally,the estimation and filtering of gyroscope random drift error can be realized.The performance of the gyro noise filtering method is evaluated by Allan variance,and the effectiveness of the method is verified by hardware-in-the-loop simulation.

Online prediction for contamination of chlortetracycline fermentation based on Dezert–Smarandache theory

Fermentative production of chlortetracycline is a complex fed-batch bioprocess. It generally takes over 90 h for cultivation and is often contaminated by undesired microorganisms. Once the fermentation system is contaminated to certain extent, the product quality and yield will be seriously affected, leading to a substantial economic loss. Using information fusion based on the Dezer–Smarandache theory, self-recursive wavelet neural network and unscented kalman filter, a novel method for online prediction of contamination is developed. All state variables of culture process involving easy-to-measure and difficult-to-measure variables commonly obtained with soft-sensors present their contamination symptoms. By extracting and fusing latent information from the changing trend of each variable, integral and accurate prediction results for contamination can be achieved. This makes preventive and corrective measures be taken promptly. The field experimental results show that the method can be used to detect the contamination in time, reducing production loss and enhancing economic efficiency.

Multi-sensor federated unscented Kalman filtering algorithm in intermittent observations

Aiming at the adverse effect caused by limited detecting probability of sensors on filtering preci- sion of a nonlinear system state, a novel muhi-sensor federated unscented Kalman filtering algorithm is proposed. Firstly, combined with the residual detection strategy, effective observations are cor- rectly identified. Secondly, according to the missing characteristic of observations and the structural feature of unscented Kalman filter, the iterative process of the single-sensor unscented Kalman filter in intermittent observations is given. The key idea is that the state estimation and its error covariance matrix are replaced by the state one-step prediction and its error covariance matrix, when the phe- nomenon of observations missing occurs. Finally, based on the realization mechanism of federated filter, a new fusion framework of state estimation from each local node is designed. And the filtering precision of system state is improved further by the effective management of observations missing and the rational utilization of redundancy and complementary information among multi-sensor observa- tions. The theory analysis and simulation results show the feasibility and effectiveness of the pro- posed algorithm.

Video stabilization motion filtering based on constraint unscented Kalman filter

A motion filtering method is proposed in this paper, which takes into consideration the existence of certain system constraints with respect to the amount of the corrective rotational and translational motions that can be applied on each video frame for stabilization. The interdependence between rotational and translational constraints is considered, and a constraint unscented Kalman filter （CUKF） algorithm is utilized to achieve a smoothly stabilized motion. The method is applied to stabilize each video frame, and the results reveal that the proposed approach improves the stabilization performance in comparison with the trivial approach.

A stealthy method to determine the relative position and velocity for satellite formation flying

To achieve the satellite formation control and the succeed formation missions, we present a new stealthy method to determine the relative states between formation satellites. In this method, the combination of a CCD camera and laser radar is used as the relative measure sensors. To reduce electromagnetic radiation, the laser radar works intermittently to minimize the probability of being discovered. And an unscented Kalman filter (UKF) is applied to estimate the relative states. The observability of this method is analyzed. The validity and effectiveness of the method is demonstrated in a typical application of formation relative navigation.

Estimation of catalytic activity using an unscented Kalman filtering in condensation reaction

The catalytic activity of cation exchange resins will be continuously reduced with its use time in a condensation reaction for bisphenol A(BPA).For online estimation of the catalytic activity,a catalytic deactivation model is studied for a production plant of BPA,state equation and observation equation are proposed based on the axial temperature distribution of the reactor and the acetone concentration at reactor entrance.A hybrid model of state equation is constructed for improving estimation precision.The unknown parameters in observation equation are calculated with sample data.The unscented Kalman filtering algorithm is then used for on-line estimation of the catalytic activity.The simulation results show that this hybrid model has higher estimation accuracy than the mechanism model and the model is effective for production process of BPA.

Integrating a model with remote sensing observations by a data assimilation approach to improve the model simulation accuracy of carbon flux and evapotranspiration at two flux sites

Model simulation and in situ observations are often used to research water and carbon cycles in terrestrial ecosystems, but each of these methods has its own advantages and limitations. Combining these two methods could improve the accuracy of quantifying the dynamics of the water and carbon fluxes of an ecosystem. Data assimilation is an effective means of integrating modeling with in situ observation. In this study, the ensemble Kalman filter(En KF) and the unscented Kalman filter(UKF) algorithms were used to assimilate remotely sensed leaf area index(LAI) data with the Biome-BGC model to simulate water and carbon fluxes at the Harvard Forest Environmental Monitoring Site(EMS) and the Dinghushan site. After MODIS LAI data from 2000–2004 were assimilated into the improved Biome-BGC model using the En KF algorithm at the Harvard Forest site, the R2 between the simulated and observed results for NEE and evapotranspiration increased by 7.8% and 4.7%, respectively. In addition, the sum of the absolute error(SAE) and the root mean square error(RMSE) of NEE decreased by an average of 21.9% and 26.3%, and the SAE and RMSE of evapotranspiration decreased by 24.5% and 25.5%, respectively. MODIS LAI data of 2003 were assimilated into the Biome-BGC model for the Dinghushan site, and the R2 values between the simulated and observed results for NEE and evapotranspiration were increased by 6.7% and 17.3%, respectively. In addition, the SAE values of NEE and ET were decreased by 11.3% and 30.7%, respectively, and the RMSE values of NEE and ET decreased by 10.1% and 30.9%, respectively. These results demonstrate that the accuracy of carbon and water flux simulations can be effectively improved when remotely sensed LAI data are properly integrated with ecosystem models through a data assimilation approach.

Tracking with nonlinear measurement model by coordinate rotation transformation

A new filtering method is proposed to accurately estimate target state via decreasing the nonlinearity between radar polar measurements(or spherical measurements in three-dimensional(3D) radar) and target position in Cartesian coordinate. The degree of linearity is quantified here by utilizing correlation coefficient and Taylor series expansion. With the proposed method, the original measurements are converted from polar or spherical coordinate to a carefully chosen Cartesian coordinate system that is obtained by coordinate rotation transformation to maximize the linearity degree of the conversion function from polar/spherical to Cartesian coordinate. Then the target state is filtered along each axis of the chosen Cartesian coordinate. This method is compared with extended Kalman filter(EKF), Converted Measurement Kalman filter(CMKF), unscented Kalman filter(UKF) as well as Decoupled Converted Measurement Kalman filter(DECMKF). This new method provides highly accurate position and velocity with consistent estimation.

Path Following Control of Underactuated Ships Based on Unscented Kalman Filter

A path following controller is proposed to force an underactuated surface ship which is suffering from disturbance to follow a predefined path.The controller is based on analytic model predictive control and unscented Kalman filter(UKF) techniques.The analytic model predictive control provides a systematic method to get appropriate controller parameters to guarantee the stability of the closed-loop system,and the well-defined relative degree is guaranteed by introducing output-redefinition.The UKF is used to estimate the states and uncertain parameters due to time-varying added mass matrices.With help of the proposed UKF-based controller,the underactuated ship with time-varying parameters can follow a desired straight path.Simulation results are presented to demonstrate the effectiveness of the proposed controller.