Measurement Update Research Articles

Using Allan variance to improve stochastic modeling for accurate GNSS/INS integrated navigation

MEMS-based integrated system of a global navigation satellite system (GNSS) and an inertial navigation system (INS) has been widely used in various navigation applications. However, such integration encounters some major limitations. On the one hand, the noisy MEMS-based INS undermines the accuracy with time during the frequently occurring GNSS outages caused by signal blockage or attenuation in certain situations such as urban canyon, tunnels, and high trees. On the other hand, the model mismatch between actual GNSS error and the assumed one would also degrade the obtained accuracy even with continuous GNSS aiding. To improve the overall performance for GNSS/MEMS-INS, better error models can be obtained using Allan variance (AV) analysis technique for modeling inertial sensor errors instead of the commonly recommended auto-regressive processes, and on the other hand, the measurement update in Kalman filter is improved using innovation filtering and AV calculation. The performance of each method and the combined algorithm is evaluated by a field test with either differential GNSS (DGNSS) or single-point positioning (SPP) as external aid. In addition to the considerable navigation enhancement brought by each method, the experimental results show the combined algorithm accomplishes overall accuracy improvements by about 18% (position), 8% (velocity), and 38% (attitude) for integration with DGNSS, and by about 15% (position), 75% (velocity), and 77% (attitude) for that with SPP, compared with corresponding traditional counterparts.

Bayesian filtering based on solving the Fokker-Planck equation

PurposeThis paper aims to propose Bayesian filtering based on solving the Fokker–Planck equation, to improve the accuracy of filtering in non-Gauss case. Nonlinear filtering plays an important role in many science and engineering fields for estimating the state of dynamic system, but the existing filtering algorithms are mainly used for solving the problem of Gauss system.Design/methodology/approachUnder the Bayesian framework, the time update of this filtering is based on solving Fokker–Planck equation, while the measurement update uses the Bayes formula directly. Therefore, this novel algorithm can be applied to nonlinear, non-Gaussian estimation. To reduce the computational complexity due to standard meshing, an adaptive meshing algorithm proposed which includes the coarse meshing, significant domain determination that is generated using extended Kalman filtering and Chebyshev’s inequality theorem, and value assignment for significant domain. Simulations are conducted on a reentry body tracking problem to demonstrate the effectiveness of this novel algorithm.FindingsIn this way, finer grid points can be placed in the regions with high conditional probability density, while the grid points with low conditional probability density can be neglected. The simulation results indicate that the novel algorithm can reduce the computational burden significantly compared to the standard meshing, while achieving similar accuracy.Practical implicationsA novel Bayesian filtering based on solving the Fokker–Planck equation using adaptive meshing is proposed, and the simulations show that algorithm can reduce the computational burden significantly compared to the standard meshing, while achieving similar accuracy.Originality/valueA novel nonlinear filtering based on solving the Fokker–Planck equation is proposed. The novel algorithm is suitable for non-Gauss system, and can achieve similar accuracy compared to the standard meshing with the significant reduction of computational burden.

On the use of decision feedback equalization for continuous active sonar

Continuous Active SONAR (CAS) systems allow duty cycles up to 100% and so lower target association errors are possible as compared to Pulse Active Sonar (PAS). Large time-bandwidth product Linear Frequency Modulated (LFM) signals are the de facto standard for this type of SONAR systems, yet, these signals suffer from low processing gains when the ocean exhibits low-spatio temporal coherence. In this work, we depart from the typical sub-band matched filter processing and propose to adopt signal processing techniques used in underwater acoustic communications. In particular, we analyze Binary Phase Shift Keying (BPSK) signals via an adaptive Decision-Feedback Equaliser (DFE). The DFE is able to adapt to environmental changes based on the known transmitted bits. The operational bandwidth is 1500–4000 Hz and the BPSK signals are transmitted in two non-overlapping bands to avoid transmit interference during reception. The performance of the proposed system is demonstrated based on field data recorded during a sea experiment off the Coast of La Spezia in October 2017. The key result here is that the Doppler measurement update rate of the echoes is as fast as the bit rate of the transmitted BPSK signal.Continuous Active SONAR (CAS) systems allow duty cycles up to 100% and so lower target association errors are possible as compared to Pulse Active Sonar (PAS). Large time-bandwidth product Linear Frequency Modulated (LFM) signals are the de facto standard for this type of SONAR systems, yet, these signals suffer from low processing gains when the ocean exhibits low-spatio temporal coherence. In this work, we depart from the typical sub-band matched filter processing and propose to adopt signal processing techniques used in underwater acoustic communications. In particular, we analyze Binary Phase Shift Keying (BPSK) signals via an adaptive Decision-Feedback Equaliser (DFE). The DFE is able to adapt to environmental changes based on the known transmitted bits. The operational bandwidth is 1500–4000 Hz and the BPSK signals are transmitted in two non-overlapping bands to avoid transmit interference during reception. The performance of the proposed system is demonstrated based on field data recorded during a ...

Utilizing Out-of-Sequence Measurement for Ambiguous Update in Particle Filtering

This paper proposes a novel method to cope with local measurement ambiguity problem in particle filtering. The ambiguity of the measurement has been attributed as a crucial cause of filter degradation and divergence. Given the observation that the ambiguous measurement update is contributed by not only the shape of the measurement model but also the prior distribution of the filter estimate, we adopt a solution to the out-of-sequence measurement problem on the framework of the particle filter with sequential importance resampling. Once an ambiguous measurement update is detected, the proposed method skips the measurement update at the time step and utilizes the measurement later when the particle distribution becomes adequate for the measurement update. This strategy provides a remedy to the ambiguity problem to obtain accurate current position estimate with lower covariance. Numerical simulation is presented to demonstrate effectiveness and performance of the proposed method. Compared to other methods, such as the standard particle filter, the auxiliary particle filter, the mixture particle filter, and the receding-horizon Kalman filter, the proposed method shows better performance in terms of root-mean-square error and estimated covariance.

A Tighter Set-Membership Filter for Some Nonlinear Dynamic Systems

In this paper, we propose a tighter set-membership filter for some nonlinear dynamic systems by using an analytic method and a boundary sampling technique. The nonlinear dynamic systems can be linearized about the current estimate, then the remainder term is bounded in real time by an optimization ellipsoid, other than a priori remainder bound. For a 2-D radar system and a quadratic system, some regular properties can be derived for the remainder term, which helps us obtain a tighter bounding ellipsoid to cover the remainder. Moreover, the prediction step and the measurement update step are derived based on the recent optimization method and the on-line bounding ellipsoid of the remainder, so that a tighter set-membership filter can be achieved. The numerical examples demonstrate the effectiveness of the proposed filter.

Robust Derivative Unscented Kalman Filter Under Non-Gaussian Noise

A robust derivative unscented Kalman filter is proposed for a nonlinear system with non-Gaussian noise and outliers based on Huber function. In this paper, the time update process can be performed using a Kalman filter (KF), and measurement update process can be carried out utilizing an unscented transform. This novel filtering algorithm differs from the traditional unscented Kalman filter (UKF) which is sensitive to non-Gaussian noise and outliers. Besides, for a nonlinear system with linear state equation, the presented filtering has the merits of both KF and UKF, and it has better performance under non-Gaussian noise and large outliers. Furthermore, the proposed filtering algorithm can not only track the target effectively but also suppress the effects of the non-Gaussian noise and large outliers. Finally, numerical simulations are conducted to verify estimation accuracy and effectiveness of the proposed filtering algorithm.

Employing economical methods for pavement defects estimation

It is a common practise that measurements of road surface conditions are made using professional and expensive apparatus. Typically a van or a truck equipped with a set of professional sensors i.e. laser scanners of surface is used, therefore the measurement update period is often quite long. Two alternative low-cost methods for estimating road pavement defects and failures were proposed and investigated by the authors. The first one is based on accelerometers application and the other one employs image analysis acquired by cameras installed on a vehicle.

Hybrid Genetic Algorithm and Kalman Filter Approach to Estimate the Clamping Force of Electro-Mechanical Brake

In thispaper, a hybrid genetic algorithm (GA) and Kalman filter approach to combining motor encoder and current sensor models is presented to accurate estimate the clamping force of an electro-mechanical brake (EMB). Elimination of the clamping force sensor and measurement cables results in lower cost and increased reliability of an EMB system, including its electric motor.A Kalman filter is a special kind of observer that provides optimal filtering of the measurement noise and inside the system if the covariances of these noises are known. The proposed combined estimator is based on Kalman filter optimized by GA in which the motor encoder is used in a dynamic stiffness model and the motor current sensor is used to give measurement updates in a torque balance model. A real-coded GA is used to optimize the noise matrices and improve the performance of the Kalman filter. Experimental results show that, by using the proposed estimator, the virtual clamping force sensor can handle highly dynamic situations, making it suitable for possible use in sensorless fault-tolerant control. It is shown that the proposed combined estimator improves the root mean square error (RMSE) performance. The developed estimator can be used in real vehicle environments because it can adapt to parameter variations.

GPS/BDS/INS tightly coupled integration accuracy improvement using an improved adaptive interacting multiple model with classified measurement update

An Extended Kalman Filter (EKF) is commonly used to fuse raw Global Navigation Satellite System (GNSS) measurements and Inertial Navigation System (INS) derived measurements. However, the Conventional EKF (CEKF) suffers the problem for which the uncertainty of the statistical properties to dynamic and measurement models will degrade the performance. In this research, an Adaptive Interacting Multiple Model (AIMM) filter is developed to enhance performance. The soft-switching property of Interacting Multiple Model (IMM) algorithm allows the adaptation between two levels of process noise, namely lower and upper bounds of the process noise. In particular, the Sage adaptive filtering is applied to adapt the measurement covariance on line. In addition, a classified measurement update strategy is utilized, which updates the pseudorange and Doppler observations sequentially. A field experiment was conducted to validate the proposed algorithm, the pseudorange and Doppler observations from Global Positioning System (GPS) and BeiDou Navigation Satellite System (BDS) were post-processed in differential mode. The results indicate that decimeter-level positioning accuracy is achievable with AIMM for GPS/INS and GPS/BDS/INS configurations, and the position accuracy is improved by 35.8%, 34.3% and 33.9% for north, east and height components, respectively, compared to the CEKF counterpart for GPS/BDS/INS. Degraded performance for BDS/INS is obtained due to the lower precision of BDS pseudorange observations.

Entropy optimization based filtering for non-Gaussian stochastic systems

This paper is concerned with the entropy optimization based filter design for a class of multivariate dynamic stochastic systems with simultaneous presence of non-Gaussian process noise and measurement noise. The filter consists of time update and measurement update two steps, where the selection of the filter gain in the measurement update equation is a key issue to be addressed. Different from the classic Kalman filter theory, entropy rather than variance is employed as the filtering performance criterion due to the non-Gaussian characteristic of the estimation error. Following the establishment of the relationship between the probability density functions of random noises and estimation error, two kinds of entropy based performance indices are provided. On this basis, the corresponding optimal filter gains are obtained respectively by using the gradient optimization technique. Finally, some numerical simulations are provided to demonstrate the effectiveness of the proposed filtering algorithms.

Data Assimilation of Ground‐Based GPS and Radio Occultation Total Electron Content for Global Ionospheric Specification

AbstractThis study presents an approach based on the Gauss‐Markov Kalman filter to assimilate the total electron content observed from ground‐based GPS receivers and space‐based radio occultation instrumentations (such as FORMOSAT‐3/COSMIC (F3/C) and FORMOSAT‐7/COSMIC‐2 (F7/C2)) into the International Reference Ionosphere. Observing System Simulation Experiments (OSSEs) show that the data assimilation procedure consisting of the forecast and the measurement update steps can better improve the accuracy of the data assimilation analysis than the assimilation procedure using the measurement update alone. Compared with F3/C, the denser F7/C2 occultation observations can improve the analysis accuracy significantly as suggested by OSSEs. The real data assimilation results are further validated with global ionosphere maps, the global ground‐based GPS measurements, and the ionospheric F2 peak height and electron density sounded by ionosondes. Both the OSSEs and validation results confirm that a number of improvements to the data assimilation procedure presented in this paper can indeed be used to reconstruct the three‐dimensional ionospheric electron density adequately.

Multiple Sensor Measurement Updates for the Extended Target Tracking Random Matrix Model

In this paper, multiple sensor measurement update is studied for a random matrix model. Four different updates are presented and evaluated: three updates based on parametric approximations of the extended target state probability density function and one update based on a Rao–Blackwellized (RB) particle approximation of the state density. An extensive simulation study shows that the RB particle approach shows best performance, at the price of higher computational cost, compared to parametric approximations.

Maximum correntropy sparse Gauss–Hermite quadrature filter and its application in tracking ballistic missile

A novel robust filter referred as maximum correntropy sparse Gauss–Hermite quadrature filter (MCSGHQF) is proposed. The novel algorithm makes use of the sparse Gauss–Hermite quadrature (SGHQ) rule to numerically compute Gaussian-weighted integrals, which are propagated through non-linear state equation, and then a weighted means and covariance is taken. As the sensor measurements are always corrupted by non-Gaussian noise which is typically glint noise or mixed Gaussian-impulsive noise, the measurement update is redesigned based on the maximum correntropy criterion instead of minimum mean square error. Therefore, the MCSGHQF could exhibit robustness to the non-Gaussian measurement noise, especially impulsive noise. In addition, the study proposes the use of MCSGHQF for ballistic missile tracking during midcourse phase to deal with the non-Gaussian noise. The tracking performance is compared with that of SGHQ filter (SGHQF), Huber-based filter and extended Kalman filter by Monte-Carlo simulations. The simulation results demonstrate that the MCSGHQF is effective in glint noise case and exhibits superior to Huber-based filter in mixed Gaussian-impulsive noise case.

A probabilistic optimization approach for motion planning of autonomous vehicles

This paper presents a novel probabilistic approach for improving the motion planning performance of autonomous driving. The proposed approach is based on the sampling-based planning algorithm, which generates an optimal trajectory from a set of trajectory candidates. In order to treat the uncertainty in the perception data and the vehicle system, the particle filter framework is applied to the motion planning algorithm with four main steps: the time update of the trajectory candidates, the perception measurement update, the trajectory selection and the motion goal resampling. Since the proposed planning algorithm recursively generates an optimal trajectory, the time update of the trajectory candidate updates the motion goals of the trajectory candidates in the previous step using the vehicle model, and it also generates a new set of candidates. In order to evaluate the optimality of each candidate with regard to the safety and the reliability, a perception measurement update is performed. In this step, the importance weight of each candidate is computed using perception data and its adaptive likelihood function. Based on the candidates with updated importance weights, an optimal trajectory is determined in the trajectory selection. Then, the motion goal resampling modifies the set of motion goals based on the importance weights for efficient management of the motion goals in the iterative planning algorithm. The developed algorithm is validated using various types of test. The results show that the proposed method not only provides an integrated probabilistic interface between the perception and the planning but also results in an excellent performance in terms of the computation efficiency.

Accurate State Estimation in Continuous-Discrete Stochastic State-Space Systems With Nonlinear or Nondifferentiable Observations

This paper presents a novel method of nonlinear Kalman filtering, which unifies the best features of the accurate continuous-discrete extended and cubature Kalman filters. More precisely, the time updates in the discussed state estimator are done as those in the first filter whereas the measurement updates are conducted with use of the third-degree spherical-radial cubature rule applied for approximating the arisen Gaussian-weighted integrals. All this allows accurate predictions of the state mean and covariance matrix to be combined with accurate measurement updates. Moreover, the new filter is particularly effective for continuous-discrete stochastic systems with nonlinear and/or nondifferentiable observations. The efficiency of this mixed-type method is shown in comparison to the performance of the original accurate continuous-discrete extended and cubature Kalman filters in severe conditions of tackling a seven-dimensional radar tracking problem, where an aircraft executes a coordinated turn, with sufficiently long sampling times.

Cooperative Localization of Connected Vehicles: Integrating GNSS With DSRC Using a Robust Cubature Kalman Filter

Cooperative localization of the connected vehicles is significant for many advanced intelligent transportation system (ITS) applications. Vehicle-to-vehicle communication using dedicated short-range communication (DSRC) has great potential to enhance global navigation satellite systems (GNSSs) for the capability of cooperative localization. In the integration of DSRC and GNSS, the tolerance against the unknown and time-varying observation conditions is a key factor to fulfill the requirements of several specific ITS applications. Under a GNSS/DSRC integrated architecture for cooperative localization, a novel robust cubature Kalman filter (CKF) is proposed in this paper to improve the performance of the data fusion under uncertain sensor observation environments. In the proposed solution, the structure of the standard CKF is enhanced using the Huber M-estimation technique, in which the original measurement update in the CKF is modified considering the probable anomalies in state estimation. Furthermore, based on the investigation of the adjustment effect from the constraint factor, an adaptive strategy for this parameter is introduced to optimize the performance comprehensively. The proposed method is validated using a specific simulation system. Results of experiment and simulations demonstrate the capability of improving the robustness and adaptive performance over the original filters under the unknown operation conditions.

Spekkens’ toy model in all dimensions and its relationship with stabiliser quantum mechanics

Spekkens’ toy model is a non-contextual hidden variable model with an epistemic restriction, a constraint on what an observer can know about reality. The aim of the model, developed for continuous and discrete prime degrees of freedom, is to advocate the epistemic view of quantum theory, where quantum states are states of incomplete knowledge about a deeper underlying reality. Many aspects of quantum mechanics and protocols from quantum information can be reproduced in the model. In spite of its significance, a number of aspects of Spekkens’ model remained incomplete. Formal rules for the update of states after measurement had not been written down, and the theory had only been constructed for prime-dimensional and infinite dimensional systems. In this work, we remedy this, by deriving measurement update rules and extending the framework to derive models in all dimensions, both prime and non-prime. Stabiliser quantum mechanics (SQM) is a sub-theory of quantum mechanics with restricted states, transformations and measurements. First derived for the purpose of constructing error correcting codes, it now plays a role in many areas of quantum information theory. Previously, it had been shown that Spekkens’ model was operationally equivalent to SQM in the case of odd prime dimensions. Here, exploiting known results on Wigner functions, we extend this to show that Spekkens’ model is equivalent to SQM in all odd dimensions, prime and non-prime. This equivalence provides new technical tools for the study of technically difficult compound-dimensional SQM.

An Implicit UKF for Satellite Stellar Refraction Navigation System

The stellar refraction navigation is a type of autonomous celestial navigation method for satellites that uses high-accuracy star sensors to obtain the stellar refraction. The apparent height and the stellar refraction angle are two kinds of measurements for the satellite stellar refraction navigation system. A better navigation performance can be achieved by the stellar refraction angle rather than the refraction apparent height. However, the measurement model of the stellar refraction angle is an implicit function, which needs an implicit filter method. A new implicit unscented Kalman filter (UKF) method is proposed and applied to the satellite stellar refraction navigation system in this paper. The main difference between the classical UKF and the implicit UKF lies in the measurement update. First, since the implicit measurement model can be rearranged into an equation whose one side is zero, the vector of zeros is regarded as the equivalent measurement, and the difference between the predicted measurement and its true value is utilized for updating the predicted state and its covariance matrix. Second, the measurement noise and its covariance matrix are transformed based on the unscented transformation principle. In addition, the implicit UKF is compared with the implicit extended Kalman filter (IEKF), the iterative IEKF, and the UKF. Simulations show that the proposed implicit UKF method can obtain about 19.0% and 17.5% improvements in three-dimensional root mean square position estimation compared to the IEKF and the iterative IEKF, respectively. Although the navigation performance of the UKF is close to the implicit UKFs, the computational time of the implicit UKF is much shorter than the UKFs. In addition, the sensitivities of the four different Kalman filters to the star sensor's faults and the atmosphere perturbation are compared, respectively.

High-Speed Resonant Surface Acoustic Wave Instrumentation Based on Instantaneous Frequency Measurement

Surface acoustic wave (SAW) resonators are used for a broad range of wireless sensing applications, some of them having high demands on the resolution as well as the measurement update rate. This paper presents a new interrogation method for precise and fast frequency determination of passive SAW resonators based on instantaneous frequency measurement by a low-cost six-port interferometer. Using a delay line, the frequency measurement is reduced to a phase measurement that can be instantaneously evaluated by the six-port network. No complex signal processing is necessary providing high update rates and low hardware costs. An in-depth analysis of the system concept and its building blocks is presented, and the advantages as well as the limitations are discussed and compared with the current state of the art. Finally, a demonstrator in the 2.4-GHz frequency band shows the feasibility and the precision of the concept with measurement times of only a few microseconds.

Design and Simulation of the Integrated Navigation System based on Extended Kalman Filter

AbstractThe integrated navigation system is used to estimate the position, velocity, and attitude of a vehicle with the output of inertial sensors. This paper concentrates on the problem of the INS/GPS integrated navigation system design and simulation. The structure of the INS/GPS integrated navigation system is made up of four parts: 1) GPS receiver, 2) Inertial Navigation System, 3) Extended Kalman filter, and 4) Integrated navigation scheme. Afterwards, we illustrate how to simulate the integrated navigation system with the extended Kalman filter by measuring position, velocity and attitude. Particularly, the extended Kalman filter can estimate states of the nonlinear system in the noisy environment. In extended Kalman filter, the estimation of the state vector and the error covariance matrix are computed by steps: 1) time update and 2) measurement update. Finally, the simulation process is implemented by Matlab, and simulation results prove that the error rate of statement measuring is lower when applying the extended Kalman filter in the INS/GPS integrated navigation system.