Measurement Update Research Articles

A novel hybrid consensus-based variational Bayesian filter with position uncertainty in multi-agent system

Most existing distributed state estimation approaches assume that the position of agent in multi-agent system (MAS) is precisely known. However, in target tracking applications, the position of agent is noisy, which makes traditional distributed state estimation methods suffer from accuracy reduction. This paper focuses on developing a novel hybrid consensus-based variational Bayesian filter (HCVB) for target tracking with position uncertainty in nonlinear MAS. To improve the nonlinear approximation accuracy, high-degree cubature information filter framework is used. To cope with agent position uncertainty, the measurement update is derived by using variational Bayesian (VB) method to approximate the joint posterior distribution of the target state and agent position, which can estimate the state and agent position jointly. To decrease the required consensus iterations, a hybrid consensus method is proposed, which can achieve global consistency of all agents with a few consensus iterations. Simulations on UAV tracking in MAS verify the superiority of the proposed method.

An In-Vehicle Smartphone RTK/DR Positioning Method Combined with OSM Road Network

In vehicle navigation scenarios, the RTK positioning results of smartphones are prone to jumps due to the interference of complex urban environments, and the heading angle of dead reckoning (DR) is prone to divergence. In order to obtain more stable and high-precision smartphone positioning results, this paper proposes an RTK/DR positioning method combined with the OpenStreetMap road network. The OpenStreetMap road network data are used to correct the heading angle during the linear motion phase to improve heading angle accuracy. In order to reduce the impact of RTK results jumping on subsequent DR, it is possible to set up a measurement update switch, which combines the RTK covariance matrix, vehicle motion state, and RTK heading angle change information to determine whether to perform a measurement update. The research uses two smartphones to carry out four vehicle positioning tests. The eight sets of test results show that the heading angle correction method based on the OpenStreetMap road network can effectively control the accumulation of heading angle errors and allow DR trajectory to be more consistent with the benchmark. Compared with RTK, the forward accuracy of RTK/DR positioning method is almost unchanged, even though the direction accuracy and lateral positioning accuracy are significantly improved. The RTK/DR horizontal positioning accuracy of both smartphones is approximately 1.3 m, which is better rather than the RTK results. The proposed RTK/DR positioning method can obtain more reliable orientation and position information than RTK.

RHM-δ-GLMB Tracking Algorithm on the Focal Plane for UAV Cluster Targets

This paper offers a new tracking algorithm for clustered targets of focal plane unmanned aerial vehicles (UAVs) by integrating the random hypersurface model (RHM) model into the δ-generalized label multi-Bernoulli (δ-GLMB) filter to guarantee a robust UAV cluster target tracking on such focal planes. We first investigated the infrared imaging features of UAV cluster targets by emphasizing the target imaging size and dispersion. Next, we designed an elliptical RHM-based measurement model to map the measurement, state parameters, scaling factors, and errors to pseudo-measurement "0", followed by establishing a pseudo-measurement equation to reflect the target’s extended shape size. Then, in order to enhance measurement estimation accuracy, the RHM model was implemented with the δ-GLMB filter and Gamma-Gaussian mixture, which can perform a real-time estimate of the targets’ centroid motion state and extended state. We also used the grid-based fast density-based spatial clustering of applications with noise (DBSCAN) segmentation algorithm to overcome the distance-based segmentation method restrictions for infrared radiation (IR) measurement data and diminish the algorithm’s complexity even more in the measurement update. Extensive simulations demonstrated that this algorithm outperformed existing matching filtering algorithms in the target centroid motion and extended states. Our investigations also revealed that the algorithm was less vulnerable to clutter and more adaptive, making it more straightforward to accomplish reliable tracking of UAV cluster targets.

UWB-Based Indoor Positioning System With Infinite Scalability

The ultra-wide band radio technology (UWB) is currently considered the de-facto standard for implementing precise indoor positioning systems. Several positioning algorithms are currently being investigated for finding the best implementation in terms of scalability, refresh rate, and energy requirements. Among all the proposed approaches, the Downlink Time Difference of Arrival (DTDoA) is currently considered one of the most promising techniques capable of tracking any number of assets without decreasing the measurement update rate. This paper proposes a model for the DTDoA and validates the algorithms on UWB data, using a motion capture system as ground truth. Results highlight the validity of the previously proposed model, showing that the proposed UWB indoor positioning system achieves a maximum 30 cm uncertainty with only a simple wireless synchronisation, avoiding wired procedure that limits the usability of the infrastructure.

A Numerically Robust Bayesian Filtering Algorithm for Gaussian Mixture Models

A Bayesian filtering algorithm is developed for a class of state-space systems that can be modelled via Gaussian mixtures. In general, the exact solution to this problem involves an exponential growth in the number of mixture terms and this is handled here by utilising a Gaussian mixture reduction step after both the time and measurement update steps. In addition, a numerically robust square-root implementation of the unified algorithm is presented and this algorithm is profiled on several simulated systems, including the state estimation for a challenging non-linear system.

Dynamic Harmonic Estimation Using a Novel Robust Filtering Strategy: Iterated Sliding Innovation Cubature Filter

Active filters (AFs) are effective tools for mitigating the detrimental effects of harmonic components on the power systems. The performance of AFs is significantly dependent on designing an accurate and robust estimator which is responsible for providing reference harmonic values. In this article, a novel technique, called sliding innovation (SI) cubature filter, is proposed to estimate the harmonic parameters, i.e., magnitude and phase, in various operating conditions. The proposed method exploits the concept of sliding mode control in the formulation of the measurement update step in the Bayesian filtering framework to enhance the robustness of the estimator. Furthermore, the iterated version of the proposed algorithm, called iterative SI cubature filter, is presented to enhance the accuracy of the estimator. The proposed method keeps its robustness and accuracy in the noisy conditions under the fault occurrence as well as power system transients. The obtained results from both simulation and experimental setup confirm that the proposed estimator is more accurate and robust with a higher convergence speed compared to the well-known discrete Fourier transform (DFT), cubature Kalman filter (CKF), iterated extended Kalman filter (IEKF), and particle filter (PF).

Enhancing topology error detection via multiple measurement scans

In today’s energy management systems, the network model being fed into state estimation (SE) is assumed to be free of topology errors. In this conventional approach, bus-branch (BB) models are created as electrical equivalents of the actual network. If any topology error goes undetected while forming BB models, the subsequent SE solution will be either biased or divergent. To deal with topology errors, in this paper, a topology tracking method, using the detailed node-breaker (NB) models, is formulated. In large systems, it is computationally intensive to run SE and the following bad data tests. Therefore, SE analysis is carried out every few minutes, which is less frequent than the measurement updates (every few seconds). Since contingencies develop quickly (less than a second), the switching device flows in a few substations can change significantly from one measurement scan to the next. To identify the substation most impacted by the event, an efficient SE procedure based on the Lasso (least absolute shrinkage and selection operator) method is developed. Then, the correct topology is obtained by running a localized SE centered around the identified substation. The efficacy of the proposed approach is demonstrated both in a small 13-bus and a large 300-bus IEEE test cases.

Set‐theoretic localization for mobile robots with infrastructure‐based sensing

AbstractIn this article, we propose a set‐membership based localization approach for mobile robots using infrastructure‐based sensing. Under an assumption of known uncertainties bounds of the noise in the sensor measurement and robot motion models, the proposed method computes uncertainty sets that over‐bound the robot 2D body and orientation via set‐valued motion propagation and subsequent measurement update from infrastructure‐based sensing. We establish theoretical properties and computational approaches for this set‐theoretic localization method and illustrate its application to an automated valet parking example in simulations, and to omnidirectional robot localization problems in real‐world experiments. With deteriorating uncertainties in system parameters and initialization parameters, we conduct sensitivity analysis and demonstrate that the proposed method, in comparison to the FastSLAM, has a milder performance degradation, thus is more robust against the changes in the parameters. Meanwhile, the proposed method can provide estimates with smaller standard deviation values.

Zonotopic multi-sensor fusion estimation with mixed delays under try-once-discard protocol: A set-membership framework

In this paper, the fusion estimation problem is investigated for a class of multi-sensor networked systems with unknown-but-bounded noises and mixed time-delays under try-once-discard protocols (TODPs). The measurements of multiple sensor nodes are sent to the remote fusion center through individual network channels, where the TODP is implemented in each channel to schedule the signal transmissions for the purpose of avoiding data collisions. To fuse the information collected from all channels, a sequential estimator is proposed whose estimator parameters are designed such that the estimation error (after each measurement update) is restrained into a zonotope with minimum F-radius at each moment. First, by using the properties of zonotopes, desired zonotopes are obtained that contain the estimation errors, and the F-radii of these zonotopes are subsequently minimized by appropriately designing the estimator parameters. It is shown that, under the proposed zonotopes-based fusion rule, the designed sequential estimator leads to the same estimation accuracy as that of the widely utilized parallel estimator. Finally, an illustrative example is provided to verify the validity of the developed fusion estimation method.

Adaptive Markov IMM Based Multiple Fading Factors Strong Tracking CKF for Maneuvering Hypersonic-Target Tracking

Hypersonic targets have complex motion states and high maneuverability. The traditional interactive multi-model (IMM) has low tracking accuracy and a slow convergence speed. Therefore, this paper proposes a strong tracking cubature Kalman filter (CKF) adaptive interactive multi-model (AIMM) based on multiple fading factors. Firstly, this paper analyzes the structure of the CKF algorithm, introduces the fading factor of the strong tracking algorithm into the covariance matrix of the time update and measurement update, and adjusts the filter gain online and in real time, which can reduce the decline infilter accuracy caused by model mismatch. Secondly, Singer model, “current” statistical (CS) model, and Jerk model are selected in the model set of IMM and introduced singular value decomposition (SVD) decomposition to solve the problem that Cholesky decomposition cannot be performed in the CKF due to the model dimension expansion. Last, an adaptive algorithm for the Markov matrix in the IMM is proposed. The transition probability was adaptively modified by the value of the model likelihood function to enhance the proportion of matching models. The simulation results show that the proposed algorithm enhanced the proportion of matching models in the IMM and improved the tracking accuracy by 16.51% and the convergence speed by 37.5%.

Gaussian process regression-based quaternion unscented Kalman robust filter for integrated SINS/GNSS

High-precision filtering estimation is one of the key techniques for strapdown inertial navigation system/global navigation satellite system (SINS/GNSS) integrated navigation system, and its estimation plays an important role in the performance evaluation of the navigation system. Traditional filter estimation methods usually assume that the measurement noise conforms to the Gaussian distribution, without considering the influence of the pollution introduced by the GNSS signal, which is susceptible to external interference. To address this problem, a high-precision filter estimation method using Gaussian process regression (GPR) is proposed to enhance the prediction and estimation capability of the unscented quaternion estimator (USQUE) to improve the navigation accuracy. Based on the advantage of the GPR machine learning function, the estimation performance of the sliding window for model training is measured. This method estimates the output of the observation information source through the measurement window and realizes the robust measurement update of the filter. The combination of GPR and the USQUE algorithm establishes a robust mechanism framework, which enhances the robustness and stability of traditional methods. The results of the trajectory simulation experiment and SINS/GNSS car-mounted tests indicate that the strategy has strong robustness and high estimation accuracy, which demonstrates the effectiveness of the proposed method.

Dense Incremental Metric-Semantic Mapping for Multiagent Systems via Sparse Gaussian Process Regression

In this article, we develop an online probabilistic metric-semantic mapping approach for mobile robot teams relying on streaming RGB-D observations. The generated maps contain full continuous distributional information about the geometric surfaces and semantic labels (e.g., chair, table, and wall). Our approach is based on online Gaussian process (GP) training and inference and avoids the complexity of GP classification by regressing a truncated signed distance function (TSDF) of the regions occupied by different semantic classes. Online regression is enabled through a sparse pseudo-point approximation of the GP posterior. To scale to large environments, we further consider spatial domain partitioning via a hierarchical tree structure with overlapping leaves. An extension to a multirobot setting is developed by having each robot execute its own online measurement update and then combine its posterior parameters via local weighted geometric averaging with those of its neighbors. This yields a distributed information processing architecture, in which the GP map estimates of all the robots converge to a common map of the environment while relying only on local one-hop communication. Our experiments demonstrate the effectiveness of the probabilistic metric-semantic mapping technique in 2-D and 3-D environments in both the single- and multirobot settings and in comparison to a deep TSDF neural network approach.

Analysis of Vehicle Location Prediction Errors for Safety Applications in Cooperative-Intelligent Transportation Systems

Cooperative-Intelligent Transportation System (C-ITS) safety applications depend on reliable location information timely exchanged by road users. Due to inter-vehicle communication delays and sampling frequency, there always exists a time gap between the state observation update time and safety decision time. Predicting the vehicle’s locations into a future time epoch common to both host and subject vehicles enables real-time collision detection. Current studies of vehicle positioning performance mostly focus on the accuracy and availability of vehicle navigation solutions at equal observation intervals. Location error propagation over the prediction time intervals and dependence on various factors is not much understood. In this paper, we analyzed how the accuracy of the location prediction degrades depending on prediction intervals and state estimate errors from the measurement updates. We adopted the Kalman Filter method to predict locations with two representative location data sets collected in real road environments. Results from a dual-frequency Global Navigation Satellite System (GNSS)/Real-time Kinematic (RTK) receiver show that the Root Mean Square Error (RMSE) of prediction locations grow from a few centimeters at the state updates to about 50 and 100 cm within the prediction intervals of 1 and 2 seconds, respectively. This implies that GNSS/RTK positioning capability is a prerequisite for C-ITS safety applications. The experimental results from a surveying-grade GNSS/Inertial Navigation System (INS) receiver show that the RMSE can remain within 10 cm for the prediction interval of 2 s. High-rate INS velocity measurements provide significant advantages in efficient control of the error growth of the predicted vehicle locations.

Resilient Interactive Sensor-Independent-Update Fusion Navigation Method

To improve the robustness and reliability of multi-sensor navigation and reduce the uncertainties and complexity of sensor management in challenging environment, a resilient interactive sensor-independent-update (ISIU) method is proposed. Inspired by the interactive cooperation theory, the contributions can be divided into two aspects. Firstly the priority of trust of navigation sensors is introduced into the information fusion in the form of transition probability matrix defined by Markov chain. Secondly every observable sensor is integrated with the propagated system in an elemental filter with sensor-independent-update structure. The multi-sensor integration is implemented in state estimation domain enhanced by interactive information fusion rather than in measurement domain implemented in traditional filter method. The overall estimation is determined by the weighted sum of average from every filter estimate. This weight of every model is dynamic updated by the prior transition information and posterior model likelihood. The same independent structure is also applied to adopt new available sensor to realize plug-and-play navigation. The kinematic vehicle experiment in sub-urban and urban canyon environment verified the superiority of the proposed method. The ISIU method shows better accuracy and reliability compared to classical Kalman filters. The introduction of priority of sensors and decoupled measurement update process make it robust and insensitive to sensor measurement noise and outliers. The interactive sensor-independent-update structure has the natural function of fault detection and exclusion without additional operations. The effect of dynamic sensor selection is achieved in this processing. The proposed ISIU method is pretty suitable for resilient navigation in challenging environments.

A Human Gait Tracking System Using Dual Foot-Mounted IMU and Multiple 2D LiDARs.

This paper proposes a human gait tracking system using a dual foot-mounted IMU and multiple 2D LiDARs. The combining system aims to overcome the disadvantages of each single sensor system (the short tracking range of the single 2D LiDAR and the drift errors of the IMU system). The LiDARs act as anchors to mitigate the errors of an inertial navigation algorithm. In our system, two 2D LiDARs are used. LiDAR 1 is placed around the starting point, and LiDAR 2 is placed at the ending point (in straight walking) or at the turning point (in rectangular path walking). Using the LiDAR 1, we can estimate the initial headings and positions of each IMU without any calibration process. We also propose a method to calibrate two LiDARs that are placed far apart. Then, the measurement from two LiDARs can be combined in a Kalman filter and the smoother algorithm to correct the two estimated feet trajectories. If straight walking is detected, we update the current stride heading and the foot position using the previous stride headings. Then, it is used as a measurement update in the Kalman filter. In the smoother algorithm, a step width constraint is used as a measurement update. We evaluate the stride length estimation through a straight walking experiment along a corridor. The root mean square errors compared with an optical tracking system are less than 3 cm. The performance of proposed method is also verified with a rectangular path walking experiment.

Tracking Multiple Targets Using Bearing-Only Measurements in Underwater Noisy Environments.

This article handles tracking multiple targets using bearing-only measurements in underwater noisy environments. For tracking multiple targets in underwater noisy environments, the Gaussian Mixture Probability Hypothesis Density (GM-PHD) filter provides good performance with its low computational load. Bearing-only measurements are passive and do not provide position information of a target. Note that the nonlinearity of the bearing-only measurements can be handled by Extended Kalman Filters (EKF) when applying the GM-PHD filter. However, range uncertainty of the target is large for bearing-only measurements. Thus, a single EKF leads to poor performance when it is applied in the GM-PHD. In this article, every bearing measurement gives birth to multiple target samples, which are distributed considering the feasible range of the passive sensor. Thereafter, every target sample is updated utilizing the measurement update step of the EKF. In this way, we run multiple EKFs associated to multiple target samples, instead of running a single EKF. To the best of our knowledge, our article is novel in tracking multiple targets in noisy environments, using the observer with bearing-only measurements. The effectiveness of the proposed GM-PHD is verified utilizing MATLAB simulations.

Comparison of Adaptive Fuzzy EKF and Adaptive Fuzzy UKF for State Estimation of UAVs Using Sensor Fusion

Development of an Adaptive Fuzzy Extended Kalman Filter (AFEKF) and an Adaptive Fuzzy Unscented Kalman Filter (AFUKF) for the state estimation of unmanned aerial vehicles (UAVs) were presented in this paper based on real flight data of a fixed wing airplane. The Adaptive Neuro Fuzzy extension helps to estimate the values of the EKF's and UKF's Rk covariance matrix at each sampling instant when measurement update step is carried out. The ANFIS monitors the EKF's and UKF's performances attempt to eliminate the gap between theoretical and real innovation sequences' covariance. The investigations show that AFUKF can provide better performance in accuracy and less error than the AFEKF in case of real flight data for maneuvering fixed wing UAVs.

A new Kalman filter approach for structural parameter tracking: Application to the monitoring of damaging structures tested on shaking-tables

In this paper, a new data assimilation framework for correcting finite element models from datasets acquired on-the-fly in low-frequency dynamics is presented. An Unscented Kalman filter algorithm is coupled with a modified Constitutive Relation Error (mCRE) observer, leading to a Modified Dual Kalman Filter algorithm (MDKF). Built as a Hermitian data-to-model distance written in the frequency domain enriched with a CRE residual accounting for model bias, the mCRE functional has shown interesting assets for model updating purposes, in particular enhanced convexity and robustness to measurement noise. The proposed data assimilation strategy integrates the latter through a metric change in the measurement update equation. It thus differs from classical nonlinear Kalman filtering for parameter estimation as the comparison between measurements and model predictions is achieved through the mCRE functional itself. Besides, the calibration of MDKF internal parameters is facilitated by a set of general guidelines that ensure the performance of the algorithm. The methodology is applied to two earthquake engineering examples. The performances of MDKF are first assessed using synthetic measurements from a plane frame subjected to random ground acceleration. Actual measurements from the SMART2013 benchmark are then assimilated in a real-time context to monitor the eigenfrequency drop of a reinforced-concrete structure submitted to a sequence of gradually damaging shaking-table tests. The nice correlation with (i) data-driven identification results, and (ii) sequential mCRE-based model updating results, illustrates the relevance of this new approach and suggests promising use of MDKF for on-the-fly adaptive control prospects and applications involving data-to-model interaction.

Deriving 3-D Surface Deformation Time Series with Strain Model and Kalman Filter from GNSS and InSAR Data

This study proposes a new set of processing procedures based on the strain model and the Kalman filter (SM-Kalman) to obtain high-precision three-dimensional surface deformation time series from interferometric synthetic aperture radar (InSAR) and global navigation satellite system (GNSS) data. Implementing the Kalman filter requires the establishment of state and observation equations. In the time domain, the state equation is generated by fitting the pre-existing deformation time series based on a deformation model containing linear and seasonal terms. In the space domain, the observation equation is established with the assistance of the strain model to realize the spatial combination of InSAR and GNSS observation data at each moment. Benefiting from the application of the Kalman filter, InSAR and GNSS data at different moments can be synchronized. The time and measurement update steps are performed dynamically to generate a 3-D deformation time series with high precision and a high resolution in the temporal and spatial domains. Sentinel-1 SAR and GNSS datasets in the Los Angeles area are used to verify the effectiveness of the proposed method. The datasets include twenty-seven ascending track SAR images, thirty-four descending track SAR images and the daily time series of forty-eight GNSS stations from January 2016 to November 2018. The experimental result demonstrates that the proposed SM-Kalman method can produce high-precision deformation results at the millimeter level and provide two types of 3-D deformation time series with the same temporal resolution as InSAR or GNSS observations according to the needs of users. The new method achieves a high degree of temporal and spatial fusion of GNSS and InSAR data.

Adaptive Masreliez–Martin fractional interpolatory cubature Kalman filter with recursive noise estimation

In this study, we propose a Masreliez–Martin fractional interpolatory cubature Kalman filter and an adaptive Masreliez–Martin fractional interpolatory cubature Kalman filter to design the estimators for fractional-order discrete-time nonlinear systems under non-Gaussian measurement noise and unknown process noise covariance. Ther Masreliez–Martin fractional interpolatory cubature Kalman filter is developed by extending the interpolatory cubature Kalman filter to the fractional nonlinear discrete system to increase the robustness of estimation under noisy environment by applying the Masreliez–Martin method, including both time update and measurement update. Meanwhile, the adaptive Masreliez–Martin fractional interpolatory cubature Kalman filter is put forward to enhance the state estimation adaptive to the fractional system with uncertain process noise through recursive estimation. Simulation results on the re-entry target tracking system have demonstrated the adaptiveness, robustness and effectiveness of the propose filters.