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This paper presents a novel methodology to localise Unmanned Ground Vehicles (UGVs) using Unmanned Aerial Vehicles (UAVs). The UGVs are assumed to be operating in a Global Navigation Satellite System (GNSS)-denied environment. The localisation of the ground vehicles is achieved using UAVs that have full access to the GNSS. The UAVs use range sensors to localise the UGV. One of the major requirements is to use the minimum number of UAVs, which is two UAVs in this paper. Using only two UAVs leads to a significant complication that results an estimation unobservability under certain circumstances. As a solution to the unobservability problem, the main contribution of this paper is to present a methodology to treat the unobservability problem. A Constrained Extended Kalman Filter (CEKF)-based solution, which uses novel kinematics and heuristics-based constraints, is presented. The proposed methodology has been assessed based on the stochastic observability using the Posterior Cramér–Rao Bound (PCRB), and the results demonstrate the successful operation of the proposed localisation method.

In bearings-only target tracking, the pseudo-linear Kalman filter (PLKF) attracts much attention because of its stability and its low computational burden. However, the PLKF’s measurement vector and the pseudo-linear noise are correlated, which makes it suffer from bias problems. Although the bias-compensated PLKF (BC–PLKF) and the instrumental variable-based PLKF (IV–PLKF) can eliminate the bias, they only work well when the target behaves with non-manoeuvring movement. To extend the PLKF to the manoeuvring target tracking scenario, an unbiased PLKF (UB–PLKF) algorithm, which splits the noise away from the measurement vector directly, is proposed. Based on the results of the UB–PLKF, we also propose its velocity-constrained version (VC–PLKF) to further improve the performance. Simulations show that the UB–PLKF and VC–PLKF outperform the BC–PLKF and IV–PLKF both in non-manoeuvring and manoeuvring scenarios.

Summary Periodic health assessment of large civil engineering structures is an effective way to ensure safe performance all through their service lives. Dynamic response‐based structural health assessment can only be performed under normal/ambient operating conditions. Existing Kalman filter‐based parameter identification algorithms that consider parameters as the only states require the measurements to be sufficiently clean in order to achieve precise estimation. On the other hand, appending parameters in an extended state vector in order to jointly estimate states and parameters is reported to have convergence issues. In this article, a constrained version of the dual extended Kalman filtering (cDEKF) technique is employed in which two concurrent extended Kalman filters simultaneously filter the measurement response (as states) and estimate the elements of state transition matrix (as parameters). Constraints are placed on stiffness and damping parameters during the estimation of the gain matrix to ensure they remain within realistic bounds. The proposed method is compared against the existing Kalman filter‐based parameter identification techniques on a three‐degrees‐of‐freedom mass‐spring‐damper system adopting both unconstrained and constrained estimation approaches. cDEKF is then employed on a numerical six‐story shear frame and a 3D space truss to validate its robustness and efficacy in identifying structural damage. The results suggest that cDEKF algorithm is an efficient online damage identification scheme that makes use of ambient vibration response.

Population aging is driving the need for unobtrusive, continuous monitoring solutions in residential care environments. Radio-frequency (RF)-based technologies such as Ultra-Wideband (UWB) and millimeter-wave (mmWave) radar are particularly attractive for providing detailed information on presence and movement while preserving privacy. Building on a UWB–mmWave localization system deployed in a senior living residence, this paper focuses on the data-processing methodology for extracting quantitative mobility indicators from long-term indoor monitoring data. The system combines a device-free mmWave radar setup in bedrooms and bathrooms with a tag-based UWB positioning system in common areas. For mmWave data, an adaptive short-term average/long-term average (STA/LTA) detector operating on an aggregated, normalized radar energy signal is used to classify micro- and macromovements into bedroom occupancy and non-sedentary activity episodes. For UWB data, a partially constrained Kalman filter with a nearly constant velocity dynamics model and floor-plan information yields smoothed trajectories, from which daily gait- and mobility-related metrics are derived. The approach is illustrated using one-day samples from three users as a proof of concept. The proposed methodology provides individualized indicators of bedroom occupancy, sedentary behavior, and mobility in shared spaces, supporting the feasibility of combined UWB and mmWave radar sensing for longitudinal routine analysis in real-world elderly care environments.

Automatic navigation based on dual-antenna real-time kinematic (RTK) positioning has been widely employed for unmanned agricultural machinery, whereas GNSS inevitably suffers from signal blocking and electromagnetic interference. In order to improve the reliability of an RTK-based navigation system in a GNSS-challenged environment, an integrated navigation system is preferred for autonomous navigation, which increases the complexity and cost of the navigation system. The information fusion of integrated navigation has been dominated by Kalman filter (KF) for several decades, but the KF cannot assimilate the known knowledge of the navigation context efficiently. In this paper, the geometric characteristics of the straight path and path-tracking error were employed to formulate the constraint measurement model, which suppresses the position error in the case of RTK-degraded scenarios. The pseudo-measurements were then imported into the KF framework, and the smoothed navigation state was generated as a byproduct, which improves the reliability of the RTK positioning without external sensors. The experiment result of the mobile vehicle automatic navigation indicates that the tracking error-constrained KF (EC-KF) outperforms the trajectory-constrained KF (TC-KF) and KF when the RTK system outputs a float or single-point position (SPP) solution. In the case where the duration of the SPP solution was 20 s, the positioning errors of the EC-KF and TC-KF were reduced by 38.50% and 24.04%, respectively, compared with those of the KF.

Tracking the kinematics of human movement usually requires the use of equipment that constrains the user within a room (e.g., optical motion capture systems), or requires the use of a conspicuous body-worn measurement system (e.g., inertial measurement units (IMUs) attached to each body segment). This paper presents a novel Lie group constrained extended Kalman filter to estimate lower limb kinematics using IMU and inter-IMU distance measurements in a reduced sensor count configuration. The algorithm iterates through the prediction (kinematic equations), measurement (pelvis height assumption/inter-IMU distance measurements, zero velocity update for feet/ankles, flat-floor assumption for feet/ankles, and covariance limiter), and constraint update (formulation of hinged knee joints and ball-and-socket hip joints). The knee and hip joint angle root-mean-square errors in the sagittal plane for straight walking were 7.6±2.6∘ and 6.6±2.7∘, respectively, while the correlation coefficients were 0.95±0.03 and 0.87±0.16, respectively. Furthermore, experiments using simulated inter-IMU distance measurements show that performance improved substantially for dynamic movements, even at large noise levels (σ=0.2 m). However, further validation is recommended with actual distance measurement sensors, such as ultra-wideband ranging sensors.

An Augmented Relative Navigation System (ARNS) is proposed for autonomous satellite formation flying in low-Earth-orbit (LEO). Inter-satellite ranging systems such as those based on radio frequency transmissions can provide additional observation information, e.g. inter-satellite distance measurement, which can be used to increase the Global Positioning System (GPS) stand-alone observation dimension, or treated as a non-linear equality constraint within a smoothly-constrained Kalman filter. Both approaches are implemented in the proposed ARNS described in this paper. An innovative phase integer ambiguity fixing and feedback scheme is implemented to increase the ambiguity fix rate of the GPS carrier phase measurements. A set of Gravity Recovery and Climate Experiment (GRACE) flight data is used to test and validate the relative navigation performance of the proposed methods. Results indicate that the augmented system can improve relative positioning accuracy by an order of magnitude.

In recent years, the error-state Kalman filter (ErKF) has been widely employed in various applications, including robotics, aerospace, and localization. However, incorporating state constraints into the ErKF framework using the estimate projection method remains ambiguous. This paper examines this issue in depth, specifically exploring whether constraints should be enforced before or after the ErKF correction step. We adopt a mathematical approach, deriving analytical solutions and analyzing their statistical properties. Our findings prove that, for a linear system with linear constraints, both methods yield statistically equivalent results. However, the filter’s behavior becomes uncertain when dealing with linearized constraints. We further identify a special case of a nonlinear constraint where the results of the linear case remain valid. To support our theoretical analysis and evaluate the filter’s performance under non-ideal conditions, we conduct two Monte Carlo simulations considering increasing initialization errors and constraint incompleteness. The simulation results validate our theoretical insights and suggest that applying constraints to the error state after the correction step may lead to superior performance compared to the alternative approach.

In order to meet the requirements of high-precision vehicle positioning in complex scenes, an observation noise adaptive robust GNSS/MIMU tight fusion model based on the gain matrix is proposed considering static zero speed, non-integrity, attitude, and odometer constraint models. In this model, the robust equivalent gain matrix is constructed by the IGG-Ⅲ method to weaken the influence of gross error, and the on-line adaptive update of observation noise matrix is carried out according to the change of actual observation environment, so as to improve the solution performance of filtering system and realize high-precision position, attitude and velocity measurement when GNSS signal is unlocked. A real test on a road over 600km demonstrates that, in about 100km shaded environment, the fixed rate of GNSS ambiguity resolution in the shaded road is 10% higher than that of GNSS only ambiguity resolution. For all the test, the positioning accuracy can reach the centimeter level in an open environment, better than 0.6m in the tree shaded environment, better than 1.5m in the three-dimensional traffic environment, and can still maintain a positioning accuracy of 0.1m within 10s when the satellite is unlocked in the tunnel scene. The proposal and verification of the algorithm model show that low-cost MIMU equipment can still achieve high-precision positioning when there are scene feature constraints, which can meet the problem of high-precision vehicle navigation and location in the urban complex environment.

(1) Background: Quantification of severity of epileptic activities, especially during electrical stimulation, is an unmet need for seizure control and evaluation of therapeutic efficacy. In this study, a parameter ratio derived from constrained square-root cubature Kalman filter (CSCKF) was formulated to quantify the excitability of local neural network and compared with three commonly used indicators, namely, band power, Teager energy operator, and sample entropy, to objectively determine their effectiveness in quantifying the severity of epileptiform discharges in mice. (2) Methods: A set of one normal and four types of epileptic EEGs was generated by a mathematical model. EEG data of epileptiform discharges during two types of electrical stimulation were recorded in 20 mice. Then, EEG segments of 5 s in length before, during and after the real and sham stimulation were collected. Both simulated and experimental data were used to compare the consistency and differences among the performance indicators. (3) Results: For the experimental data, the results of the four indicators were inconsistent during both types of electrical stimulation, although there was a trend that seizure severity changed with the indicators. For the simulated data, when the simulated EEG segments were used, the results of all four indicators were similar; however, this trend did not match the trend of excitability of the model network. In the model output which retained the DC component, except for the CSCKF parameter ratio, the results of the other three indicators were almost identical to those using the simulated EEG. For CSCKF, the parameter ratio faithfully reflected the excitability of the neural network. (4) Conclusion: For common EEG, CSCKF did not outperform other commonly used performance indicators. However, for EEG with a preserved DC component, CSCKF had the potential to quantify the excitability of the neural network and the associated severity of epileptiform discharges.