Angle Estimation Method Research Articles

High‐resolution angle estimation method in partly calibrated subarray‐based bistatic multiple‐input multiple‐output radar with unknown non‐uniform noise

Uniformly distributed white noise is often the desirable noise assumption for partly calibrated subarray-based radar systems. However, this assumption may practically not always be guaranteed. In this study, the angle estimation problem of the partly calibrated multi-subarray-based bistatic multiple-input multiple-output radar, where intersubarray calibration errors and non-uniform noise coexist, is considered. In addition, an inverse transformation-based enhanced Capon method is proposed to adapt to such a challenging situation. First, the noise-free covariance matrix of each subarray is obtained by formulating an imaginary selecting matrix following a covariance matrix invariance approach which performs an inverse transformation of the matrix. Thus, the noise identities at the different antennas of the subarray are estimated as nuisance parameters at the expense of the target signals. Second, assuming that the calibration within each subarray is well configured such that the steering vector of a subarray is known, knowledge is required of the intersubarray calibration mismatches. To this, a high-resolution Capon estimator which applies a combination of root and local searching orientation of the antenna arrays is implemented. The proposed approach resolves the intersubarray calibration errors and ultimately leads to obtaining the joint direction of departure and direction of arrival estimation of the target. Evidence of the proposed algorithm's validity and effectiveness over existing methods is demonstrated in numerical simulations under varying conditions.

Prediction of Lower Extremity Multi-Joint Angles during Overground Walking by Using a Single IMU with a Low Frequency Based on an LSTM Recurrent Neural Network.

The joint angle during gait is an important indicator, such as injury risk index, rehabilitation status evaluation, etc. To analyze gait, inertial measurement unit (IMU) sensors have been used in studies and continuously developed; however, they are difficult to utilize in daily life because of the inconvenience of having to attach multiple sensors together and the difficulty of long-term use due to the battery consumption required for high data sampling rates. To overcome these problems, this study propose a multi-joint angle estimation method based on a long short-term memory (LSTM) recurrent neural network with a single low-frequency (23 Hz) IMU sensor. IMU sensor data attached to the lateral shank were measured during overground walking at a self-selected speed for 30 healthy young persons. The results show a comparatively good accuracy level, similar to previous studies using high-frequency IMU sensors. Compared to the reference results obtained from the motion capture system, the estimated angle coefficient of determination () is greater than 0.74, and the root mean square error and normalized root mean square error (NRMSE) are less than 7° and 9.87%, respectively. The knee joint showed the best estimation performance in terms of the NRMSE and among the hip, knee, and ankle joints.

Dynamic subspace angle estimation method for bistatic MIMO radar with system imperfections

The development of high-resolution methods that can withstand unpleasant radar conditions for target localization is challenging. In this paper, a novel dynamic subspace method to address the problem of angle estimation of the bistatic Multiple-input multiple-output (MIMO) radar with system imperfections brought about by the coexistence of mutual coupling and coherent signals with large power differences is proposed. The proposed dynamic subspace angle estimation method comprises two subspace approaches; the dynamic subspace resampling with coupling calibration approach and the dynamic subspace superresolution with coupling calibration approach. The implementation of both approaches is such that they apply a linear transformation technique by way of exploiting the topology of the array structure to attain signal decoupling. In addition, the proposed approaches devise the decimation of the signal samples and the formulation of a beamforming framework to induce decorrelation and achieve signal resolution. Finally, a 1D pairwise spectral estimator which exploits matrix inversion mechanism coupled with a grid refining technique is introduced to resolve the target angle with obvious power differences.In contrast with the existing methods, the proposed method has an extra advantage of its applicability to colored noise scenarios due to its inherent noise suppression ability. This, therefore, augments its high suitability to imperfect systems. Evidence of the proposed algorithm's validity and effectiveness over existing methods is demonstrated in terms of numerical simulations under varying conditions.

Load Asymmetry Angle Estimation Using Multiple view Videos.

A robust computer vision-based approach is developed to estimate the load asymmetry angle defined in the revised NIOSH lifting equation (RNLE). The angle of asymmetry enables the computation of a recommended weight limit for repetitive lifting operations in a workplace to prevent lower back injuries. An open-source package OpenPose is applied to estimate the 2D locations of skeletal joints of the worker from two synchronous videos. Combining these joint location estimates, a computer vision correspondence and depth estimation method is developed to estimate the 3D coordinates of skeletal joints during lifting. The angle of asymmetry is then deduced from a subset of these 3D positions. Error analysis reveals unreliable angle estimates due to occlusions of upper limbs. A robust angle estimation method that mitigates this challenge is developed. We propose a method to flag unreliable angle estimates based on the average confidence level of 2D joint estimates provided by OpenPose. An optimal threshold is derived that balances the percentage variance reduction of the estimation error and the percentage of angle estimates flagged. Tested with 360 lifting instances in a NIOSH-provided dataset, the standard deviation of angle estimation error is reduced from 10.13° to 4.99°. To realize this error variance reduction, 34% of estimated angles are flagged and require further validation.

Millimeter-Wave Angle Estimation of Multiple Targets Using Space–Time Modulation and Interferometric Antenna Arrays

A new method of angle estimation of multiple targets using a distributed interferometric antenna array and wideband space-time modulation is presented in this work. Interferometric array measurements of angle of arrival are generally ambiguous in the presence of one or more targets. We propose a new method of mitigating ambiguities in interferometric measurements by multiplying the angle pseudo-spectra from multiple antenna baselines, resulting in detections at only the angles of the targets. Using a single linear frequency modulated (LFM) transmitter and a receive interferometric array with $N$ elements we show a simple and computationally efficient technique to estimate the angle of up to $\mathcal{O}(N^2)$ targets. We describe the theory behind the technique, present detailed simulations, and an experimental verification using a three-element millimeter-wave measurement system.

Finger joint angle estimation based on sEMG signals by Attention-MLP

sEMG(Surface electromyography) signal was widely applied in human-machine interactive field, especially in robotic arm control. In this paper, we built the Attention-MLP (Multilayer Perceptron) model to implement a type of continuous joint angle estimation method based on sEMG for six grasp movements, we tested this model on Ninapro dataset and the average Pearson correlation coefficient (CC) and the average root mean square error (RMSE) of the proposed Attention-MLP method achieved 0.812±0.02 and 10.51±1.98; the average CC and RMSE of this method are better than Sparse Pseudo-input Gaussian processes (SPGP), its average CC and RMSE are 12.14±2.30 and 0.727±0.07. Compared with the traditional method SPGP, our model performed better on continuously estimation of ten main hand joint angles under 6 grip movements.

DOA estimation in beamspace for monostatic MIMO radar utilizing real polynomial rooting

A novel angle estimation method in beamspace for monostatic multiple-input multiple-output (MIMO) radar based on a real polynomial rooting technique is presented. In order to eliminate the redundancy of the received data, the reduced-dimensional matrix is used to reduce the dimension of the received data. To further reduce computational complexity, the reduced-dimensional data is transformed into the beamspace. In order to avoid computationally expensive spectrum search, we will introduce conformal transformation to determine the extreme value of the MUSIC spectrum by utilizing the real polynomial rooting technique. Finally, the DOA of the target can be obtained from these extreme values. Numerical results demonstrate the effectiveness of the proposed algorithm.

Landmark-Assisted Compensation of User's Body Shadowing on RSSI for Improved Indoor Localisation with Chest-Mounted Wearable Device.

Nowadays, location awareness becomes the key to numerous Internet of Things (IoT) applications. Among the various methods for indoor localisation, received signal strength indicator (RSSI)-based fingerprinting attracts massive attention. However, the RSSI fingerprinting method is susceptible to lower accuracies because of the disturbance triggered by various factors from the indoors that influence the link quality of radio signals. Localisation using body-mounted wearable devices introduces an additional source of error when calculating the RSSI, leading to the deterioration of localisation performance. The broad aim of this study is to mitigate the user’s body shadowing effect on RSSI to improve localisation accuracy. Firstly, this study examines the effect of the user’s body on RSSI. Then, an angle estimation method is proposed by leveraging the concept of landmark. For precise identification of landmarks, an inertial measurement unit (IMU)-aided decision tree-based motion mode classifier is implemented. After that, a compensation model is proposed to correct the RSSI. Finally, the unknown location is estimated using the nearest neighbour method. Results demonstrated that the proposed system can significantly improve the localisation accuracy, where a median localisation accuracy of 1.46 m is achieved after compensating the body effect, which is 2.68 m before the compensation using the classical K-nearest neighbour method. Moreover, the proposed system noticeably outperformed others when comparing its performance with two other related works. The median accuracy is further improved to 0.74 m by applying a proposed weighted K-nearest neighbour algorithm.

Joint Angle and Frequency Estimation in Linear Arrays Based on Covariance Reconstruction and ESPRIT

Joint angle and frequency estimation, one of the key technologies in wireless communication and radar science, has been extensively studied by scholars. For linear arrays, this paper proposes a joint angle and frequency estimation method based on covariance reconstruction and the estimation of signal parameters via rotational invariance techniques (CR-ESPRIT). We first use the received conjugate signal to reconstruct a covariance matrix. Then, we use the least squares-ESPRIT (LS-ESPRIT) algorithm to estimate the desired frequencies. Finally, we estimate the angles according to the reconstructed matrix. The proposed method can estimate signal parameters via automatic pairing and without an additional parameter pairing process under the condition of a uniform or a nonuniform array. Moreover, this method has high estimation accuracy, excellent and stable anti-noise performance, and strong algorithmic robustness. Through a computer simulation analysis, we can confirm the reliability and validity of the proposed parameter estimation method. A comparison with other methods further proves the performance advantages of the developed method. The method in this paper can be easily applied to many signal processing contexts, such as electronic reconnaissance and wireless communication.

Estimation of seismic wave incident angle using vibration response data and stacking ensemble algorithm

The determination of the incident angle of an earthquake is one of the critical research issues in modeling the seismic input mechanism at a dam site and it is also for geological exploration. At present, the incident angle calculation methods mostly rely on accurate geological models, complex theoretical formulations, and complicated procedures. To this end, an incident angle estimation method using dam vibration response data and a machine learning algorithm is presented in this study. First, a three-dimensional finite element gravity dam-foundation system model is constructed. A wave input method based on the viscous-spring artificial boundary is used to simulate the multi-angle incidence of P and SV waves. The vibration responses of key dam points are obtained. Nine features that have geometric interpretation are constructed by the response data and the new data are substituted into a stacking ensemble algorithm for training. Finally, the angles of obliquely incident P and SV waves are estimated using the trained stacking ensemble estimation model. The results reveal correlation between dam responses and the incident angle with the average R2 values of the estimation model of 0.996 (P waves) and 0.996 (SV waves), and the average root mean square errors of 1.765° (P waves) and 0.546° (SV waves). It is thus confirmed that the estimation model integrated multiple features from several measurement points with high accuracy and stability. In addition, the proposed method can be extended to other types of large structures because of its universality.

Autonomous Vehicles Sideslip Angle Estimation: Single Antenna GNSS/IMU Fusion With Observability Analysis

Taking advantage of available measurement in Internet of Things (IoT) for intelligent transportation systems, a sideslip angle estimation method for autonomous vehicles is presented and experimentally verified by fusing global navigation satellite system (GNSS) and inertial measurement unit (IMU), and by constructing an observability index (OI). The correlation between the vehicle sideslip error and the inertial navigation system (INS) heading error is presented first. Then, the observability for the heading error in a velocity-based Kalman filter is discussed and a novel index is defined to check the observability of the heading error. The course from a single antenna GNSS in an autonomous vehicle is augmented to estimate the heading error when the observability of the heading error is low. To reject the course measurement for scenarios that include sideslip movement, a binary hypothesis test approach is applied to indicate whether the vehicle is sidesliping. In addition, based on the OI and the sideslip indicator, a hybrid feedback strategy is designed for the heading error correction. To improve the convergence rate of the heading error in the velocity-based Kalman filter, a tuning strategy is presented. The stochastical observability of the designed Kalman observer is investigated for known and stochastic initial conditions. Finally, the proposed sideslip angle estimator is experimentally validated through a vehicle test platform in critical driving scenarios. The results confirm that the proposed OI can effectively identify when the heading error is observable, and also corroborate the effectiveness of the hybrid feedback strategy and adaptation method in the Kalman observer.

Transient Synchronization Stability Control for LVRT With Power Angle Estimation

Power synchronization control (PSC) is an effective control method for a voltage-source converter (VSC) connected with a weak grid, where the short-circuit ratio is close to 1. The grid voltage sag will induce the synchronization instability of PSC-VSC and then trigger the catastrophic cascading failure in the power system. This letter presents the transient power angle nature of PSC under the grid disturbance by phase portrait, and the critical condition of transient synchronization instability for PSC is derived. The virtual orthogonal power (VOP) is elaborated and the power angle estimation method is presented by VOP. Then, a mode adaptive transient synchronization stability control scheme is proposed for the low-voltage ride through with the power angle estimation scheme. By using the proposed transient synchronization stability control scheme, the PSC-VSC can maintain synchronization with the grid during the fault of grid voltage sag. The control method theoretical analysis is verified by the experimental tests.

Elevation Angle Estimation in 2D Acoustic Images Using Pseudo Front View

A novel method to estimate the missing dimension in 2D acoustic images for 3D reconstruction is proposed in this paper. Acoustic cameras can acquire high resolution 2D images in underwater environment insusceptible to water turbidity and light condition. However, the formulation of acoustic images leads to the missing dimension problem. Estimating the unknown elevation angle dimension is a difficult task which has recently drawn the attention of researchers. The non-bijective characteristic between 3D points and 2D pixels increases the complexity of the problem. In this paper, a novel elevation angle estimation method is proposed. The method transfers the acoustic view to pseudo front view using a deep neural network. The proposed network can estimate the missing dimension and resolve the non-bijection problem of the 2D-3D correspondence. Because of the difficulty of acquiring depth information in underwater environments, the network is trained using simulated images. To mitigate the sim-real gap, a neural style transfer method is implemented to generate a realistic image dataset for training. Simulation experiments were carried out for evaluation and real data proved the feasibility of the proposed method.

An Improved Estimation Method of Mutual Inductance Angle for a Two-Dimensional Wireless Power Transfer System

The improvement of power transmission efficiency (PTE) is an important issue in the design of a wireless power transfer (WPT) system. The WPT system with multiple transmitting (Tx) or receiving (Rx) coils is a way to improve the PTE. This paper deals with the estimation of the mutual inductance angle for a two-dimensional (2D) WPT system with two Tx coils and one Rx coil. The mutual inductance angle is one of the most important parameters to determine the PTE in the 2D WPT system. The condition for the maximum PTE is investigated and the mutual inductance angle is defined for the 2D WPT system. An improved estimation method of the mutual inductance angle is proposed based on the phase-locked loop (PLL) technique using the voltages and currents of the Tx coils. The simulation and experimental results are provided to validate the effectiveness of the proposed method.

Correlation method and Kalman filter-based adaptive angle rate estimation for time-varying periodic signals of the attitude and heading reference system

An angle differential estimation method is needed for the attitude and heading reference system (AHRS), which is unavailable to measure the angle rate directly. Differential estimation accuracy is seriously affected by the model error of existing differential filters for time-varying periodic angles provided by the AHRSs. To address this challenge, an adaptive angle rate estimation method based on the Kalman filter and correlation method is proposed. The Kalman filter based on the jerk model is selected to estimate the angle rate. The process noise covariance model of the Kalman filter is established considering amplitude and period fluctuations of the periodic signals. The correlation method is then combined with the Kalman filter to estimate the amplitude and period of the periodic signals, which are utilized to optimize the process noise covariance matrix of the Kalman filter. Compared with traditional differential estimation methods, the proposed method improves the angle rate estimation accuracy by adjusting the parameter of the differential filter according to the model error of the time–varying periodical angle. A simulation is conducted to verify the performance of the proposed method by continuously changing the amplitude and period of the signals. Simulation results show that the proposed method is least affected by model error and achieves the best performance compared with seven other traditional rate estimation methods. Turntable and sea tests also demonstrate the correctness and effectiveness of the proposed angle rate estimation method.

Target Bearing Estimation for Ship-Borne HFSWR Using Doppler Effect and Very Small Antenna Array

In this article, a new target bearing angle estimation method for ship-borne high-frequency surface-wave radar (HFSWR) is presented. This new method is designed to give bearing angle estimation of ship targets. It relies on platform motion instead of antenna aperture to acquire bearing angle resolving capability, and hence can be applied to ship-borne HFSWRs that only have very small antenna arrays, and gives small vessels over-the-horizon (OTH) detection capability. This new method requires little modification to existing HFSWR hardware, and only a small amount of additional memory and computing power is needed. Both theoretic analysis and implementation details are given in this article. The new method is tested using real-measured ship-borne HFSWR radar data. The test result proved the effectiveness of the new method.

Sparse Nested Arrays With Spatially Spread Square Acoustic Vector Sensors for High-Accuracy Underdetermined Direction Finding

In acoustic sensing systems, acoustic vector sensor (also known as vector hydrophone for underwater applications) arrays are widely used. Most of the acoustic vector sensor array signal processing methods presume the minimum spacing between two adjacent sensors or sensor components to be within a half-wavelength in order to avoid azimuth-elevation angle estimation aliasing. This would limit the effective array aperture, thereby reducing the potential estimation accuracy. Furthermore, they are unapplicable to the underdetermined scenarios, where the number of sources exceeds that of sensor components. Exploiting the recently proposed nested array concept, we present a new type of nested array, termed as Sparse Nested spatially spread Square Acoustic Vector sensor Array (SNSAVA) to realize underdetermined 2-D direction finding with increased estimation accuracy. In SNSAVA, interspacing of two sensors and two components of a sensor can be spread to be much higher than a half-wavelength so that the effective array aperture will be significantly extended. An unambiguous angle estimation method is further derived to make this fully sparse array configuration practically feasible. Performance studies focused on underdetermined high-accuracy azimuth-elevation angle estimation are provided via numerical examples. The estimation performance for the SNSAVA is also compared with that of the nested acoustic vector sensor arrays, proposed in [33], and with the Cramér-Rao bound.

A Novel PWA Lateral Dynamics Modeling Method and Switched T-S Observer Design for Vehicle Sideslip Angle Estimation

In this article, a novel vehicle sideslip angle estimation method is proposed using the Takagi–Sugeno (T–S) observer based on a piecewise affine (PWA) lateral dynamics model. Since conventional lateral dynamics models have complex structures and nonlinearities, difficulties in sideslip angle observer design and online implementation are inevitable. To address nonlinearities, the PWA and T–S fuzzy modeling approaches are applied in this article. First, a nominal PWA model is obtained using the nominal tyre load and tyre-road friction coefficient. An explicit relationship between the PWA model parameters and the tyre load, tyre-road friction coefficient is deduced based on the Dugoff tyre model. Then, a novel PWA lateral dynamics model is obtained considering a varying tyre load and tyre-road friction coefficient. Due to the residual nonlinear terms, this PWA model is further converted into a T–S fuzzy model. Finally, a switched T–S observer is designed as it is computationally simple and efficient enough for online estimation. To validate the effectiveness of the proposed approach, experiments are conducted on both low- and high-friction coefficient roads. Experimental results show that the proposed PWA modeling technique is effective and the T–S observer can estimate the sideslip angle well under both stable and unstable steering maneuvers.

Sleeve for Knee Angle Monitoring: An IMU-POF Sensor Fusion System.

The knee flexion-extension angle is an important variable to be monitored in various clinical scenarios, for example, during physical rehabilitation assessment. The purpose of this work is to develop and validate a sensor fusion system based on a knee sleeve for monitoring of physical therapy. The system consists of merging data from two inertial measurement units (IMUs) and an intensity-variation based Polymer Optical Fiber (POF) curvature sensor using a quaternion-based Multiplicative Extended Kalman Filter (MEKF). The proposed data fusion method is magnetometer-free and deals with sensors' uncertainties through reliability intervals defined during gait. Walking trials were performed by twelve healthy participants using our knee sleeve system and results were validated against a gold standard motion capture system. Additionally, a comparison with other three knee angle estimation methods, which are exclusively based on IMUs, was carried out. The proposed system presented better performance (mean RMSE 3.3 °, LFM coefficients, a1 = 0.99 ± 0.04, a0 = 0.70 ± 2.29, R2 = 0.98 ± 0.01 and ρC 0.99) when compared to the other evaluated methods. Experimental results demonstrate the usability and feasibility of our system to estimate knee motion with high accuracy, repeatability, and reproducibility. This wearable system may be suitable for motion assessment in rehabilitation labs in future studies.

Integrator-Less Method for Phase Angle Estimation of Fundamental Frequency Positive-Sequence Component Under Adverse Condition

This article proposes an integrator-less method for phase angle estimation of unbalanced three-phase voltage systems under adverse conditions. It mainly unites abc-to- dq transform, delayed signal cancellation scheme, and a phase error compensation algorithm. It does not demand online operation of integrators, and thus, associated discretization error and instability issue are not present in the proposed method. It is also an unconditionally stable technique as it uses a real open-loop structure. Moreover, the method is relatively simple and computationally efficient due to circumventing online operations of the complex functions, such as square root, trigonometric, and inverse trigonometric. Under alike transient time conditions, the proposed method is more resistant to harmonic disturbances when compared to integrator-based similar competing techniques, such as an enhanced frequency adaptive demodulation approach and a phase error compensation-based open-loop method. The usefulness of the offered method is proved using simulated and experimental results.