Position Determination Algorithm Research Articles

An Enhanced Direct Position Determination of Mixed Circular and Non-Circular Sources Using Moving Virtual Interpolation Array.

In this study, a moving single-station direct position determination (DPD) algorithm based on virtual interpolated arrays is proposed. Existing moving single-station algorithms face challenges such as the incomplete utilization of sparse array apertures and insufficient consideration of mixed circular and non-circular signals. To address these issues, we propose an enhanced gridless DPD algorithm, suitable for multiple mixed circular and non-circular sources. Through constructing a non-zero unconjugated covariance matrix from the non-circular components of the mixed signals, the data dimensionality is expanded, and the gridless method is used to fill the voids in the coarray, significantly improving localization performance. Additionally, a unitary transformation method is applied to reduce computational complexity. This method transforms complex operations into real operations by applying unitary transformations to steering vectors and subspaces. Simulation results demonstrate that the proposed algorithm offers significant advantages in terms of array degrees of freedom and localization accuracy.

Direct position determination algorithm based on wideband array signal model in external illuminator system

Abstract Target location and tracking are among the most critical applications for external illuminator systems. Most traditional array signal direct position determination (DPD) techniques are based on narrowband signals. With the advancement of communication technology, various wideband signals are extensively utilized in communication systems, leading to the failure of some traditional DPD techniques. To address this issue, this article proposes a new DPD algorithm for wideband array signals. First, we suppress the direct wave (DW) interference in the received signal. Then, a cost function for the target coordinate is constructed based on the Maximum Likelihood (ML) criterion, and a phase matching matrix is created for the problem of unknown signal transmission time. Finally, the position estimation is obtained from the peak of the cost function. Simulation results demonstrate that the proposed algorithm outperforms traditional two-step localization methods based on the time difference of arrival of signals, particularly in cases where DW interference is present in the received signal.

An enhanced direct position determination of non-circular sources via sparse Bayesian inference and grid refinement strategy

In this study, an off-grid sparse Bayesian inference (OGSBI) based direct position determination (DPD) algorithm is investigated. Existing SBI-based DPD algorithms are confronted with the challenge of excessive computational loads and lack of consideration for non-circular (NC) signals. To address these limitations, we present an enhanced OGSBI-based DPD algorithm for multiple non-circular sources. By utilizing the conjugate information of the NC signals, we expand the dimensionality of the data matrix to achieve a significant improvement in the localization performance. Additionally, a grid refinement strategy is developed to alleviate the computational loads, which involves an initial search to determine the approximate source locations, followed by fine localization using a denser grid. Moreover, the computational complexity and Cramér-Rao lower bound are derived to provide a comprehensive analysis of the proposed algorithm. Numerical simulations demonstrate the superiority of the proposed algorithm in terms of both localization accuracy and computational efficiency.

Vehicle Position Detection Based on Machine Learning Algorithms in Dynamic Wireless Charging.

Dynamic wireless charging (DWC) has emerged as a viable approach to mitigate range anxiety by ensuring continuous and uninterrupted charging for electric vehicles in motion. DWC systems rely on the length of the transmitter, which can be categorized into long-track transmitters and segmented coil arrays. The segmented coil array, favored for its heightened efficiency and reduced electromagnetic interference, stands out as the preferred option. However, in such DWC systems, the need arises to detect the vehicle's position, specifically to activate the transmitter coils aligned with the receiver pad and de-energize uncoupled transmitter coils. This paper introduces various machine learning algorithms for precise vehicle position determination, accommodating diverse ground clearances of electric vehicles and various speeds. Through testing eight different machine learning algorithms and comparing the results, the random forest algorithm emerged as superior, displaying the lowest error in predicting the actual position.

5G Positioning: An Analysis of Early Datasets.

Global Navigation Satellite Systems (GNSSs) are nowadays the prevailing technology for positioning and navigation. However, with the roll-out of 5G technology, there is a shift towards 'hybrid positioning': indeed, 5G time-of-arrival (ToA) measurements can provide additional ranging for positioning, especially in environments where few GNSS satellites are visible. This work reports a preliminary analysis, the processing, and the results of field measurements collected as part of the GINTO5G project funded by ESA's EGEP programme. The data used in this project were shared by the European Space Agency (ESA) with the DICA of Politecnico di Milano as part of a collaboration within the ESALab@PoliMi research framework established in 2022 between the two organizations. The ToA data were collected during a real-world measurement campaign and they cover a wide range of user environments, such as indoor areas, outdoor open sky, and outdoor obstructed scenarios. Within the test area, eleven self-made replica 5G base stations were set up. A trolley, carrying a self-made 5G receiver and a data storage unit, was moved along predefined trajectories; the trolley's accurate trajectories were determined by a total station, which provided benchmark positions. In the present work, the 5G data are processed using the least squares method, testing and comparing different strategies. Therefore, the primary goal is to evaluate algorithms for position determination of a user based on 5G observations, and to empirically assess their accuracy. The results obtained are promising, with positional accuracy ranging from decimeters to a few meters in the worst cases.

Accurate spectrogram restoration algorithm for an echelle spectrometer based on adaptive parameters.

The echelle spectrometer is a high-resolution spectrometer that can realize transient direct readings of a full spectrum. To improve the accuracy of the spectrogram restoration model in calibration, multiple-integral time fusion, and an improved adaptive-threshold centroid algorithm are used to overcome noise and improve the accuracy of calculating the light spot position. A seven-parameter pyramid-traversal method is proposed to optimize the parameters of the spectrogram restoration model. The deviation of the spectrogram model is significantly reduced after the parameters are optimized, and the deviation curve fluctuation becomes mild, which greatly improves the model's accuracy after curve fitting.The test results show that the accuracy of the spot position determination algorithm proposed in this paper is 0.1 pixels. In addition to this, the accuracy of the spectral restoration model is controlled within 0.3 pixels in a short-wave stage and 0.7 pixels in a long-wave stage. Compared with the traditional algorithm, the accuracy of spectrogram restoration is more than two times, and the spectral calibration time is less than 45 min.

Closed-Form Rectilinear Emitters Localization With Multiple Sensor Arrays: Phase Alignment and Optimal Weighted Least-Square Method

Position determination algorithms of rectilinear emitters (also called strictly second-order noncircular emitters) with multiple sensor arrays (SAs) allow for higher localization accuracy and more achievable degrees of freedom compared to the conventional version with circular emitters. However, it also brings additional computational complexity and noise. In this article, we develop a position determination algorithm of rectilinear emitters in closed-form on the basis of phase alignment and optimal weighted least square (OWLS), which is termed the PAOWLS method. First, we utilize the polynomial root-finding method to obtain the angle of arrival (AOA) and estimate rectilinear phases to align AOA. Then, we construct a least-square (LS) constraint to estimate the positions of emitters directly (termed the PALS method). Finally, we construct a weighted LS constraint and deduce the optimal weight to compensate for the position estimation bias. Extensive numerical results verify the outstanding performance of the proposed algorithm in terms of localization accuracy, resolution capability, and computational complexity.

A Computationally Efficient Direct Position Determination Algorithm Based on OFDM System

Based on the orthogonal frequency division multiplexing (OFDM) system, a computationally attractive implementation for the traditional single source maximum likelihood (SML) direct position determination (DPD) algorithm is proposed. The proposed algorithm implements fast Fourier transform (FFT) to the received frequency-domain signals after deconvolution. Then, the cost function for all points can be obtained from the same FFT output set. As a consequence, some repeated calculation in the traditional SML DPD algorithm is avoided. Simulation results demonstrate that the proposed modified SML DPD algorithm can achieve a comparable performance to traditional SML-DPD while significantly reducing the computational complexity.

Direct position determination algorithm for non‐circular sources in the presence of mutual coupling and its theoretical performance analysis

AbstractThis article proposes a direct position determination (DPD) algorithm for non‐circular sources observed by a moving array using the self‐calibration technique in the presence of mutual coupling. The method first utilises the symmetric Toeplitz property of uniform linear array matrices with mutual coupling and cyclic Toeplitz property of uniform circular array coupling matrix, realising the decoupled estimations of target position parameters and sensor error parameters. Then the position parameters of multiple non‐circular are directly determined based on the subspace data fusion criterion in a decoupled manner, where the subspaces are obtained using the extended array data model with the non‐circular properties of the sources. This results in a significant improvement in the accuracy of the target position estimation and the number of distinguishable sources compared to the traditional mutual coupling calibration algorithm. In addition, the theoretical mean square error expression for the position estimations of the proposed algorithm under the influence of finite sampling is derived based on the matrix perturbation analysis theory, and the corresponding Cramér‐Rao bound is given. Finally, the correctness of the theoretical derivation and the superiority of the method is verified by simulation experiments.

A Fast Direct Position Determination Algorithm for LFM Signal Based on Spectrum Detection

For the purpose of simultaneously estimating and locating the linear frequency modulation (LFM) emitter with unknown parameters, an innovative approach, i.e., Fast Direct Position Determination (FDPD), is introduced. The proposed algorithm is based on maximum likelihood estimation (MLE) and spectrum detection. To improve the accuracy and overcome the dramatic complexity of plain maximum likelihood formulation, we further derive the objective function equation of Direct Position Determination (DPD) algorithm and present an enhanced strategy to solve the highly nonlinear optimization problem. By combining the two-step localization method, one-step localization method, and short-time Fourier transform (STFT), our approach realizes jointly estimation of the transmitted signal parameters and emitter localization. Simulation results show that the proposed method is superior compared to the existing DPD, and two-step localization algorithms in terms of localization error and computational complexity, especially for low signal-to-noise ratio (SNR).

A reduced dimension multiple signal classification–based direct location algorithm with dense arrays

Aiming at the issue of parameter matching in conventional two-step location, a reduced dimension multiple signal classification direct position determination algorithm based on multi-array is proposed. Based on the idea of dimension reduction, the algorithm avoids multi-dimensional search in spatial domain and attenuation coefficient domain and reduces the search complexity. Simulation results show that the performance of the algorithm is better than the traditional angle of arrival two-step localization algorithm and subspace data fusion direct localization algorithm.

Efficient Direct Localization of OFDM Emitters in Multipath Environment With Mobile Receivers

For the purpose of locating the orthogonal frequency division multiplexing (OFDM) signal emitter efficiently and accurately in multipath environment, an innovative direction position determination (DPD) algorithm based on the multiple carrier characteristic of OFDM signals is proposed in this paper. The time of the arrival (TOA), angle of arrival (AOA) and Doppler frequency shift information contained in the observed data are jointly employed to locate the emitter. High-dimensional search can be avoided by decoupling unknown parameters and the estimation performance is improved due to the expansion of the subspace. The compact closed-form expressions of the Cramer-Rao lower bound (CRLB) corresponding to the parameters of interest are also derived. Simulation results show that compared with the traditional DPD based on MUSIC algorithm, the localization performance of the proposed algorithm can attain the CRLB at higher noise levels.

Direct Position Determination for Augmented Coprime Arrays via Weighted Subspace Data Fusion Method

Direct position determination (DPD) for augmented coprime arrays is investigated in this paper. Augmented coprime array expands degree of freedom and array aperture and improves positioning accuracy. Because of poor stability and noise sensitivity of the subspace data fusion (SDF) method, we propose two weighted subspace data fusion (W-SDF) algorithms for direct position determination. Simulation results show that two W-SDF algorithms have a prominent promotion in positioning accuracy than SDF, Capon, and propagator method (PM) algorithm for augmented coprime arrays. SDF based on optimal weighting (OW-SDF) is slightly better than SDF based on SNR weighting (SW-SDF) in positioning accuracy. The performance for DPD of the W-SDF method with augmented coprime arrays is better than that of the W-SDF method with uniform arrays.

MODEL AND ALGORITHMS FOR DETERMINING THE LOCATION AND POSITION OF AGRICULTURAL MACHINERY DURING THE MOVEMENT

The subject of research is the navigation subsystem of autonomous control system to determine the location and position of agricultural machinery during the movement. The purpose of the work is to develop and research model and algorithms to determine the location and position of mobile agricultural machinery using a physical model. The following tasks are solved in the article: development of agricultural machinery physical model to collect information from sensors during movement, further development and research of applicability of algorithms for location and position determination. The following methods are used: methods of mathematical statistics, methods of information systems theory and data processing, methods of random signals filtration. The following results were obtained: during research, the agricultural machinery physical model to collect information from sensors during movement was created. The model includes a GPS receiver, an accelerometer, gyroscope and infrared encoders, to count the rotation of the wheels, as well as its own four wheelbase of agricultural machinery. The modernized GPS coordinate filtration algorithm using a geochex algorithm is proposed, which according to several successively obtained GPS coordinates calculates the hash received coordinates; if the coordinates have the same hash, it can be argued that the vehicle is in the segment of the area that corresponds to this hash. To determine the physical model position during the movement data from the accelerometer and the gyroscope was processed using Savitzky-Golay and Madgwick filters. With the use of wheels’ rotation data, the odometric algorithms for movement and location determining of the agricultural machinery physical model in motion were implemented. Conclusions: to improve the accuracy of estimating the location and position agricultural machinery, algorithms complexation of indicators from different navigation systems should be used to reduce the total error. Research results can be applied in the development of new and modifications of existing navigation subsystems of agricultural machinery autonomous control systems.

Node placement optimization using particle swarm optimization and iterated local search algorithm in wireless sensor networks

SummaryCoverage and connectivity are the two most challenging issues in target‐based wireless sensor networks (WSNs). For that, node placement is one of the fundamental concerns that affect the performance of coverage and connectivity in WSN. This paper introduces a new approach by combining particle swarm optimization and iterated local search (PSO‐ILS) to have an optimum coverage and connectivity rate with the minimum number of nodes. In one side, to maintain the full coverage of targets, the PSO‐ILS is used to deploy the minimum number of sensor nodes. In other side, to achieve the full connectivity, the optimal position determination (OPD) algorithm was conceived to identify the optimal candidate positions which can be used by the PSO‐ILS to place the minimum number of relay nodes. The obtained results considered over a number of runs are compared with canonical PSO, differential evolution (DE), and genetic algorithms (GAs). The outcomes derived from this comprehensive analysis determine that PSO‐ILS provides an effectual improvement in contrary to the methods PSO, DE, and GA in terms of the selected potential positions to ensure full coverage of target points and the number of relay nodes required to achieve full connectivity.

Novel prior position determination approaches in particle filter for ultra wideband (UWB)‐based indoor positioning

<h3>Abstract</h3> Filtering-based indoor positioning using ultra wideband (UWB) requires known velocity to predict prior position in the prediction stage. Velocity can be obtained from an inertial measurement unit (IMU) sensor or the posterior state vector at the previous time stamp. Both methods have limitations when using them in practice. This paper proposes two novel velocity determination approaches, which use measurements to approximate velocity in a self-contained way. They are integrated into particle filtering algorithms for prior position determination. The test result shows that the particle filter with the proposed approaches performs similarly to the Rao-Blackwellized particle filter and slightly better than the particle filter with IMU. Compared with the standard particle filter, the particle filters with our proposed approaches achieve similar positioning accuracies with less computation time. Moreover, it is found that the integration of Angle-of-Arrival measurements in particle-filter-based positioning improves the 3-D positioning accuracy by about 37.3% on average.

Non-Cooperative Passive Direct Localization Based on Waveform Estimation

This paper considers a non-cooperative passive localization system wherein widely distributed receivers are used to localize a transmitter radiating a periodical pulse pair signal. Two possible pulse modulation models, noncoherent and coherent pulses, are fully considered for practical application, and are effectively unified as a general model for the algorithm design. To achieve highly accurate and robust localization performance, an enhanced direct position determination (DPD) algorithm based on waveform estimation (WE) is devised to jointly estimate the transmitter position and the waveform profile. The optimal objective function based on a least square (LS) principle is first derived to directly determine the position of the transmitter. Due to the complete lack of knowledge on the transmitted signal, the processing center calculates the objective function at each searched grid of interest by using estimated pulses instead of the real ones, while extraction of pulse samples and estimation of waveform are executed. Theoretical derivation gives the solution to estimate the non-parameterized waveform with a structure of maximum Rayleigh quotient. Additionally, simulation results verify the effectiveness of the proposed algorithm for many common waveform types in the cases of transmitting noncoherent and coherent pulses, and also show the excellent advantage over the classical DPD algorithm at low signal-to-noise ratio (SNR).

A new Wi-Fi dynamic selection of nearest neighbor localization algorithm based on RSS characteristic value extraction by hybrid filtering

Fingerprinting localization based on Wi-Fi received signal strength (RSS) is the most widely used indoor localization method. It typically includes offline training and online matching phases. The selection of the RSS characteristic value is a key step. The weighted K nearest neighbor (WKNN) algorithm is the most commonly used position-determination algorithm. The mean value of the RSS data collected over a time interval is usually taken as its characteristic value. However, the RSS measurements contain Gaussian and non-Gaussian noise, which cannot be filtered out effectively by the mean value method. The traditional WKNN algorithm adopts a fixed . However, reference points far away from the test point (TP) may be selected as the nearest neighbors to participate in the position calculation, which may result in accuracy degradation. This paper proposes the weighted dynamic K nearest neighbor algorithm (WDKNN-HF), which utilizes a hybrid of particle filtering and Kalman filtering to extract the RSS characteristic value. In the online matching phase, a dynamic K matching algorithm based on Euclidean distances is developed to determine the coordinates of TPs. Two experiments are conducted in two different indoor scenes. Experimental results demonstrate that the proposed algorithm can obtain better positioning accuracy than existing algorithms, such as KNN, WKNN, enhanced-WKNN (EWKNN) and self-adaptive weighted K nearest neighbor (SAWKNN).

Direct Position Determination Sensitivity to NLOS Propagation Effects on Doppler-Shift

In this paper, we consider the Direct Position Determination (DPD) algorithm for Doppler-shift based localization of radio-emitters. The DPD emitter location estimate is the location candidate that maximizes the largest eigenvalue of a location-dependent matrix. The sensitivity to multipath is analyzed by Small Error Analysis, which requires expressions for the derivatives of the largest eigenvalue with respect to the multipath parameters. We consider multipath conditions in which the line-of-sight path is obstructed and the receivers intercept a non-line-of-sight (NLOS) component. We provide compact closed-form expressions for these derivatives. Our theoretical results are corroborated by numerical experiments.

A Fast Algorithm of Direct Position Determination Using TDOA and FDOA

Weiss’s Direct position determination (WDPD) method compensate the received signals of the M stations to the transmitted signals by the Delay-Doppler operator, and Delay-Doppler operator is computed M times to compensate the time delay and Doppler shift for every search point, and the dimension of the Delay-Doppler operator is related to the size of data points N. And Delay-Doppler operator is equal to four matrices multiplying continuously, whose size is N×N, and matrix multiplication needs lots of time and memory, limiting the size of N. This paper deduces the DPD that don’t need to compensate to the transmitted signals. In practice, any one of M stations maybe is the reference station, and the signal of the reference station can compensate to the receiving signals of other stations by Delay-Doppler operator, and the objective function of the DPD is given. Through the DPD, Delay Doppler operator only is calculated M-1 times for every search point, and reduce the computation complexity, especially M is small. And for DPD algorithm, there are a lot of redundant computations in the Delay Doppler operator, so the fast algorithm of DPD (FDPD) is proposed. The experimental results verify that DPD reduce the computation complexity and FDPD saves the computation time and maintain the performance of the DPD algorithm simultaneously.