High-precision Estimation Research Articles

Design of robust Gaussian approximate filter and smoother with latency probability identification

The Kalman filter is a linear optimal estimator when it can accurately receive measurements and the noise obeys a Gaussian distribution. However, the measurement noise may have heavy-tailed characteristics because of outlier interference. Actually, real-world measurement information may have one-step randomly delayed measurements (ORDMs) with unknown latency probability (LP) due to exogenous disturbances. Moreover, systems are usually not linear. To overcome the influence of the state estimator of nonlinear systems from heavy-tailed measurement noise (HMN) and the unknown LP, this paper focuses on the robust Gaussian approximate (GA) filter and smoother for the above issues. First, the one-step predicted probability density function (PDF) is modeled as a Gaussian distribution, and the likelihood PDF is modeled as a Normal–Gamma–Beta (NGBM) distribution. Furthermore, novel robust Gaussian approximate filter and smoother are proposed based on the variational Bayesian technique. They provide general estimation frameworks for estimating state of nonlinear systems with HMN and ORDMs, and different nonlinear estimators can be implemented using different numerical techniques. In addition, the computational complexity of the proposed algorithms is calculated. Finally, taking a univariate nonstationary growth model, a passive ranging problem, and target tracking as examples, the effectiveness and superiority of the proposed robust algorithms contrasted with the existing algorithms are shown. The outcomes show that the proposed methods have higher estimation precision; however, the computational burden is marginally increased.

Monitoring of Possible Activities of Yangsan Fault Zone Using GNSS

After the Gyeongju earthquake in 2016 and the subsequent one in Pohang the following year, there is an imminent necessity to evaluate the risk of earthquakes accurately as well as respond to the risks on the Korean peninsula. For this purpose, the existence and movement of a fault should be investigated in the area. In this study, we calculated the displacement of the crust around the mass production fault using GNSS (Global Navigation Satellite System) data and analyzed the deformation characteristics by applying the method of stress calculation. The Yangsan Fault Zone has been analyzed with a total of 24 GNSS stations between 2018 and 2021. Data processing was conducted with Bernese GNSS Software, which requires high-precision orbit, satellite clock, ionosphere information for high-precision position estimation. By accumulating daily solutions over the three years to produce the final solution with the velocity of the stations, the Yangsan Fault Zone moved about 32 mm per year southeast on average. Based on the results, the movements of the stations on either side of the Faults are almost the same. Stress analysis of the Yangsan Fault Zone showed a large east–west expansion during 2018–2019 but decreased in stress afterwards, thus it is evaluated to be relatively stable compared to the past. However, due to the nature of crustal variation continuous monitoring research with long-term data processing should be followed, which will be discussed in further research.

Stimulus Selection in a Q-learning Model Using Fisher Information and Monte Carlo Simulation

Reinforcement learning models have been extensively studied for decision-making tasks with reward feedback. However, in designing an experiment to collect data for Q-learning models, the quantitative effect of a presented stimulus on the estimation precision of participant parameters has generally not been considered. That is, the lack of a mathematical framework has prevented researchers from designing an optimal experiment. To tackle this problem, this study analytically derives the Fisher information. Furthermore, this study formulates a stochastic representation of the Q-learning model, which is one of the most commonly applied reinforcement learning models. With this derivation, a two-step procedure is proposed to select the optimal stimuli in terms of estimation precision, in which low-cost Fisher information evaluation and more detailed finite-sample Monte Carlo simulation are combined. The simulation studies show that reward probability reversal leads to a high estimation precision for the learning rate parameter. By contrast, for the inverse temperature parameter, a larger difference in reward probability between options leads to higher estimation precision. These results reveal that the optimal experimental design is dependent on which trait parameters of the Q-learning model are of interest to researchers. Further, it is found that the use of undesirable stimuli in terms of trait parameter precision leads to a large bias in the correlation coefficient estimate. Based on the results, the approaches to designing experiments in the Q-learning model are discussed.

Integrating Sentinel-1 and 2 with LiDAR data to estimate aboveground biomass of subtropical forests in northeast Guangdong, China

ABSTRACT Accurate monitoring of forest aboveground biomass (AGB) is vital for sustainable forest management. Generally, the AGB is estimated by combining satellite images and field measurements. Nevertheless, field plots are inaccessible in complex forest areas. Due to the limitations related to either optical or SAR data alone, combining the two data types is indispensable. Here, we explored the LiDAR-derived biomass as training/testing samples for the combination of yearly time-series of Sentinel-1 and Sentinel-2 images to estimate AGB in north-eastern Conghua, Guangdong province, China. The AGB reference map derived from airborne LiDAR data and field plots could provide more samples for satellite-based AGB estimation with a limited amount of sampling plots. We designed four groups of experiments based on diverse Sentinel-1 and Sentinel-2 variables, including backscatter, backscatter indices, texture features, spectral bands, vegetation indices, and biophysical features. Four different prediction methods (support vector regression, multi-layer perceptron neural network, K-nearest neighbour, and random forest (RF)) were separately used to estimate AGB. Results showed that the RF model achieved the best accuracy for AGB mapping. All Sentinel-1 and Sentinel-2 experiment (R2: 0.72, RMSEr: 17.65%) performed better than the monthly complementary experiment (R2: 0.66, RMSEr: 19.01%). Additionally, the arid period images were observed to be sensitive for estimating AGB. The most contributing Sentinels predictors were determined via a sequential forward selection. Consequently, the proposed methodology has great potential for low-cost, large-scale, and high-precision AGB estimation.

Research on the state of health estimation of lithium-ion batteries for energy storage based on XGB-AKF method

With the advantages of high energy density, long cycle life and high stability, lithium-ion batteries have been used in a large number of fields such as electric vehicles and grid scale energy storage. To ensure the safe and reliable operation of battery systems, it is important to make an accurate and rapid estimation of the state of health (SOH) of Li-ion cells. A Li-ion cell is a complex nonlinear dynamic system. The SOH of a Li-ion can not be measured directly in actual working conditions; it can only be estimated indirectly by external characteristic parameters that reflects the extent of cell aging. It is difficult to ensure the reliability of method based on a single aging feature or model. Therefore, this paper proposes a multi-feature SOH estimation method that combines data-driven XGBoost and a Kalman filter. Firstly, a principal component analysis algorithm to reconstruct multiple battery aging features based on data is used, and an XGBoost online estimation model incorporating multiple features based on the reconstructed feature data is constructed. Finally, the joint optimal estimation of SOH of Li-ion cells by introducing a time-domain Kalman filter based on the real-time correction of the XGBoost model is achieved in this method. The results show that the method improves the accuracy and robustness of the estimation model and achieves a high-precision joint estimation of SOH for Li-ion cells.

Attitude Determination for Unmanned Cooperative Navigation Swarm Based on Multivectors in Covisibility Graph

To reduce costs, an unmanned swarm usually consists of nodes with high-accuracy navigation sensors (HAN) and nodes with low-accuracy navigation sensors (LAN). Transmitting and fusing the navigation information obtained by HANs enables LANs to improve their positioning accuracy, which in general is called cooperative navigation (CN). In this method, the accuracy of relative observation between platforms in the swarm have dramatic effects on the positioning results. In the popular research, constructing constraints in three-dimensional (3D) frame could only optimize the position and velocity of LANs but neglected the attitude estimation so LANs cannot maintain a high attitude accuracy when utilizing navigation information obtained by sensors installed during maneuvers over long periods. Considering the performance of the inertial measurement unit (IMU) and other common sensors, this paper advances a new method to estimate the attitude of LANs in a swarm. Because the small unmanned nodes are strictly limited by relevant practical engineering problems such as size, weight and power, the method proposed could compensate for the attitude error caused by strapdown gyroscopic drift, which only use visual vectors built by the targets detected by cameras with the function of range finding. In our method, the coordinates of targets are mainly given by the You Only Look Once (YOLO) algorithm, then the visual vectors are built by connecting the targets in the covisibility graph of the nodes in the swarm. The attitude transformation matrices between each camera frame are calculated using the multivector attitude determination algorithm. Finally, we design an information filter (IF) to determine the attitude of LANs based on the observation of HANs. Considering the problem of positioning reference, the field test was conducted in the open air and we chose to use two-wheeled robots and one UAV to carry out the experiment. The results show that the relative attitude error between nodes is less than 4 degrees using the visual vector. After filtering, the attitude divergence of LANs’ installed low precision IMU can be effectively constrained, and the high-precision attitude estimation in an unmanned CN swarm can be realized.

Frequency Estimation Enhancement for Industrial Free Induction Decay Signals Under Low SNR via Hankelization and Modified Covariance

The frequency of a free induction decay (FID) signal from an industrial proton precession magnetometer (PPM) is proportional to the magnetic field strength. To achieve high-precision frequency estimation for an FID signal with a low signal-to-noise ratio (SNR), a long estimation period is always required which limits the application scenarios of the PPMs, such as aeromagnetic detection. To break through the contradiction between frequency estimation precision and time, this paper proposes an enhanced frequency estimation method via Han-kelization and modified covariance, dubbed EFE-HMC. First, the collected one-dimensional FID signal is constructed as a third-order tensor through Hankelization, and then the noise tensors are removed by multi-linear singular value decomposition to improve the SNR; second, the pre-processed third-order tensor is inverted into a one-dimensional signal, and the modified covariance is employed to estimate the corresponding signal frequency; and third, an experimental test platform is constructed to compare the proposed EFE-HMC with three state-of-the-art methods including Carry Chain, equal precision, and Dn-ResUnet. The results demonstrate that when the SNR is lower than -10 dB and the estimation time varies from 50 ms to 200 ms, the frequency estimation precision is improved by 60% on average. Moreover, the frequency estimation time is reduced by about 150 ms when the frequency estimation precision is better than 0.03 Hz.

D-LIOM: Tightly-Coupled Direct LiDAR-Inertial Odometry and Mapping

Simultaneous localization and mapping via LiDAR-Inertial fusion is a crucial technology in many automation-related applications. Recently, a number of approaches based on geometric features have evolved, yielding impressive results via tightly-coupled estimation. This sort of feature-based techniques, however, are inextricably linked to the scanning mechanism of the LiDAR, relying on stable feature detection, and thus are difficult to adapt to multi-LiDAR systems. A few direct solutions, on the other hand, register the raw point cloud with the built probability map, which is more computationally efficient and easy to be extended. But, the existing direct approaches are all loosely-coupled, lacking correction of the IMU biases, and thus only work well in 2D cases. To this end, we present D-LIOM, a tightly-coupled Direct LiDAR-Inertial Odometry and Mapping framework. In D-LIOM, a scan is directly registered to a probability submap, and the LiDAR odometry, the IMU pre-integration, and the gravity constraint are integrated to build a local factor graph in the submap's time window, allowing the system to perform real-time high-precision pose estimation. Furthermore, to eliminate accumulated errors in time, we detect loops and adjust the sparse pose graph based on mutual matching of projected 2D submaps, allowing D-LIOM to run stably in large-scale scenes. In addition, to improve its flexibility to varied sensor combinations, D-LIOM supports multi-LiDAR inputs and facilitates the initialization with a common 6-axis IMU. Extensive experiments demonstrate that D-LIOM largely outperforms the existing state-of-the-art counterparts in mapping effect and localization accuracy as well as with high time efficiency. Lastly, to ensure that our results are entirely reproducible, all necessary data and codes are made open-source available. One introduction video can also be found on the online website.

TDFCAM: A method for estimating stable isotope trophic discrimination in wild populations.

Stable isotope mixing models (SIMMs) are widely used for characterizing wild animal diets. Such models rely upon using accurate trophic discrimination factors (TDFs) to account for the digestion, incorporation, and assimilation of food. Existing methods to calculate TDFs rely on controlled feeding trials that are time-consuming, often impractical for the study taxon, and may not reflect natural variability of TDFs present in wild populations.We present TDFCAM as an alternative approach to estimating TDFs in wild populations, by using high-precision diet estimates from a secondary methodological source-in this case nest cameras-in lieu of controlled feeding trials, and provide a framework for how and when it should be applied.In this study, we evaluate the TDFCAM approach in three datasets gathered on wild raptor nestlings (gyrfalcons Falco rusticolus; peregrine falcons Falco perigrinus; common buzzards Buteo buteo) comprising contemporaneous δ13C & δ15N stable isotope data and high-quality nest camera dietary data. We formulate Bayesian SIMMs (BSIMMs) incorporating TDFs from TDFCAM and analyze their agreement with nest camera data, comparing model performance with those based on other relevant TDFs. Additionally, we perform sensitivity analyses to characterize TDFCAM variability, and identify ecological and physiological factors contributing to that variability in wild populations.Across species and tissue types, BSIMMs incorporating a TDFCAM outperformed any other TDF tested, producing reliable population-level estimates of diet composition. We demonstrate that applying this approach even with a relatively low sample size (n < 10 individuals) produced more accurate estimates of trophic discrimination than a controlled feeding study conducted on the same species. Between-individual variability in TDFCAM estimates for ∆13C & ∆15 N increased with analytical imprecision in the source dietary data (nest cameras) but was also explained by natural variables in the study population (e.g., nestling nutritional/growth status and dietary composition).TDFCAM is an effective method of estimating trophic discrimination in wild animal populations. Here, we use nest cameras as source dietary data, but this approach is applicable to any high-accuracy method of measuring diet, so long as diet can be monitored over an interval contemporaneous with a tissue's isotopic turnover rate.

Wearable Leg Movement Monitoring System for High-Precision Real-Time Metabolic Energy Estimation and Motion Recognition

Comprehensive and quantitative assessment of human physical activity in daily life is valuable for healthcare, especially for those who suffer from obesity and neurological disorders or are at high risk of dementia. Common wearable devices, e.g., smartwatches, are insufficient and inaccurate for monitoring highly dynamic limb movements and assessing human motion. Here, we report a new wearable leg movement monitoring system incorporating a custom-made motion sensor with machine learning algorithm to perceive human motion accurately and comprehensively during diverse walking and running actions. The system enables real-time multimodal perceptions of personal identity, motion state, locomotion speed, and energy expenditure for wearers. A general law of extracting real-time metabolic energy from leg movements is verified although individual gaits show differences. In addition, we propose a novel sensing configuration combining unilateral lower leg movement velocity with its angular rate to achieve high accuracy and good generalizability while simplifying the wearable system. Advanced performances in personal identification (accuracy of 98.7%) and motion-state recognition (accuracy of 93.7%) are demonstrated. The wearable system also exhibites high-precision real-time estimations of locomotion speed (error of 3.04% to 9.68%) and metabolic energy (error of 4.18% to 14.71%) for new subjects across various time-varying conditions. The wearable system allows reliable leg movement monitoring and quantitative assessment of bodily kinematic and kinetic behaviors during daily activities, as well as safe identity authentication by gait parameters, which would greatly facilitate smart life, personal healthcare, and rehabilitation training.

ISSA Online Estimation Method for Guided Projectile Angular Rate Based on Magnetoresistive Sensors

Due to the complex and harsh launching and flying environment of guided projectile, gyros strapdown to projectile is easy to fail, and projectile angular rate cannot be accurately sensed. In this article, an online estimation model of projectile angular rate is established, which describes the mathematical relationship among output information of magnetoresistive sensors, the angular rate of gyro output, and attitude matrix. In order to realize the real-time estimation of projectile angular rate, an improved sparrow search algorithm (ISSA) is proposed. This method combines adaptive dynamic step strategy with dynamic compression search strategy, improving the traditional SSA. This method takes angular rate as the optimization object and uses the ISSA diagonal rate estimation model to solve and obtain high-precision estimation of angular rate. The simulation results verify the correctness and feasibility of the online estimation model of projectile angular rate only using magnetoresistive sensors, and the precision of angular rate estimation based on the ISSA is better than that of the traditional intelligent optimization algorithm.

A Novel Method of Situ Measurement Algorithm for Oudemansiella raphanipies Caps Based on YOLO v4 and Distance Filtering

Oudemansiella raphanipies has gradually gained more and more popularity in the market for its delicious taste, while enhancing human immunity and regulating human body functions as well. To achieve the high-throughput and automatic monitoring of the phenotypes of Oudemansiella raphanipies, a novel method, based on YOLO v4 and Distance Filter (DF), was proposed for high-precision diameter estimation of Oudemansiella raphanipies caps. To begin with, a dataset of Oudemansiella raphanipies was established by the laboratory cultivation and collection of factory samples. The improved YOLO v4 target detection model with added CBAM modules to each convolution block in the backbone was trained to locate the caps and, thus, obtain an approximate bounding box. Secondly, the approximate contour of the cap was gained through the H component, canny edge detection operators, and distance filtering to conduct the noise elimination. Finally, the center of the fitted circle and its accurate contour of the cap could be obtained by the constrained least square method, and the diameter of the fitted circle was estimated by the calibration data. The results of practical tests showed that this method achieved an accuracy of 95.36% in recognizing Oudemansiella raphanipies caps in the growing bed, and the fitting effect of caps was superior to Circle Hough Transform (CHT), the least square method (LS), and Ransac, with no manual adjustment on parameters. Compared with the manual measurement, the mean absolute error (MAE) of this method was 0.77 mm, the coefficient of determination (R2) was 0.95, and the root mean square error (RMSE) was 0.96 mm. Therefore, the model had high-cost performance and could meet the needs of continuous and long-term tracking of the cap shape of Oudemansiella raphanipies, providing the basis for future high-throughput breeding and machine picking.

Wideband spectrum sensing using step-sampling based on the multi-path nyquist folding receiver

Wideband spectrum sensing with a high-speed analog-digital converter (ADC) presents a challenge for practical systems. The Nyquist folding receiver (NYFR) is a promising scheme for achieving cost-effective real-time spectrum sensing, which is subject to the complexity of processing the modulated outputs. In this case, a multipath NYFR architecture with a step-sampling rate for the different paths is proposed. The different numbers of digital channels for each path are designed based on the Chinese remainder theorem (CRT). Then, the detectable frequency range is divided into multiple frequency grids, and the Nyquist zone (NZ) of the input can be obtained by sensing these grids. Thus, high-precision parameter estimation is performed by utilizing the NYFR characteristics. Compared with the existing methods, the scheme proposed in this paper overcomes the challenge of NZ estimation, information damage, many computations, low accuracy, and high false alarm probability. Comparative simulation experiments verify the effectiveness of the proposed architecture in this paper.

A novel convolutional informer network for deterministic and probabilistic state-of-charge estimation of lithium-ion batteries

Accurate and real-time state-of-charge (SOC) estimation for lithium-ion batteries (LiB) is crucial for battery management system. However, the nonlinearity and complex dynamic properties of LiB pose a great challenge to the estimation of SOC. Some previous methods have undertaken high-precision SOC point estimation; however, the reliability of the estimated results has not been evaluated. These methods are too conservative and unreliable to describe the SOC sequence with random fluctuation characteristics by a certain number. In this study, a novel method for deterministic and probabilistic SOC estimation is proposed, called the Laplace distribution-based convolutional Informer network. The convolutional neural network (CNN) was used to extract spatial characteristics from the original input and enhance the ability of the model to capture sequential location information. An Informer network integrating the attention mechanism was used to learn the mapping relationship between these high-dimensional characteristics extracted by CNN and the SOC. This design makes the model suitable for fully extracting feature information from these data with complex temporal degradation properties. Considering the universality of measurement error and the importance of uncertainty estimation, the Laplace-based loss function was derived and used to train the proposed convolutional Informer network, reducing the influence of outliers on the estimated results and making the proposed model achieve uncertainty quantization. The effectiveness of the proposed model was evaluated on two public battery datasets. The results demonstrated that the proposed model produced accurate SOC point estimates and reliable interval estimates for different batteries under various operating conditions.

A Learning-Based Vehicle-Cloud Collaboration Approach for Joint Estimation of State-of-Energy and State-of-Health

The state-of-energy (SOE) and state-of-health (SOH) are two crucial quotas in the battery management systems, whose accurate estimation is facing challenges by electric vehicles' (EVs) complexity and changeable external environment. Although the machine learning algorithm can significantly improve the accuracy of battery estimation, it cannot be performed on the vehicle control unit as it requires a large amount of data and computing power. This paper proposes a joint SOE and SOH prediction algorithm, which combines long short-term memory (LSTM), Bi-directional LSTM (Bi-LSTM), and convolutional neural networks (CNNs) for EVs based on vehicle-cloud collaboration. Firstly, the indicator of battery performance degradation is extracted for SOH prediction according to the historical data; the Bayesian optimization approach is applied to the SOH prediction combined with Bi-LSTM. Then, the CNN-LSTM is implemented to provide direct and nonlinear mapping models for SOE. These direct mapping models avoid parameter identification and updating, which are applicable in cases with complex operating conditions. Finally, the SOH correction in SOE estimation achieves the joint estimation with different time scales. With the validation of the National Aeronautics and Space Administration battery data set, as well as the established battery platform, the error of the proposed method is kept within 3%. The proposed vehicle-cloud approach performs high-precision joint estimation of battery SOE and SOH. It can not only use the battery historical data of the cloud platform to predict the SOH but also correct the SOE according to the predicted value of the SOH. The feasibility of vehicle-cloud collaboration is promising in future battery management systems.

Relative Pose Estimation of Non-Cooperative Space Targets Using a TOF Camera

It is difficult to determine the accurate pose of non-cooperative space targets in on-orbit servicing (OOS). The visual camera is easily affected by the extreme light environment in space, and the scanning lidar will have motion distortion when the target moves at high speed. Therefore, we proposed a non-cooperative target pose-estimation system combining a registration and a mapping algorithm using a TOF camera. We first introduce the projection model of the TOF camera and proposed a new calibration method. Then, we introduce the three modules of the proposed method: the TOF data preprocessing module, the registration module and the model mapping module. We assembled the experimental platform to conduct semi-physical experiments; the results showed that the proposed method has the smallest translation error 8 mm and Euler angle error 1° compared with other classical methods. The total time consumption is about 100 ms, and the pose tracking frequency can reach 10 Hz. We can conclude that the proposed pose-estimation scheme can achieve the high-precision pose estimation of non-cooperative targets and meet the requirements necessary for aerospace applications.

An ultra-precise fast fourier transform

<h2>Abstract</h2> The Fast Fourier Transform (FFT) is a cornerstone of digital signal processing, generating a computationally efficient estimate of the frequency content of a time series. Its limitations include: (1) information is only provided at discrete frequency steps, so further calculation, for example interpolation, is often used to obtain improved estimates of peak frequencies and amplitudes; (2) ‘energy' from spectral peaks may ‘leak' into adjacent frequencies, potentially causing lower amplitude peaks to be distorted or hidden; (3) the FFT, like many other DSP algorithms, is a discrete time approximation of continuous time mathematics. This paper describes a new FFT calculation which uses two windowing functions, derived from Prism Signal Processing. Separate FFT results are obtained from each windowing function applied to the data set. Calculations based on the two FFT results yields high precision estimates of spectral peak location (frequency), amplitude and phase. This technique addresses FFT limitations as follows: (1) spectral peak parameters are calculated directly, unrestricted by FFT frequency step discretization; (2) the windowing functions have narrowband characteristics which attenuate and localize spectral leakage; (3) the windowing functions incorporate a Romberg Integration mechanism to overcome the discrete/continuous time approximation.

A fast TDOA and VDOA estimation method of the wideband frequency hopping signal

In the mobile multi-station passive positioning scenario, the carrier frequency hopping of the wideband frequency hopping communication signal will produce a changing Doppler frequency shift. Therefore, it is not possible to directly estimate the Doppler frequency difference of the observed signal containing multiple pulses. In this case, only the time difference and frequency difference of the single-hop signal can be estimated, but the accuracy is low. The existing methods often need the carrier frequency of each FH pulse signal as a priori information, and the high computational complexity of the two-dimensional search method of the time difference and frequency difference is difficult to overcome. Aiming at the above problems, a fast and high-precision estimation algorithm for the time difference of arrival and velocity difference of wideband frequency hopping signals is proposed in this paper. Firstly, the wideband frequency hopping signal is segmented in the time domain with multiple pulses as the unit, the signal model of time-varying time difference is established, and the time difference of each short-time segment is estimated by the generalized cross-correlation algorithm. The estimated values of the initial time difference and Doppler velocity difference can be worked out by least squares fitting of the time difference sequence obtained from the single pulse estimation. Finally, taking the Link16 data link signal as an example, the simulation experiment of the proposed method is conducted, which verifies the correctness and performance superiority of the algorithm.

Differential Evolution Algorithm-Aided Time-Varying Carrier Frequency Offset Estimation for OFDM Underwater Acoustic Communication

Orthogonal frequency division multiplexing (OFDM) is the preferred scheme for high-speed communication in the field of underwater acoustic communication. However, it is very sensitive to the carrier frequency offset (CFO). This study used a time-varying CFO estimation method aided by the differential evolution (DE) algorithm to accurately estimate the CFO of an OFDM system. This method was based on the principle that the received OFDM signal with inter-carrier interference could be considered by a Multi Carrier-code division multiple access (MC-CDMA) system on the receiver side because MC-CDMA is a technology that combines OFDM and code division multiple access (CMDA). Because it is suitable for solving problems where there are dependencies between adjacent variables, the DE algorithm was used to capture the varying CFO values on the adjacent blocks. The spreading code of the MC-CDMA was obtained based on the estimated CFO values, which were elements in the DE solutions. Then the received signal was reconstructed. The Root-Mean-Square Error between the reconstructed and actual received signals was used as the cost function, and the CFO was estimated using the DE algorithm because of its powerful parallel search capability. The simulation results showed that the proposed method had a high estimation accuracy. Compared with other intelligent optimization algorithms such as the genetic algorithm and simulated annealing mutated-genetic algorithm, the time-varying CFO estimation performance of the DE algorithm was better because of its unique ability to solve problems with dependencies between adjacent variables. Specifically, under the condition of a high signal-to-noise ratio, the improvement of estimation accuracy reaches 36.13%, and the Bit Error Rate of demodulation is thus reduced by 75%, compared with the reference algorithms. In addition, the proposed method also has good applicability to modulation methods. For phase-shift keying and quadrature amplitude modulation, in particular, the proposed method not only achieved high-precision time-varying CFO estimation values, but also reduced the demodulation deterioration caused by noise.

Distributed satellite autonomous navigation using X-ray pulsars

Distributed X-ray pulsar-based navigation (DXNAV) is an effective method to realize earth-orbit satellite positioning under weak pulsar signal conditions. In this paper, we propose a new DXNAV method based on multiple information fusion. The DXNAV system principle and the pulse phase estimate Cramér-Rao lower bound are deduced. To suppress the calculation complexity and the error source, the X-ray pulsar photon time-of-arrival detected by each satellite is equivalently converted to the leading satellite directly using the inter-satellite link ranging and starlight angular distance measurement. A high precision estimate model of the pulse phase is built using pulsar standard profile, observed profile, and star-geocentric angular distance from distributed satellites. The estimated pulse phase is real-time supplied to the navigation system, which is established in the form of a deviation equation. The two-stage Kalman filter is designed to estimate the pulse phase in profile histogram bin step and the leader position in real-time step. Compared separately with the maximum likelihood phase estimate method and the celestial navigation method using only the star-geocentric angular distance, the simulation analysis shows that the estimation precisions of position and velocity are improved by 29% and 25%.