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It is a challenging task to localize and track an in-hand object in robotic domain. Researchers were mainly using the vision as major modality for extracting object's pose. The vision approaches are fragile when the object is occluded by the robotic arm and hand. To this end, we propose a tactile-based DTI-Tracker (tracking object's pose via Dynamic Tactile Interaction) approach and formalize the object's tracking as a filter problem. An Extended Kalman Filter (EKF) is used to estimate the in-hand object pose exploiting the high spatial resolution tactile feedback. Given the initial estimation error, the proposed approach rapidly converges the estimation result to the real pose and the statistic evaluation shows the robustness of the proposed approach. We evaluate this method in physics simulation and real multi-fingered grasping setup while the object is static and movable. The proposed method is a potential tool to foster future research on dexterous manipulation using multifingered robotic hand. [ABSTRACT FROM AUTHOR]

In order to avoid catastrophic events that degrade the quality of machined products, such as tool breakage, it is vital to have a prognostic system for monitoring tool wear during the micro-milling process. Despite the long history of the tool wear monitoring field, creating such a system to track, monitor, and foresee the rapid progression of tool wear still needs to be improved in the application of micro-milling. On the other hand, digital twin technology has recently become widely recognized as significant in manufacturing and, notably, within the Industry 4.0 ecosystem. Digital twin technology is considered a potential breakthrough in developing a prognostic tool wear monitoring system, as it enables the tracking, monitoring, and prediction of the dynamics of a twinned object, e.g., a CNC machine tool. However, few works have explored the digital twin technology for tool wear monitoring, particularly in the micro-milling field. This paper presents a novel tool wear monitoring system for micro-milling machining based on digital twin technology and an extended Kalman filter framework. The proposed system provides wear progression notifications to assist the user in making decisions related to the machining process. In an evaluation using four machining datasets of slot micro-milling, the proposed system achieved a maximum error mean of 0.038 mm from the actual wear value. The proposed system brings a promising opportunity to widen the utilization of digital twin technology with the extended Kalman filter framework for seamless data integration for wear monitoring service. [ABSTRACT FROM AUTHOR]

This paper presents a particle swarm optimization-guided maximum likelihood estimation enabled (MLE) adaptive extended Kalman filter (EKF) with unknown inputs algorithm for estimating the dynamic nonlinear thermal states for an indoor heating ventilation and air conditioning system. The concept of MLE has been introduced to enhance the speed of convergence of the filtering parameters in adaptive EKF. The nonlinear indoor environment has been modelled employing equivalent RC network taking relative humidity into account. At the outset, an EKF-based method accommodating the unknown inputs and an adaptive estimator-based variant of it are developed for estimating the temperature of the walls of a laboratory-scale realistic environment. Subsequently the proposed scheme comes into play to deal with the scenarios associated with undesirable divergence and poor initialization utilizing the metaheuristically adapted optimal regularizer. The proposed technique outperforms the other contemporary state-of-the-art counterparts in terms of mean squared error. [ABSTRACT FROM AUTHOR]

The increasing demand for indoor positioning information has led to a growing emphasis on indoor localization. Non-Line-of-Sight (NLOS) conditions diminish the accuracy of Ultra-Wide Band (UWB) system positioning, while over time, Inertial Navigation Systems (INS) suffer from accumulating positioning errors. To address these issues, this paper proposes a method that combines UWB and INS sensors. Compared to individual system positioning methods, this approach effectively enhances localization precision, leveraging the complementary strengths of both systems. The paper utilizes Extended Kalman Filtering (EKF) to fuse residual positioning information, and the obtained residual position results are processed using the Multiple Fading Factor Square Root Kalman Filter technique (MSTSCKF). Moreover, during temporal asynchrony, it updates INS positioning and yaw angle information using EKF output for subsequent INS positioning until the next data correction. To further mitigate NLOS effects, a k-means preprocessing method is applied to UWB data. Root Mean Square Error (RMSE) is used as an evaluation metric. Simulation and experimental results demonstrate that the proposed method effectively accounts for NLOS error influences, thereby enhancing navigation and positioning accuracy.

ObjectiveHigh-precision localization technology serves as the crucial foundation in enabling the autonomous navigation operations of intelligent agricultural robots. However, the traditional global navigation satellite system (GNSS) localization method faces numerous limitations, such as tree shadow, electromagnetic interference, and other factors in the agricultural environment brings challenges to the accuracy and reliability of localization technology. To address the deficiencies and achieve precise localization of agricultural robots independent of GNSS, a localization method was proposed based on the fusion of three-dimensional light detection and ranging (LiDAR) data and inertial measurement unit (IMU) information to enhance localization accuracy and reliability.MethodsLiDAR was used to obtain point cloud data in the agricultural environment and realize self-localization via point cloud matching. By integrating real-time motion parameter measurements from the IMU with LiDAR data, a high-precision localization solution for agricultural robots was achieved through a specific fusion algorithm. Firstly, the LiDAR-obtained point cloud data was preprocessed and the depth map was used to save the data. This approach could reduce the dimensionality of the original LiDAR point cloud, and eliminate the disorder of the original LiDAR point cloud arrangement, facilitating traversal and clustering through graph search. Given the presence of numerous distinct crops like trees in the agricultural environment, an angle-based clustering method was adopted. Specific angle-based clustering criteria were set to group the point cloud data, leading to the segmentation of different clusters of points, and obvious crops in the agricultural environment was effectively perceived. Furthermore, to improve the accuracy and stability of positioning, an improved three-dimensional normal distribution transform (3D-NDT) localization algorithm was proposed. This algorithm operated by matching the LiDAR-scanned point cloud data in real time with the pre-existing down sampled point cloud map to achieve real-time localization. Considering that direct down sampling of LiDAR point clouds in the agricultural environment could result in the loss of crucial environmental data, a point cloud clustering operation was used in place of down sampling operation, thereby improving matching accuracy and positioning precision. Secondly, to address potential constraints and shortcomings of using a single sensor for robot localization, a multi-sensor information fusion strategy was deployed to improve the localization accuracy. Specifically, the extended Kalman filter algorithm (EKF) was chosen to fuse the localization data from LiDAR point cloud and the IMU odometer information. The IMU provided essential motion parameters such as acceleration and angular velocity of the agricultural robot, and by combining with the LiDAR-derived localization information, the localization of the agricultural robot could be more accurately estimated. This fusion approach maximized the advantages of different sensors, compensated for their individual limitations, and improved the overall localization accuracy of the agricultural robot.Results and DiscussionsA series of experimental results in the Gazebo simulation environment of the robot operating system (ROS) and real operation scenarios showed that the fusion localization method proposed had significant advantages. In the simulation environment, the average localization errors of the proposed multi-sensor data fusion localization method were 1.7 and 1.8 cm, respectively, while in the experimental scenario, these errors were 3.3 and 3.3 cm, respectively, which were significantly better than the traditional 3D-NDT localization algorithm. These findings showed that the localization method proposed in this study could achieve high-precision localization in the complex agricultural environment, and provide reliable localization assistance for the autonomous functioning of agricultural robots.ConclusionsThe proposed localization method based on the fusion of LiDAR data and IMU information provided a novel localization solution for the autonomous operation of agricultural robots in areas with limited GNSS reception. Through the comprehensive utilization of multi-sensor information and adopting advanced data processing and fusion algorithms, the localization accuracy of agricultural robots could be significantly improved, which could provide a new reference for the intelligence and automation of agricultural production.

Abstract This article studies a distributed consensus‐based estimation problem for discrete time‐varying non‐linear systems with missing measurements and Denial of Service (DoS) attacks. The probability of missing measurements is independent for each sensor. The communication link between sensor nodes is unreliable and subjected to DoS attacks. To achieve accurate state estimation against missing measurements, a local estimator with compensation mechanism is designed for each sensor node. A stochastic event‐triggered mechanism is used to lessen additional information transfer. Based on this, a distributed consensus‐based estimator is constructed by continually fusing local neighbours information matrixs and vectors. Moreover, the analysis of the designed estimator boundedness is presented. Finally, the effectiveness of the proposed algorithm is verified by three numerical examples.

To effectively eliminate the nonlinear distortion caused by the modulation depth (C value) drift and carrier phase delay (θ) in the phase-generated carrier (PGC) demodulation scheme, the PGC-PDC-EKF joint algorithm is presented, which combines phase delay compensation (PDC) with an extended Kalman filter (EKF). The θ is accurately extracted and compensated by the PDC module. Furthermore, with the EKF algorithm, the harmonic distortion of the demodulated signal due to the fluctuation of C value is suppressed. The experimental results indicate that θ is compensated accurately with a resolution of 0.01745 rad. The signal-to-noise and distortion ratio (SINAD) of the improved scheme reaches 54.01 dB, which is 18.03 dB higher than the PGC-Arctan algorithm on average. The total harmonic distortion (THD) is as low as −62.28 dB, which is 26.04 dB lower than the PGC-Arctan algorithm. The linearity of the demodulation system exceeds 99.99%. The proposed method provides a significant reference for demodulation schemes of interferometric fiber optic sensing systems in practical applications.

In farmland environments where GNSS signals are obstructed, such as forested areas or in adverse weather conditions, traditional GNSS/INS integrated navigation systems suffer from positioning errors and instability. To address this, a model-assisted integrated navigation system is proposed, combining Convolutional Neural Networks (CNN) and Bidirectional Long Short-Term Memory (BiLSTM) networks. The CNN-BiLSTM model is trained under normal GNSS conditions and used to predict positioning when GNSS signals are interrupted, effectively replacing GNSS to ensure stable and accurate navigation. Experimental validation is conducted using field data from tractor simulations. The results show that, during a 100-s GNSS denial, the CNN-BiLSTM model reduces the average position error by 79.3% compared to pure inertial navigation and by 5.4% compared to traditional LSTM. In a 30-s GNSS denial, the average position error is reduced by 41% compared to inertial navigation and 6.2% compared to LSTM. The model maintains positioning accuracy within 3% of the GNSS/INS output under normal conditions, demonstrating its feasibility and effectiveness. This approach offers a promising solution for autonomous tractor navigation in GNSS-denied agricultural environments, contributing to precision agriculture.

The development of the GPS (Global Positioning System) and related advances have made it possible to conceive of an outdoor positioning system with great accuracy; however, for indoor positioning, more efficient, reliable, and cost-effective technology is required. There are a variety of techniques utilized for indoor positioning, such as those that are Wi-Fi, Bluetooth, infrared, ultrasound, magnetic, and visual-marker-based. This work aims to design an accurate position estimation algorithm by combining raw distance data from ultrasonic sensors (Marvelmind Beacon) and acceleration data from an inertial measurement unit (IMU), utilizing the extended Kalman filter (EKF) with UDU factorization (expressed as the product of a triangular, a diagonal, and the transpose of the triangular matrix) approach. Initially, a position estimate is calculated through the use of a recursive least squares (RLS) method with a trilateration algorithm, utilizing raw distance data. This solution is then combined with acceleration data collected from the Marvelmind sensor, resulting in a position solution akin to that of the GPS. The data were initially collected via the ROS (Robot Operating System) platform and then via the Pixhawk development card, with tests conducted using a combination of four fixed and one moving Marvelmind sensors, as well as three fixed and one moving sensors. The designed algorithm is found to produce accurate results for position estimation, and is subsequently implemented on an embedded development card (Pixhawk). The tests showed that the designed algorithm gives accurate results with centimeter precision. Furthermore, test results have shown that the UDU-EKF structure integrated into the embedded system is faster than the classical EKF. [ABSTRACT FROM AUTHOR]

This paper deals with a discrete-time observer-based state feedback control design by taking into consideration bounded parameter uncertainty, actuator faults, and stochastic noise in an inner control loop which is extended in a cascaded manner by outer PI- and P-control loops for velocity and position regulation. The aim of the corresponding subdivision of the quadrotor model is the treatment of the control design in a systematic manner. In the inner loop, linear matrix inequality techniques are employed for the placement of poles into a desired area within the complex z-plane. A robustification of the design towards noise is achieved by optimizing both control and observer gains simultaneously guaranteeing stability in a predefined bounded state domain. This procedure helps to reduce the sensitivity of the inner control loop towards changes induced by the outer one. Finally, a model-based optimization process is employed to tune the parameters of the outer P/PI controllers. To allow for the validation of accurate trajectory tracking, a comparison of the novel approach with the use of a standard extended Kalman filter-based linear-quadratic regulator synthesis is presented to demonstrate the superiority of the new design. [ABSTRACT FROM AUTHOR]

In general, the extended Kalman filter (EKF) has a wide range of applications, aiming to minimize symmetric loss function (mean square error) and improve the accuracy and efficiency of state estimation. As the nonlinear model complexity increases, rounding errors gradually amplify, leading to performance degradation. After multiple iterations, divergence may occur. The traditional extended Kalman filter cannot accurately estimate the nonlinear model, and these errors still have an impact on the accuracy. To improve the filtering performance of the extended Kalman filter (EKF), this paper proposes a new extended Kalman filter (REKF) method that utilizes the statistical properties of the rounding error to enhance the estimation accuracy. After establishing the state model and measurement model, the residual term is used to replace the higher-order term in the Taylor expansion, and the least squares method is applied to identify the residual term step by step. Then, the iterative process of updating the extended Kalman filter is carried out. Within the Kalman filter framework, a higher-order rounding error-based extended Kalman filter (REKF) is designed for the joint estimation of rounding error and random variables, and the solution method for the rounding error is considered for the multilevel approximation of the original function. Through numerical simulations on a general nonlinear model, the higher-order rounding error-based extended Kalman filter (REKF) achieves better estimation results than the extended Kalman filter (EKF) and improves the filtering accuracy by utilizing the higher-order rounding error information, which also proves the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Autonomous robots have gained significant attention in research due to their ability to facilitate human work. Navigation systems, particularly localization, present a challenge in autonomous robots. The inertial navigation system is a localization system that uses inertial sensors and a wheel odometer to estimate the robot's relative position to the initial position. However, the system is susceptible to continuous error accumulation over time due to factors like sensor noise and wheel slip. To address these issues, external sensors are required to measure the robot's position in the environment. The extended Kalman filter (EKF) method is utilized to estimate the robot's position based on wheel odometer and light detection and ranging (LIDAR) sensor measurements. In the prediction stage, the input to the EKF is the position measurement from the wheel odometer, while the LIDAR sensor's position measurement is used in the update stage to improve the prediction stage results. The test results reveal that the EKF's estimated position has a lower average error compared to the position measurement using the wheel odometer. Therefore, it can be concluded that the EKF technique is effectively applied to the robot and can correct the wheel odometer's cumulative error with the assistance of the LIDAR sensor. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Signal Processing is the property of Journal of Signal Processing and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper develops a model for lithium-ion batteries under dynamic stress testing (DST) and federal urban driving schedule (FUDS) conditions that incorporates associated hysteresis characteristics of 18650-format lithium iron-phosphate batteries. Additionally, it introduces the adaptive sliding mode observer algorithm (ASMO) to achieve robust and swiftly accurate estimation of the state of charge (SOC) of lithium-iron-phosphate batteries during electric vehicle duty cycles. The established simplified hysteresis model in this paper significantly enhances the fitting accuracy during charging and discharging processes, compensating for voltage deviations induced by hysteresis characteristics. The SOC estimation, even in the face of model parameter changes under complex working conditions during electric vehicle duty cycles, maintains high robustness by capitalizing on the easy convergence and parameter insensitivity of ASMO. Lastly, experiments conducted under different temperatures and FUDS and DST conditions validate that the SOC estimation of lithium-iron-phosphate batteries, based on the adaptive sliding-mode observer and the simplified hysteresis model, exhibits enhanced robustness and faster convergence under complex working conditions and temperature variations during electric vehicle duty cycles. [ABSTRACT FROM AUTHOR]

Copyright of Smart Agriculture is the property of Smart Agriculture Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The objective of this study was to model a new drought index called the Fusion-based Hydrological Meteorological Drought Index (FHMDI) to simultaneously monitor hydrological and meteorological drought. Aiming to estimate drought more accurately, local measurements were classified into various clusters using the AGNES clustering algorithm. Four single artificial intelligence (SAI) models—namely, Gaussian Process Regression (GPR), Ensemble, Feedforward Neural Networks (FNN), and Support Vector Regression (SVR)—were developed for each cluster. To promote the results of single of products and models, four fusion-based approaches, namely, Wavelet-Based (WB), Weighted Majority Voting (WMV), Extended Kalman Filter (EKF), and Entropy Weight (EW) methods, were used to estimate FHMDI in different time scales, precipitation, and runoff. The performance of single and combined products and models was assessed through statistical error metrics, such as Kling–Gupta efficiency (KGE), Mean Bias Error (MBE), and Normalized Root Mean Square Error (NRMSE). The performance of the proposed methodology was tested over 24 main river basins in Iran. The validation results of the FHMDI (the compliance of the index with the pre-existing drought index) revealed that it accurately identified drought conditions. The results indicated that individual products performed well in some river basins, while fusion-based models improved dataset accuracy more compared to local measurements. The WMV with the highest accuracy (lowest NRMSE) had a good performance in 60% of the cases compared to all other products and fusion-based models. WMV also showed higher efficiency in 100% of the cases than all other fusion-based and SAI models for simultaneous hydrological and meteorological drought estimation. In light of these findings, we recommend the use of fusion-based approach to improve drought modeling. [ABSTRACT FROM AUTHOR]

The main aim of this article is to extend on the application of the grey Lotka-Volterra model by Wu et al. [1] with a linear programming method. We used this method for estimating the parameters of behavioral variables under the criterion of the minimization of mean absolute percentage error (MAPE). Our empirical analysis indicates that the adaptive extended Kalman filter (EKF) approach performs far better compared to traditional Lotka-Volterra model in the prediction of the relevant parameters. Comparisons of empirical results with the linear programming method for parameter estimation of the grey Lotka-Volterra model demonstrate that the EKF approach has more powerful and efficient prediction performance. [ABSTRACT FROM AUTHOR]

We develop an extended Kalman filter-based vehicle tracking algorithm, specifically designed for uniform planar array layouts and vehicle platoon scenarios. We first propose an antenna placement strategy to design the optimal antenna array configuration for precise vehicle tracking in vehicle-to-infrastructure networks. Furthermore, a vehicle tracking algorithm is proposed to improve the position estimation performance by specifically considering the characteristics of the state evolution model for vehicles in the platoon. The proposed algorithm enables the sharing of corrected error transition vectors among platoon vehicles, for the purpose of enhancing the tracking performance for vehicles in unfavorable positions. Lastly, we propose an array partitioning algorithm that effectively divides the entire antenna array into sub-arrays for vehicles in the platoon, aiming to maximize the average tracking performance. Numerical studies verify that the proposed tracking and array partitioning algorithms improve the position estimation performance. [ABSTRACT FROM AUTHOR]

Extended Kalman filtering with unknown input (EKF-UI) is often used to estimate the structural system state, parameters and unknown input in structural health monitoring. However, the real-time performance of EKF-UI is bound to whether the measurement equation has a direct feedthrough of unknown input, which great limits its application scope. Based on the zero-order-hold assumption and random walk assumption of unknown input, a novel adaptive discrete state equation is derived in this paper. The new equation establishes a connection between the current state and the current input and allows the adjustment of the sensitivity matrix of the unknown input. Then, based on the adaptive discrete state equation and minimum variance unbiased estimation principle, an adaptive generalized extended Kalman filter with unknown input is derived. The proposed algorithm eliminates the limitation that the real-time performance is restricted by whether the measurement equation has a direct feedthrough of the input and realizes the optimization of the state and input estimates in the sense of minimum variance. To demonstrate the feasibility of the proposed method, numerical example of a shear frame structure with Bouc–Wen hysteresis nonlinearity and experimental test of a five-story shear frame are conducted. The comparison with existing methods shows the advantages of the proposed method. [ABSTRACT FROM AUTHOR]

A fuzzy control improvement method is proposed with an integral line-of-sight (ILOS) guidance principle to meet the needs of autonomous navigation and high-precision control of ship trajectories. Firstly, a three-degree-of-freedom ship motion model was established with the battery-powered container ship ZYHY LVSHUI 01 built by the COSCO Shipping Group. Secondly, a ship path-following controller based on the ILOS algorithm was designed. To satisfy the time-varying demand of the look-ahead distance parameters during the following process, especially under different navigation conditions, fuzzy logic controllers were designed for different navigation conditions to automatically adjust the look-ahead distance parameters. Thirdly, a controller was applied that uses a five-state extended Kalman filter (EKF) to estimate the heading, speed, and heading rate based on the ship's motion model with the assistance of Global Navigation Satellite System (GNSS) position measurements. This provides the necessary navigational information, reduces the algorithm's dependence on sensors, and improves its generalizability. Finally, path-following experiments were carried out in the MATLAB experimental platform, and the results were compared with different following algorithms. The simulation results showed that the new algorithm has a better following performance, and it can maintain a smooth rudder angle output. The research results provide a reference for the path-following control of ships. [ABSTRACT FROM AUTHOR]

Mobility for disabled individuals is a crucial issue in their daily lives. The navigation system is one of the most commonly employed techniques for smart wheelchairs in the domain of mobile robotic-Maurice Audin, providing them with autonomy and social integration opportunities. Indeed, its simplicity and reliability can bring benefits to the users. This paper deals with intelligent wheelchair navigation through the development of multi-sensor data fusion using a hybrid filter (HF) approach by combining the extended Kalman filter (EKF) and the modified particle filter (PF). This combination overcomes the limitations of each other and leverages their respective strengths to achieve more accurate and robust localization. Indeed, the proposed hybrid filter aims to minimize estimation errors and improve the dynamic localization and navigation system. The applicability and effectiveness of the developed HP approach are demonstrated by simulation, and the results obtained were compared with those found in the literature. It has been found that the mean absolute error (MAE) and the percentage estimation error of the present method are better than those of EKF and both data fusion methods. [ABSTRACT FROM AUTHOR]

To prevent flow maldistribution and imbalanced temperature, a disturbance observer-based control strategy is presented for microchannel cooling systems with multiple heat exchangers. A disturbance observer is designed using the extended Kalman filter for estimating the states and disturbance. The performance of the observer is validated using experimental data from a pumped liquid cycle testbed. Disturbance observer-based control is applied to systems with two and three heat exchangers. The findings demonstrate that the wall temperatures and the temperature differences for the heat exchangers could be maintained at the desired values. When the heat exchangers are subjected to heat loads in the form of square, sinusoidal, and sawtooth functions, the temperature fluctuation could be suppressed by 60%-80% and the temperatures could be maintained at the same values. Our research demonstrates that the proposed control strategy has acceptable accuracy and robustness for the system with multiple heat exchangers undergoing various operating situations. [ABSTRACT FROM AUTHOR]

Summary: One of the most challenging subsystems for the CubeSats is the attitude determination and control system (ADCS) because it involves hardware and software integration, advanced strategies and algorithms to determine and control the attitude that impacts on space maneuvering and well working of a large set of payload (e.g., the optical payload). Although ADCS is largely studied, it still requires further investigations and analysis in order to achieve high‐performance and a reduced efforts. This paper presents an effective and reliable solution for the ADCS of CubeSats involved in Earth observation missions. The solution is based on an innovative framework that leverages the strengths of two distinct methodologies—H‐infinity optimal output feedback control and the extended Kalman filter (EKF)‐to significantly enhance the pointing stability of satellite systems. While H‐infinity optimal output feedback control is traditionally associated with partial state knowledge, we intentionally extend its application to scenarios with complete state information. The study includes a comparative performance analysis involving three algorithm configurations: the classic combination of EKF and model predictive control (MPC), the utilization of H‐infinity optimal output feedback control without EKF, and our proposed integrated approach. Performance evaluations are based on extrinsic indicators, demonstrating the advantages of our method in terms of pointing stability and overall control system performance. This research underscore the significance of combining innovative thinking with well‐established methodologies, unlocking new possibilities for stability enhancement in a range of engineering applications. [ABSTRACT FROM AUTHOR]

Currently, satellite navigation systems on cars provide a promising means of making these vehicles unmanned in the future. There is a common problem with these systems due to the unavailability of satellite signals in tunnels, forests, and noisy areas. One of the methods used to solve this problem is by using inertial navigation systems as an auxiliary system. This system works by modeling errors and correcting them when GNSS signals are absent. A number of methods are available for error modeling such as Kalman filters, neural networks, and so on, each of which has its own advantages and disadvantages. The error of inertial navigation is modeled using LSTM deep neural networks in this article. In this neural network, the relationship between current and past data is modeled as long as the GNSS satellite signal is available to improve the output position of the inertial navigation system when the GNSS satellite signal can no longer be received. The proposed method has been tested on real car driving data, and the calculated position from the inertial navigation system in four maneuvers has been compared with the Extended Kalman Filter method outputs. According to the results of the experiments, the proposed algorithm has improved the position estimation by 60% on average during 30, 60, and 120 seconds without GNSS signals, compared to the inertial navigation system based on Extended Kalman filter.. [ABSTRACT FROM AUTHOR]