GNSS/IMU/ODO/LiDAR-SLAM Integrated Navigation System Using IMU/ODO Pre-Integration.

In this paper, we proposed a multi-sensor integrated navigation system composed of GNSS (global navigation satellite system), IMU (inertial measurement unit), odometer (ODO), and LiDAR (light detection and ranging)-SLAM (simultaneous localization and mapping). The dead reckoning results were obtained using IMU/ODO in the front-end. The graph optimization was used to fuse the GNSS position, IMU/ODO pre-integration results, and the relative position and relative attitude from LiDAR-SLAM to obtain the final navigation results in the back-end. The odometer information is introduced in the pre-integration algorithm to mitigate the large drift rate of the IMU. The sliding window method was also adopted to avoid the increasing parameter numbers of the graph optimization. Land vehicle tests were conducted in both open-sky areas and tunnel cases. The tests showed that the proposed navigation system can effectually improve accuracy and robustness of navigation. During the navigation drift evaluation of the mimic two-minute GNSS outages, compared to the conventional GNSS/INS (inertial navigation system)/ODO integration, the root mean square (RMS) of the maximum position drift errors during outages in the proposed navigation system were reduced by 62.8%, 72.3%, and 52.1%, along the north, east, and height, respectively. Moreover, the yaw error was reduced by 62.1%. Furthermore, compared to the GNSS/IMU/LiDAR-SLAM integration navigation system, the assistance of the odometer and non-holonomic constraint reduced vertical error by 72.3%. The test in the real tunnel case shows that in weak environmental feature areas where the LiDAR-SLAM can barely work, the assistance of the odometer in the pre-integration is critical and can effectually reduce the positioning drift along the forward direction and maintain the SLAM in the short-term. Therefore, the proposed GNSS/IMU/ODO/LiDAR-SLAM integrated navigation system can effectually fuse the information from multiple sources to maintain the SLAM process and significantly mitigate navigation error, especially in harsh areas where the GNSS signal is severely degraded and environmental features are insufficient for LiDAR-SLAM.

Implementation and Performance of a Deeply-Coupled GNSS Receiver with Low-Cost MEMS Inertial Sensors for Vehicle Urban Navigation.

In urban environments, Global Navigation Satellite Systems (GNSS) signals are frequently attenuated, blocked or reflected, which degrades the positioning accuracy of GNSS receivers significantly. To improve the performance of GNSS receiver for vehicle urban navigation, a GNSS/INS deeply-coupled software defined receiver (GIDCSR) with a low cost micro-electro-mechanical system (MEMS) inertial measurement unit (IMU) ICM-20602 is presented, in which both GPS and BDS constellations are supported. Two key technologies, that is, adaptive open-close tracking loops and INS aided pseudo-range weight control algorithm, are applied in the GIDCSR to enhance the signal tracking continuity and positioning accuracy in urban areas. To assess the performance of the proposed deep couple solution, vehicle field tests were carried out in GNSS-challenged urban environments. With the adaptive open-close tracking loops, the deep couple output carrier phase in the open sky, and improved pseudo-range accuracy before and after GNSS signal blocked. Applying the INS aided pseudo-range weight control, the pseudo-range gross errors of the deep couple decreased caused by multipath. A popular GNSS/INS tightly-coupled vehicle navigation kit from u-blox company, M8U, was tested side by side as benchmark. The test results indicate that in the GNSS-challenged urban areas, the pseudo-range quality of GIDCSR is at least 25% better than that of M8U, and GIDCSR's horizontal positioning results are at least 69% more accurate than M8U's.

Pole-Like Object Extraction and Pole-Aided GNSS/IMU/LiDAR-SLAM System in Urban Area.

Vision-based sensors such as LiDAR (Light Detection and Ranging) are adopted in the SLAM (Simultaneous Localization and Mapping) system. In the 16-beam LiDAR aided SLAM system, due to the difficulty of object detection by sparse laser data, neither the grid-based nor feature point-based solution can avoid the interference of moving objects. In an urban environment, the pole-like objects are common, invariant and have distinguishing characteristics. Therefore, it is suitable to bring more robust and reliable positioning results as auxiliary information in the process of vehicle positioning and navigation. In this work, we proposed a scheme of a SLAM system using a GNSS (Global Navigation Satellite System), IMU (Inertial Measurement Unit) and LiDAR sensor using the position of pole-like objects as the features for SLAM. The scheme combines a traditional preprocessing method and a small scale artificial neural network to extract the pole-like objects in environment. Firstly, the threshold-based method is used to extract the pole-like object candidates from the point cloud, and then, the neural network is applied for training and inference to obtain pole-like objects. The result shows that the accuracy and recall rate are sufficient to provide stable observation for the following SLAM process. After extracting the poles from the LiDAR point cloud, their coordinates are added to the feature map, and the nonlinear optimization of the front end is carried out by utilizing the distance constraints corresponding to the pole coordinates; then, the heading angle and horizontal plane translation are estimated. The ground feature points are used to enhance the elevation, pitch and roll angle accuracy. The performance of the proposed navigation system is evaluated through field experiments by checking the position drift and attitude errors during multiple two-min mimic GNSS outages without additional IMU motion constrain such as NHC (Nonholonomic Constrain). The experimental results show that the performance of the proposed scheme is superior to that of the conventional feature point grid-based SLAM with the same back end, especially in congested crossroads where slow-moving vehicles are surrounded and pole-like objects are rich in the environment. The mean plane position error during two-min GNSS outages was reduced by 38.5%, and the root mean square error was reduced by 35.3%. Therefore, the proposed pole-like feature-based GNSS/IMU/LiDAR SLAM system can fuse condensed information from those sensors effectively to mitigate positioning and orientation errors, even in a short-time GNSS denied environment.

Requirement Assessment of the Relative Spatial Accuracy of a Motion-Constrained GNSS/INS in Shortwave Track Irregularity Measurement.

Modern railway track health monitoring requires high accuracy measurements to ensure comfort and safety. Although Global Navigation Satellite System/Inertial Navigation System (GNSS/INS) integration has been extended to track geometry measurements to improve the work efficiency, it has been questioned due to its positioning accuracy at the centimeter or millimeter level. We propose the relative spatial accuracy based on the accuracy requirement of track health monitoring. A requirement assessment of the spatial relative accuracy is conducted for shortwave track irregularity measurements based on evaluation indicators and relative accuracy calculations. The threshold values of the relative spatial accuracy that satisfy the constraints of shortwave track irregularity measurements are derived. Motion-constrained GNSS/INS integration is performed to improve the navigation accuracy considering the dynamic characteristics of the track geometry measurement trolley. The results of field tests show that the mean square error and the Allan deviation of the relative position errors of motion-constrained GNSS/INS integration are smaller than 0.67 mm and 0.16 mm, respectively, which indicates that this approach meets the accuracy requirements of shortwave track irregularities, especially vertical irregularities. This work can provide support for the application of GNSS/INS systems in track irregularity measurement.

A Hybrid Sliding Window Optimizer for Tightly-Coupled Vision-Aided Inertial Navigation System.

The fusion of visual and inertial measurements for motion tracking has become prevalent in the robotic community, due to its complementary sensing characteristics, low cost, and small space requirements. This fusion task is known as the vision-aided inertial navigation system problem. We present a novel hybrid sliding window optimizer to achieve information fusion for a tightly-coupled vision-aided inertial navigation system. It possesses the advantages of both the conditioning-based method and the prior-based method. A novel distributed marginalization method was also designed based on the multi-state constraints method with significant efficiency improvement over the traditional method. The performance of the proposed algorithm was evaluated with the publicly available EuRoC datasets and showed competitive results compared with existing algorithms.

Artificial Marker and MEMS IMU-Based Pose Estimation Method to Meet Multirotor UAV Landing Requirements.

The fully autonomous operation of multirotor unmanned air vehicles (UAVs) in many applications requires support of precision landing. Onboard camera and fiducial marker have been widely used for this critical phase due to its low cost and high effectiveness. This paper proposes a six-degrees-of-freedom (DoF) pose estimation solution for UAV landing based on an artificial marker and a micro-electromechanical system (MEMS) inertial measurement unit (IMU). The position and orientation of the landing maker are measured in advance. The absolute position and heading of the UAV are estimated by detecting the marker and extracting corner points with the onboard monocular camera. To achieve continuous and reliable positioning when the marker is occasionally shadowed, IMU data is fused by an extended Kalman filter (EKF). The error terms of the IMU sensor are modeled and estimated. Field experiments show that the positioning accuracy of the proposed system is at centimeter level, and the heading error is less than 0.1 degrees. Comparing to the marker-based approach, the roll and pitch angle errors decreased by 33% and 54% on average. Within five seconds of vision outage, the average drifts of the horizontal and vertical position were 0.41 and 0.09 m, respectively.

Design of a Smartphone Indoor Positioning Dynamic Ground Truth Reference System Using Robust Visual Encoded Targets.

Smartphone indoor positioning ground truth is difficult to directly, dynamically, and precisely measure in real-time. To solve this problem, this paper proposes and implements a robust smartphone high-precision indoor positioning dynamic real-time ground truth reference system using color visual scatter-encoded targets based on machine vision and photogrammetry. First, a kind of novel high-precision color vision scatter-encoded patterns with a robust recognition rate is designed. Then we use a smartphone to obtain a sequence of images of an experimental room and extract the base points of the color visual scatter-encoded patterns from the sequence images to establish the indoor local coordinate system of the encoded targets. Finally, we use a high-efficiency algorithm to decode the targets of a real-time dynamic shooting image to obtain accurate instantaneous pose information of a smartphone camera and establish the high-precision and high-availability smartphone indoor positioning direct ground truth reference system for preliminary real-time accuracy evaluation of other smartphone positioning technologies. The experimental results show that the encoded targets of the color visual scatter-encoded pattern designed in this paper are easy to detect and identify, and the layout is simple and affordable. It can accurately and quickly solve the dynamic instantaneous pose of a smartphone camera to complete the self-positioning of the smartphone according to the artificial scatter feature visual positioning technology. It is a fast, efficient and low-cost accuracy-evaluation method for smartphone indoor positioning.

Robust Pedestrian Dead Reckoning Based on MEMS-IMU for Smartphones.

This paper proposes a pedestrian dead reckoning (PDR) algorithm based on the strap-down inertial navigation system (SINS) using the gyros, accelerometers, and magnetometers on smartphones. In addition to using a gravity vector, magnetic field vector, and quasi-static attitude, this algorithm employs a gait model and motion constraint to provide pseudo-measurements (i.e., three-dimensional velocity and two-dimensional position increment) instead of using only pseudo-velocity measurement for a more robust PDR algorithm. Several walking tests show that the advanced algorithm can maintain good position estimation compare to the existing SINS-based PDR method in the four basic smartphone positions, i.e., handheld, calling near the ear, swaying in the hand, and in a pants pocket. In addition, we analyze the navigation performance difference between the advanced algorithm and the existing gait-model-based PDR algorithm from three aspects, i.e., heading estimation, position estimation, and step detection failure, in the four basic phone positions. Test results show that the proposed algorithm achieves better position estimation when a pedestrian holds a smartphone in a swaying hand and step detection is unsuccessful.

Fast Signals of Opportunity Fingerprint Database Maintenance with Autonomous Unmanned Ground Vehicle for Indoor Positioning.

Indoor positioning technology based on Received Signal Strength Indicator (RSSI) fingerprints is a potential navigation solution, which has the advantages of simple implementation, low cost and high precision. However, as the radio frequency signals can be easily affected by the environmental change during its transmission, it is quite necessary to build location fingerprint database in advance and update it frequently, thereby guaranteeing the positioning accuracy. At present, the fingerprint database building methods mainly include point collection and line acquisition, both of which are usually labor-intensive and time consuming, especially in a large map area. This paper proposes a fast and efficient location fingerprint database construction and updating method based on a self-developed Unmanned Ground Vehicle (UGV) platform NAVIS, called Automatic Robot Line Collection. A smartphone was installed on NAVIS for collecting indoor Received Signal Strength Indicator (RSSI) fingerprints of Signals of Opportunity (SOP), such as Bluetooth and Wi-Fi. Meanwhile, indoor map was created by 2D LiDAR-based Simultaneous Localization and Mapping (SLAM) technology. The UGV automatically traverse the unknown indoor environment due to a pre-designed full-coverage path planning algorithm. Then, SOP sensors collect location fingerprints and generates grid map during the process of environment-traversing. Finally, location fingerprint database is built or updated by Kriging interpolation. Field tests were carried out to verify the effectiveness and efficiency of our proposed method. The results showed that, compared with the traditional point collection and line collection schemes, the root mean square error of the fingerprinting-based positioning results were reduced by 35.9% and 25.0% in static tests and 30.0% and 21.3% respectively in dynamic tests. Moreover, our UGV can traverse the indoor environment autonomously without human-labor on data acquisition, the efficiency of the automatic robot line collection scheme is 2.65 times and 1.72 times that of the traditional point collection and the traditional line acquisition, respectively.

Indoor Positioning Based on Pedestrian Dead Reckoning and Magnetic Field Matching for Smartphones.

This paper presents an ambient magnetic field map-based matching (MM) positioning algorithm for smartphones in an indoor environment. To improve the low distinguishability of a magnetic field fingerprint at a single point, a magnetic field sequence (MFS) combined with the measured trajectory contour coming from pedestrian dead-reckoning (PDR) is used for MM. Based on the fast approximation of magnetic field gradient, a Gauss-Newton iterative (GNI) method is used to find a rigid transformation that optimally aligns the measured MFS with a reference MFS coming from the magnetic field map. Then, the position of the reference MFS is used to control the position drift error of the inertial navigation system (INS) based PDR by an extended Kalman filter (EKF) and to further improve the accuracy of the trajectory contour. Finally, we conduct several experiments to evaluate the navigation performance of the proposed MM algorithm. The test results show that the position estimation error of the MM algorithm is 0.64 m (RMS) in an office building environment, 1.87 m (RMS) in a typical lobby environment, and 2.34 m (RMS) in a shopping mall environment.

A Railway Track Geometry Measuring Trolley System Based on Aided INS.

Accurate measurement of the railway track geometry is a task of fundamental importance to ensure the track quality in both the construction phase and the regular maintenance stage. Conventional track geometry measuring trolleys (TGMTs) in combination with classical geodetic surveying apparatus such as total stations alone cannot meet the requirements of measurement accuracy and surveying efficiency at the same time. Accurate and fast track geometry surveying applications call for an innovative surveying method that can measure all or most of the track geometric parameters in short time without interrupting the railway traffic. We provide a novel solution to this problem by integrating an inertial navigation system (INS) with a geodetic surveying apparatus, and design a modular TGMT system based on aided INS, which can be configured according to different surveying tasks including precise adjustment of slab track, providing tamping measurements, measuring track deformation and irregularities, and determination of the track axis. TGMT based on aided INS can operate in mobile surveying mode to significantly improve the surveying efficiency. Key points in the design of the TGMT's architecture and the data processing concept and workflow are introduced in details, which should benefit subsequent research and provide a reference for the implementation of this kind of TGMT. The surveying performance of proposed TGMT with different configurations is assessed in the track geometry surveying experiments and actual projects.

Tightly-Coupled Integration of Multi-GNSS Single-Frequency RTK and MEMS-IMU for Enhanced Positioning Performance.

Dual-frequency Global Positioning System (GPS) Real-time Kinematics (RTK) has been proven in the past few years to be a reliable and efficient technique to obtain high accuracy positioning. However, there are still challenges for GPS single-frequency RTK, such as low reliability and ambiguity resolution (AR) success rate, especially in kinematic environments. Recently, multi-Global Navigation Satellite System (multi-GNSS) has been applied to enhance the RTK performance in terms of availability and reliability of AR. In order to further enhance the multi-GNSS single-frequency RTK performance in terms of reliability, continuity and accuracy, a low-cost micro-electro-mechanical system (MEMS) inertial measurement unit (IMU) is adopted in this contribution. We tightly integrate the single-frequency GPS/BeiDou/GLONASS and MEMS-IMU through the extended Kalman filter (EKF), which directly fuses the ambiguity-fixed double-differenced (DD) carrier phase observables and IMU data. A field vehicular test was carried out to evaluate the impacts of the multi-GNSS and IMU on the AR and positioning performance in different system configurations. Test results indicate that the empirical success rate of single-epoch AR for the tightly-coupled single-frequency multi-GNSS RTK/INS integration is over 99% even at an elevation cut-off angle of 40°, and the corresponding position time series is much more stable in comparison with the GPS solution. Besides, GNSS outage simulations show that continuous positioning with certain accuracy is possible due to the INS bridging capability when GNSS positioning is not available.

An IMU Evaluation Method Using a Signal Grafting Scheme.

As various inertial measurement units (IMUs) from different manufacturers appear every year, it is not affordable to evaluate every IMU through tests. Therefore, this paper presents an IMU evaluation method by grafting data from the tested IMU to the reference data from a higher-grade IMU. The signal grafting (SG) method has several benefits: (a) only one set of field tests with a higher-grade IMU is needed, and can be used to evaluate numerous IMUs. Thus, SG is effective and economic because all data from the tested IMU is collected in the lab; (b) it is a general approach to compare navigation performances of various IMUs by using the same reference data; and, finally, (c) through SG, one can first evaluate an IMU in the lab, and then decide whether to further test it. Moreover, this paper verified the validity of SG to both medium- and low-grade IMUs, and presents and compared two SG strategies, i.e., the basic-error strategy and the full-error strategy. SG provided results similar to field tests, with a difference of under 5% and 19.4%-26.7% for tested tactical-grade and MEMS IMUs. Meanwhile, it was found that dynamic IMU errors were essential to guarantee the effect of the SG method.

Design and Performance Evaluation of a Dual Antenna Joint Carrier Tracking Loop.

In order to track the carrier phases of Global Navigation Satellite Systems (GNSS) signals in signal degraded environments, a dual antenna joint carrier tracking loop is proposed and evaluated. This proposed tracking loop processes inputs from two antennas, namely the master antenna and the slave antenna. The master antenna captures signals in open-sky environments, while the slave antenna capture signals in degraded environments. In this architecture, a Phase Lock Loop (PLL) is adopted as a master loop to track the carrier phase of the open-sky signals. The Doppler frequency estimated by this master loop is utilized to assist weak carrier tracking in the slave loop. As both antennas experience similar signal dynamics due to satellite motion and clock frequency variations, a much narrower loop bandwidth and possibly a longer coherent integration can be adopted to track the weak signals in slave channels, by utilizing the Doppler aid from master channels. PLL tracking performance is affected by the satellite/user dynamics, clock instability, and thermal noise. In this paper, their impacts on the proposed phase tracking loop are analyzed and verified by both simulation and field data. Theoretical analysis and experimental results show that the proposed loop structure can track degraded signals (i.e., 18 dB-Hz) with a very narrow loop bandwidth (i.e., 0.5 Hz) and a TCXO clock.

Modeling and development of INS-aided PLLs in a GNSS/INS deeply-coupled hardware prototype for dynamic applications.

A GNSS/INS deeply-coupled system can improve the satellite signals tracking performance by INS aiding tracking loops under dynamics. However, there was no literature available on the complete modeling of the INS branch in the INS-aided tracking loop, which caused the lack of a theoretical tool to guide the selections of inertial sensors, parameter optimization and quantitative analysis of INS-aided PLLs. This paper makes an effort on the INS branch in modeling and parameter optimization of phase-locked loops (PLLs) based on the scalar-based GNSS/INS deeply-coupled system. It establishes the transfer function between all known error sources and the PLL tracking error, which can be used to quantitatively evaluate the candidate inertial measurement unit (IMU) affecting the carrier phase tracking error. Based on that, a steady-state error model is proposed to design INS-aided PLLs and to analyze their tracking performance. Based on the modeling and error analysis, an integrated deeply-coupled hardware prototype is developed, with the optimization of the aiding information. Finally, the performance of the INS-aided PLLs designed based on the proposed steady-state error model is evaluated through the simulation and road tests of the hardware prototype.

Collaborative WiFi Fingerprinting Using Sensor-Based Navigation on Smartphones.

This paper presents a method that trains the WiFi fingerprint database using sensor-based navigation solutions. Since micro-electromechanical systems (MEMS) sensors provide only a short-term accuracy but suffer from the accuracy degradation with time, we restrict the time length of available indoor navigation trajectories, and conduct post-processing to improve the sensor-based navigation solution. Different middle-term navigation trajectories that move in and out of an indoor area are combined to make up the database. Furthermore, we evaluate the effect of WiFi database shifts on WiFi fingerprinting using the database generated by the proposed method. Results show that the fingerprinting errors will not increase linearly according to database (DB) errors in smartphone-based WiFi fingerprinting applications.

Tightly coupled integration of ionosphere-constrained precise point positioning and inertial navigation systems.

The continuity and reliability of precise GNSS positioning can be seriously limited by severe user observation environments. The Inertial Navigation System (INS) can overcome such drawbacks, but its performance is clearly restricted by INS sensor errors over time. Accordingly, the tightly coupled integration of GPS and INS can overcome the disadvantages of each individual system and together form a new navigation system with a higher accuracy, reliability and availability. Recently, ionosphere-constrained (IC) precise point positioning (PPP) utilizing raw GPS observations was proven able to improve both the convergence and positioning accuracy of the conventional PPP using ionosphere-free combined observations (LC-PPP). In this paper, a new mode of tightly coupled integration, in which the IC-PPP instead of LC-PPP is employed, is implemented to further improve the performance of the coupled system. We present the detailed mathematical model and the related algorithm of the new integration of IC-PPP and INS. To evaluate the performance of the new tightly coupled integration, data of both airborne and vehicle experiments with a geodetic GPS receiver and tactical grade inertial measurement unit are processed and the results are analyzed. The statistics show that the new approach can further improve the positioning accuracy compared with both IC-PPP and the tightly coupled integration of the conventional PPP and INS.

LiDAR Scan Matching Aided Inertial Navigation System in GNSS-Denied Environments.

A new scan that matches an aided Inertial Navigation System (INS) with a low-cost LiDAR is proposed as an alternative to GNSS-based navigation systems in GNSS-degraded or -denied environments such as indoor areas, dense forests, or urban canyons. In these areas, INS-based Dead Reckoning (DR) and Simultaneous Localization and Mapping (SLAM) technologies are normally used to estimate positions as separate tools. However, there are critical implementation problems with each standalone system. The drift errors of velocity, position, and heading angles in an INS will accumulate over time, and on-line calibration is a must for sustaining positioning accuracy. SLAM performance is poor in featureless environments where the matching errors can significantly increase. Each standalone positioning method cannot offer a sustainable navigation solution with acceptable accuracy. This paper integrates two complementary technologies-INS and LiDAR SLAM-into one navigation frame with a loosely coupled Extended Kalman Filter (EKF) to use the advantages and overcome the drawbacks of each system to establish a stable long-term navigation process. Static and dynamic field tests were carried out with a self-developed Unmanned Ground Vehicle (UGV) platform-NAVIS. The results prove that the proposed approach can provide positioning accuracy at the centimetre level for long-term operations, even in a featureless indoor environment.

High-precision image aided inertial navigation with known features: observability analysis and performance evaluation.

A high-precision image-aided inertial navigation system (INS) is proposed as an alternative to the carrier-phase-based differential Global Navigation Satellite Systems (CDGNSSs) when satellite-based navigation systems are unavailable. In this paper, the image/INS integrated algorithm is modeled by a tightly-coupled iterative extended Kalman filter (IEKF). Tightly-coupled integration ensures that the integrated system is reliable, even if few known feature points (i.e., less than three) are observed in the images. A new global observability analysis of this tightly-coupled integration is presented to guarantee that the system is observable under the necessary conditions. The analysis conclusions were verified by simulations and field tests. The field tests also indicate that high-precision position (centimeter-level) and attitude (half-degree-level)-integrated solutions can be achieved in a global reference.

Fast thermal calibration of low-grade inertial sensors and inertial measurement units.

The errors of low-cost inertial sensors, especially Micro-Electro Mechanical Systems (MEMS) ones, are highly dependent on environmental conditions such as the temperature. Thus, there is a need for the development of accurate and reliable thermal compensation models to reduce the impact of such thermal drift of the sensors. Since the conventional thermal calibration methods are typically time-consuming and costly, an efficient thermal calibration method to investigate the thermal drift of a full set of gyroscope and accelerometer errors (i.e., biases, scale factor errors and non-orthogonalities) over the entire temperature range in a few hours is proposed. The proposed method uses the idea of the Ramp method, which removes the time-consuming process of stabilizing the sensor temperature, and addresses its inherent problems with several improvements. We change the temperature linearly for a complete cycle and take a balanced strategy by making comprehensive use of the sensor measurements during both heating and cooling processes. Besides, an efficient 8-step rotate-and-static scheme is designed to further improve the calibration accuracy and efficiency. Real calibration tests showed that the proposed method is suitable for low-grade IMUs and for both lab and factory calibration due to its efficiency and sufficient accuracy.