Hybrid Projectile Body Angle Estimation for Selectable Range Increase

The NewSpace landscape for microlaunchers is highly competitive. The cost is one of the main drivers in this competition. Several microlauncher companies have decided to outsource the GNC sub-system to external providers, procuring low-cost commercial-of-the-shelf solutions. Lately, Astos has been involved in several activities related with GNC for (micro-)launchers. Astos’ work has been focused on providing GNC development tools and flexible and easily reconfigurable GNC software that can be applied to a wide range of launch vehicles. Navigation is one of the main drivers for launcher orbital injection accuracy and it is also one of the main drivers for cost in the GNC sub-system. Usually, this cost is driven by the Inertial Navigation System (INS) or Inertial Measurement Unit (IMU), in which expensive technologies are employed such as ring-laser gyroscopes. In traditional inertial propagation algorithms, errors are accumulated due to integration resulting in a steady divergence of the position and attitude estimate. Therefore, the performance of the navigation mainly depends on the performance of the IMU. This makes an investment into a highly accurate inertial sensors, especially the gyroscope, necessary to meet the navigation requirements. Lately, the use of hybrid navigation solutions that fuse the inertial measurements with Global Navigation Satellite Systems (GNSS) measurements has diminished, in some degree, the reliance of the navigation algorithm on the IMU performance. Although this is true for translational states, as position and velocity, the same cannot be said with the same degree of validity for attitude determination and, more specifically, for roll angle estimation. One possible way to reduce the cost of inertial sensors is by using microelectromechanical systems (MEMS). The advantages of using this technology, apart from the large reduction in cost, are the significant saves in mass and power required to operate these sensors. The disadvantage is clearly the lower performance, especially in high-vibration environments such as encountered in launcher vehicles. Lately, efforts to improve the performance of MEMS navigation solutions were driven by the demand of industries such as the wearables and unmanned aerial systems. This led to the development of solutions that utilize multiple low-cost inertial measurement units. By that, the hardware cost is not gravely increased in exchange for higher navigation accuracy, reliability, and redundancy. In this paper, a navigation algorithm is proposed that incorporates the measurements from multiple low-grade MEMS IMUs. The algorithm implements parallel Extended Kalman Filters (EKF), one for each IMU, combining the inertial measurements with the position, velocity, and time solutions provided by a single GNSS receiver. The algorithm has a loosely coupled architecture and the inertial propagation is regularly reset using the fused estimates of the vehicle’s state and IMU biases (closed-loop implementation). The navigation solution, providing estimates of position, velocity, and attitude, is then a combination of the individual EKF results through weighted means based on the covariance of the individual estimates. This formulation utilizing parallel filters is called in the literature as Federated Kalman Filter architecture. An analysis will be presented relating the performance of the navigation architecture with the number of sensors used and their distribution on the launch vehicle’s body. The assessment is performed with relation to a baseline navigation architecture also implementing a loosely coupled, closed-loop, hybrid structure but employing a single low-grade IMU. The analysis will determine the most promising sensor constellation, based on navigation performance, cost and implementation complexity. The selected multiple IMU solution is then compared with two different navigation architectures: Strapdown inertial propagation utilizing a single high-grade IMU; and hybrid navigation scheme implementing a loosely coupled, closed-loop architecture with a medium grade IMU. The performance evaluation is conducted utilizing simulated measurements retrieved from high-fidelity 6 degrees-of-freedom non-linear simulator of a representative microlauncher scenario. The simulators’ dynamics, kinematics, environment, and sensor modelling are provided by the ASTOS tool. Astos intends to further study the feasibility and performance of the proposed Inertial/GNSS hybrid navigation architecture with multiple IMUs. In the roadmap for raising the algorithm’s technology readiness level, more advanced simulations are foreseen, with improved sensor error modelling and previously unmodelled dynamical effects such as flexibility and sloshing. Additionally, processor- and hardware-in-the-loop tests with real sensor data are planned.

Abstract. With the continuous improvement of the hardware level of the inertial measurement unit (IMU), indoor pedestrian dead reckoning (PDR) using an inertial device has been paid more and more attention. Typical PDR system position estimation is based on acceleration obtained from accelerometers to measure the step count, estimate step length and generate the position with the heading received from angular sensors (magnetometers and gyroscopes). Unfortunately, collected signals are very responsive to the alignment of sensor devices, built-in instrumental errors and distortions from the surrounding environment. In our work, a pedestrian positioning method using step detection based on a shoe-mounted inertial unit is arranged and put to the test, and the final results are analyzed. The extended Kalman filter (EKF) provides estimation of the errors which are acquired by the XSENS IMU sensor biases. The EKF is revised with acceleration and angular rate computations by the ZUPT (zero velocity update) and ZARU (zero angular rate update) algorithms. The step detection associated with these two solutions is the perfect choice to calculate the current position and distance walked and to estimate the IMU sensors' collected errors by using EKF. The test with a shoe-mounted IMU device was performed and analyzed in order to check the performance of the recommended method. The combined PDR final results were compared to GPS/Beidou postprocessing kinematic results (outdoor environment) and to a real route which was prepared and calculated for an indoor environment. After the comparison, the results show that the accuracy of the regular-speed walking under ZUPT and ZARU combination in the case of outdoor positioning did not go beyond 0.19 m (SD) and for indoor positioning accuracy did not exceed 0.22 m (SD). The authors are conscious that built-in drift errors coming from accelerometers and gyroscopes, as well as the final position obtained by XSENS IMU, are only stable for a short time period. Based on this consideration, our future work will be focused on supporting the methods presented with radio technologies (WiFi) or image-based solutions to correct all IMU imperfections.

Navigation, guidance and control for small space vehicles require inertial measurement sensors which are small, inexpensive, low power, reliable and accurate. Micro inertial sensors, such as MEMS gyroscopes, can provide small, inexpensive, low power devices; however, the accuracy of these devices is insufficient for many space applications. Signal processing methods can be used to provide the necessary accuracy. The individual outputs of many nominally identical micro sensors can be combined to generate a single accurate measurement. An extended Kalman filter (EKF) (A.R. Stubberud and X.-H. Yu, 2000) which includes the dynamics of every sensor can be used for such a combination; however, the 'curse of dimensionality' limits the number of sensors which can be used. In this paper, a new EKF technique for combining many sensors is proposed which, using a common nominal model for the micro sensors and a single EKF with the state dimension of a single sensor, has accuracy comparable to the high dimensional EKF and is significantly more accurate than a single sensor.

Terrestrial mobile gravimetry using temperature-stabilized Inertial Measurement Units (IMUs) is emerging as an efficient technique for acquiring high-accuracy gravity data in dynamic environments. This study explores the integration of the iCORUS-2 IMU system with GNSS along the Cebeci-Elmadağ route in Ankara, Türkiye. The iTempStab technology was incorporated into the iCORUS-2 system to stabilize temperature variations to enhance the accuracy of gravity measurements. Notably, this research represents the results of vehicle-based terrestrial mobile gravimetry using a thermally stabilized IMU. An Extended Kalman Filter (EKF) was applied to integrate IMU and GNSS data. The advantage of terrestrial mobile gravimetry over airborne methods is the ability to make static updates for vertical gravity, zero gravity gradient and zero velocity measurements, which can be introduced into the EKF as measurement updates. The method was tested by analyzing the statistical impact of these updates at varying intervals: without any gravity measurement updates, and by applying updates at approximately 2 km, 3 km, 4 km, 5 km, 6 km, and 7 km intervals. Results indicated that without updates, a root mean square error (rmse) value between external terrestrial gravity data and mobile gravimetry estimates is 1.362 mGal. However, with updates at approximately 2 km intervals, the rmse value significantly decreased to 0.948 mGal, representing a %30.4 reduction in rmse and achieving sub-mGal accuracy. The inclusion of temperature stabilization and frequent gravity measurement updates demonstrated a marked improvement in data accuracy and consistency. These advancements not only validate the potential of mobile gravimetry for geophysical surveys but also broaden its applications in fields requiring precise gravity data acquisition.

Knowing vehicle sideslip angle accurately is critical for active safety systems such as Electronic Stability Control (ESC). Vehicle sideslip angle can be measured through optical speed sensors, or dual-antenna GPS. These measurement systems are costly (∼$5k to $100k), which prohibits wide adoption of such systems. This paper demonstrates that the vehicle sideslip angle can be estimated in real-time by using two low-cost single-antenna GPS receivers. Fast sampled signals from an Inertial Measurement Unit (IMU) compensate for the slow update rate of the GPS receivers through an Extended Kalman Filter (EKF). Bias errors of the IMU measurements are estimated through an EKF to improve the sideslip estimation accuracy. A key challenge of the proposed method lies in the synchronization of the two GPS receivers, which is achieved through an extrapolated update method. Analysis reveals that the estimation accuracy of the proposed method relies mainly on vehicle yaw rate and longitudinal velocity. Experimental results confirm the feasibility of the proposed method.

The first ground test results of the UCLA formation flight control computer (FFCC) are presented. The FFCC are designed to calculate real time, relative states of multiple aircraft accurately enough to fly two F-18 A/C autonomously in formation flight for a drag reduction experiment. This paper compares three schemes of differing complexity for the estimation of relative position, velocity, and attitude of two FFCC. Each scheme processes measurements from a GPS receiver and an INS on each vehicle. In the first scheme, each FFCC estimates its own absolute state using an extended Kalman filter (EKF) and the relative state is found by differencing the absolute state estimates from each filter. In the second scheme, one vehicle processes the single vehicle EKF while the second processes the differential range and Doppler measurements to estimate the relative state. In the third scheme, differential carrier phase measurements are added to the relative state estimation filter. The third scheme meets the target values for flying two NASA F-18 A/C in flight formation. Relative position is estimated within 10 cm, and relative attitude within 0.5 deg.

This letter presents a simple, low-cost teleoperation system. The leader device is a handheld camera integrated with an Inertial Measurement Unit (IMU), making it feasible to use a modern smartphone for this purpose. Existing leader devices require hardware and sensors to measure both the user interactions, and to control the follower device. By contrast, the proposed method uses the handheld camera both as a leader device and as a sensor to control the position of the follower device through visual servoing. To the best of the author's knowledge, this visual servoing scenario where the camera is held by a user has not been thoroughly studied. The measurements from the handheld device and the follower are fused together in an Extended Kalman Filter (EKF) to improve further the pose estimation. A Virtual Camera and IMU (VCI) concept is introduced to filter hand tremors for teleoperation efficiency without hindering the bandwidth of the relative pose control loop. The EKF and the VCI performance are assessed experimentally by teleoperating a Suspended Aerial Manipulator (AMES) prototype.

Nowadays, magnetic and inertial measurement units (MIMUs) have become useful tools for determining the attitude of moving objects. An attitude calculation algorithm (ACA) is programed into an MIMU, which determines the attitude by fusing three built-in sensors, namely, gyroscope, accelerometer, and magnetometer. Attitude is often represented by Euler angles, quaternion, or rotation matrix. Despite that great development has been achieved, how to eliminate the negative effect of magnetic disturbance on the pitch and roll estimation is still difficult for an ACA. This article aims to propose an Extended Kalman Filter (EKF)-based approach for problem solving. Inspired by the fact that the Euler angles are computed by using some elements of the rotation matrix, a diagonalizable regulation matrix (DRM) is multiplied to the right half part of the gain matrix (which is multiplied to the residual of the magnetometer measurement in the update stage of EKF). The determination of DRM is based on the principle that these elements can be appropriately regulated by the DRM so as to make the magnetometer measurement only participate in the computation of azimuth. No further revision to EKF is made except the Kalman gain matrix, hence the proposed EKF behaves similar as traditional EKF, except its ability of eliminating the negative effect of magnetic disturbance on the pitch and roll estimation. The superiority of the proposed EKF is validated by comparing it with four other competing algorithms through simulation and experimental experiments.

This paper presents the integration of an Ultra Short Base Line (USBL) acoustic modem and positioning device in a two-parallel Extended Kalman Filter (EKF) multisensor navigation schema for an Autonomous Underwater Vehicle (AUV). The system consists of a first odometric EKF position estimator fed with the measurements provided by an Inertial Measurement Unit (IMU), a Doppler Velocity Log (DVL), a visual tracker and a pressure sensor, and a second corrective EKF that fuses the previous sensors with the Global Positioning System (GPS) and the corrected delayed-state Ultra Short Base Line (USBL) position data. The first filter is aimed to compute a highly reliable vehicle position estimation from the sensor suit that produces high frequency relative navigation data. This estimation is essential to correct the delay of the USBL position measurements. The objective of the second filter is to give the vehicle a global pose, eliminating the drift inherent to dead-reckoning sensors by integrating absolute positions (GPS and USBL) provided at low frequencies. The effects of the USBL integration in the global localization module are evaluated in a simulated environment, and compared to a ground truth trajectory with the pose estimates given by the first EKF, the USBL raw data and the output of the second EKF, showing an effective reduction of the trajectory error.

Traffic conditions nowadays are in a grim situation caused by daily congestion and accidents. Thus, traffic state forecasting is considered as one of the most important traffic management techniques on roadway networks. Owing to financial and economic constraints, uses of sensors and cameras along the road are not a feasible option. Henceforth, probe vehicles equipped with GPS and other sensors are gaining prominence and are frequently used in developed countries to collect traffic data. In the probe vehicle concept, vehicles themselves are acting as roving traffic detectors, which are not bound to specific and fixed locations along the road infrastructure. In this paper, a sensor fusion model based on the extended Kalman filter and measurement inputs from a global positioning system (GPS) receiver and inertial measurement unit (IMU) sensors to improve absolute position estimation and to collect traffic data using ultrasonic sensors and dashcam has been presented. The proposed methodology has been tested for prevailing mixed traffic conditions in Prayagraj city. On the basis of the analysis of collected data, this paper presents a systematic solution to efficiently estimate the traffic state of large-scale urban road networks.

In this paper, machine-learning-based tools are utilized to learn a model of the functionality of a commercial chip with built-in signal processing and sensor fusion algorithms. Specifically, a fully integrated 9-axis Inertial Measurement Unit (IMU) with embedded algorithms providing the three-axis attitude and corresponding quaternion by fusing all the sensors is considered. Traditionally, extended Kalman filters are used for fusing IMU sensors; however, subtle algorithmic fixes (e.g., magnetic and angular alignment calibration for all sensors, Kalman filter tuning, temperature drift compensation, dynamic magnetic effects) need to be deployed to attain precise attitude (especially heading). A recurrent neural network (RNN) was trained using the chip to substitute for the built-in algorithms of the IMU Chip to output the approximate attitude given the 9-axis sensor data. We show the efficacy of our approach by mounting two IMUs on a board and utilize one IMU, which has its own internal algorithms, to train a machine learning system to fuse the raw data from the sensors on the second IMU to generate comparable accuracy (and in some cases, even outperform the original IMU).

A new integrated navigation system designed for small size Unmanned Aerial Vehicles (UAVs) is presented. The proposed system is based on a number of low-cost avionics sensors, including Global Navigation Satellite Systems (GNSS), Micro-Electro-Mechanical System (MEMS) based Inertial Measurement Unit (IMU) and Vision Based Sensors (VBS). The use of an Aircraft Dynamics Models (ADMs) to provide additional information to compensate for the shortcomings of Vision Based Navigation (VBN) and MEMS-IMU sensors in high-dynamics attitude determination tasks is also considered. Additionally, the research concentrates on the potential of carrier-phase GNSS for Attitude Determination (GAD) using interferometric techniques. The main objective is to design a compact, light and relatively inexpensive system capable of providing the required navigation performance (position and attitude data) in all phases of flight of small UAVs, with a special focus on precision approach and landing, where VBN techniques can be fully exploited in a multi-sensor data fusion architecture. An Extended Kalman Filter (EKF) is developed to integrate the information provided by the different sensors and to provide estimates of position, velocity and attitude of the UAV platform in real-time. Three different integrated navigation system architectures are implemented. The first architecture uses VBN at 20 Hz and GNSS at 1 Hz to augment the MEMS-IMU running at 100 Hz. The second mode also includes the ADM (computations performed at 100 Hz) to provide augmentation of the attitude channel. The third fusion architecture uses GNSS based attitude values. The simulations are carried out on the AEROSONDE UAV performing high-dynamics manoeuvres repre-sentative of the UAV operational flight envelope. Simulation of the VBN-IMU-GNSS (VIG) integrated navigation system shows that the system can attain position, velocity and attitude accuracies complying with Category Two (CAT II) precision approach requirements. Simulation of the VBN-IMU-GNSS-ADM (VIGA) system also shows promising results, since the achieved attitude accuracy is higher using the ADM-VBN-IMU than using VBN-IMU only. However, due to rapid divergence of the ADM virtual sensor, there is a need for frequent re-initialisation of the ADM data module, which is strongly dependent on the UAV flight dynamics and the specific manoeuvring transitions performed. In the simulation of the third integrated navigation system, the VIG system is augmented by employing the GAD, forming the VIG-GAD (VIGGA) system architecture. The performances achieved with the VIG, VIGA and VIGGA integrated Navigation and Guidance System (NGS) are presented and are in line with the International Civil Aviation Organization (ICAO) precision approach requirements.

Miniature inertial measurement units (IMUs) are wearable sensors that measure limb segment or joint angles during dynamic movements. However, IMUs are generally prone to drift, external magnetic interference, and measurement noise. This paper presents a new class of nonlinear state estimation technique called state-dependent coefficient (SDC) estimation to accurately predict joint angles from IMU measurements. The SDC estimation method uses limb dynamics, instead of limb kinematics, to estimate the limb state. Importantly, the nonlinear limb dynamic model is formulated into state-dependent matrices that facilitate the estimator design without performing a Jacobian linearization. The estimation method is experimentally demonstrated to predict knee joint angle measurements during functional electrical stimulation of the quadriceps muscle. The nonlinear knee musculoskeletal model was identified through a series of experiments. The SDC estimator was then compared with an extended kalman filter (EKF), which uses a Jacobian linearization and a rotation matrix method, which uses a kinematic model instead of the dynamic model. Each estimator's performance was evaluated against the true value of the joint angle, which was measured through a rotary encoder. The experimental results showed that the SDC estimator, the rotation matrix method, and EKF had root mean square errors of 2.70°, 2.86°, and 4.42°, respectively. Our preliminary experimental results show the new estimator's advantage over the EKF method but a slight advantage over the rotation matrix method. However, the information from the dynamic model allows the SDC method to use only one IMU to measure the knee angle compared with the rotation matrix method that uses two IMUs to estimate the angle.

The application of unmanned vehicles in civilian and military fields is increasingly widespread. Traditionally, unmanned vehicles primarily rely on Global Positioning Systems (GPSs) for positioning; however, GPS signals can be limited or completely lost in conditions such as building obstructions, indoor environments, or electronic interference. In addition, countries are actively developing GPS jamming and deception technologies for military applications, making precise positioning and navigation of unmanned vehicles in GPS-denied or constrained environments a critical issue that needs to be addressed. In this work, authors propose a method based on Visual–Inertial Odometry (VIO), integrating the extended Kalman filter (EKF), an Inertial Measurement Unit (IMU), optical flow, and feature matching to achieve drone localization in GPS-denied environments. The proposed method uses the heading angle and acceleration data obtained from the IMU as the state prediction for the EKF, and estimates relative displacement using optical flow. It further corrects the optical flow calculation errors through IMU rotation compensation, enhancing the robustness of visual odometry. Additionally, when re-selecting feature points for optical flow, it combines a KAZE feature matching technique for global position correction, reducing drift errors caused by long-duration flight. The authors also employ an adaptive noise adjustment strategy that dynamically adjusts the internal state and measurement noise matrices of the EKF based on the rate of change in heading angle and feature matching reliability, allowing the drone to maintain stable positioning in various flight conditions. According to the simulation results, the proposed method is able to effectively estimate the flight trajectory of drones without GPS. Compared to results that rely solely on optical flow or feature matching, it significantly reduces cumulative errors. This makes it suitable for urban environments, forest areas, and military applications where GPS signals are limited, providing a reliable solution for autonomous navigation and positioning of drones.

Robot localization is vital for the operation of an automated guided vehicle (AGV) but is susceptible to problems such as wheel slip. With more sensors fused together, the more environmental information can be collected by the AGV, which helps with the localization of AGV. Inertial measurement unit (IMU) and global positioning unit (GPS) are usually implemented to improve robot localization but are susceptible to noise and are effective outdoors. Indoors, however, are more suitable with light detection and ranging (lidar) device. This paper implements extended Kalman filter (EKF) and unscented Kalman filter (UKF) for robot localization on AGV. AGV localization was tested with EKF and UKF on three different test tracks with different turn conditions. The performance of the EKF and UKF was compared to each other. Different sensors were implemented along with sensor fusion. UKF generates better odometry estimation than EKF with 24.07% better accuracy. With the usage of lidar, wheel slip was compensated.KeywordsAutomated guided vehicleAGVRobot localizationSensor fusion