Attitude And Heading Reference System Research Articles

Use of Attitude and Heading Reference System (AHRS) to Analyze the Impact of Safety Nets on the Accelerations Occurring in the Human Body During a Collision.

The article presents accelerations occurring in the human body when falling onto a safety net. An attitude and heading reference system (AHRS) consists of sensors on three axes that provide attitude information for objects, including pitch, roll, and yaw. These sensors are made of microelectromechanical systems (MEMS) gyroscopes, accelerometers, and magnetometers. Usually, they are used in aircraft flight instruments due to their high precision. In the present article, these sensors were used to test safety nets, protecting people or objects falling from heights. The measurement was made for two heights: 6 m and 3.5 m. During the research, a type of mannequin that is a representative model of the human body for the largest segment of the adult population was used. The measurement was carried out using two independent measurement systems. One recorded the accelerations at the chest of the tested object, while the sensors of the second system were placed at the head, arms, and legs. The compiled measurement results were related to the permissible acceleration values that do not threaten human health and life.

An Algorithm for Affordable Vision-Based GNSS-Denied Strapdown Celestial Navigation

Celestial navigation is rarely seen in modern Uncrewed Aerial Vehicles (UAVs). The size and weight of a stabilized imaging system, and the lack of precision, tend to be at odds with the operational requirements of the aircraft. Nonetheless, celestial navigation is one of the few non-emissive modalities that enables global navigation over the ocean at night in Global Navigation Satellite System (GNSS) denied environments. This study demonstrates a modular, low cost, lightweight strapdown celestial navigation solution that is utilized in conjunction with Ardupilot running on a Cube Orange to produce position estimates to within 4 km. By performing an orbit through a full rotation of compass heading and averaging the position output, we demonstrate that the biases present in a strapdown imaging system can be nullified to drastically improve the position estimate. Furthermore, an iterative method is presented which enables the geometric alignment of the camera with the Attitude and Heading Reference System (AHRS) in-flight without an external position input. The algorithm is tested using real flight data captured from a fixed wing aircraft. The results from this study offer promise for the application of low cost celestial navigation as a redundant navigation modality in affordable, lightweight drones.

Development of a reliable adaptive estimation approach for a low‐cost attitude and heading reference system

AbstractA main challenge within inertial navigation systems involves attitude determination, which refers to the process of estimating the angles that define orientations. A new algorithm is presented to estimate a reliable and proper model for a low‐cost attitude and heading reference system (AHRS), while also, including long‐term global navigation satellite system (GNSS) outages with various dynamical manoeuvres. In the proposed approach, the initial AHRS model is continuously refined at each time step through the incorporation of complementary terms using a new prediction method. These complementary terms are determined using attitude information from the accelerometers output and the GNSS as reference systems. The proposed estimation technique undergoes mathematical analysis to ascertain stochastic stability and is further assessed through real‐world aerial experimental tests conducted with hardware‐in‐the‐loop mechanisation. The obtained results demonstrate a significant enhancement in the reliability and accuracy of the AHRS through the proposed estimation algorithm, even under GNSS blockages. The comparative results highlight the higher performance of the suggested data fusion scheme in providing a reliable and accurate model for the AHRS in normal conditions and assisting a powerful neural network‐based algorithm to provide reliable heading information even during long‐term GNSS outages under dynamical manoeuvres.

Integration of Deep Sequence Learning-Based Virtual GPS Model and EKF for AUV Navigation

To address the issue of increasing navigation errors in low-cost autonomous underwater vehicles (AUVs) operating without assisted positioning underwater, this paper proposes a Virtual GPS Model (VGPSM) based on deep sequence learning. This model is integrated with an Extended Kalman Filter (EKF) to provide a high-precision navigation solution for AUVs. The VGPSM leverages the time-series characteristics of data from sensors such as the Attitude and Heading Reference System (AHRS) and the Doppler Velocity Log (DVL) while the AUV is on the surface. It learns the relationship between these sensor data and GPS data by utilizing a hybrid model of Long Short-Term Memory (LSTM) and Bidirectional Long Short-Term Memory (Bi-LSTM), which are well-suited for processing and predicting time-series data. This approach constructs a virtual GPS model that generates virtual GPS displacements updated at the same frequency as the real GPS data. When the AUV navigates underwater, the virtual GPS displacements generated using the VGPSM in real-time are used as measurements to assist the EKF in state estimation, thereby enhancing the accuracy and robustness of underwater navigation. The effectiveness of the proposed method is validated through a series of experiments under various conditions. The experimental results demonstrate that the proposed method significantly reduces cumulative errors, with navigation accuracy improvements ranging from 29.2% to 69.56% compared to the standard EKF, indicating strong adaptability and robustness.

Design and implementation of an adaptive unscented Kalman filter with interval Type-3 fuzzy set for an attitude and heading reference system considering gyroscope bias

Low-cost microelectromechanical sensors used in attitude and heading reference systems (AHRS) suffer from unstable on–off biases, scaling errors, and nonlinearities that lead to an increase of navigation errors over time. To damp these errors and uncertainties from ultimate attitude and heading angles, the bias term of gyroscopes is augemented in under estimation state vector for high frequency feedback compensation. In this paper, an adaptive estimation algorithm to combine the strong tracking filter (STF) and interval type-3 fuzzy set (IT3FS) with an unscented Kalman filter (UKF) is proposed to deal with the large uncertainties in the microelectromechanical AHRS. The UKF, involving strong capability of dealing with nonlinearity, is limited by large instable bias uncertainty. By combining the STF to adaptively tuning of the UKF gain matrix and the IT3FS to determine the STF fading factor as well, the new IT3FS-STUKF algorithm is developed for high estimation performance against the significant uncertainties. To validate the proposed IT3FS-STUKF, real experiments are conducted with ground vehicles in urban areas, which show an improved accuracy compared to the extended Kalman filter (EKF) at reasonable computational burden.

Adaptive UAV Navigation Method Based on AHRS.

To address the inaccuracy of the Constant Acceleration/Constant Velocity (CA/CV) model as the state equation in describing the relative motion state in UAV relative navigation, an adaptive UAV relative navigation method is proposed, which is based on the UAV attitude information provided by Attitude and Heading Reference System (AHRS). The proposed method utilizes the AHRS output attitude parameters as the benchmark for dead reckoning and derives a relative navigation state equation with attitude error as process noise. By integrating the extended Kalman filter output for relative state estimation and employing an adaptive decision rule designed using the innovation of the filter update phase, the proposed method recalculates motion states deviating from the actual motion using the Tasmanian Devil Optimization (TDO) algorithm. The simulation results show that, compared with the CA/CV model, the proposed method reduces the relative position errors by 12%, 23%, and 32% in the X, Y, and Z directions, respectively, and that it reduces the relative velocity errors by 350%, 330%, and 300%, respectively. There is a significant improvement in the relative navigation accuracy.

A fuzzy adaptive complementary filter for attitude estimation based on norm judgment

Unmanned aerial vehicle (UAV) has great application prospect because of its capability of three-dimensional space operation. The reliability of attitude and heading reference system (AHRS) for UAV attitude estimation is crucial for the application of UAV. When a UAV is subjected to unknown electromagnetic interference and force interference in flight, its attitude detection system can suffer from reduced accuracy or even failure. In this paper, a fuzzy adaptive complementary filter (CF) for attitude estimation based on norm judgment is proposed to solve the problem that the sensor is easily disturbed by the complex flight environment and the fixed filter parameters are difficult to obtain the UAV attitude accurately under different flight states. Firstly, the correction model of the gyroscope, which includes four filter parameters, namely accelerometer weight, magnetometer weight, proportional gain P and integral gain I, is established. Secondly, the influence of the four parameters on the estimation accuracy is analyzed. Finally, the adaptive adjustment rules are designed to adjust the filter parameters online and thus achieve the accurate and reliable measurement of UAV attitude. The feasibility of the proposed algorithm is verified through static, dynamic and interference experiments with the specially designed AHRS test platform. And the results show that the attitude estimation algorithm designed in this paper can ensure the high accuracy of the system in both steady state and high-speed rotation, shield the pitch and roll angles from the acceleration of motion, and keep the yaw angle from the external magnetic field.

Global Navigation Satellite System Spoofing Detection in Inertial Satellite Navigation Systems

The susceptibility of global navigation satellite systems (GNSSs) to interference significantly limits the possibility of their use. From the standpoint of possible consequences, the most dangerous interference is the so-called spoofing. Simultaneously, in most cases of GNSS use, an inertial navigation system (INS) or an attitude and heading reference system (AHRS) is also present on the board of mobile objects. In this regard, the research goal is to assess the possibility of detecting GNSS spoofing in inertial satellite navigation systems. This paper examines the method for detecting GNSS spoofing by combining a pair of commercially available GNSS receivers and antennas with an INS or AHRS. The method is based on a comparison of the double differences of GNSS carrier phase measurements performed by receivers under conditions of resolved integer ambiguity and the values of the range double differences predicted using an INS. GNSS carrier phase integer ambiguity can be resolved using a strapdown inertial navigation system (SINS) or AHRS data. The mathematical model of GNSS phase difference measurements and the SINS-predicted satellite range differences model are given. The proposed algorithm calculates the moving average of the residuals between the SINS-predicted satellite range double differences and the measured GNSS carrier phase double differences. The primary criterion for spoofing detection is the specified threshold excess of the moving average of the double difference residuals. Experimental studies are performed using simulation and hardware-in-the-loop simulation. The experimental results allow us to evaluate the efficiency of the proposed approach and estimate the potential characteristics of the spoofing detection algorithm based on it.

An Improved Fault Detection and Isolation Method for Airborne Inertial Navigation System/Attitude and Heading Reference System Redundant System

The integrity of airborne inertial navigation systems (INSs) is the key to ensuring the safe flight of civil aircraft. The airborne attitude and heading reference system (AHRS) is introduced into the construction of a redundant inertial navigation system. As a backup system for an airborne INS, the AHRS exhibits a different device performance. A sequential weighted generalized likelihood ratio test (SWGLT) method, based on a principal component parity vector (PPV), is proposed. The PPV method improves the adaptability of the detection threshold to the inertial sensors’ noise and improves the probability of correct detection. At the same time, the multiscale problem of a heterogeneous redundant system error is solved by sequential weighting, and the false alarm rate is reduced. Simulation experiments show that the proposed method can improve fault detection sensitivity, reduce false alarm rates, and ensure the integrity of civil aircraft navigation systems.

Measurements of nearshore ocean-surface kinematics through coherent arrays of free-drifting buoys

Abstract. Surface gravity wave breaking occurs along coastlines in complex spatial and temporal patterns that significantly impact erosion, scalar transport, and flooding. Numerical models are used to predict wave breaking and associated processes but many lack sufficient evaluation with observations. To fill the need for more nearshore wave measurements, we deployed coherent arrays of small-scale, free-drifting buoys named microSWIFTs. The microSWIFT is a small buoy equipped with a GPS module to measure the buoy's position, horizontal velocities, and an inertial measurement unit (IMU) to directly measure the buoy's rotation rates, accelerations, and heading. Measurements were collected over a 27 d field experiment in October 2021 at the US Army Corps of Engineers Field Research Facility in Duck, NC. The microSWIFTs were deployed as a series of coherent arrays, meaning they all sampled simultaneously with a common time reference, leading to a rich spatial and temporal dataset during each deployment. Measurements spanned offshore significant wave heights ranging from 0.5 to 3 m and peak wave periods ranging from 5 to 15 s over the entire experiment. The completed dataset consists of 67 deployment files that contain 971 drift tracks that contain all associated data. We use an attitude and heading reference system (AHRS) 9-degrees-of-freedom Kalman filter to rotate the measured accelerations from the reference frame of the buoy to the Earth reference frame. We then use the corrected accelerations to compute the vertical velocity and sea-surface elevation. We give example evaluations of wave spectral energy density estimates from individual microSWIFTs compared with a nearby acoustic wave and current (AWAC) sensor. A zero-crossing algorithm is applied to each buoy time series of sea-surface elevation to extract realizations of measured surface gravity waves, yielding 116 307 wave realizations throughout the experiment. We also compute significant wave height estimates from the aggregate wave realizations and compare these estimates with the nearby AWAC estimates. An example of spatial variability in cross-shore velocity and vertical acceleration is explored. Wave-breaking events, detected by high-intensity vertical acceleration peaks, are explored, and the cross-shore distribution of all breaking events detected in the experiment is shown. A total of 3419 wave-breaking events were detected across the entire experiment. These data are available at https://doi.org/10.5061/dryad.hx3ffbgk0 (Rainville et al., 2023) and will be used to investigate nearshore wave kinematics, transport of buoyant particles, and wave-breaking processes.

Urban localization using robust filtering at multiple linearization points

We propose a robust Bayesian filtering framework for state and multi-modal uncertainty estimation in urban settings by fusing diverse sensor measurements. Our framework addresses multi-modal uncertainty from various error sources by tracking a separate probability distribution for linearization points corresponding to dynamics, measurements, and cost functions. Multiple parallel robust Extended Kalman filters (R-EKF) leverage these linearization points to characterize the state probability distribution. Employing Rao–Blackwellization, we combine the linearization point distribution with the state distribution, resulting in a unified, efficient, and outlier-resistant Bayesian filter that captures multi-modal uncertainty. Furthermore, we introduce a gradient descent-based optimization method to refine the filter parameters using available data. Evaluating our filter on real-world data from a multi-sensor setup comprising camera, Global Navigation Satellite System (GNSS), and Attitude and Heading Reference System (AHRS) demonstrates improved performance in bounding position errors based on uncertainty, while maintaining competitive accuracy and comparable computation to existing methods. Our results suggest that our framework is a promising direction for safe and reliable localization in urban environments.

Online hydrodynamic forces estimation system based on the artificial lateral line system

Vehicles that operate beneath or on the surface of water (e.g., boats, remotely operated vehicles, unmanned underwater vehicles, etc.) are subjected to external hydrodynamic forces and require an online hydrodynamic observer for precise autonomous control. The accurate calculation of current forces requires accurate sensor data and computational fluid dynamics, which impose a huge computational burden and cannot be applied in the real-time control of such vehicles. Fish can accurately perceive the effects of ocean currents, a function that can be achieved through an artificial lateral line system. In this study, an online hydrodynamic observer is proposed that uses an artificial lateral line system to estimate the resultant forces acting on water vehicles in real time for the autonomous control of the vehicle. A small three-layer artificial neural network is used to construct the hydrodynamic observer to evaluate various hydrodynamic forces in the form of a six-axis resultant force, such as the damping effects of currents and effects of wind and waves. In this study, an artificial lateral line system is designed for vehicles of any geometry. The system consists of a multipressure sensor array, data acquisition unit, and computational unit. Each pressure sensor is packaged as a separate unit that can be assembled on the surface of an underwater robot. These pressure sensors measure the pressure changes caused by the ocean current forces, while the data acquisition unit collects, collates, and sends the pressure sensor and attitude and heading reference system (AHRS) data to the processing unit. The processing unit uses an artificial neural network to estimate the ocean current forces acting on the vehicle body coordinate system based on the pressure sensor array, and converts them into the inertial reference system in the geoid based on the data acquired from the AHRS. This study explores the effects of the number of sensors and their locations on the accuracy of the estimated results. It investigates whether a scale factor can be used to estimate other available observers of the same size and geometry to enable the rapid deployment of artificial lateral devices to different vehicles. To evaluate the generalization performance of the proposed hydrodynamic observer, tests were conducted in dynamic water environments, such as rivers and oceans.

Robust Attitude and Heading Estimation under Dynamic Motion and Magnetic Disturbance.

Robust and accurate attitude and heading estimation using Micro-Electromechanical System (MEMS) Inertial Measurement Units (IMU) is the most crucial technique that determines the accuracy of various downstream applications, especially pedestrian dead reckoning (PDR), human motion tracking, and Micro Aerial Vehicles (MAVs). However, the accuracy of the Attitude and Heading Reference System (AHRS) is often compromised by the noisy nature of low-cost MEMS-IMUs, dynamic motion-induced large external acceleration, and ubiquitous magnetic disturbance. To address these challenges, we propose a novel data-driven IMU calibration model that employs Temporal Convolutional Networks (TCNs) to model random errors and disturbance terms, providing denoised sensor data. For sensor fusion, we use an open-loop and decoupled version of the Extended Complementary Filter (ECF) to provide accurate and robust attitude estimation. Our proposed method is systematically evaluated using three public datasets, TUM VI, EuRoC MAV, and OxIOD, with different IMU devices, hardware platforms, motion modes, and environmental conditions; and it outperforms the advanced baseline data-driven methods and complementary filter on two metrics, namely absolute attitude error and absolute yaw error, by more than 23.4% and 23.9%. The generalization experiment results demonstrate the robustness of our model on different devices and using patterns.

A proposal of AHRS yaw angle correction with the use of roll angle

PurposeAttitude and heading are very important measurements on board aircraft. In modern solutions they are measured by the attitude and heading reference system (AHRS). In some small unmanned systems, the GPS track angle is used for heading corrections instead of the magnetometer; then, the system measures the track angle instead of heading. With a temporary lack of correction signals, the measurement error increases very quickly. Similarly, a quick increase in the measurement error is observed when a magnetic heading sensor used for correction stops working properly. This study aims to propose measurement of the roll angle for yaw angle correction.Design/methodology/approachAHRS algorithms were designed; typical maneuvers were analyzed. The method was verified by simulation and in flight testing analysis. For quantitative analyses, a performance index was proposed.FindingsThe method enables reduction of the yaw angle error caused by the gyros bias error. This study presents the idea, results of simulations and flight testing data analysis and discusses advantages and limitations of the presented method.Practical implicationsThe presented methodology can be implemented in AHRS systems for manned and unmanned aircraft.Originality/valueThis study enables more accurate measurement of the yaw angle in the case of missing correction signals.

Methods and experiments for collecting information and constructing models of bottom-layer contours in paddy fields

To realize intelligent, accurate, and efficient operation of paddy field machinery that drive the paddy field bottom-layer below the tillage layer, the paddy field bottom-layer contours must be known. However, surface measurement systems cannot directly measure paddy field bottom-layer contours, making it difficult to collect and digitally model. In this study, an agricultural machine without a shock-absorbing suspension on the rear axle was used as an acquisition platform. Combined with a global navigation satellite system (GNSS) and attitude and heading reference system (AHRS) positional measurement technology, a 1/4 single-degree-of-freedom model of the vehicle body collected bottom-layer contour information of paddy fields. Based on the Delaunay triangulation principle, a digital model of the bottom-layer contour was established based on the collected bottom-layer contour point set. Subsequently, the ray method, used to extract specific triangles containing predicted points, and the point-plane intersection principle, used to estimate the elevation of arbitrary points in the whole area of bottom-layer, were used. Straight line contour acquisition on concrete road slope, contour acquisition on the bottom-layer surface of a paddy field, and elevation estimation of arbitrary points in the whole area were performed as verification tests. The results indicate that, in the x, y, and z axes, the average errors of the cement slope profile collection were 0.86, 0.68, and 0.55 cm, respectively, with standard errors of 0.99, 0.78, and 0.67 cm, respectively. Further, the average errors of the bottom-layer contour collection of the paddy field were 1.57, 0.91, and 1.25 cm, respectively, with standard errors of 1.87, 1.01, and 1.55 cm, respectively. The average error of elevation estimation at any point in the whole area was 1.25 cm with a standard error of 1.49 cm. The presented method can continuously and accurately acquire bottom-layer contour information, construct a digital model of the bottom-layer contour, accurately predict the location coordinates of any point within the field, and provide a reference for the walking environment of intelligent farming machines and measurement methods for the production of high-precision topographic maps.

An Observation Model From Linear Interpolation for Quaternion-Based Attitude Estimation

This article aims to solve multiple problems associated with attitude estimation; the complexity of Kalman filter (KF) calculations in the attitude and heading reference system (AHRS), the interference sensitivity of magnetic, angular rate, and gravity (MARG) sensors, and the low accuracy of the factored quaternion algorithm (FQA). It presents a two-layer linear KF using MARG sensors to obtain attitude estimation in quaternions. First, data from a triaxial accelerometer and magnetometer is processed by a novel algorithm, which fuses the quaternion estimator (QUEST) algorithm and FQA by the linear interpolation (LERP) to obtain an observation model. Second, the process model in the two-layer KF was obtained by using LERP to fuse an optimum quaternion obtained from a gyroscope and FQA. The LERP can eliminate gyro bias drift, and integral error, and compensate for unexpected conditions, such as fast rotation and temporary strong magnetic disturbances. The proposed algorithm presents higher accuracy and lower computational load than QUEST or FQA used with a KF alone. The performance of the proposed algorithm is verified through simulation and experiments.

The depth-keeping performance of autonomous underwater vehicle advancing in waves integrating the diving control system with the adaptive fuzzy controller

This study aims to develop an experimental-based adaptive fuzzy controller for the diving control system (DCS) of autonomous underwater vehicle (AUV) to ensure high stability and rapid integration. The DCS is designed with a depth sensor and an attitude and heading reference system (AHRS) to sense the attitude vector and the current depth of AUV in real-time as the control inputs of attitude close-loop and to calculate yaw and pitch controls of AUV. Therefore, the DCS can integrate depth-keeping and attitude stability controls into the AUV. To verify the robustness and adaptability of the DCS with adaptive fuzzy control, the DCS with universal fuzzy control (A-type DCS), improved fuzzy control (B-type DCS), and adaptive fuzzy control (C-type DCS) have been analyzed. The experimental analysis indicates that the C-type DCS features higher robustness to external force interference than the other types of DCS. The present study establishes an adaption function based on depth-keeping control experiments and demonstrates robustness of the adaptive fuzzy control DCS to environmental disturbances. Consequently, the proposed adaptive fuzzy control DCS is a model-free design that resolves the problem of depth-keeping and attitude stability controls of AUV with unknown hydrodynamic coefficients, rudder dynamics and time-varying external forces.

Multilayer Low-Cost Sensor Local-Global Filtering Fusion Integrated Navigation of Small UAV

Aimed at improving the nonlinear integrated navigation solution performance of multiple low-cost sensors fusion, this paper presents a multilayer loosely-coupled, local-global, and step-optimized MF5DCKF (Multisensor Federated fifth-degree Cubature Kalman filter) state estimation algorithm for the small unmanned aerial vehicle (UAV). This method establishes a multilayer nonlinear integrated navigation model composed of the nonlinear attitude and heading reference system (AHRS) error model, strapdown inertial navigation system/global positioning system (SINS/GPS) error model, and strapdown inertial navigation system/barometer (SINS/BARO) error model to enhance the robustness and richness of the navigation module. Further, based on the above navigation models, a loosely-coupled error state fusion frame is designed to obtain the local convergent state vector. Simultaneously, a three-layer fifth-degree Cubature Kalman filter is proposed to improve the local state estimation accuracy. Subsequently, to optimize the estimated local state, this paper presents a novel distributed MF5DCKF scheme fusing the local state vector to calculate the global optimal state parameters in a step-optimized process. The experimental flight test results show that the proposed algorithm achieves a higher state solution accuracy and a better convergent performance compared with some conventional multisensor fusion algorithms. The new algorithm framework can provide applicability and reliability for the small UAV during the flight.

Three-Step Autonomous Calibration Method for Low-Cost MEMS Inertial/Magnetic Sensors

The inherent error of low-cost microelectromechanical system (MEMS) inertial/magnetic sensor directly affects the measurement accuracy of attitude and heading reference system (AHRS), and the error calibration of inertial/magnetic sensor can significantly improve its performance and measurement accuracy. Based on the above problem existing in the magnetometer, accelerometer, and rate gyro (MARG) sensors, this article proposes a new three-step auxiliary autonomous calibration method (TSAAC) based on the combination of MEMS inertial/magnetic sensors, and the effectiveness and feasibility of the proposed method are jointly verified through numerical simulation and physical verification. The experimental results show that the actual calibration effect of the TSAAC is close to the calibration effect assisted by the high-precision turntable, which can achieve the autonomous calibration of the inertial/magnetic sensor combination without any external equipment assistance.

9-DOF IMU-Based Attitude and Heading Estimation Using an Extended Kalman Filter with Bias Consideration.

The attitude and heading reference system (AHRS) is an important concept in the area of navigation, image stabilization, and object detection and tracking. Many studies and works have been conducted in this regard to estimate the accurate orientation of rigid bodies. In most research in this area, low-cost MEMS sensors are employed, but since the system’s response will diverge over time due to integration drift, it is necessary to apply proper estimation algorithms. A two-step extended Kalman Filter (EKF) algorithm is used in this study to estimate the orientation of an IMU. A 9-DOF device is used for this purpose, including a 6-DOF IMU with a three-axis gyroscope and a three-axis accelerometer, and a three-axis magnetometer. In addition, to have an accurate algorithm, both IMU and magnetometer biases and disturbances are modeled and considered in the real-time filter. After applying the algorithm to the sensor’s output, an accurate orientation as well as unbiased angular velocity, linear acceleration, and magnetic field were achieved. In order to demonstrate the reduction of noise power, fast Fourier transform (FFT) diagrams are used. The effect of the initial condition on the response of the system is also investigated.