An adaptive attitude estimationfor unidentified flying objects

This paper presents a novel adaptive method for attitude estimation of unidentified flying object based on acceleration sensors and gyroscope sensors. Because the external acceleration is the main error source of estimation error.

Electronics and Automation AN ADAPTIVE ATTITUDE ESTIMATIONFOR UNIDENTIFIED FLYING OBJECTS Nguyen Dang Tien* Abstract: This paper presents a novel adaptive method for attitude estimation of unidentified flying object based on acceleration sensors and gyroscope sensors Because the external acceleration is the main error source of estimation error Therefore, in this paper, we proposed a new method, in which the extended Kalman filter is combined with compensating external acceleration to reduce the effect of measurement noise and increase the accuracy of estimation process Finally, the simulation results are presented to demonstrate the effectiveness of the proposed estimation method Keywords: Adaptive attitude estimation, Extended Kalman filter, Unidentified flying object PROBLEM STATEMENT Adaptive attitude estimation is widely used for various applications such as missiles, submarines, unmanned aircraft and satellites In the past, there are numerous mechanical systems used to locate and estimate object’s motion parameters However, these systems usually have a high cost and low accuracy Recently, micro-electromechanical system (MEMS) technology has achieved significant development and many MEMS products have low cost, small size, high accuracy and can be applied widely in practice Acceleration sensors and gyroscope sensors are popular products of MEMS Technology Normally, adaptive estimation equipment only has to use acceleration sensors to locate the position of the object by measuring the gravity’s direction of the object However, there are various errors as well as external acceleration which affect the accuracy of measuring when only acceleration sensors are being used Therefore, the gyroscope sensors are utilized to enhance the accuracy of measuring and reduce the effect of noise The main challenge here is how to integrate the acceleration sensor and gyroscope sensor to bring the highest quality result Recent works almost focused on using Kalman filter to solve this issue such as: Adaptive attitude estimation for robotic [1-2], missiles [3-4], aircraft [5-6] and satellites [7-8] However, these works only focus on using linear Kalman filter In addition, when the object is affected by external acceleration, the result of linear Kalman filter has low quality In this paper, to overcome the disadvantage of existing works, we propose a new extended Kalman filter in which, a compensating external acceleration is used to enhance the quality of estimation result in any case PROBLEM ESTABLISHMENT 2.1 Sensors in Attitude estimation In this paper, the attitude is defined as the rotation angle between y axis and x axis of the object in Euler coordinate system The rotation angle around z axis is not considered in this paper Euler angle is the rotation angle between a fixed reference frame x f , y f , z f   and an object attached reference frame  xb , yb , z b  To estimate the attitude of object, we use measurement values: a x , a y , a z : are the output acceleration values of coordinate frame  xb , yb , zb   78  N.D.Tien, “An adaptive attitude estimation for unidentified…” Research g , g x y , g z  : are output inertia values which are used to estimate angular velocities  ,  ,   of object in coordinate frame  x , y , z  x y b z b b Simply, object’s attitude can be estimated through accelerate sensors by measuring gravitational acceleration g  9.8   sin 1 (a x ) and   sin 1 ( ay cos( ) ) (1) While the output accelerate are normalized with gravitational acceleration Note that only ax and a y are used in equation (1), however, az plays a significant role in our algorithm The value of attitude in equation (1) can be very large when having external acceleration because the acceleration sensor is not capable of distinguishing gravitational acceleration and external acceleration To solve this issue, gyroscope sensors are used in the process of estimating attitude However, there is an issue when using gyroscope sensors while the error will be cumulative over time due to the integral process Therefore, gyroscope sensor only brings good result in short time interval Therefore, the main issue of integrating acceleration sensors and gyroscope sensors for estimation process is how to evaluate the roles of each type of sensor For example, when the estimated object is affected by external acceleration, we will count on the measured value which is collected by gyroscope sensors than the acceleration sensors because in that case, acceleration sensor measured values are less accurate due to external acceleration 2.2 Extended Kalman filter 2.2.1 Standard extended Kalman filter State variable x (t) and measured values are defined as below [9] x(t)     x z (t)   ax ay gx  y  z  gy T g z  (2) T State equation and observation equation are presented as x (t)  A(t) x(t)  w(t) (3) z (t)  f ( x(t))  v(t) in which system noise w(t) measurement noise v (t) are assumed to follow Gaussian distribution with variances are Q and R 0 0  Q  0  0 0 0 0 0 q1 0 0 q1 0  r1 0 r  0  T   E w(t) w(t)  ; R   0   0 0  0 q1  0 0 r3 0 r3 0 Journal of Military Science and Technology, Special Issue, No 48A, - 2017 0    E v(t)v(t)T   0 r3  79 Electronics and Automation 0 0  A  0  0 0 0 0 0 0 cos  (t) sin  (t)   sin  (t) cos  (t)     f ( x(t))   x   y     z  sin  (t)  sin  (t) tan  (t) cos  (t) tan  (t)  ; 0  0   0 When the data is taken according to sample, Equation (3) is discretized Suppose that the time taking in sampling process is T , discretized equations are presented in [9] as below: xk 1   k xk  wk (4) zk  f ( xk )  vk in which xk  x(kT) and zk  z (kT)  I W (kT) T   k  exp(A(kT) T)    I 0  cos  (kT)  sin  (kT) 0  W (kT)    1 sin  (kT) tan  (kT) cos  (kT) tan  (kT)  The variance of system noise can be calculated as below 1 q1T 3W (kT)W (kT)T  Qk  E wk wk T     q T 2W (kT)T  1  q1T 2W (kT)    q1TI  Linearized above equation, we have Hk   f ( x)  x x  xˆ  k  cos ˆ(kt)  cos ˆ(kt) cos ˆ(kt)    0   0  0  0 0  0 0 0  0  0 1 (5) 2.2.2 Proposed extended Kalman filter The disadvantage of extended Kalman filter is that the error will be very large when the object is affected by external acceleration of the environment To overcome this issue, in this paper, the Rehbinder’s external acceleration compensator [10] is utilized to compensate the effect of external acceleration    ; rg  rg   rg (6) where , rg are variances of acceleration sensors and gyroscope sensors Compensating external acceleration is calculated based on this constraint when   80 N.D.Tien, “An adaptive attitude estimation for unidentified…” Research Finally, the extended Kalman filter is constructed as Figure.1 Figure.1.Extended Kalman filter In Figure.1, we present the working processes of the new extended Kalman filter When we combine accelerometers and gyroscopes for attitude estimation, the key challenge is how to weight each sensor output When the object is affected by external acceleration, we rely more heavily on gyroscope outputs because accelerometer outputs contain unwanted external acceleration noise Therefore, in our proposed filter, the external acceleration is detected in advanced and then, we adaptively change the covariance of measurement devices (R) RESULTS AND DISCUSSION 3.1 Experiment tools The proposed algorithm has been implemented in Matlab IMU model is taken from Gimbal IMU of Matlab Aerospace Blockset IMU configuraton parameters are based on Xsen’s Mti 28A53G35 IMU with static variances of acceleration sensor and gyroscope sensor are  1.7735e  004 and rg  8.4053e  005 The input parameters which are acceleration values and gyroscope values around (x,y,z) axes are randomly selected from IMU sensors 3.2 Discussion The experimental result is presented in Figs and It is clearly seen that our proposed algorithm has better accuracy as well as smooth in comparison to standard Kalman filter This happens because our proposed extended Kalman filter is capable of identifying external acceleration by using external acceleration compensator The error and noise in measurement process are eliminated The result shows high applicability of this Journal of Military Science and Technology, Special Issue, No 48A, - 2017 81 Electronics and Automation filter to identify unidentified flying object in the process of military modernization of Vietnam Figure Estimation result of standard extended Kalman filter Figure Estimation result of proposed extended Kalman filter CONCLUSION In this paper, we propose an extended Kalman filter for estimating the attitude of unidentified flying object The main contribution of this research is the process of compensation of external acceleration, which causes most error in estimation process The experimental result shows that our proposed extended Kalman filter outperforms the standard extended Kalman filter In near future, this proposed Kalman filter will be applied in practice to detect unidentified flying object REFERENCES [1] B Barshan et al, “Evaluation of a Solid-State Gyroscope for Robotic Application,” IEEE Trans On Instrumentation and Measurement, Vol 44, No 1(1994), pp 61-67 [2] B Barshan et al, “Inertial Navigation System for Mobile Robots,” IEEE Trans Robot Automat., Vol 11, No 3(1995), pp 328-342 82 N.D.Tien, “An adaptive attitude estimation for unidentified…” Research [3] P Bristeau et al, “Trajectory estimation for a hybrid rocket,” AIAA Guidance Navigration and Control Conference, Chicago, US 2009 [4] B Barshan et al, “Using data fusion of DMARS-R-IMU and GPS data for improving attitude determination accuracy,” Space Ops Conferences, 2016, Korea [5] P Tomé et al, “Integrating Multiple GPS Receivers With A Low Cost IMU For Aircraft Attitude Determination,” ION 1999 National Technical Meeting, Jan 1999 [6] T S Bruggemann et al, “GPS Fault Detection with IMU and Aircraft Dynamics,” IEEE Transactions on Aerospace and Electronic Systems, Vol 47, No (2011), pp 305-316 [7] F Qin et al, “Performance assessment of a low-cost inertial measurement unit based ultra-tight global navigation satellite system/inertial navigation system integration for high dynamic applications,” IET Radar, Sonar Navigat., vol 8, no (2014), pp 828-836 [8] A Golovan et al, “Small satellite attitude determination based on GPS/IMU data fusion,” ICNPAA 2014: 10th International Conference on Mathematical Problems in Engineering Aerospace and Sciences AlP Conference Proceedings, Vol 1637 (2014), pp 341-348 [9] R G Brown et al, “Introduction to Random Signals and Applied Kalman Filtering,” 1997, John Wiley & Sons [10] H Rehbinder et al, “Drift-free attitude estimation for accelerated rigid bodies” Science Direct - Automatica, April, Vol 40, No (2004), pp 653 TÓM TẮT BỘ ƯỚC LƯỢNG TƯ THẾ THÍCH NGHI CHO THIẾT BỊ BAY KHƠNG XÁC ĐỊNH Bài báo khoa học trình bày phương pháp ước lượng tư thích nghi cho vật thể bay khơng xác định sử dụng cảm biến góc quay cảm biến gia tốc Bởi gia tốc ngoại nguyên nhân chủ yếu dẫn đến sai số phương pháp ước lượng tư truyền thống Do đó, báo đề xuất phương pháp ước lượng mới, lọc Kalman mở rộng kết hợp với bù thích nghi gia tốc ngoại vật thể nhằm làm giảm ảnh hưởng nhiễu lên phép đo qua làm tăng độ xác cho phương pháp ước lượng Kết vượt trội phương pháp kiểm chứng thơng qua mơ thực nghiệm Từ khóa: Bộ ước lượng tư thế, Bộ lọc Kalman mở rộng, Vật thể bay không xác định Received date, 5thFebruary 2017 Revised manuscript, 25th March 2017 Published on 26th April 2017 Author affiliations: People's Police University of Technique and Logistics, Ministry of Public Security *Corresponding author: dangtient36@gmail.com Journal of Military Science and Technology, Special Issue, No 48A, - 2017 83 ... of standard extended Kalman filter Figure Estimation result of proposed extended Kalman filter CONCLUSION In this paper, we propose an extended Kalman filter for estimating the attitude of unidentified. .. Kalman filter outperforms the standard extended Kalman filter In near future, this proposed Kalman filter will be applied in practice to detect unidentified flying object REFERENCES [1] B Barshan... variances of acceleration sensors and gyroscope sensors Compensating external acceleration is calculated based on this constraint when   80 N.D.Tien, An adaptive attitude estimation for unidentified ”