Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 185149, 14 pages

http://dx.doi.org/10.1155/2015/185149

## Line-of-Sight Rate Estimation Based on UKF for Strapdown Seeker

^{1}Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun, Jilin 130033, China^{2}University of Chinese Academy of Sciences, Beijing 100039, China

Received 10 March 2015; Revised 18 June 2015; Accepted 18 June 2015

Academic Editor: Oscar Reinoso

Copyright © 2015 Tingting Sun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Aiming at the problem that the strapdown imaging seeker cannot measure line-of-sight (LOS) rate directly, this paper presents an effective algorithm for LOS rate estimation. To address the problem, the reference frames and angles are defined. According to the relative kinematics and attitude relationship between missile and target, the nonlinear state equations and measurement equations of LOS rate are derived, and the estimation algorithm based on unscented Kalman filter (UKF) is proposed. Considering the estimation accuracy mainly depends on body LOS (BLOS) angle accuracy and gyro accuracy, the paper is unprecedented to research how these two factors impact the LOS angle and rate accuracy by simulation. Semiphysical simulation experiment verifies the correctness and accuracy of the algorithm, and the result shows that the estimation algorithm can meet the accuracy and real-time requirements of guidance system simultaneously. Thus LOS rate estimation algorithm based on UKF provides a theoretical basis for engineering applications of strapdown imaging seeker.

#### 1. Introduction

Optical imaging seekers have been widely used in military fields due to the high precision, such as the three-mode cooled imaging seekers of JAVELIN missile and the uncooled infrared strapdown seeker Direct Attack Munition Affordable Seeker (DAMASK) of JDAM missile. With the rapid development of large area-array complementary metal oxide semiconductor (CMOS) image sensors, automatic target recognition, and high-performance image trackers, the application of strapdown imaging seeker to guidance system has become an important research topic, such as the excellent application of the SPIKE missile in the United States. Strapdown imaging seeker which mounted to missile body rigidly has some advantages [1], such as compact structure, high reliability, unlimited LOS rate tracking capability, and instant field of view (FOV) equal to total FOV. However, only BLOS angle information can be measured directly; thus the LOS angles will couple with body attitude motion which finally leads to strong nonlinearity. The strong nonlinearity makes it very difficult to distill the LOS rate which is essential to the proportional guidance law. Therefore, how to estimate the LOS rate in real time to meet the accuracy requirement of guidance system is a key issue for strapdown guidance technology and application.

Researchers have studied LOS rate estimation of strapdown seeker in recent years. An “additional rate compensation + differential network” method was adopted to reconstruct the single-channel LOS rate in [2] and then offered the signal to guidance system after it passed through a low-pass filter. LOS rate generated by a self-adaptive jitter filter and differential network method [3] was only applicable for low maneuvering guided weapons. Disturbance observer was used to estimate the LOS rate in single channel [4]. The relative relationship and frame transformation between missile and target were employed to derive the relationship among the LOS rate, BLOS rate, and attitude angles, where the BLOS rate can be obtained by a differential network [5]. Extended Kalman filter (EKF) was utilized to estimate the inertial LOS rate [6]. The target motion was negligible with respect to the missile in [7, 8], the relative distance, velocity, and acceleration were assumed to be zero, and then LOS rate was estimated using UKF and Particle Filter (PF), separately. *α*-*β* filter [9] was employed to estimate BLOS rate, and then the LOS rate was reconstructed. Further, the filtering bandwidth can also be adjusted. The linear and nonlinear mixed differentiator based on the sliding mode [10] were adopted to estimate the LOS rate.

All mentioned algorithms above are either mainly based on differential network and the reconstruction method or ignoring too much relative motion information between missile and target; then nonlinear Kalman filtering algorithms are employed to estimate LOS rate, which failed to get high accuracy and cannot meet the real-time requirement. This paper proposes an effective nonlinear algorithm to estimate the LOS rate, we take the relative motion between the missile and target and the missile attitude into account to derive the estimation model, and then LOS rate is estimated using UKF. The correctness and accuracy of the algorithm are verified through the semiphysical simulation experiment.

The remainder of this paper is organized as follows. Section 2 defines the reference frames and angles. The LOS rate model including standard LOS rate and kinematic model of LOS rate estimation were introduced in Section 3. Section 4 proposes the LOS rate estimation algorithm based on UKF. Different performance seekers and gyros impacts on the LOS rate accuracy are simulated in Section 5. The semiphysical simulation experiment is designed; result and discussion are also shown in Section 6. Section 7 illustrates the conclusion of this paper.

#### 2. Reference Frames and Angles

In order to study the LOS rate estimation algorithm for strapdown imaging seeker, the definitions of earth frame , body frame , LOS frame , and BLOS frame are shown in Figure 1, where the subscripts , , , and represent earth, body, LOS, and BLOS. For the convenience, the influence of earth spin is neglected so that earth frame is coincident with inertial frame. Earth frame is defined as follows: the origin is selected as launching point, orients upwards and directs the plumb, axis directs the takeoff direction in the horizon plane, and axis forms right-handed system with and . Body frame is defined as follows: the origin is selected as rotating center of missile, axis directs the direct axis, is upward and perpendicular to in the longitudinal plane, and axis forms right-handed system with and . LOS frame is defined as follows: the origin is selected as optical center of optical system, axis points to the target along the LOS, is upward and perpendicular to in the plumb plane which contained , and axis forms right-handed system with and . BLOS frame is defined as follows: the origin is selected as optical center of optical system, axis points to the target along the LOS, is upward and perpendicular to in the longitudinal plane which contained , and axis forms right-handed system with and . and are LOS vertical angle and azimuth angle; and are BLOS vertical angle and azimuth angle.