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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

The second and third phases of the Chinese Lunar Exploration Program (CLEP) are planning to achieve Moon landing, surface exploration and automated sample return. In these missions, the inertial navigation system (INS) and celestial navigation system (CNS) are two indispensable autonomous navigation systems which can compensate for limitations in the ground based navigation system. The accurate initialization of the INS and the precise calibration of the CNS are needed in order to achieve high navigation accuracy. Neither the INS nor the CNS can solve the above problems using the ground controllers or by themselves on the lunar surface. However, since they are complementary to each other, these problems can be solved by combining them together. A new celestial assisted INS initialization method is presented, in which the initial position and attitude of the explorer as well as the inertial sensors’ biases are estimated by aiding the INS with celestial measurements. Furthermore, the systematic error of the CNS is also corrected by the help of INS measurements. Simulations show that the maximum error in position is 300 m and in attitude 40″, which demonstrates this method is a promising and attractive scheme for explorers on the lunar surface.

The Moon is the only natural satellite of Earth. There is great potential to develop new technologies and to make use of the Moon’s valuable resources. Up to now, the Moon has been visited by the explorers of the Soviet Union (SU), the United States (US), the European Space Agency (ESA), Japan (JP), China (CHN) and India (IN). There are many lunar exploration programs currently happening or being planned.

China’s lunar exploration is a three-phase mission. In phases I and II, China launched its first and second lunar probes, Chang’e-1 and Chang’e-2, which have successfully finished their missions and obtained 3D images of the lunar surface. In the next few years of the phase II, an unmanned lander, which will carry a lunar rover for the exploration of the Moon’s surface, will softly land on the Moon. In phase III, a return vehicle will collect samples of lunar soil and carry them back to the Earth. In these upcoming missions to the Moon, explorers such as Rovers, Landers, Descenders and Ascenders will use INS and CNS for navigation to compensate for the limited capacity of ground tracking networks. The accuracy of INS and CNS mainly depends upon the accuracy with which these systems are initialized or calibrated, so the accurate initialization of the INS and the precise calibration of the CNS are needed.

The initialization of INS is the process of determining some initial values of the system, such as position, attitude, and sensors biases [

A celestial assisted INS initialization method for explorers on the lunar surface is presented. An unscented Kalman filter is used for fusing information from various INS and CNS sensors. The initial position, attitude as well as biases of INS sensors are estimated effectively and the systematic error of CNS is corrected at the same time. The feasibility of this new method is validated using a ground test bed. Simulations show that the maximum error in position is 300 m and in attitude 40″. These results verify that this method is a promising and attractive scheme for lunar explorers.

This paper is systematized in five sections. After this introduction, the basic principle of INS and CNS is outlined in Section 2. Then the state model and measurement model of this celestial assisted INS initialization method is described in details in Section 3. Simulations in Section 4 demonstrate the performance and conclusions are drawn in Section 5.

Reference frames used in this paper are defined as follows:

The inertial frame (_{i}X_{i}Y_{i}Z_{i}

The Moon fixed frame (_{m}X_{m}Y_{m}Z_{m}

The navigation frame (_{n}X_{n}Y_{n}Z_{n}

The explorer body frame (_{b}X_{b}Y_{b}Z_{b}

An INS usually includes a navigation computer and an inertial measurement unit (IMU), which typically consists of three orthogonal accelerometers and three orthogonal gyroscopes. By tracking both the current angular velocity and the current linear acceleration of the explorer measured by IMU, the INS determines the linear acceleration of the explorer in the inertial frame. Thus, if the original velocity and position are known, the inertial velocity of the explorer can be obtained by integration of the inertial acceleration, and integration again yields the inertial position. There are two types of inertial navigation systems: platform inertial navigation system and strap-down inertial navigation system (SINS). In the platform inertial navigation system, IMU is mounted on a mechanical platform, which can isolate explorer’s motion and is held in alignment with the expected navigation frame. The main disadvantages of this system are that the mechanical platform is expensive and its moving parts tend to wear out or jam. In the SINS, IMU is mounted rigidly onto the explorer, and a mathematical platform takes the place of the mechanical platform. This reduces the cost and size, increases the reliability by eliminating the moving parts. In this study, SINS is used for navigation of the lunar explorer. The basic equations of inertial navigation in the navigation frame can be simply expressed as follows [^{T}_{x}_{y}_{z}^{T}^{b}_{m}^{−6} rad/s.
_{m}^{2}]^{T}

From the principle of INS we can see that an initialization is needed before INS can properly work. INS initialization is the process of determining initial values for position, velocity, and attitude in the navigation frame, and in some cases, inertial sensor errors are also estimated. INS attitude initialization is called alignment, which is the process of determining the initial values of the coordinate transformation from the body frame to the navigation frame in SINS [

As a relatively mature technology, initial alignment of INS on the Earth has been widely studied in the literature. The main research directions include: INS error models [

Stars always move in the regular way, their positions can be known exactly at a specific time. Celestial navigation is a kind of technology of finding one’s position through astronomical observations. CNS is usually comprised of a star sensor (or sun sensor) and an inclinometer. The star sensor is used to measure the direction of the star and the inclinometer is used to measure local vertical direction. Thus the star altitude, which is the angle between the horizon and the line of sight to the star, can be subtended. The star altitude is a function of the explorer’s position and the geographic position (GP) of the star, which is expressed in the Moon fixed frame as follows:
_{LHA}_{LHA}_{GHA}_{GHA}_{LHA}

When there are enough measurements, the explorer’s position can be determined by the intercept method or the filter method [

The traditional INS initialization method on the earth based on Kalman filter usually uses the INS error model as the state model [

Because the lunar explorer is stationary, the state model in the Moon fixed frame is defined as:
_{x}_{y}_{z}_{x}_{y}_{z}

To make all state variables observable, the star altitude, star orientation and outputs of IMU are chosen as the measurement variables.

Star altitude. From _{e}_{e}_{e}_{e}_{H}

Star direction vector. The observation information measured by star sensor also provides an indication of the lunar explorer’s attitude information. Given the 2-D star centroid from the threshold star image, a 3-D star-direction unit vector _{b}_{b}_{b}_{b}^{T}_{m}_{m}_{m}_{m}^{T}_{LHA}_{LHA}^{T}_{b}_{m}

Output of accelerometers:
^{b}_{t}_{Δ} is the vector of accelerometers biases.

Output of gyros:
^{b}_{t}_{Δ} is the vector of gyros biases. Using

The Kalman filter (KF), which is optimal for application to linear and Gaussian systems, is often used in the INS initialization [

This section presents simulations of this celestial assisted INS initialization method. All simulation data comes from the lunar explorer INS/CNS simulation system shown in

In simulations, measurement errors are separated from the real data and used to create simulation measurements on the lunar surface. The error characteristics of the accelerometers and gyroscopes are shown in

Similar to

The estimated attitude also converges to the real attitude quickly. The root mean square (RMS) attitude errors are 11.3343″, 5.9231″ and 2.8087″ respectively in yaw, roll and pitch angle. The maximum estimation errors of these angles are 36.3830″, 19.7239″ and 10.2493″. From these results, it can be concluded that this celestial assisted INS initialization method can enhance the position and attitude estimation accuracy. The maximum error in position is 300 m and in attitude 40″, which is much better than that sent by ground stations.

In this study, a new celestial assisted INS initialization method for lunar explorers, which could solve the INS initialization and CNS calibration problems at the same time, is presented. To make the state model simple and observable, position, attitude, and main error resources are used as state variables. All original information provided by the sensors of the INS and the CNS is used as measurements. An unscented Kalman filter is used to deal with these measurements and estimate the states. The method is tested using a ground simulation system. The estimation error of initial position is within 300 m and the estimation error of initial attitude is within 40″. Both the inertial sensors’ biases in the INS and the systematic error in the CNS are estimated effectively. Results allow the conclusion that this celestial assisted INS initialization method is a promising method for the high accuracy initialization of a lunar explorer. It should be noted that the proposed approach is general and may be used on any kind of lunar explorers on the lunar surface, such as lunar rovers, landers and ascenders, with an equivalent set of sensors. Future directions of research include applications (extensions) of this method to cases where the INS and CNS are fused with other navigation sensors (e.g., vision sensors, beacons

The work described in this paper was supported by National Natural Science Foundation of China (60874095) and Hi-tech Research and Development Program of China. The author would like to thank all members of the Inertial Technology Key Laboratory, for their useful comments regarding this work effort.

Reference frames.

Parameters in the Moon fixed frame.

Celestial assisted INS initialization algorithm.

Lunar explorer INS/CNS simulation system.

Accelerometer and gyro errors.

The measurement errors of the star sensor and the inclinometer.

The position estimation and its error.

The attitude estimation and its error.

The estimation of accelerometer and gyroscope errors

The estimation of star altitude error.