Journal of Sensors

Volume 2018, Article ID 7342896, 14 pages

https://doi.org/10.1155/2018/7342896

## A Preferable Airborne Integrated Navigation Method Based on INS and GPS

School of Instrumentation Science and Optoelectronics Engineering, Beihang University, Beijing 100191, China

Correspondence should be addressed to Xiaoyue Zhang; nc.ude.aaub@euyoaixgnahz

Received 24 August 2017; Revised 10 January 2018; Accepted 6 February 2018; Published 19 June 2018

Academic Editor: Eduard Llobet

Copyright © 2018 Xiaoyue Zhang and Kaiwen Ning. 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

An integrated navigation method based on INS and GPS was proposed for airborne navigation. The influence of scale factor error and misalignment error of gyroscope and accelerometer on navigation accuracy was analyzed. Compared with traditional INS/GPS integrated navigation method, scale factor error and misalignment error were added to the state model of the integrated navigation system. The observability of scale factor error and misalignment error was analyzed combined with typical airborne movement. Then the integrated system was optimized, and the new navigation model of the integrated system was obtained. The optimized INS/GPS integrated model was validated by numerical simulation and turntable test. Comparing the proposed model with traditional integrated model (integrated system error states do not include scale factor error and misalignment error), the results showed that the proposed integrated navigation method can improve the accuracy from 8% to 28% of the east, north, and upward positions.

#### 1. Introduction

Inertial navigation system (INS) is an autonomous navigation system that does not depend on any external information [1, 2]. However, the characteristics of the location error accumulate with time, making it difficult to work independently for a long time. Global Positioning System (GPS) can measure three-dimensional position and velocity accurately, but the disadvantage is susceptible to interference and control [3–5]. Therefore, INS and GPS have complementary characteristics. Since the 1990s, INS/GPS integrated navigation system has been a great success at home and abroad, and it has developed into a specialized technology [6, 7].

INS/GPS integrated navigation system works as follows: when GPS signal is good, the system selects the integrated navigation mode. The precision of integrated navigation basically depends on GPS precision, and the inertial measurement unit (IMU) errors can be estimated and compensated online. When GPS signal is disturbed or shielded, the system automatically shifts into inertial navigation mode. At this point, navigation accuracy basically depends on the precision of IMU [8]. Therefore, the estimation accuracy of IMU errors in integrated navigation can affect the accuracy of the subsequent inertial navigation [9, 10]. In airborne INS/GPS integrated navigation system, however, the errors of IMU only consider the bias of gyroscope and accelerometer without considering scale factor and misalignment at present. A method of the dynamic parameter identification of the scale factor error and misalignment error was designed based on Kalman filter. The observability of the scale factor error and misalignment error with different maneuvers was analyzed in [11]. Zhou et al. described the error dynamic system equation and observation equation of inertial navigation system and the singular value of the system states of online calibration [12]. Therefore, a more advanced method can be designed to make the IMU errors (including bias, scale factor, and misalignment) be more accurate in estimation and compensation in the integrated navigation process. When entering the inertial navigation mode, it can get higher navigation accuracy.

For the application of airborne navigation, this paper analyzes the influence of scale factor error and misalignment error on the accuracy of integrated navigation. Based on the analysis, the scale factor error and the misalignment error are added to the error model of the integrated navigation system. Then the observability of the scale factor error and misalignment error is analyzed combined with the typical airborne movement. According to the observability analysis results, the integrated system is optimized and the new error model of the integrated navigation system is obtained. Finally, the optimized INS/GPS integrated model proposed in this paper is validated by numerical simulation and turntable test, and then the proposed model is compared with the traditional integrated model.

#### 2. Error Analysis of Airborne Inertial Measurement Unit

The errors of inertial measurement unit mainly include bias, scale factor error and misalignment error. The error model of INS and IMU is given in the following passage, and the influence of IMU errors on the navigation accuracy is analyzed combined typical airborne movement.

##### 2.1. Error Model of Inertial Navigation System

where , , and represent the longitude error, the latitude error, and the altitude error, respectively, and and are the curvature radius of the meridian and prime vertical. and represent velocity error and attitude error, respectively, and represents the accelerometer measurement error, which contains accelerometer bias, scale factor error, and misalignment error. represents the gyroscope measurement error, which contains gyroscope bias, scale factor error, and misalignment error.

##### 2.2. Error Model of Inertial Measurement Unit

where , , and are the gyroscope scale factor errors of the *x*-axis, *y*-axis, and *z*-axis. , , , , , and are the gyroscope misalignment errors. , , and are the gyroscope biases. , , and are the gyroscope ideal outputs.
where , , and are the accelerometer scale factor errors of the *x*-axis, *y*-axis, and *z*-axis. , , , , , and are the accelerometer misalignment errors. , , and are the accelerometer biases. , , and are the accelerometer ideal outputs [13].

##### 2.3. Analysis of the Influence of IMU Errors on Navigation Accuracy

In order to facilitate quantitative analysis, combined with the actual low-precision inertial navigation systems commonly used in airborne navigation, the error parameters of the IMU are set as follows:

###### 2.3.1. Analysis of Attitude Error

In order to more clearly and easily analyze the influence of gyroscope scale factor error and misalignment error on attitude error, we temporarily do not consider other terms. The attitude error equation can be simplified as

When the airframe turns, the angular velocity of the Earth and the platform are small relative to the IMU rotation rate. So we ignore the influence of angular velocity of the Earth and the platform on the attitude error; the attitude error equation is further simplified [14]:

When the system only changes the pitch angle, the roll angle and heading angle change could be assumed to be zero, then

Combined with the gyroscope error parameters given above and (8), the influence of gyroscope scale factor error on attitude error is greater than that of gyroscope bias on attitude error when ; the influence of gyroscope misalignment errors and on attitude error is greater than that of gyro bias and on attitude error when . Therefore, when the body pitch angle changes, the influence of gyroscope scale factor error and misalignment error on attitude error cannot be ignored.

Similarly, when the system roll angle changes or heading angle changes, then is

Substituting (9) into (6), we can get the same conclusion.

###### 2.3.2. Error Analysis of Velocity and Position

The most common movements of the aircraft are uniform motion and accelerated motion, this paper mainly analyzes the influence of the accelerometer errors on position error and velocity error in these two kinds of motion. To simplify the analysis, this paper also does not consider other error terms, so velocity error equation can be simplified as

When the system only changes the pitch angle, the roll angle and heading angle change could be assumed to be zero; the attitude matrix can be simplified as

In uniform motion (), according to the accelerometer error parameters and (12), we can conclude that . The influence of accelerometer misalignment errors and on the east and north velocity errors is about 40% of the bias and . In addition, . The influence of the accelerometer scale factor error on upward velocity error is about 60% of accelerometer bias . Therefore, the influence of the accelerometer scale factor error and misalignment error on velocity error cannot be ignored in uniform motion.

In accelerated motion (), according to the accelerometer error parameters and (12), we can conclude that when and , the influence of the accelerometer scale factor errors and on the north velocity error and upward velocity error is greater than that of accelerometer bias and .When and , the influence of the accelerometer misalignment errors and on the north velocity error and upward velocity error is greater than that of accelerometer bias and . In the actual motion, the acceleration of aircraft is about 0.3. According to the analysis above, the influence of the accelerometer scale factor error on velocity error is about 18% of the accelerometer bias and the influence of accelerometer misalignment error on velocity error is 12% of the accelerometer bias in accelerated movement.

Similarly, when the system’s roll angle changes or heading angle changes, attitude matrix is

Substituting (13) into (10), we can get the same conclusion.

In summary, the influence of scale factor error and misalignment error of gyroscope and accelerometer on navigation cannot be ignored.

#### 3. Model Establishment

##### 3.1. INS/GPS Integrated Navigation Model

From what has been analyzed above, we can conclude that the influence of scale factor error and misalignment error on navigation cannot be ignored in airborne navigation. Therefore, the scale factor error and misalignment error need to be considered in the INS/GPS integrated error model. In this paper, INS/GPS integrated navigation is realized by using Kalman filter. The position and velocity differences between GPS and INS are taken as measurement errors. IMU errors and navigation errors can be online estimated and compensated, so the high navigation accuracy can be acquired. INS/GPS integrated navigation schematic diagram is shown in Figure 1.