Application Case

# FOG Inertial Navigation System Comparison Test

1. Introduction to the inertial navigation system

Inertial Navigation System (INS), also known as inertial reference system, is an autonomous navigation system that does not rely on external information and does not radiate energy externally (such as radio navigation). Its working environment includes not only air, ground, but also underwater. The basic working principle of inertial navigation is based on Newton’s laws of mechanics. By measuring the acceleration of the carrier in the inertial reference system, integrating it with time and transforming it into the navigation coordinate system, it can be obtained in the navigation coordinate system. Information such as speed, yaw angle and position.

The inertial navigation system belongs to the inferred navigation mode, that is, the position of the next point is calculated from the position of a known point according to the continuously measured moving body heading angle and speed, so that the current position of the moving body can be continuously measured. The gyroscope in the inertial navigation system is used to form a navigation coordinate system, so that the measurement axis of the accelerometer is stabilized in the coordinate system, and the heading and attitude angles are given; the accelerometer is used to measure the acceleration of the moving body, after the time one point gets the speed, and the speed is then integrated by one time to get the displacement.

2. Importance

Inertial technology is one of the key technologies for navigating the carrier. Inertial technology is a technology that uses the principle of inertia or other related principles to autonomously measure and control the motion process of the carrier. It is inertial navigation, inertial guidance, inertial measurement and inertial sensor technology. The general term. With the support of the strong funds of various governments, modern inertial technology has penetrated into the civilian sector from the initial military application. Inertial technology plays a very important role in defense equipment technology. For inertial guided medium- and long-range missiles, the hit accuracy of 70% is generally determined by the accuracy of the guidance system. For missile nuclear submarines, their position and speed are variable due to long snorkeling time. These data are the initial parameters of the missile launch, which directly affect the missile’s hit accuracy. Therefore, it is necessary to provide high-precision position, velocity and vertical alignment signals. The only navigation device currently available for submarines is the inertial navigation system. Inertial navigation relies entirely on the carrier’s own equipment to navigate independently and independently, without relying on external information, and has the advantages of good concealment, work without weather conditions and human disturbance, and high precision. For long-range cruise missiles, inertial guidance systems plus map matching technology or other guidance techniques ensure that they can hit targets with high precision after flying thousands of kilometers. Inertial technology has been gradually extended to aerospace, aviation, marine, petroleum development, geodesy, marine survey, geological drilling control, robotics and railways. With the emergence of new inertial sensors, inertial technology in the automotive industry, medical electronics The application is available in the device. Therefore, inertial technology not only occupies a very important position in the modernization of national defense, but also shows its great role in various fields of the national economy.

3. Product overview

3.1. Introduction

ER-FGI1100 Inertial navigation system using triaxial fiber optic gyro sensitive vector angular motion, the proportion of digital signal output with the carrier movement angular rate; three orthogonal collocation of quartz flexure accelerometer gauge carrier sensitive linear acceleration, output with the proportion of current signal and current after I-F conversion circuit switching frequency signal input navigation computer. Computer navigation gyro, accelerometer, external data of GPS receiver, system error compensation calculation, navigation solution and to the provisions of the cycle guide through the monitoring port for external sending real-time speed, position, attitude and navigation information.

3.2. Some technical information

 ER-FGI1100 inertial   navigation system Pure inertial mode GNSS assisted navigation mode（External receiver） Azimuth alignment accuracy ≤ 0.1° sec lat (1σ) Azimuth alignment accuracy ≤ 0.1° sec lat (1σ) Horizontal attitude alignment accuracy ≤ 0.02° (1σ) Horizontal attitude alignment accuracy ≤ 0.02° (1σ) Azimuth holding accuracy 0.05° /h Azimuth holding accuracy ≤0.05°sec lat (1σ) Horizontal attitude holding accuracy 0.03° /h Horizontal attitude holding accuracy ≤ 0.01° (1σ) Positioning accuracy (50%CEP) ≤ 2nm/h (10min Static alignment ) Positioning accuracy ≤ 5m (1σ) Horizontal velocity precision(RMS) ≤ 2m/s (10min Static alignment ) Speed accuracy ≤ 0.1m/s (1σ) Positioning accuracy (50%CEP) ≤ 1nm/h (Two   position alignment，Alignment time is less than 30min) Horizontal velocity precision (RMS) ≤ 1m/s (Two position alignment，Alignment time is less than 30min) Power and environment Data measurement frequency Maximum 100Hz Power Supply 23~31V DC Power Supply, Nominal Supply Voltage27V Power Normal temperature steady-state power consumption is less than 17W, High and low temperature steady-state power consumption is less than 20W, Start transient power consumption is less than 50W Working Temp -40° C~+60°C Storge Temp -45° C~+80° C Installment Dimension 180mm×180mm×160mm Quality ﹤6kg Fiber optic gyroscope index Quartz accelerometer index Time to Prepare≤ 15s Measurement Range：-20g~+20g Bias   Stability (the average time 100s) ≤ 0.02 °/h(1σ) The Threshold   Value：≤ 5×10-6g Bias repeatability (Stable environment，average time 100s) Bias: ≤6×10-3g ≤ 0.02 °/h (1σ) Scale Factor Repeatability: ≤ 3.5×10-5 (1σ) Random Walk Coefficient≤ 0.005° / √ Hz Scale   Factor Temperature Coefficient: ≤ 6×10-5/°C (-40° C~+60° C) Scale Factor Nonlinearity≤ 50ppm The Second Order Nonlinear Coefficient: ≤ 3×10-5g/g2 Scale Factor   Repeatability≤ 50ppm (1σ) Bias：≤ 6×10-3g Gyro Measurement Range≥ ±300° /s Bias Repeatability: ≤ 2.5×10-5g (1σ) Bias Temp   Coefficient: ≤ 2.5×10-5g/° C (-40° C ～ +60° C) Band width: ≥ 800Hz

Figure 1. Part of the technical parameters

4. Comparison test between the company’s products and other products of the same type

4.1  Experimental Environments

Two rough alignment experiments were performed under the same environment. One is an alignment experiment on a swing base based on a three-axis turntable, while the other is an alignment experiment on a moving base based on the vehicle. The characteristics of the inertial measurement unit (IMU) used in the experiments are as follows, the constant drift stability of each gyro is less than 0.01(◦)/h(1σ), random walk coefficient is less than 0.01(◦)/h(1σ), the bias of each quartz flexible accelerometer is less than 5 × 10−5g. The initial position of the experiment is 32.05◦ (N) and 118.0◦(E).

The experiment environment on a swing base is shown in Figure 2, and the corresponding structural diagram is shown in Figure 3. It mainly consists of a fiber optic gyro inertial system, a navigation computer (alignment algorithm is running in it), a computer used for storing, a GPS receiver, and the three-axis turntable. The navigation computer infuses outputs of the IMU and GPS receiver, and sends the result to the storing computer through the network. The storing computer compares the result of the coarse alignment from navigation computer with the attitude values of the turntable, and calculates the alignment accuracy. Figure 2. Experiment environment based on three-axis turntable. Figure 3. Structure diagram of experiment environment

The structure diagram of the vehicle-based alignment experiment is shown in Figure 4. In order to evaluate the accuracy, the high-precision fiber optic gyro SINS (PHINS), produced by French company iXBlue, was chosen as a reference. The PHINS and  ER-FGI1100 are mounted on a rigid board with parallel heading angles, as shown in Figure 5. The experiment environment is shown in Figure 6. PHINS operates in the mode of integrated navigation aided by GPS, and sends the result to the storing computer, which is regarded as the real alignment reference. DVL provides the velocity to the navigation computer for assisting ER-FGI1100  to complete the initial alignment. The storing computer stores the alignment results of ER-FGI1100 and PHINS, and assesses the alignment accuracy of proposed algorithm. The project is used in the underwater environment. Since the experiment condition is limited, we use the vehicle experiment instead. The reference velocity is provided by PHINS with a constant error of 0.2 m/s and a random error of 0.005 m/s. Figure 4. Structure diagram of alignment experiment based on vehicle. Figure 5. Installation method of the fiber optic gyro inertial system (FOSN) and the high-precision fiber optic gyro SINS (PHINS). Figure 6. Experiment environment based on vehicle.

4.2 Alignment Experiment on Swing Base Based on Turntable

A ER-FGI1100  is mounted on the three-axis turntable, whose swing mode is set as follows: (1) the swing center of pitch is 2◦, swing amplitude is 8◦, and swing frequency is 0.15 Hz; (2) the swing center of roll is −2◦, swing amplitude is 10◦, and swing frequency is 0.2 Hz; (3) the swing center of heading is set at multiple angles, namely 0◦, 45◦, 90◦, 135◦, 180◦, 225◦, 270◦, and 315◦, swing amplitude is 6◦, and swing frequency is 0.125 Hz. Figure 7. Attitude error curves of coarse alignment (the swing center of heading is 45◦). (a) The error curves of pitch angle; (b) the error curves of roll angle; (c) the error curves of heading angle.

The means and standard deviations of their alignment errors for heading are respectively 0.1431◦ and 0.1232◦, and 0.1302◦ and 0.0315◦.

4.3  Alignment Experiment on Moving base Based on Vehicle

An alignment experiment based on vehicle is carried out. The route of the vehicle is shown in Figure 8. This experiment mainly focuses on the influence of external velocity on the alignment results. Figure 8. Route of the vehicle.

4.4  Influence of Filtering Frequency of External Velocity on Alignment

In this experiment, DVL provides the external velocity, and its frequency is set at different value,

such as 200 Hz, 50 Hz and 1 Hz. The attitude error of the improved quaternion filter algorithm

is shown in Figure 9. Figure 9. Alignment error curves at different output frequency of velocity. (a) The error curves of pitch angle; (b) the error curves of roll angle; (c) the error curves of heading angle.

In Figure 9, it is shown that, at 1 Hz, the heading angle converges slowly and obviously fluctuates. With increasing velocity output frequency, the convergence rate is faster and the alignment result is better. At 300 s, the heading angle errors at 1 Hz, 50 Hz, and 200 Hz are respectively −1.788◦, −1.389◦,and −1.384◦. In a low frequency situation such as 1Hz, the heading angle error accumulates mainly in the acceleration and deceleration process of the vehicle, because the estimation of velocity difference in every SINS calculation period is inaccurate. The compensation method is shown in Figure 10, where the velocity difference in velocity output period is evenly distributed across every strapdown calculation cycle. Ts is the SINS calculation frequency, T is the velocity output period, a is the velocity difference in SINS calculation period, and V(Ti) is the velocity value at the moment of Ti. Figure 10. Compensation mode of velocity difference

4.5 Influence of Constant Error of External Velocity

The constant error of external velocity is set to different values, such as 2 m/s, 1 m/s and 0.1 m/s.

Corresponding to different constant errors of external velocity, the alignment results of the  on moving base are shown in Figure 11. Figure 11. Alignment error curves of different constant errors. (a) The error curves of pitch angle;

(b) the error curves of roll angle; (c) the error curves of heading angle.

In Figure 11, it can be seen that, under conditions of different constant error of velocity, horizontal attitude error can converge fast, while the error of the heading angle increases with the increasing of constant error. The heading angle errors are similar when constant errors are 0.1m/s and 1 m/s, at which point the heading angle errors are −1.787° and −1.807°. In comparison, the heading  angle error is −2.099° when constant error is 2m/s. The constant error of external reference velocity  influences the alignment accuracy in accordance with the term of acceleration b b ωib × v , but its  influence is limited.

4.6  Influence of Random Error of External Velocity

The constant error is assumed to be zero to analyze the influence of random error of velocity on the alignment accuracy. Three different values of white noise random errors are selected: 0.05 time, 0.1 time and 0.2 time. The alignment error is shown in Figure 12. Figure 12. Alignment error curves with different random errors.

(a) The error curves of pitch angle;

(b) the error curves of roll angle;

(c) the error curves of heading angle.

In Figure 12 it is shown that with increasing random velocity error, the alignment result converges more slowly. At the alignment moment of 300 s, heading angle errors corresponding to the random error are, from smallest to largest, −2.292◦, −3.284◦, and −5.722◦. Compared with the influence of constant error of velocity, the influence of random error is larger. This is because random error of velocity influences the alignment accuracy by both of differential velocity .Vb and ωbibb x Vb . Therefore, as shown in Figure 10 and Equation (5), during the whole process of alignment, random error has been accumulating within the external reference velocity update period.

The three experiments described above show that when the output frequency of external velocity is low, such as 1 Hz, the alignment error will increase, with external velocity becoming larger. Further,the influence of random error of external velocity on alignment result is more obvious than that of constant error.  It is more practical to assume that the velocity error model consists of constant error than random error, as in the four cases shown in the Table 3.

Table 3. Four cases of external reference velocity.  Figure 12. Alignment error curves with different random errors.

(a) The error curves of pitch angle;

(b) the error curves of roll angle;

(c) the error curves of hea