FU Jun, JIANG Sai, QIN Fang-jun, FENG Ka-li

(1. Electrical Engineering College, Naval University of Engineering, Wuhan 430033, China; 2. Office of R&D Naval University of Engineering, Wuhan 430033, China)

Novel piecewise compensation method for FOG temperature error

FU Jun1, JIANG Sai2, QIN Fang-jun1, FENG Ka-li1

(1. Electrical Engineering College, Naval University of Engineering, Wuhan 430033, China; 2. Office of R&D Naval University of Engineering, Wuhan 430033, China)

The temperature characteristics of fiber optic gyro(FOG) is analyzed, and its large-range temperature test is designed. The effects of different temperatures and temperature rates on the output of FOG are studied, and different temperature characteristics in different temperature ranges of FOG are achieved. In order to improve the compensation precision for temperature error, a novel idea of multi-model piecewise fitting is proposed based on the gyro temperature characteristics in low, middle and high temperature ranges respectively by using an artificial neutral net. The temperature errors are compensated based on the established models, and the results indicate that the model can effectively reduce the FOG temperature bias, and the precision is improved by one order of magnitude.

fiber optic gyro; temperature bias; multi-model; artificial neutral net

Fiber optic gyro is a kind of inertial measurement instrument based on the sagnac effect, which forms the core of marine strapdown inertial navigation system, and makes use of the full optical fiber structure of solid carrier rotating angular velocity measurement[1-2]. Compared with the traditional mechanical gyroscope, FOG has many outstanding advantages, such as high precision, impact resistance, good vibration resistance, large dynamic range, not sensitive to acceleration of gravity, etc.[2]. FOG has broad and bright prospect. In recent years because of its potential advantages, fiber optic gyroscope is widely used in car navigation, attitude control rocket, arms control and other fields[2-5].

For practical application of fiber optic gyro, it is generally required to have wide working temperature range. As the core of the inertial navigation system device, the main components such as optical fiber ring of fiber optic gyro, integrated optical device, coupler and so on are very sensitive to temperatures[6], when the environment temperature changes, the gyro bias significantly increases, the scale factor linearity is also significantly worse[7]. Therefore, to study the temperature characteristic of fiber optic gyroscope, modeling and compensation in order to improve the precision of gyro is very necessary. Domestic research on fiber optic gyro temperature modeling mainly concentrates in the single model, ignoring the fact that the influence of temperatures on the optical fiber gyro in different temperature range is different. Based on the study , the temperature models can be divided into three differentmodels according to temperature changes from low, medium to high scope. neural network based on piecewise multiple model of fiber optic gyro temperature error compensation method is put forward, which can effectively improve the precision of fiber optic gyro temperature error compensation.

1 Temperature influence mechanism analysis

The influence of temperature on the optical fiber gyro includes two aspects. One is the gyro working environment temperature influence on the working state of gyro. The second is the gyro material properties sensitive to temperature[6]. The core component of fiber optic gyroscope is sensitive to temperature, temperature change, which will lead to ring optical fiber refractive index changes. The two beams back propagation of optical fiber will have a different optical path to form the reciprocal effect. Gyro bias is mainly caused by the mutual out phase shift[8].

When the two beam interference light ,which is called by clockwise (CW) light and counterclockwise (CCW)light respectively, transmitting through the length of L, the phase delay of clockwise and counter-clockwise is respectively as follows[9]:

Where n is the refractive index of fiber ring, c is the speed of light propagation in optical fiber ring, z is the distance to the endpoint, time T for light through the optical fiber ring.

The reciprocal phase delay of fiber optic ring induced by temperature change is:

Where waveguide.

From the above analysis, the temperature error of fiber optic gyroscope can be quantitatively measured.nc is the speed of light in the

2 Modeling method and data processing

Fiber optic gyro temperature changes and causes for the nonlinear relationship between the temperature and gyro bias. So nonlinear model is adopted to improve the modeling accuracy. Artificial Neural Network (ANN) is a kind of simple calculation parameters and nonparametric model. The RBF neural network is a kind of three layer forward network, which has a simple structure, concise training and fast convergence rate. RBF can approximate any nonlinear function[9-10].

Temperature compensation is to use the method of software to modify the temperature error of gyro, compensation for gyro bias caused by temperature change[10-11]. So it is necessary to establish the relevant temperature and drift model. Based on the model, according to the measurement of temperature we predict the value of gyro bias with respect to the corresponding temperature, then get the temperature induced gyro bias from actual measured drift and predicted one.

In experiment a gyros labeled as X is put into a temperature box. The temperature is changed from 15～45 ℃ gradually. Test data is saved every 1 ms. Using MATLAB to average the test data, we find out three kinds of interesting phenomenon. Within the scope of the 15 ～0 ℃, gyro bias is approximately proportional to the temperature changes. Within the range of 0～30 ℃, gyro bias is approximately inverse proportional to the temperature changes. Within the scope of the 30 ～45 ℃, gyro bias is approximated as a quadratic function relation with the temperature changes. According to the findings, the temperature is divided into the following three interval: -15～0℃, 0～30℃and 30～45 ℃. The temperature value and temperature change rate are inputs, gyro bias is the output of RBF network. By connecting three models of different temperature scope, a complete model of the temperature bias compensation is formed. For an example, gyro, the effect of temperature on the X gyro bias and compensation effect is shown in Fig.1.

Fig.1 Compensation effect

Fig.2 Compensation effect of the first temperature scope

Before the compensation, the overall average for optical fiber gyro bias was 11.49 (°)/h, the maximum was 11.64 (°)/h. After compensation the average becomes 0.011 (°)/h, maximum becomes 0.14 (°)/h. It can be seen that the compensation effect is obvious.

In the test experiment, compensation effect of the first temperature scope is shown in the Fig.2.

Fig.3 Compensation effect of the second temperature scope

Before compensation the average gyro bias was 11.50 (°)/h, the maximum was 11.64 (°)/h. After compensation the average becomes 0.024 (°)/h, maximum becomes 0.18 (°)/h.

In the test experiment, compensation effect of the second temperature scope is shown in the Fig.3.

Before compensation the average gyro bias was 11.49 (°)/h the maximum was 11.62 (°)/h. After compensation the average becomes -0.019 (°)/h, maximum becomes 0.13 (°)/h.

In the test experiment, compensation effect of the third temperature scope is shown in the Fig.4.

Fig.4 Compensation effect of the third temperature scope

Before compensation the average gyro zero-bias was 11.48 (°)/h, the maximum was 11.63 (°)/h. After compensation the average becomes 0.028 (°)/h, maximum becomes 0.16 (°)/h. Experiment results are listed in the following table 1.

Tab.1 Compensation for temperature bias (°)/h

Temperature errors are compensated based on the established models. The results indicate that the model can effectively reduce the FOG temperature bias, the precision is greatly improved by one order of magnitude.

3 Summary

On the basis of a large number of experimental data analysis, the study found that the temperature influence on the gyro bias in different models with the different temperature range. Using RBF neural network fitting, we use Piecewise Compensation Method with different models. Test results show that within the temperature range -15～45 ℃, before compensation the mean overall gyro bias was 11.49 (°)/h. After compensation the mean overall gyro bias becomes 0.11 (°)/h. The compensation effect is obvious, and the precision is greatly improved by one order of magnitude.

From the results of compensation, we see obvious residual temperature bias, which cannot be fully eliminated by the compensation method. So in future research work, we will focus on analyzing the influence factors of residual temperature bias, with more factors, and a more detailed model of the temperature bias.

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1005-6734(2016)02-0242-03

一種光纖陀螺溫度誤差分段補(bǔ)償新方法

傅 軍1，江 賽2，覃方君1，馮卡力1

（1. 海軍工程大學(xué) 電氣工程學(xué)院，武漢 430033；2. 海軍工程大學(xué)科研部，武漢 430033）

分析了光纖陀螺的溫度特性，設(shè)計(jì)了大范圍的溫度測試，研究了不同溫度和溫度變化率對光纖陀螺輸出的影響，研究了光纖陀螺在不同溫度范圍內(nèi)的溫度特性。為了提高溫度誤差補(bǔ)償精度，根據(jù)陀螺溫度特性將溫度分為低、中、高三個(gè)區(qū)間，分別利用人工神經(jīng)網(wǎng)絡(luò)進(jìn)行誤差建模，提出了一種多模型分段擬合的新方法。根據(jù)建立的模型進(jìn)行溫度誤差補(bǔ)償，補(bǔ)償結(jié)果表明，建立的模型能有效地減小了光纖陀螺的溫度漂移，精度提高了一個(gè)量級。

光纖陀螺；溫度漂移；多模型；人工神經(jīng)網(wǎng)絡(luò)

A

2015-12-23

國家自然科學(xué)基金（41404002）；總裝預(yù)研基金（14JB11378）

傅軍（1975—），男，講師，從事慣性導(dǎo)航技術(shù)及應(yīng)用、組合導(dǎo)航研究。E-mail: fjsd@21cn.com

10.13695/j.cnki.12-1222/o3.2016.02.019