Based on the temperature drift characteristic of fiber optic gyroscope (FOG), a novel modeling and compensation method which integrated the artificial fish swarm algorithm (AFSA) and backpropagation (BP) neural network is proposed to improve the output accuracy of FOG and the precision of inertial navigation system. In this paper, AFSA is used to optimize the weights and threshold of BP neural network which determine precision of the model directly. In order to verify the effectiveness of the proposed algorithm, the predicted results of BP optimized by genetic algorithm (GA) and AFSA are compared and a quantitative evaluation of compensation results is analyzed by Allan variance. The comparison result illustrated the main error sources and the sinusoidal noises in the FOG output signal are reduced by about 50%. Therefore, the proposed modeling method can be used to improve the FOG precision.
FOG is one kind of inertial sensors, which is based on the Sagnac effect and has been widely used in inertial system and engineering application at present. The surrounding environment of FOG is often accompanied with a wide temperature range or a fast temperature change rate. Besides, the optical components of FOG are sensitive to the environment temperature change, which will bring errors to the output of FOG [
From the study of complex mechanism of FOG, we can see that the temperature variation will cause different refractive index of optical fiber in every sector of the fiber coil and the thermal nonreciprocity effect will be induced; the thermal effect had been described by Shupe and is known as Shupe effect [
As for modeling the nonlinear question of describing the FOG output between temperature gradients, many methods have been proposed such as the timesequence autoregressive and moving average model [
Since the artificial fish swarm algorithm (AFSA) firstly proposed by Li et al. [
The paper is organized as follows. Theory analysis of FOG temperature effect and the temperature experiments are described in Section
From the analysis of FOG’s output, the FOG drift can be divided into two aspects: noises and bias drifts. Noises determine the minimum detectable phase shift, which consist of temperature noise, light source noise, electronic noise, and others. Drifts determine the bias in the output and show the longterm changes characteristic of gyroscope.
In 1980s, Shupe [
A majority of the modeling and compensation methods to deal with the accuracy improvement of FOG are through using the model to fit the output characteristics of temperature drift data. Most modeling ideas are based on IEEE standard (IEEE Std 9521997) [
The
When a certain temperature change happened to FOG, the nonreciprocal phase noises can be calculated, so we should pay more attention to the bias drifts [
In the experiment, an interferometric FOG is installed on a stationary base which has a temperature box; FOG’s static output is acquired under different change rates. The sampling frequency is 100 Hz, and sampling time is 40 minutes. Two sets of temperature change rate are within range of −5°C/min to 5°C/min and −8°C/min to 8°C/min; the sampling interval of FOG’s output and temperature sensors’ output are set at 1 second.
Besides, in order to improve the modeling performance of the neural network and reduce the randomness parts in FOG output, we cited wavelet transform method and other preprocessing steps to eliminate constant drift and trend extraction in FOG output [
FOG original and denoising data under
The AFSA is a novel global optimization algorithm which was inspired by the natural social behavior of fish swarm in searching, swarming, and following. Each individual fish can search its own local optimum and pass on information in the fish swarm, and finally the swarm will achieve a global optimum. Its main feature is parallel processing, independent of initial values, avoidance of converging to a local minimum, and fast training and convergence speed. The related concepts and mathematic description are as follows.
Suppose that the searching space is
The evaluation criterion is based on the problem that we are to address; the usual method is to judge whether the value of MSE repeatedly is less than its allowable error and cannot exceed the extreme of visual and numbers. The MSE of the actual value
Based on the advantages of AFSA, we used AFSA as the learning algorithms to determine the parameters of BP neural network. In the training step, construct the artificial fish individuals and take the MSE of the neural network’s output as the food consistence of current state.
The structure of threelayered BP neural network is shown in Figure
Structure of threelayer BP neural network.
In order to construct the artificial fish model, we set the size of artificial fish scale as
The AFSABP algorithm optimizing steps can be described as follows.
Initialize the BP neural network: three layers,
The optimized weights and threshold constitute the matrix
Parameters of artificial fish swarm initialization including popsize, Visual, Step,
Set the initial number of iteration Gen as 0, and generate the popsize artificial fishes randomly, which also constitute the initialized swarm; all the arguments consist of weights and threshold and are between the range of
Calculate the food consistence of every individual artificial fish; compare all the
The four behaviors mentioned above are applied to the fish swarm; each fish simulates the follow and swarm behavior and choose the behavior with bigger
After each iteration, the value of bulletin board is updated when meeting the conditions.
Judge the end condition. When Gen reaches the MaxGen or the MSE meets the target value
The flowchart of AFSABP algorithm is shown in Figure
The flowchart of AFSABP.
In order to compare the performance of the different modeling methods which are mentioned and cited in this paper, different from the normal methods of comparing the accuracy when the iterations increased, we take the FOG output data under varied temperature as the input data of models. The different applied methods are BP neural network and GA optimized BP neural network which contain crossover and mutation operation and the AFSABP algorithm. By comparing the prediction error curves after training and from the curve figure we can easily identify the algorithm which has better superiority and predict accuracy.
The FOG temperature drift model is based on the AFSABP algorithm which is mentioned above; the input of the model is temperature and FOG’s temperature drift after denoising processing. Besides, a comparison of the modeling and compensation result with BP neural network and GA optimized BP neural network is expressed. The training data of AFSABP neural network is FOG temperature drift data under
Compensation comparison results of the three algorithms.
In order to have a quantitative evaluation of compensation result of FOG’s temperature drift, the Allan variance method was applied to analyse the drift compensation result. Allan variance method is a time essential analysis technique and has advantages in evaluating and identifying random noise coefficients [
The analysis result is shown in Table
Allan variance analysis of FOG’s output.
Original data  After denoising data  Compensation result  

GABP  AFSA  

149.37  129.58  1.48  1.17 

0.94  0.79  0.009  0.007 

28.09  24.52  0.14  0.09 

176.34  154.15  3.64  1.72 

229  197.57  5.12  2.45 
Figure
Allan variance analysis of the different algorithm FOG output after compensation.
In this paper, a new hybrid algorithm BP neural network optimized by AFSA is presented and used to describe the temperature drift characteristic of FOG. First, the theory about Shupe effect of FOG was introduced; then the AFSA is used to determine the linking weight and threshold of BP neural network and in order to validate the effectiveness of the method, a set of temperature experiments of FOG under
In order to verify the effectiveness of our algorithm, the predicted accuracy of three algorithms, BP neural network and BP optimized by AFSA and GA, are observed by error prediction curve. Besides, the Allan variance method is applied to get a quantitative evaluation of compensation result of FOG’s output before and after a set of processes. The results well validate the main error sources and the sinusoidal noises can be compensated by AFSABP neural network and the fiber optic gyroscope precision can be improved.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported in part by the National Natural Science Foundation of China (nos. 51375087 and 50975049), Specialized Research Fund for the Doctoral Program of Higher Education (no. 20110092110039), Ocean Special Funds for Scientific Research on Public Causes (no. 20120503509), and the Program Sponsored for Scientific Innovation Research of College Graduate in Jiangsu Province, China (no. CXLX13_083).