Study On Aeromagnetic Compensation Of Helicopter-towed Birds

Aeromagnetic survey is an important method for geological research and mineral exploration.In recent years,the surge of high-sensitivity sensors has promoted the development of small-scale and high-precision aeromagnetic surveys,making helicopter towed bird a popular carrier.Helicopter-towed-bird aeromagnetic surveys place the sensor in a bird far away from the helicopter,so that the influence of the helicopter can be largely avoided.But the magnetic interference generated by the bird still degrades the accuracy of the measurement.High-precision aeromagnetic compensation methods for helicopter towed birds need to be studied urgently.This paper first builds a helicopter-towed-bird aeromagnetic system and then uses this system to collect data for the study of compensation methods.The system uses an optical pump to measure the magnetic strength.Therefore,a frequency counting circuit with a sampling rate of 10 Hz and a resolution of 0.0324 Hz is designed.Tolles-Lawson(T-L)model and Neural Model are two compensation models for fixed-wing aircraft.This paper first studies the compensation method of helicopter towed birds based on T-L model.Unlike fixed-wing aircraft,the bird does not have a power system.Its uncontrollable movement during flight makes the model subject to the co-called collinearity problem.This paper uses singular value decomposition(SVD)to study the collinearity of the T-L feature matrix.It is found that the high-pass filter can reduce the linear relationship between features.The cut-off frequency of the high-pass filter determines the compensation quality.Therefore,the frequency distribution of the magnetic interference of the bird is studied in this paper.It is found that the interference consists of a low-frequency(0.025~0.098 Hz)component caused by the bird's swings and a high-frequency(higher than 0.098 Hz)component resulting from the bird's rotations.In order to reduce the influence of collinearity,the model parameters should be solved using the high-frequency component.On this basis,this paper further studies the regularization method of the T-L model and finds that the bird's motion has high randomness,and thus the minor components of the TL feature matrix also have a large impact on the parameter solution.Therefore,the L2 regularization is better than the truncated SVD for helicopter towed bird compensation.Finally,by using a high-pass filter of 0.098 Hz and the L2 regularization with a coefficient of 0.00072,this paper increased the improvement ratio(IR)of the T-L model to 1.276.The T-L model is a linear model with only 16 parameters.It has a small capacity which is not enough to represent the complicated magnetic interference caused by the bird.Therefore,this paper instead studies the compensation methods based on neural networks.This paper first based on the neural model for fixed-wing aircraft builds a neural network suitable for helicopter towed bird compensation,and finds that the model's compensation performance is poor and unstable.The reason for this result is that the neural model has to estimate the aeromagnetic interference as a hidden variable.This paper analyzes the hidden space of the model and finds two ways to improve compensation quality and stability.The first one is to introduce random variables into the model to achieve regularization of the neural network.The general neural model can only estimate the expectation of aeromagnetic interference but not its standard deviation(SD).This paper by using the reparameterization trick introduces random variables into the model and realizes the synchronous estimation of aeromagnetic interference's expectation and SD.The introduced random variable in 100 repeated experiments increased the average of IR from 1.135 to 1.310,while reducing its SD from 0.120 to 0.059.By analyzing the training process of the model,this paper finds that reparameterization trick adds random noise to the back-propagation(BP)of error,playing the role of regularization.This paper also finds that the regularization effect is related to the structure of the model.This paper first studies the influence of shared nodes in the network and finds that shared nodes establish a path for random noise during the BP of error.This path guarantees that the gradients can obtain sufficient noise during the late stages of training.On this basis,this paper further studies the influence of the network's activation function on the noise path and finds that when the SD of aeromagnetic interference is small,the absolute function does not affect the noise in the path,while the Sigmoid function blocks the noise path.The SD of aeromagnetic interference can give the uncertainty of the compensation result for each sampling point.Accordingly,the dynamic fusion of the neural network model and the T-L model can be realized.This paper compares dynamic fusion with general fusion methods based on a fixed SD and finds that dynamic fusion has better compensation performance.Another method to improve the quality and stability of compensation is to use prior results to constraint the hidden variable of the model.By analyzing the hidden space of the neural model,this paper finds that the general least-squares-based training method is equivalent to maximizing the evidence lower bound(ELBO)of the model,and maximizing the ELBO can bring aeromagnetic interference close to its true value.Based on this fact,this paper derives a model training method with prior constraints from the ELBO.The prior constraints can guide the neural model to converge to a reasonable interval,thereby improving the stability of performance.At the same time,a properly selected prior constraint can also improve the compensation quality of the model.By using the extended T-L model as a prior constraint,this paper increased the expectation of the IR from 1.135 to 1.312,while reducing its SD from 0.120 to 0.024.This paper further studies the convergence of the model under a prior constraint and finds that the guiding effect of the constraint shows only in the initial stage of training,and then it starts to hinder the neural network from fitting the training data.In order to solve this problem,this paper studies the decaying method of the prior constraint during training.The experimental results show that the exponential decaying of the prior constraint can increase the IR's SD without changing its expectation.By using the exponential decay of the prior constraint,this paper improved the IR of helicopter-towed-bird data to 1.453.