复杂环境下基于自监督LSTM网络的导航误差建模补偿.pdf

第32卷第2期 中国惯性技术学报 Vol.32 No.2 2024 年 02 月 Journal of Chinese Inertial Technology Feb.2024 收稿日期：收稿日期：2023-09-18；修回日期：修回日期：2024-01-02 基金项目：基金项目：航空基金重点项目（201908018001）作者简介：作者简介：成果达（1988），男，高级工程师，从事惯性导航技术研究。文章编号：文章编号：1005-6734(2024)02-0115-10 doi.10.13695/ki.12-1222/o3.2024.02.002 Modeling and compensation of navigation error based on self-supervised LSTM network in complex environment CHENG Guoda1,2,YUE Yazhou2,WEI Yanyi2,LI Sihai1(1.School of Automation,Northwestern Polytechnical University,Xian 710072,China;2.AVIC Xian Flight Automatic Control Research Institute,Xian 710065,China)Abstract:Aiming at the problems that the inertial navigation system has interactive effects and navigation errors are difficult to identify in complex environment,a navigation error compensation method based on self-supervised long short term memory(LSTM)network intelligent combination model is proposed.The self-supervised temperature change rate module is proposed to overcome the limit of temperature sensor precision and provide temperature change rate in real time,which further improves the ability of the model to identify navigation error.In the experiment section,the effectiveness of the self-supervised module is verified through ablation experiments under various complex environment.Taking the northward velocity of flight test data as an example,the maximum absolute velocity error before compensation is 1.607 m/s,and 0.357 m/s after.Experimental results prove that the velocity and position error under complex physics environment could be effectively reduced,and the pure inertial navigation performance is therefore improved.Key words:inertial navigation;long short term memory network;navigation error compensation;self-supervised learning 复杂环境下基于自监督复杂环境下基于自监督 LSTM 网络的导航误差建模补偿网络的导航误差建模补偿 成果达1,2，岳亚洲2，韦彦一2，李四海1（1.西北工业大学 自动化学院，西安 710072；2.西安飞行自动控制研究所，西安 710065）摘要：摘要：针对复杂环境下惯导系统存在交互影响和导航误差难以辨识的问题，提出了一种基于自监督长短期记忆（LSTM）网络智能组合模型的导航误差补偿方法。模型中的自监督温变速率模块不受到温度传感器精度的限制，从而实时计算更精确的温变速率，进一步提升了模型导航误差辨识的能力。在实验部分，基于多种复杂环境下的实验数据，通过消融实验验证了自监督模块的有效性。以飞行数据的北向速度为例，补偿前后的最大速度绝对误差分别为 1.607 m/s 和 0.357 m/s。实验结果说明了所提方法可以减小复杂环境下的速度和位置误差，从而提升惯性导航精度。关关 键键 词：词：惯性导航；长短期记忆网络；导航误差补偿；自监督学习 中图分类号：中图分类号：U666.1 文献标志码：文献标志码：A The navigation performance of the strap-down inertial navigation system(SINS)is directly affected by the inertial measurement units(IMUs),and the performance of the IMUs fluctuates greatly due to the environmental influence.The SINS does not have a physical platform to isolate the angular motion of the aircraft,and the IMU is directly attached to the moving aircraft.Therefore,the gyroscope and accelerometer in the IMU will be directly sensitive to the angular and linear motion of the aircraft.Compared with the platform inertial navigation,the measurement range of the IMU in the strap-down inertial navigation,especially the angular velocity range of the gyroscope measurement,is much larger.Under high dynamic conditions,the SINS needs to 116 中国惯性技术学报 第 32 卷 accurately model and compensate for dynamic errors of gyroscopic and accelerometer to ensure navigation performance1.When combined with global navigation satellite system(GNSS),the accumulative error could be diminished using Kalman filter2.However,the satellite signal is not always available,resulting in deficiency of navigation performance.On the one hand,the study of navigation error modelling compensation still requires further exploration.In the field of modelling the dynamic error of laser inertial navigation,state-of-the-art researches mainly focus on compensating for the dynamic error of accelerometer3,while the study of gyroscopic dynamic error is relatively limited.The angular velocity measurement error model presented in Ref.4 takes the anisoelasticity error caused by high-frequency jitter devices into consideration.Ref.5 divides nonelastic error by device level and system level,and derives the drift error under certain specific motion conditions based on the relationship between gyroscope output and rotation vector.On the other hand,the error mechanism of the entire IMU is not clear and the closed-form expression is difficult to establish.In reality,the non-rigid nature of the IMU caused by the mechanical jitter of the laser gyroscope may result in the actual error model much more complex beyond imagination.IMUs are not only sensitive to the temperature of individual time steps6,7,but may also be related to other parameters(such as gradient and changing rate of temperature,etc.)of the temperature field around.Such quantities are difficult to collect through the relevant sensors.Hence,there is an urgent need to find a suitable method to build the part of the model that is difficult to obtain by simply analyzing physical properties.Artificial intelligence and neural networks have attracted attention in study of nonlinear systems due to their superior representation ability,among which long short term memory networks(LSTMs)have brought fresh insights for time series data.The excellent learning ability of neural networks has made them widely adopted as a kind of general approximator in the identification of nonlinear dynamic systems8.The theoretical analysis is rigorous and the system is mature for the classic function approximation theory.Neural networks provide a very effective black box tool for identification of nonlinear systems with their excellent function approximation ability.When dealing with time series data,recurrent neural networks(RNNs)are proved to be effective and gain widespread application.But there exists the inevitable long-term dependencies problem of RNN in practical use.In this case,LSTM was proposed to exploit long-term information by integrating gating mechanisms9,therefore overcoming the internal possible gradient vanishing or explosion problems of RNNs.LSTM has been extensively applied in fields of computer vision,natural language processing and financial time forecasting.More recently,LSTM has been integrated with multiple techniques for exploiting the character and information of time series data.Ref.1010 combined LSTM with encoder-decoder structure for sequence-to-sequence mapping and information compressing in power electronics converter modelling.Ref.11 introduced advanced LSTM models by adding attention module on different layers.LSTM networks have been adopted to enhance navigation performance in recent years,but the usage of temperature change rate requires further improvement.In recent years,LSTM networks have also been adopted in navigation era in order to compensate for the unknown time series navigation error model12.Among the error models including black box model such as neural networks and white box model such as polynomial model,input variables commonly cover acceleration,temperature,magnetic information,etc.Temperature change rate has also been proven to be statistically significant as one of the input variables in error modelling13.However,the accurate temperature change rate is difficult to acquire directly due to the precision limit of thermometers attached to IMUs.Under regular circumstances,the temperature of IMUs changes slowly over time and the thermometers is unable to reach ideal precision.Hence the ideal slope of temperature change rate could easily reduce to binary numerical temperature with the unit of minimum temperature measurement scale.While the linear filters could be easy to calculate and smoothen the temperature measurements in time domain,the filtered series still contain noises of certain level and have time lag with the length of the window.As a result,the precision of temperature change rate needs to be enhanced.Self-supervised learning can exploit information from unsupervised data itself with the help of pretext 第 2 期 成果达等：复杂环境下基于自监督 LSTM 网络的导航误差建模补偿 117 model.Similar to regular regression task,the outcome of self-supervised learning is supposed to fit certain pattern.Unlike supervised learning where the labels are given in advance manually,the labels in self-supervised learning are produced with the assistance of pretext model during the learning stage.Although the pretext model is discarded during the prediction stage,its information is contained in the learned model.The self-supervised models are normally sorted into context-based,temporal-based and contrastive-based model.The ones based on temporal data have the assumption that the data have similarity over time,where the data of adjoining time are alike.Self-supervised learning could improve the performance of downstream tasks.More specifically,the navigation error is likely to be reduced with the usage of self-supervised module.In order to improve the accuracy of inertial navigation,this paper presents a hybrid compensation method combining LSTM network with self-supervised temperature change rate for navigation error identification.In this paper,LSTM and self-supervised neural network are adopted to modelling the navigation error in addition to physical model to further improve navigation accuracy.Besides,the proposed algorithm introduces temperature change rate learned via the self-supervised neural network into the input variables.In this way,the information within temperature change rate could be utilized efficiently discarding the primitive noises.The contributions of this paper are as follows:1)A hybrid navigation error compensation model is presented,which aims at enhancing the performance of the deterministic navigation model with the LSTM based self-supervised neural network model.2)A self-supervised temperature change rate module is proposed to overcome the limit of thermometer precision and provide temperature change rate in real time.3)The effectiveness of the hybrid error model and the self-supervised module is verified through experiments under various complex environment.The rest of the paper is organized as follow.Section 1 briefly introduces neural networks and LSTM;Section 2 introduces the navigation error transfer model,analyses the influence of complex physical environment on navigation accuracy,and establishes a hybrid network model combining the navigation model and the neural network model;and Section 3 verifies the effectiveness of the hybrid model through experiments.1 LSTM neural network Neural networks form the connections among neurons with learnable linear parameters and nonlinear activation functions.In this paper,we adopt LSTM network to compose the mathematical model from the available inertial sensor measurement to the navigation error in complex physics environment.1.1 RNNs Among various network structures,RNNs are effective when handling time series data with variable length.A fully connected RNN updates its parameters by integrating the input of the neurons on the previous layer as well as its own information preserved from the previous time step.The property that the recurrent units share the parameters along time dimension enables RNNs to deal with time series data with variable length.Eq.(1)is an illustration of the update formula of the neuron h by time t:1ttthUhWxb (1)11xxe (2)Where tx denotes the input of neuron th from the previous layer,U is the transition matrix of the recurrent unit,W and b are the weight and bias parameters respectively,and is the sigmoid activation function as Eq.(2).Fig.1 is an expansion structure of how the recurrent unit passes the information of the input tx and output ty along time dimension.Nevertheless,nave RNN could face the problems of gradient vanishing and explosion in the back-propagation process when fitting a time series with long-term dependence.Fig.1 Recurrent unit of nave RNN 1.2 LSTM For the purpose of alleviating the problem of long-term dependencies of RNN,LSTM incorporates gating mechanism to update the internal nodes inside the 118 中国惯性技术学报 第 32 卷 recurrent unit.The recurrent unit of LSTM includes internal node tc for state update,external node th for information flow,and candidate cell state tc obtained from linear transformation.Fig.2 demonstrates the flowchart inside the recurrent unit of LSTM,including three types of soft threshold gates:Forget gate tf that determines the forgetting proportion from the external node 1th to the internal node 1tc,Input gate ti that determines the input proportion from candidate state tc to internal node tc,Output gate to that determines the output proportion from the internal node tc to the external node th.In Fig.2,denotes element-wise multiplication of two vectors,denotes element-wise addition and denotes vector concatenation.Fig.2 Recurrent unit of LSTM network More specifically,the update process is calculated as Eq.(3).11111tanhtanhtttttttttttctctittitftftftototocfcichoccU hW xbiU hWxbfU hW xboU hW xb (3)Where tc,th and tc denote the internal node,external node and candidate state in time step t.kU,kW,kb(,kf i o )denote the transition matrices,weights and bias parameters of three types of gates respectively.2 Navigation error mechanism and model establishment The main error sources of the navigation solution error are the initial condition error and the IMU error.The attitude alignment error in the initial condition also mainly depends on the IMU error.The other influencing factor is the solution error under high dynamic conditions.Among them,the performance of IMUs can be affected by the environment fluctuations greatly.Due to the lack of understanding the pattern how the environment(such as temperature,vibration,magnetic field,etc.)affects the accuracy of IMUs,it is difficult to accurately compensate for this part of the error,especially when the satellite signal is interrupted and pure inertial navigation is required.2.1 Proposed hybrid model As is shown in Fig.3,the hybrid model consists of a deterministic model of the navigation solution process and the LSTM-based self-supervised model.To be more specific,the outcome of IMUs first serve as the input of the mathematical model and are used to produce regular navigation metrics including attitude,velocity and position,as well as the deterministic error compensation process.The measurements are also conveyed to the unknown error modelling part to be fitted using the LSTM network for fine tuning the navigation error using time series measurement data.In this stage,the temperature change rate of high accuracy is first estimated by a pretrained self-supervised neural network,which later turns into one of the input variables of the LSTM error compensation model.The output of the two stages are then combined as the final navigation result.The deterministic and black box model are detailed in the following two parts accordingly.Fig.3 Hybrid model structure 2.2 Deterministic navigation model The deterministic model of attitude,velocity and position are calculated via the following mathematical expressions,as Eq.(4).T2sec,nnbnnbbibbinnnbnnnnbsfieennnnNEUMNvvLLhvRhRhCCCvC fvg (4)Where bib and bsff are the angular velocity and the acceleration measured by the IMU respectively.nbC,nv,L,and h are attitude