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The strapdown inertial navigation system (SINS) and the global navigation satellite system (GNSS) are traditionally combined into one integrated navigation system, which allows to maintain the advantages and compensate for the disadvantages inherent in each system separately. Currently, the Kalman filter is the most widely used integrated navigation algorithm, but in difficult environmental conditions, in particular, in the presence of strong noise, the effect of filter divergence is often observed. In combination with the accumulation of inertial system errors, this can significantly degrade navigation accuracy.
The federated filter as a method with parallel processing of information has advantages in terms of low system load and high reliability and is widely used in the integration of multisensor data [1]. A federated filter consists of a main filter and subfilters [2]. In the presence of two navigation sources — an inertial navigation system and a GNSS, the output signals of the SINS are fed to the input of subfilter 1, and the output signals of the GNSS are fed to the input of subfilter 2. The corresponding estimates and the covariance matrix of the subfilters are fed to the main filter for optimal combining information and estimating the system state vector.
Artificial neural networks can be supervised trained to achieve non-linear input-output mappings when simulating very complex and non-linear stochastic systems. Their use in integrated navigation systems brings good results.
Recently, there has been a lot of research on the application of neural networks in integrated navigation systems. In particular, the author Yimin Zhou combined a BP (BackPropagation) neural network with a Kalman filter to improve navigation accuracy [3]. The authors FANG Wei, JIANG Jin-guang and XIE Dong-peng used MLPNN (multilayer perceptron neural networks) to support the integrated navigation system [4]. But most of the existing methods based on artificial neural networks are based on the correlation of inertial navigation system errors with the corresponding output signals without taking into account the influence of past knowledge about the errors. In this work, recurrent neural networks (RNN, Recurrent Neural Network, RNN) are used to process the readings of the integrated navigation system. RNN allows to determine the relationship between the current output signal and the previous input signal. RNN consists of input, hidden and output layers. After this neural network receives input at the moment , the hidden layer has value , and the output layer has value . The main specificity of the method consists in the fact that the value of depends not only on , but also on the output of the hidden layer at the last moment, that is, . Thus, the method for calculating the forward propagation of the RNN can be expressed as follows:
where and — activation function of the output and hidden layers.
An integrated navigation system using a recurrent neural network uses neural networks to train a SINS error model in the presence of a satellite signal, while establishing a relationship between the navigation information of the carrier and the error model. When satellite communication is lost, the trained neural network is used to predict SINS errors and correct its output signals, thereby continuing to provide reliable navigation information to the carrier.
In general, the federated filtering algorithm using a neural network proposed in this work consists in using a federated filter to integrate information from inertial and satellite navigation systems in the presence of GNSS signals. At the same time, the neural network collects the output information from the inertial elements as input and uses the navigation information from the federated filter as the desired output for training. When the GNSS signal is interrupted, the neural network switches to predictive mode. At the same time, the neural network still collects the output information from the inertial elements as input and uses the previously trained network model to predict more accurate navigation information, which is used to correct the SINS readings.
