Adaptive neuro-fuzzy module for inertial navigation system/global positioning system integration utilising position and velocity updates with real-time cross-validation

Recently, methods based on artificial intelligence (AI) have been suggested to provide reliable positioning information for different land vehicle navigation applications. The majority of these applications utilise both the global positioning system (GPS) and the inertial navigation system (INS). These AI modules were trained to mimic the latest vehicle dynamics so that, in case of GPS outages, the system relies on INS and the recently updated AI module to provide the vehicle position. Several neural networks and neuro-fuzzy techniques were implemented in real-time in a de-centralised fashion and provided acceptable accuracy for short GPS outages. It was reported that these methods provided poor positioning accuracy during relatively long GPS outages. In order to prevail over this limitation, this study optimises the Al-based INS/GPS integration schemes utilising adaptive neuro-fuzzy inference system with performing, in real-time, both GPS position and velocity updates. In addition, a holdout cross validation method during the update procedure was utilised in order to ensure generalisation of the model. The proposed system is tested using differential GPS and both navigational and tactical grades INS field test data obtained from a land vehicle experiment. The results showed that the effectiveness of the proposed system over both the existing Al-based and the conventional INS/GPS integration techniques, especially during long GPS outages. This method may have one limitation related to the unusual significant changes of the vehicle dynamics between the update and the prediction stages of operation which may influence the overall positioning accuracy.     

Adaptive Fuzzy Prediction of Low-Cost Inertial-Based Positioning Errors

Kalman filter (KF) is the most commonly used estimation technique for integrating signals from short-term high performance systems, like inertial navigation systems (INSs), with reference systems exhibiting long-term stability, like the global positioning system (GPS). However, KF only works well under appropriately predefined linear dynamic error models and input data that fit this model. The latter condition is rather difficult to be fulfilled by a low-cost inertial measurement unit (IMU) utilizing microelectromechanical system (MEMS) sensors due to the significance of their long- and short-term errors that are mixed with the motion dynamics. As a result, if the reference GPS signals are absent or the Kalman filter is working for a long time in prediction mode, the corresponding state estimate will quickly drift with time causing a dramatic degradation in the overall accuracy of the integrated system. An auxiliary fuzzy-based model for predicting the KF positioning error states during GPS signal outages is presented in this paper. The initial parameters of this model is developed through an offline fuzzy orthogonal-least-squares (OLS) training while the adaptive neuro-fuzzy inference system (ANFIS) is implemented for online adaptation of these initial parameters. Performance of the proposed model has been experimentally verified using low-cost inertial data collected in a land vehicle navigation test and by simulating a number of GPS signal outages. The test results indicate that the proposed fuzzy-based model can efficiently provide corrections to the standalone IMU predicted navigation states particularly position.     

Analysis and Modeling of Inertial Sensors Using Allan Variance

It is well known that inertial navigation systems can provide high-accuracy position, velocity, and attitude information over short time periods. However, their accuracy rapidly degrades with time. The requirements for an accurate estimation of navigation information necessitate the modeling of the sensors' error components. Several variance techniques have been devised for stochastic modeling of the error of inertial sensors. They are basically very similar and primarily differ in that various signal processings, by way of weighting functions, window functions, etc., are incorporated into the analysis algorithms in order to achieve a particular desired result for improving the model characterizations. The simplest is the Allan variance. The Allan variance is a method of representing the root means square (RMS) random-drift error as a function of averaging time. It is simple to compute and relatively simple to interpret and understand. The Allan variance method can be used to determine the characteristics of the underlying random processes that give rise to the data noise. This technique can be used to characterize various types of error terms in the inertial-sensor data by performing certain operations on the entire length of data. In this paper, the Allan variance technique will be used in analyzing and modeling the error of the inertial sensors used in different grades of the inertial measurement units. By performing a simple operation on the entire length of data, a characteristic curve is obtained whose inspection provides a systematic characterization of various random errors contained in the inertial-sensor output data. Being a directly measurable quantity, the Allan variance can provide information on the types and magnitude of the various error terms. This paper covers both the theoretical basis for the Allan variance for modeling the inertial sensors' error terms and its implementation in modeling different grades of inertial sensors.