Enhanced Kalman Filter using Noisy Input Gaussian Process Regression for Bridging GPS Outages in a POS

Abstract

A Position and Orientation System (POS) integrating an Inertial Navigation Systems (INS) and the Global Positioning System (GPS) is a key component of remote sensing motion compensation. It can provide reliable and high-frequency high-precision motion information using a Kalman Filter (KF) during GPS availability. However, the performance of a POS significantly degrades during GPS outages. To maintain reliable POS outputs, this paper proposes a new hybrid predictor based on modelling the nonlinear time-series data-driven INS-errors using Noisy Input Gaussian Process Regression (NIGPR), which takes the input noise into account. The proposed approach is used to learn the nonlinear INS-errors model when GPS signals are available. When GPS outages occur, it starts to predict the observation measurement, and then feeds it to a KF as a virtual update to estimate all the INS errors. The proposed approach is verified in a real airplane, which combines a POS and Synthetic Aperture Radar (SAR). Experimental results show that the proposed approach significantly improves the performance of the POS, with improvements more than 90% better than a KF and 10% better than a Gaussian Process Regression (GPR/KF) combination during various GPS outages.

A LSTM Algorithm Estimating Pseudo Measurements for Aiding INS during GNSS Signal Outages

“…In Equation (7), ω n in = ω n ie + ω n en , φ means the misalignment angles vector and C n b is called the direction cosine matrix (DCM) transforming the coordinates from the b-frame to the n-frame. Equation (8) indicates the velocity error equation, where δ f b is the accelerometer zero offset error, f b is the output of accelerometer unit in b-frame and δg n is the gravity error, g n is gravity vector in n-frame. Equations (9)-(11) represent the position error, where δL and δλ represent the position error in latitude and longitude, δh represents the position error in height, and the R M and R N denote the radius of curvature in longitude and latitude, respectively.…”

“…Shown above, φ E,N,U are the misalignment angles calculated in Equation (7) in the n-frame. δV E,N,U are the velocity errors of three axes calculated from Equation (8) in the n-frame, while δL, δλ, and δh represent the position errors of latitude, longitude, and height, respectively, calculated from Equations (9)-(11) in n-frame. ∇ x , ∇ y , ∇ z , x , y , and z represent the accelerometer biases and gyroscope biases in three axes in the b-frame.…”

“…Because of their complementary properties, INS and GNSS are commonly integrated by a Kalman filter (KF) for providing continuous and high precision navigation [3][4][5][6]. In an INS/GNSS system, GNSS aids INS by estimating its errors in KF [7,8]. Besides, INS connects the GNSS signal gap and helps the GNSS signal reacquisition after an outage [9,10].…”

Deep Gaussian Process Regression for Performance Improvement of POS During GPS Outages

“…On this basis, a RBFNN/KF hybrid model is developed to suppress POS errors during GPS outages [1]. However, a major shortcoming is the difficulty of choosing the number of hidden units and local minimum in the training procedure [17].…”

“…However, the standard GPR ignores input noise, which easily leads to poor modelling performance and over-fitting. In order to overcome the problem, Ye et al [17] merges Noisy Input GPR into KF to improve the performance of POS during GPS outages. Because that the predictive capability of GPR models is limited by the expressiveness of the kernel function, there is still room for improvement of the performance in the long-term GNSS outages.…”