Neural Network Augmented Kalman Filtering in the Presence of Unknown System Inputs

We present an approach for augmenting a linear, time-varying Kalman filter with an adaptive neural network (NN) for the state estimation of systems with linear process models acted upon by unknown inputs. The application is to the problem of tracking maneuvering targets. The unknown system inputs represent the effect of unmodeled disturbances acting on the system and are assumed to be continuous and bounded. The NN is trained online to estimate the unknown inputs. The training signal for the NN consists of two error signals. The first error signal is the residual of the Kalman filter that is augmented with the NN output. The second error signal is obtained after deriving a linear parameterization model of available system signals in terms of the ideal, unknown NN weights that linearly parameterize the unknown system inputs. The combination of two different sources of error signals to train the NN represents a composite adaptation type approach to adaptive state estimation. The approach is applied in a vision-based formation flight simulation of a leader and a follower unmanned aerial vehicle (UAV). The adaptive estimator onboard the follower UAV estimates the range, azimuth angle, and elevation angle to the leader UAV, the derivatives of these LOS variables, and the unknown leader aircraft acceleration along the axes of the Cartesian coordinate inertial frame. Simulation results with the presented approach are greatly improved when compared to those obtained with just a linear, time-varying Kalman filter and a particular adaptive state estimation method that utilizes just one source of error signals to train the NN [17].