Robust Real-Time Multistatic Sonar Tracking with Missed Detections and Measurement Bias Using Gaussian Long Short-Term Memory Networks

We analyze the use of Long Short-Term Memory (LSTM) networks and Gaussian LSTM networks (G-LSTMs) for object localization and tracking based on bistatic sonar measurements in scenarios involving moving receivers, missing detections, and potentially biased Gaussian measurements. We formally derive the Cramér-Rao Lower Bound (CRLB) for the situation including incorporating past information for noisy nonlinear models. Performance is analyzed on decaying coordinated turn tracks and found to be close to the CRLB and the performance of the Extended Kalman Filter (EKF), despite having no explicit prior knowledge of the movement or measurement models. The Gaussian and non-Gaussian LSTMs exhibit robustness against missing detections and measurement bias and are able to quantify such biases (if present). This Gaussian architecture shows promise, as performance is slightly worse with their nonGaussian counterparts but offers a covariance estimate and only exhibits a slight underconfidence in predictions. The Gaussian neural networks considered here show the ability to capture environmental uncertainty as given by the dynamic probability of detection. Inference times are small enough to allow for real-time tracking.