State Estimation of an Agent with Stochastic Dynamics Using Recurrent Filters

The paper proposes a method for estimating the state vector of an agent in a multi-agent biological system based on noisy measurements using recurrent filters. It addresses the issues of scalability in existing approaches to monitoring the behavior of laboratory rodents and the absence of a unified mathematical framework. A mathematical description of an agent in the biological system is provided, along with the formulation of the task of estimating its state. The mathematical model is built upon a non-linear discrete-time system in state space. The solution to this problem is demonstrated using the example of skeletal keypoints in a Wistar rat, which are detected using a pre-trained detector. A fully connected neural network is proposed to parameterize the unknown dynamics of the system. The particle filter (a sequential Monte Carlo method) and the unscented Kalman filter were selected for a comparative analysis. The comparison of the methods was conducted on a collected and preprocessed dataset comprising images with a resolution of 1060×548 pixels and annotations of rat skeletal keypoints. The experimental results demonstrate the high efficacy of the proposed method and its advantage over an analytical description of the system's nonlinear dynamics. Among the compared methods, the dual estimation of both the state vector and the neural network parameters using two unscented Kalman filters achieved the minimal mean error of 6.4 pixels. However, for practical applications in real-time scenarios, a single filter employing a pre-trained neural network proves to be more advantageous. Moreover, the unscented Kalman filter in this case demonstrated higher accuracy than the particle filter (mean error of 8.1 pixels vs. 12.0 pixels). The results of this study can be used to solve the task of automated registration of Wistar rat behavior by parameterizing the functions that link state vectors with the output vectors of individual and group behavior.