Computer Vision News - April 2019

The update step computes the optimal Kalman gain , along with the observed measurement , to estimate the mean and covariance of : = ෢′ ( ෢′ + ) −1 ෞ = ෢′ + ( ෝ − ෢′ ) ෢ = ( − ) ෢ The model uses LSTM components: you can review details about LSTMs in this previous article of ours. Three LSTM components are used: , and respectively modeling , and ෢ . Each component is described in the illustration below. Note there are two different configurations for each LSTM component -- for larger networks (on the left) and smaller networks (on the right). At any point in time , takes the former prediction ෞ −1 as input and produces (the covariance matrix). At the same time, is taken as input by to produce the matrix as output. Then, ෢ ′ and , as well as matrices and ෢ enter as input into a standard Kalman filter, undergoing the process described in equations of the Kalman Filter above. And finally, the network produces a new estimation ෝ . Note that Q and R are diagonal positive definite matrices. Loss: Initially, the authors used standard Euclidean loss for all training stages, but they found that the module failed to learn a reasonable mapping. They therefore added an additional loss term to improve the gradient flow to the module for improving the training process, resulting in the following overall loss function: 7 Research Computer Vision News Long Short-Term Memory Kalman Filters