Method and system for a continuous discrete recurrent kalman network
A computer-implemented method utilizing a continuous discrete recurrent Kalman network, wherein the method includes receiving, at an encoder, an input from one or more sensors, wherein the input includes one or more time series data associating data at one or more points in time; outputting, to a Kalman filter, a latent observation and uncertainty estimate in response to the input at the encoder; determining a latent state prior and latent state posterior utilizing the Kalman filter; and outputting, via a decoder, a filtered observation utilizing at least the latent state posterior.
1 . A computer-implemented method utilizing a continuous discrete recurrent Kalman network, comprising:
receiving, at an encoder, an input from one or more sensors, wherein the input includes one or more time series data associating data at one or more points in time, wherein the encoder is configured to network map an observation into a latent observation space;
outputting, to a Kalman filter, a latent observation and uncertainty estimate in response to mapping of the input at the encoder and the latent observation space;
determining a prior latent state and posterior latent state utilizing the Kalman filter configured to solve a Stochastic Differential Equation (SDE) associated with the prior latent state and posterior latent state; and
outputting, via a decoder, a filtered observation utilizing at least the posterior latent state in response to the decoder mapping the prior latent state back to the input.
2 . The computer-implemented method of claim 1 , wherein the Kalman filter, the encoder, and the decoder each include model parameters configured to be trained with backpropagation in an end-to-end manner.
3 . The computer-implemented method of claim 1 , wherein the decoder is configured to map the filtered observation to the time series data.
4 . The computer-implemented method of claim 1 , wherein the input includes image sequences and the encoder and decoder include a convolutional neural network.
5 . The computer-implemented method of claim 1 , wherein the Kalman filter is a recurrent continuous-discrete Kalman filter.
6 . The computer-implemented method of claim 1 , wherein the method includes, utilizing the Kalman filter, outputting a discrete observation at an arbitrary time interval.
7 . The computer-implemented method of claim 1 , wherein the one or more sensors includes a camera, global positioning system (GPS) sensor, temperature sensor, oxygen sensor, speed sensor, or a vehicle sensor.
8 . A system that includes a continuous discrete recurrent Kalman network, comprising:
an encoder configured to receive an input from one or more sensors, wherein the input includes one or more time series data associating data at one or more points in time, wherein the encoder is configured to network map an observation into a latent observation space;
a recurrent continuous-discrete Kalman filter configured to receive as output from the encoder, a latent observation and uncertainty estimate in response to the input at the encoder and the latent observation space, and further configured to determine prior latent state and posterior latent state; and
a decoder configured to output a filtered observation utilizing at least the posterior latent state in response to the decoder mapping the prior latent state back to the input.
9 . The system of claim 8 , wherein the Kalman filter, the encoder, and the decoder each include model parameters configured to be trained with backpropagation.
10 . The system of claim 8 , wherein the latent observation is output in response to a stochastic differential equation.
11 . The system of claim 8 , wherein the decoder is configured to map the filtered observation to the time series data.
12 . The system of claim 8 , wherein the input includes image sequences and the encoder and decoder include a convolutional neural network.
13 . The system of claim 8 , wherein the Kalman filter is further configured to output a discrete observation at an arbitrary time interval.
14 . The system of claim 8 , wherein the one or more sensors includes a camera, global positioning system (GPS) sensor, temperature sensor, oxygen sensor, speed sensor, or a vehicle sensor.
15 . A system that includes a continuous discrete recurrent Kalman network, comprising:
a processor programmed to:
receive, at an encoder, an input from one or more sensors, wherein the input includes one or more time series data associating data at one or more points in time, wherein the encoder is configured to network map an observation into a latent observation space;
output, to a Kalman filter, a latent observation and an uncertainty estimate in response to the input at the encoder and the latent observation space;
determine a prior latent state and posterior latent state utilizing the Kalman filter configured to solve a Stochastic Differential Equation (SDE) associated with the prior latent state and posterior latent state; and
output, via a decoder, a filtered observation utilizing at least the posterior latent state in response to the decoder mapping the prior latent state back to the input.
16 . The system of claim 15 , wherein the processor is further programmed to output, via a decoder, a filtered observation utilizing at least the posterior latent state.
17 . The system of claim 15 , wherein the filtered observation indicates data associated with a future time.
18 . The system of claim 15 , wherein the Kalman filter is further configured to utilize the latent observation and the uncertainty estimate to update the prior latent state.
19 . The system of claim 15 , wherein the decoder is further configured to map the posterior latent state to an observation space.
20 . The system of claim 15 , wherein the Kalman filter is a recurrent continuous-discrete Kalman filter.