System and method for estimating errors in a sensor network implementing high frequency (HF) communication channels
One embodiment can provide a method and system for estimating a remote quantity of interest (QoI). During operation, the system can receive, over a communication channel, a radio frequency (RF) signal carrying an estimate of the QoI measured by a sensor. The system can estimate probability distributions of a set of random channel parameters associated with the HF communication channel. The system can further reconstruct the estimate based on the probability distributions of the channel parameters and the received RF signal, determine a level of uncertainty associated with the reconstructed estimate, and combine reconstructed estimates from multiple sensors based on the determined level of uncertainty associated with each reconstructed estimate to output a combined estimate of the QoI.
1 . A method for estimating a remote quantity of interest (QoI), the method comprising:
receiving, at a receiver, a radio frequency (RF) signal carrying an estimate of the QoI measured by a sensor, wherein the RF signal is received over a communication channel;
estimating probability distributions of a set of random channel parameters associated with the communication channel;
reconstructing the estimate of the QoI based on the probability distributions of the channel parameters and the received RF signal;
determining a level of uncertainty associated with the reconstructed estimate, wherein the determination comprises computing a covariance matrix of a joint probability distribution of the reconstructed estimate and the channel parameters; and
combining reconstructed estimates from multiple sensors based on the determined level of uncertainty associated with each reconstructed Kalman filter estimate to output a combined estimate of the QoI.
2 . The method of claim 1 , wherein the communication channel comprises a high-frequency (HF) communication channel, and wherein estimating the probability distributions of the random channel parameters further comprises:
training a surrogate channel model having a channel parameter space with a reduced dimension; and
simulating behaviors of the HF communication channel using the trained surrogate channel model.
3 . The method of claim 2 , wherein training the surrogate channel model further comprises training the surrogate channel model jointly with a variational autoencoder (VAE) model that is configured to output channel parameters defined in the channel parameter space with the reduced dimension.
4 . The method of claim 3 , wherein the surrogate channel model and the variational autoencoder (VAE) model are trained jointly using training samples generated by a high-fidelity physics-based channel model.
5 . The method of claim 1 , further comprising encoding the estimate of the QoI into an RF signal to be transmitted over the communication channel using a quadrature amplitude modulation (QAM)-based orthogonal frequency-division multiplexing (OFDM) encoder.
6 . The method of claim 1 , wherein reconstructing the estimate comprises using a previously trained machine-learning decoder to directly learn probability distributions of symbols representing the Kalman filter estimate.
7 . The method of claim 1 , wherein computing the covariance matrix comprises performing spectral expansion on the reconstructed estimate.
8 . The method of claim 1 , wherein computing the covariance matrix comprises computing an unscented transform on the reconstructed estimate.
9 . The method of claim 1 , wherein combining the reconstructed estimates from the multiple sensors comprises assigning a weight to each reconstructed estimate, wherein the weight is inversely proportional to a trace of the covariance matrix.
10 . A computer system for estimating a remote quantity of interest (QoI), the computer system comprising:
a processor; and
a storage device coupled to the processor and storing instructions, which when executed by the processor cause the processor to perform a method, the method comprising:
receiving, over a communication channel, a radio frequency (RF) signal carrying an estimate of the QoI measured by a sensor;
estimating probability distributions of a set of random channel parameters associated with the HF communication channel;
reconstructing the estimate based on the probability distributions of the channel parameters and the received RF signal;
determining a level of uncertainty associated with the reconstructed estimate, wherein the determination comprises computing a covariance matrix of a joint probability distribution of the reconstructed estimate and the channel parameters; and
combining reconstructed estimates from multiple sensors based on the determined level of uncertainty associated with each reconstructed estimate to output a combined estimate of the QoI.
11 . The computer system of claim 10 , wherein the communication channel comprises a high-frequency (HF) communication channel, and wherein estimating the probability distributions of the random channel parameters further comprises:
training a surrogate channel model having a channel parameter space with a reduced dimension; and
simulating behaviors of the HF communication channel using the trained surrogate channel model.
12 . The computer system of claim 11 , wherein training the surrogate channel model further comprises training the surrogate channel model jointly with a variational autoencoder (VAE) model that is configured to output channel parameters defined in the channel parameter space with the reduced dimension.
13 . The computer system of claim 12 , wherein the surrogate channel model and the variational autoencoder (VAE) model are trained jointly using training samples generated by a high-fidelity physics-based channel model.
14 . The computer system of claim 10 , wherein the method further comprises encoding the estimate of the QoI into an RF signal to be transmitted over the communication channel using a quadrature amplitude modulation (QAM)-based orthogonal frequency-division multiplexing (OFDM) encoder.
15 . The computer system of claim 10 , wherein reconstructing the estimate comprises using a previously trained machine-learning decoder to directly learn probability distributions of symbols representing the estimate.
16 . The computer system of claim 10 , wherein computing the covariance matrix comprises performing spectral expansion on the reconstructed estimate.
17 . The computer system of claim 10 , wherein computing the covariance matrix comprises computing an unscented transform on the reconstructed estimate.
18 . The computer system of claim 10 , wherein combining the reconstructed estimates from the multiple sensors comprises assigning a weight to each reconstructed estimate, wherein the weight is inversely proportional to a trace of the covariance matrix.