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In this study, we consider a remote estimation system that estimates a time-varying target based on sensor data transmitted over wireless channel. Due to transmission errors, some data packets fail to reach the receiver. To mitigate this, the receiver uses a buffer to store recently received data packets, which allows for more accurate estimation from the incomplete received data. Our research focuses on optimizing the transmission scheduling policy to minimize the estimation error, which is quantified as a function of the age of information vector associated with the buffered packets. Our results show that maintaining a buffer at the receiver results in better estimation performance for non-Markovian sources. 

In this paper, we analyze the monotonicity of infor-mation aging in a remote estimation system, where historical observations of a Gaussian autoregressive AR(p) process are used to predict its future values. We consider two widely used loss functions in estimation: (i) logarithmic loss function for maximum likelihood estimation and (ii) quadratic loss function for MMSE estimation. The estimation error of the AR(p) process is written as a generalized conditional entropy which has closed-form expressions. By using a new information-theoretic tool called ϵ -Markov chain, we can evaluate the divergence of the AR(p) process from being a Markov chain. When the divergence ϵ is large, the estimation error of the AR(p) process can be far from a non-decreasing function of the Age of Information (AoI). Conversely, for small divergence ϵ, the estimation error is close to a non-decreasing AoI function. Each observation is a short sequence taken from the AR(p) process. As the observation sequence length increases, the parameter ϵ progressively reduces to zero, and hence the estimation error becomes a non -decreasing AoI function. These results underscore a connection between the monotonicity of information aging and the divergence of from being a Markov chain. 

We study the design of a goal-oriented sampling and scheduling strategy through a channel with highly variable two-way random delay, which can exhibit memory (e.g., Delay and Disruption Tolerant Networks). The objective of the communication is to optimize the performance of remote inference, where an inference algorithm (e.g., a trained neural network) on the receiver side predicts a time-varying target signal using the data samples transmitted by a sensor. Previous formulations to this problem either assumed a channel with IID transmission delay, neglecting feedback delay or considered the monotonic relation that the performance only gets worse as the input information ages. We show how, with delayed feedback, one can effectively exploit the knowledge about delay memory through an index-based threshold policy. This policy minimizes the expected time-average inference error that can be monotone or non-monotone in age. The index function is expressed in terms of the Age of Information (AoI) on the receiver side and a parameter regarding the distribution of subsequent transmission delay, both of which can readily be tracked.