A compensation-oriented algorithm for difference-driven identification under binary-valued observations and data packet dropout

Abstract

This paper investigates the identification problem for finite impulse response (FIR) systems with binary-valued observations under event-triggered communication mechanism and data packet dropout. The challenge lies in the inability to distinguish between untriggered events and packet loss when no information is received, which prevents us from obtaining the statistical properties of the binary-valued sequence. A compensation-oriented difference-driven identification (CODD) algorithm is proposed to estimate the parameter by recovering the mean of the original binary-valued sequence, where different values for the observation estimates are assigned when receiving 0, 1 or nothing. Even though, the convergence analysis of the parameter estimate is still challenging since the assigned values are dependent. To tackle this difficulty, the estimate error is divided into two parts: an initial assigned value related part, which is demonstrated to be convergent through the construction of an auxiliary set, and the remaining component, which happens to be a convergent martingale-difference sequence. As a result, the almost sure convergence and the asymptotic normality of the CODD algorithm are established when data packet loss probability is less than $\frac{1}{2}$. By calculating the communication rate, it is proven that the difference-driven mechanism can save 50% of the communication cost compared to original binary-valued systems. Furthermore, when data packet loss probability is high, an $m$-channel compensation-oriented identification ($m$-CODD) algorithm is constructed by utilizing retransmission of the each observation for $m$ times, which is designed based on the packet loss probability. The properties of $m$-CODD algorithm including convergence, asymptotic normality and communication rate are established. Numerical simulations are illustrated to show the theoretical results.