Over the last few years, kernel adaptive filters have gained in importance as the kernel trick started to be used in classic linear adaptive filters in order to address various regression and time-series prediction issues in nonlinear environments.In this paper, we study a recursive method for identifying finite impulse response (FIR) nonlinear systems based on binary-value observation systems. We also apply the kernel trick to the recursive projection (RP) algorithm, yielding a novel recursive algorithm based on a positive definite kernel. For purposes, our approach is compared with the recursive projection (RP) algorithm in the process of identifying the parameters of two channels, with the first of them being a frequency-selective fading channel, called a broadband radio access network (BRAN B) channel, and the other being a a theoretical frequency-selective channel, known as the Macchi channel. Monte Carlo simulation results are presented to show the performance of the proposed algorithm.