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Description
Kernel ridge regression (KRR) has emerged as an effective approach to sound field estimation (SFE). By constructing the kernel and its associated reproducing kernel Hilbert space (RKHS) appropriately, the optimal KRR solution can be guaranteed to satisfy the wave equation. Such kernels and RKHSs have so far only been derived in the frequency domain and discrete-time domain. Therefore, in this paper a continuous-time kernel and associated RKHS is proposed, which enforces the wave equation by construction. The kernel function has a simple closed-form expression which is shown to have lower computational cost compared to similar discrete-time methods. A KRR-based method for SFE with the proposed model is then presented. The proposed SFE method is flexible, naturally supporting moving microphones and non-uniform sampling. The proposed method is evaluated using simulated data with both stationary and moving microphones, demonstrating the value of the approach in terms of both estimation performance and computational cost.