Preventing output saturation in active noise control: An output-constrained Kalman filter approach

TL;DR

This paper tackles output saturation in Kalman-filter-based active noise control (ANC) when disturbances are large. It introduces a Kalman filter with an output power constraint (KF-OPC) that scales the disturbance used in the KF update by a constraint factor α, where α is derived from the rated output power ρ_o, the secondary path gain G_s, and the disturbance power δ^2_d, via α = min{ sqrt(ρ_o G_s / δ^2_d), 1 }. The KF update is modified to ŵ(n|n) = K(n)[α d̂(n) - x'^T(n)ŵ(n|n-1)] added to the standard KF correction, ensuring the output power is effectively bounded. Across tonal, broadband, and real-path simulations, KF-OPC prevents amplifier saturation, maintains fast convergence, and delivers stable, nearly linear anti-noise performance under practical hardware constraints.

Abstract

The Kalman filter (KF)-based active noise control (ANC) system demonstrates superior tracking and faster convergence compared to the least mean square (LMS) method, particularly in dynamic noise cancellation scenarios. However, in environments with extremely high noise levels, the power of the control signal can exceed the system's rated output power due to hardware limitations, leading to output saturation and subsequent non-linearity. To mitigate this issue, a modified KF with an output constraint is proposed. In this approach, the disturbance treated as an measurement is re-scaled by a constraint factor, which is determined by the system's rated power, the secondary path gain, and the disturbance power. As a result, the output power of the system, i.e. the control signal, is indirectly constrained within the maximum output of the system, ensuring stability. Simulation results indicate that the proposed algorithm not only achieves rapid suppression of dynamic noise but also effectively prevents non-linearity due to output saturation, highlighting its practical significance.

Figures (6)

• Figure 1: The state space model for the ANC system
• Figure 2: The block diagram of ANC using KF approach, where $P(z)$ and $S(z)$ are the primary and secondary path, respectively. $\hat{S}(z)$ denotes the estimated secondary path and $W(z)$ is the control filter. $x(n)$, $y(n)$, $y'(n)$, and $e(n)$ are the reference signal, control signal, anti-noise, and residual error.
• Figure 3: The block diagram of KF with output power constraint (KF-OPC) method for the ANC system to avoid output saturation problem
• Figure 4: Noise reduction performance with limited output power: (a) Power spectrum of the error signal in different algorithms, (b) the anti-noise signal waves of different algorithms, (c) the control signal waves output from secondary source, and (d) the time history of one control filter weight in different algorithms.
• Figure 5: Noise reduction performance with broadband noise: (a) Noise reduction performance with different algorithms, (b) The power spectrum of error signal with different algorithms, and (c) The disturbance and KF-OPC anti-noise waveform with the output power $0.79971$ and the rated power $\rho_o = 0.8$.