The data produced by laser inertial navigation systems are quantified pulse increments, with the process of quantization adding complexity to the system's error profile. This quantification often masks small variations in error, complicating fault detection in redundant systems. Traditional fault detection algorithms, particularly those based on the equivalent space method, face challenges in effectively identifying and isolating these faults. In response, this paper leverages Singular Value Decomposition (SVD) to refine the equivalent space method, proposing an enhanced SVD-based fault detection and isolation algorithm that incorporates a three-channel filter. This novel approach employs fuzzy logic for the adaptive tuning of filter parameters, offering a departure from conventional practices where the determination of fault detection thresholds and observation intervals rely on empirical values. Instead, we adopt the Monte Carlo method to set these thresholds, aiming for precise detection and isolation of minor faults. The efficacy of this refined algorithm in diagnosing faults within redundant laser inertial navigation systems is confirmed through simulation, showcasing its potential for improved accuracy and reliability in fault diagnosis.