Lock-In Amplifier With Enhanced Filter Structure for NMR Gyroscope

To maintain the functionality of the nuclear magnetic resonance (NMR) gyroscope, extracting the precession phase and compensating for the transverse driving field is essential. The digital lock-in amplifier (DLIA) effectively captures amplitude and phase information from weak signals. The performance of the low-pass filter (LPF) within the DLIA is significant. To achieve high precision, the finite impulse response (FIR) filter requires an extremely low cut-off frequency, which results in higher order, complex operations, and significant resource consumption. The moving average filter (MAF) has high attenuation at specific frequencies and low attenuation at others. Meanwhile, lengthy windows result in increased resource consumption, higher latency, and the inability to capture rapidly changing signals. To address these challenges, a cascade filter structure is proposed, where a low-order FIR filter is cascaded with a small window MAF. This structure utilizes the FIR filter for high stopband attenuation, while the MAF further attenuates at specified frequencies and narrows the transition band. Consequently, this improvement effectively reduces the FIR filter order and MAF window length, preventing the attenuation of swiftly changing signals caused by extended window lengths. To minimize resource consumption, a dual FIR filters resource optimization method is introduced based on time-division multiplexing (TDM) and parallel distributed algorithms (PDAs), allowing two FIR filters to share one coefficient table. Subsequently, the performance of the proposed DLIA is evaluated under various conditions and implemented in a field-programmable gate array (FPGA). The results indicate that the proposed DLIA exhibits superior performance, low computational complexity, and low resource utilization.

I. Introduction

Nuclear magnetic resonance (NMR) gyroscopes, which have the advantages of small size and high accuracy, and are unaffected by environmental factors, have great potential in the field of inertial navigation [1], [2], [3]. NMR gyroscopes operate on the principle of Larmor precession, utilizing the embedded magnetometer and signal processing system to capture rotational information [4], [5], [6]. Compared with single-species, dual-species can eliminate the impact of the static magnetic field on measurement accuracy [7]. To ensure continuous measurement of the angular velocity, the system needs to work in a closed-loop system to address real-time phase detuning and compensate for the transverse driving field [6]. In the case of a closed-loop NMR gyroscope based on⁸⁷Rb–¹²⁹Xe/¹³¹Xe, by demodulating at the first harmonic of the rubidium atomic magnetic moment component, the signal containing the progression phase can be obtained. The complexity of the NMR gyroscope system encompasses tasks, such as vapor cell temperature control, laser frequency stabilization, three-axis magnetic field control, and angular velocity resolution [8]. This intricate system needs extensive digital signal processing and substantial hardware resources underscoring the importance of accurately determining the precession phase with minimal resource consumption.