Fiber optic gyroscope is a high-precision angular velocity sensor based on Sagnac effect, with the advantages of all solid state, small size, low cost and easy maintenance. It is widely used in national defense, aviation, aerospace and other fields. Due to the characteristics of optical components and environmental factors, the output signal of fiber optic gyroscope is usually a non-smooth, nonlinear random signal. Noise interference in the output signal is the main factor affecting the performance of fiber optic gyroscope. In engineering, low-pass filtering is usually used for the noise reduction of the output signal of fiber optic gyroscope. However, since the frequency bands of effective signal and noise overlap with each other, this method cannot suppress the low frequency noise interference. At present, the main adaptive filters are least mean square (LMS) adaptive filter and recursive least square (RLS) adaptive filter. LMS adaptive filter minimizes the performance function by stochastic gradient descent method, which has the advantages of low computational complexity and easy implementation. Compared with LMS adaptive filter, RLS adaptive filter has obvious advantages in convergence speed, and the adaptation of RLS adaptive filter is also better than LMS adaptive filter under non-smooth random signal conditions. However, RLS adaptive filtering has not been implemented on any hardware platform due to its high computational complexity, which makes it difficult to be applied in engineering.

In this paper, we analyze the principle of RLS adaptive filtering and propose a real-time noise reduction technique of RLS adaptive filtering for fiber optic gyroscope based on field programmable gate array (FPGA) to address the above problems. According to the principle of RLS adaptive filtering, the most direct parallel operation and the traditional serial operation can be implemented. Parallel operation can complete all operations of a filter in one clock cycle, but it will consume a lot of computing resources. Serial operation requires less computing resources, but it takes more computing time to complete a filter. We design a new alternate storage multiply-accumulate pipeline structure based on FPGA to implement RLS adaptive filtering, which ensures the operation accuracy of RLS adaptive filter by double precision floating point operation, reduces the storage space by tactfully designing the alternate storage structure, and saves the FPGA logic resources by realizing the time-division multiplexing of multiply-accumulate structure with multiple switches. The filtering effects of the LMS adaptive filter and the RLS adaptive filter are experimentally compared under static conditions, and the post-filter performance indexes are analyzed using Allan variance. The difference in delay between the LMS adaptive filter and the RLS adaptive filter is studied under dynamic conditions.

The experimental results show that the RLS algorithm shows a superior performance in noise reduction of the fiber optic gyroscope output signal due to its better adaptability to non-smooth signals. In the low frequency band, the noise amplitude after LMS adaptive filtering is comparable to that before filtering, while the RLS adaptive filter produces a certain degree of noise suppression; in the high frequency band, both the LMS adaptive filter and the RLS adaptive filter produce some suppression of the noise (Fig. 6). Compared with the 10th order LMS adaptive filter, the 4th order RLS adaptive filter improves the fiber optic gyroscope accuracy by about 50% (Table 2). For the swing experiments at 5 Hz and 10 Hz, the delays of RLS adaptive filter are 0.24 ms and 0.25 ms, respectively, while the delays of LMS adaptive filter are 0.38 ms and 0.37 ms, respectively. The delay of the RLS adaptive filter mainly comes from the sample hold of the input signal, which is about 1 sample clock cycle in size, while the delay of the LMS filter mainly comes from the 2nd order averaging of the desired signal on the input signal, which is about 1.5 sample clock cycles in size. Under dynamic conditions, the RLS adaptive filter reduces the phase delay by about 30% compared with the LMS adaptive filter (Fig. 7).

Using the alternate storage multiply-accumulate pipeline structure proposed in this paper, when the system clock is 40 MHz, the RLS adaptive filter can complete the calculation within 3 μs, and the highest sampling rate can reach more than 370 kHz, which can meet the demand of real-time noise reduction of most fiber optic gyroscopes. The research in this paper makes RLS adaptive filtering in fiber optic gyroscope noise reduction technology have engineering practical value, effectively suppressing noise in fiber optic gyroscope output signal and improving its control accuracy in high precision stable tracking platform and high maneuverability aircraft.