A LMS adaptive filter design method based on high-precision control system
By setting performance indicators, sampling rate, weight update step and filter order in the LMS adaptive filter, the optimized design realizes high-precision filtering in a high dynamic environment, solving the dynamic and static performance in the existing technology and The problem of insufficient delay characteristics achieves higher filtering accuracy and lower delay.
Patent Information
- Application Number
- CN202011539234.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2020-12-23
- Publication Date
- 2024-12-13
- Estimated Expiration
- 2040-12-23
AI Technical Summary
The existing LMS adaptive filters cannot meet the filtering requirements of high-precision control systems under high dynamic conditions, mainly because they fail to take into account dynamic and static performance requirements and delay characteristics.
By setting performance indicators, sampling rate, weight update step μ, and expected signal d(n) and filter order M, an optimized LMS adaptive filter is designed to ensure high-precision filtering in a high dynamic environment , and reduce delay.
The optimized LMS adaptive filter shows filtering accuracy and delay performance beyond traditional FIR filters in high-dynamic and high-precision control systems, and is suitable for control systems of high-speed and high-motorized aircraft.
Smart Images
Figure CN112803918B_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the field of digital signal processing and relates to a LMS adaptive filter design method based on a high-precision control system. Background Art
[0002] High-speed and highly maneuverable aircraft have outstanding characteristics such as fast time-varying, strong coupling, nonlinearity and uncertainty, which brings severe challenges to the high-precision control of the system. Fiber optic gyroscopes have the advantages of advanced working principles, simple structure, no moving parts and strong impact resistance. They are ideal angular motion sensitive elements for high-precision closed-loop control. However, compared with traditional mechanical gyroscopes, the output signal of fiber optic gyroscopes is easily disturbed by random noise in the optical path and circuit, and the resulting angular rate drift will seriously affect the control accuracy of the system. In order to achieve high-precision control of the system, it is necessary to filter the feedback signal in the control system - the output of the fiber optic gyroscope.
[0003] At present, low-pass filters are widely used in engineering to filter gyro signals. The filter's cutoff frequency, passband and other parameters are mainly determined according to engineering requirements and experience. Since traditional low-pass filters use fixed filter coefficients, it is difficult to meet the precise filtering requirements of non-stationary random signals of fiber optic gyroscopes. Adaptive filters can adjust the filter coefficients at the current moment in real time to adapt to the time-varying statistical characteristics of random signals, and can achieve optimal filtering in a certain sense. Therefore, they are more suitable for filtering the output signals of fiber optic gyroscopes. In the design of adaptive filters, the least mean square (LMS) algorithm uses the method of stochastic gradient descent to minimize the cost function. It has the advantages of low computational complexity, no prior knowledge of statistical data, and unbiased convergence of the mean to the Wiener solution. It has become the most widely used adaptive algorithm. In order to solve various practical problems, relevant scholars have proposed many variable step size LMS algorithms and transform domain LMS algorithms. In response to the problem of fiber optic gyroscope output noise, the literature proposes a denoising method based on the normalized LMS algorithm for the forward linear prediction filter, which improves the initial alignment accuracy of the inertial navigation. The literature proposes a variable step-size sign LMS adaptive denoising method. Experimental results show that this method has certain advantages in comprehensive performance such as filtering stability, filtering accuracy and real-time performance. However, most of the current research on LMS adaptive filters uses static filtering accuracy as the main design indicator without considering the delay characteristics. It is suitable for scenarios with low dynamic requirements such as gyro north finding and initial alignment, but cannot meet the filtering requirements of control systems under high dynamic conditions. Summary of the invention
[0004] The technical problem solved by the present invention is: to overcome the deficiencies of the prior art and propose an LMS adaptive filter design method based on a high-precision control system, taking into account dynamic and static performance requirements, suitable for high-precision large dynamic control systems, and having the advantages of simple structure and convenient engineering implementation.
[0005] The solution of the present invention is:
[0006] A LMS adaptive filter design method based on a high-precision control system comprises the following steps:
[0007] Step 1: Set the performance index of the LMS adaptive filter;
[0008] Step 2: According to the performance index of step 1, set the sampling rate of the LMS adaptive filter;
[0009] Step 3: According to the performance index of step 1, set the weight update step size μ of the LMS adaptive filter;
[0010] Step 4: Optimize the expected signal d(n) of the LMS adaptive filter; set the number of sampling points Δ according to the expected signal d(n);
[0011] Step 5: Set the order M of the LMS adaptive filter; complete the design of the LMS adaptive filter.
[0012] In the above-mentioned LMS adaptive filter design method based on a high-precision control system, in the step 1, the performance indicators of the LMS adaptive filter are: the amplitude change generated for the input signal with an angular frequency below 20 Hz is not greater than 1 dB; and the phase delay generated by the sinusoidal input signal with an angular frequency of 20 Hz is ensured to be no more than 0.2618 rad.
[0013] In the above-mentioned LMS adaptive filter design method based on a high-precision control system, in the step 2, the selected sampling rate of the LMS adaptive filter is 500 Hz.
[0014] In the above-mentioned LMS adaptive filter design method based on a high-precision control system, in step three, the weight update step length μ is set to 0.8.
[0015] In the above-mentioned LMS adaptive filter design method based on a high-precision control system, in step 4, the optimized desired signal d(n) is:
[0016]
[0017] In the formula, Δ is the number of sampling points;
[0018] n is the current time;
[0019] i is the time sequence number;
[0020] u(ni) is the sampling value at the current moment minus the sampling value at time i;
[0021] M is the filter order.
[0022] In the above-mentioned LMS adaptive filter design method based on a high-precision control system, in step 4, the number of sampling points Δ is set to 2.
[0023] In the above-mentioned LMS adaptive filter design method based on high-precision control system, in step five, the order M of the LMS adaptive filter is set to 10.
[0024] The beneficial effects of the present invention compared with the prior art are:
[0025] (1) The optimized LMS adaptive filter of the present invention takes into account both dynamic and static performance requirements, and its filtering accuracy and delay are superior to those of the traditional FIR filter commonly used in engineering, and can meet the filtering requirements of high-dynamic and high-precision control systems;
[0026] (2) In order to realize the optimal design of LMS adaptive filter, the present invention needs to comprehensively consider three parameters: weight update step size μ, expected signal d in unknown environment and filter order M. The design process needs to combine the performance requirements of the actual control system for the filter and the experimental data of fiber optic gyroscope, analyze the influence of relevant parameters on the filtering performance, and realize the design of high dynamic and high precision control of LMS adaptive filter. BRIEF DESCRIPTION OF THE DRAWINGS
[0027] Figure 1 Design flow chart of LMS adaptive filter of the present invention;
[0028] Figure 2 It is a schematic diagram of the structure of the LMS adaptive filter of the present invention;
[0029] Figure 3 Schematic diagram of the transverse filter of the present invention. DETAILED DESCRIPTION
[0030] The present invention will be further described below in conjunction with the embodiments.
[0031] Aiming at the requirements of high-dynamic and high-precision control systems for high-frequency noise elimination and time delay of filters, the present invention designs an optimized LMS adaptive filter after comprehensively considering the influencing factors such as the expected signal, filter order and signal sampling rate. The filter takes into account the requirements of dynamic and static performance, is suitable for high-precision and large dynamic control systems, and has the advantages of simple structure and convenient engineering implementation.
[0032] Principle of LMS adaptive filter
[0033] The structure of the least mean square (LMS) adaptive filter is as follows: Figure 2 As shown in Figure 1, it includes two parts: transverse filter and LMS algorithm. Figure 3 As shown, the Wiener filter is essentially a FIR structure, and its output It is a linear combination of the input signal U(n-1). The LMS algorithm is based on the expected signal d and The error adjusts the weight coefficient vector of the transverse filter to adapt to the time-varying statistical characteristics of the random signal.
[0034] The output of the LMS adaptive filter is the estimated value of the current sample value u(n), The calculation formula is as follows:
[0035]
[0036] In the formula, B T =[b1,b2,b3,…b M ] is a vector of transverse filter coefficients; U(n-1) = [u(n-1), u(n-2), u(n-3), ... u(nM)] T is the filter input vector.
[0037] Define the estimation error f M for:
[0038]
[0039] Taking the minimum mean square error of the estimation error as the optimal statistical criterion, the cost function J is defined as:
[0040]
[0041] Wherein, the change of J over time characterizes the convergence speed and convergence accuracy of the filter; E represents the mathematical expectation of the square of the estimation error.
[0042] The problem that needs to be solved is how to choose the weights of the filter so that the mean square error is minimized, or in other words, the weights of the filter are optimal when J is minimized. opt It can be expressed as
[13] :
[0043] B opt =R -1 r xd
[0044] Where R is the autocorrelation matrix of the input signal, r xdis the cross-correlation vector between the input signal and the expected response. In practical systems, especially when the environment is unknown, it is generally difficult to obtain the statistical characteristics of the filter input signal and the expected response (R and r xd ), therefore, an adaptive LMS algorithm with learning ability for non-stationary environment is used to estimate the weight coefficient vector in real time, gradually approaching the optimal weight value. According to the LMS algorithm, the tap weight is gradually approaching its optimal solution by repeatedly iterating the following formula
[13] :
[0045] B(n+1)=B(n)+μf M (n)U(n-1)
[0046] Where μ is the weight update step size, and the convergence range of μ is:
[0047]
[0048] λ max is the maximum eigenvalue of the autocorrelation matrix R of the input signal.
[0049] Relevant scholars have proposed many optimization algorithms based on the traditional LMS algorithm. Among them, the normalized LMS algorithm adopts a variable update step size, which has the advantages of faster convergence speed and smaller filter delay. Therefore, it is suitable for filtering requirements of high dynamic and high precision control systems. Its weight iteration formula is:
[13] :
[0050]
[0051] In the formula, γ is a very small constant to ensure that the denominator is not zero, and the convergence range of μ is:
[0052] 0<μ≤1
[0053] In order to achieve the optimal design of LMS adaptive filter in view of the performance requirements of high-precision control system for filter, it is necessary to comprehensively consider the influence of various factors on filter performance. The performance of normalized LMS adaptive filter mainly depends on three parameters: weight update step size μ, expected signal d in unknown environment and filter order M. The design process needs to combine the performance requirements of actual control system for filter and fiber optic gyroscope experimental data to analyze the influence of relevant parameters on filter performance.
[0054] LMS adaptive filter design method based on high-precision control system, such as Figure 1 As shown, the specific steps include:
[0055] Step 1: Set the performance indicators of the LMS adaptive filter; 1) The amplitude change generated for the input signal with an angular frequency below 20Hz is no more than 1dB; 2) The phase delay is as small as possible to ensure that the phase delay generated by the sinusoidal input signal with an angular frequency of 20Hz does not exceed 0.2618rad; 3) When the signal changes, the filter can quickly track the signal changes; 4) The noise reduction capability is as strong as possible.
[0056] Step 2: According to the performance indicators of step 1, set the sampling rate of the LMS adaptive filter; most of the current related literature analyzes a specific sampling rate, and the sampling rate is very important for the design of the filter. The filter input signal obtained by high-frequency sampling is usually noisy. By properly smoothing the high-frequency sampling data, the high-frequency noise can be effectively reduced, but it will cause an increase in the filter delay. In order to be suitable for the control system, the sampling rate of the LMS adaptive filter is 500Hz.
[0057] Step 3. According to the performance indicators of step 1, set the weight update step size μ of the LMS adaptive filter; the step size μ affects the convergence speed and filtering accuracy. As μ increases, the convergence speed becomes faster, but the fluctuation amplitude near the optimal solution becomes larger after convergence, and the steady-state accuracy decreases accordingly; if μ is too small, although the filtering accuracy can be guaranteed, the convergence time is greatly increased, and the real-time performance of the system cannot be guaranteed. Therefore, it is necessary to select μ (0<μ≤1) based on the compromise between convergence speed and filtering accuracy. The control system of high-speed and highly maneuverable aircraft requires that the filter can converge quickly under dynamic mutation environment. Compared with the lower magnitude of fluctuation amplitude after convergence, the selection of μ should focus on the convergence speed. In order to make the filter adapt to extreme situations such as dynamic mutation, the weight update step size μ is set to 0.8.
[0058] Step 4: Optimize the expected signal d(n) of the LMS adaptive filter; set the number of sampling points Δ according to the expected signal d(n); in the currently published relevant literature, the expected signal of the adaptive filter usually uses the signal sampling value at the current moment, that is, d(n) = u(n), but the current moment sampling value u(n) contains a large noise, which causes the fluctuation of the expected signal and affects the filtering accuracy. In order to reduce the influence of the instability of the expected signal, the present invention optimizes the selection of the expected signal and selects the average value of the sampling values at the past moment as the expected signal, that is, the optimized expected signal d(n) is:
[0059]
[0060] In the formula, Δ is the number of sampling points;
[0061] n is the current time;
[0062] i is the time sequence number;
[0063] u(ni) is the sampling value at the current moment minus the sampling value at time i;
[0064] M is the filter order.
[0065] The principle of Δ selection is to effectively reduce the noise of the current sampling value, and not affect the true value of the current sampling value or produce too much delay. As Δ increases, the noise intensity of the current signal decreases, but the delay of the filter output signal increases. In addition, as Δ increases, the correlation with the current signal gradually decreases, which will also affect the determination of the true value of the expected signal at the current moment. According to the analysis of experimental data, different Δ are obtained to obtain the corresponding expected signal, and the phase delay caused is shown in Table 1:
[0066] Table 1
[0067]
[0068] Under the premise of ensuring that the phase delay generated by the sinusoidal input signal with an angular frequency of 20 Hz does not exceed 0.2618 rad in step 1, the number of sampling points Δ is set to 2.
[0069] Step 5: Set the order M of the LMS adaptive filter. As the filter order M increases, the filtering accuracy improves, but the filter convergence speed decreases significantly. In view of the demand for short filter delay for high-precision control, the selection of the filter order M must also give priority to the convergence speed. According to the filter indicators, the order M = 10 is selected as a compromise.
[0070] In summary, the optimized selected LMS adaptive filter parameters are shown in the following formula.
[0071]
[0072] Complete the design of LMS adaptive filter.
[0073] Although the present invention has been disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solution of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.
Claims
1. A LMS adaptive filter design method based on high-precision control system, Features: The steps include: Step 1: Set the performance index of the LMS adaptive filter; In the step 1, the performance indicators of the LMS adaptive filter are: the amplitude change generated by the input signal with an angular frequency below 20 Hz is not greater than 1 dB; the phase delay generated by the sinusoidal input signal with an angular frequency of 20 Hz is ensured to be no more than 0.2618 rad; Step 2: According to the performance index of step 1, set the sampling rate of the LMS adaptive filter; Step 3: According to the performance index of step 1, set the weight update step size μ of the LMS adaptive filter; Step 4: Optimize the expected signal d(n) of the LMS adaptive filter; set the number of sampling points Δ according to the expected signal d(n); In step 4, the optimized expected signal d(n) is: In the formula, Δ is the number of sampling points; n is the current time; i is the time sequence number; u(ni) is the sampling value at the current moment minus the sampling value at time i; M is the filter order; Step 5: Set the order M of the LMS adaptive filter; complete the design of the LMS adaptive filter.
2. According to claim 1, a LMS adaptive filter design method based on a high-precision control system, Features: In the step 2, the sampling rate of the LMS adaptive filter is 500 Hz.
3. The LMS adaptive filter design method based on a high-precision control system according to claim 2, Features: In step three, the weight update step size μ is set to 0.
8.
4. The LMS adaptive filter design method based on a high-precision control system according to claim 3, Features: In step 4, the number of sampling points Δ is set to 2.
5. The LMS adaptive filter design method based on a high-precision control system according to claim 4, Features: In the step five, the order M of the LMS adaptive filter is set to 10.