CN107664499B - On-line noise reduction method for accelerometer of ship strapdown inertial navigation system - Google Patents
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Abstract
The invention discloses an accelerometer online noise reduction method of a ship strapdown inertial navigation system, and belongs to the technical field of accelerometer noise reduction. The invention aims to realize the on-line noise reduction of an accelerometer of a ship strapdown inertial navigation system, which comprises the steps of firstly modeling useful signals of the accelerometer, then reserving signals with strong correlation with a model in the signals of the accelerometer through an adaptive filter, thereby realizing the on-line noise reduction of the signals of the accelerometer, and finally analyzing and providing a parameter selection method. The method solves the problem of high noise of the accelerometer of the ship strapdown inertial navigation system, realizes online noise reduction of the accelerometer of the ship strapdown inertial navigation system, improves the accuracy of the accelerometer of the ship strapdown inertial navigation system, has the advantages of good noise reduction effect, high real-time performance, moderate calculation amount and the like, and has wide development prospect.
Description
Technical Field
The invention belongs to the technical field of accelerometer noise reduction, and particularly relates to an accelerometer online noise reduction method of a ship strapdown inertial navigation system.
Background
The inertial measurement unit is widely used in an inertial navigation system, wherein zero offset stability, constant value error, scale coefficient error, non-linear error and random noise of the inertial measurement unit play a decisive role in the alignment accuracy and navigation solution accuracy of the inertial navigation system.
The inertial navigation does not depend on satellite signals, and the positioning function can still be realized in places without the satellite signals. However, the error becomes larger and larger with the lapse of time. The strapdown inertial navigation system is an autonomous navigation system, does not depend on any external signal or send any signal to the outside, and has great advantages in certain fields compared with other navigation systems.
The accelerometer is an important sensitive element of the strapdown inertial navigation system, is an indispensable part of the strapdown inertial navigation system, can measure the speed, the acceleration and other motion information of a carrier, outputs a signal proportional to the motion acceleration of a carrier, and has direct influence on the positioning precision of the strapdown inertial navigation system, so the accelerometer and the gyroscope are the most critical components of the strapdown inertial navigation system, and the precision requirement is quite high.
The environment of the ship strapdown inertial navigation system is complex, such as the conditions of long system working time, large ship body vibration, high environment humidity, complex interference condition and the like, and the output noise of the accelerometer of the ship strapdown inertial navigation system is large, so that certain influence is caused on the working performance of the strapdown inertial navigation system. Therefore, it is very important to improve the measurement accuracy and reliability of an inertial measurement unit such as an accelerometer, and an effective method for improving the measurement accuracy of the accelerometer is to reduce the measurement noise of the accelerometer and improve the signal-to-noise ratio.
In the early days, the simplest method for reducing the noise of the inertial measurement unit mainly focuses on the design of a low-pass filter, but the low-pass filter only has a good filtering effect on the noise with a fixed bandwidth, so that the method can only effectively process specific information under a specific environment, and is not suitable for any maneuvering environment and the problem of time delay of the low-pass filter is serious.
With the improvement of computer performance, the discrete wavelet transform technology is also widely applied to the noise reduction processing of the inertial measurement unit, the application of the method in a static environment has a good effect, but the method fails in a dynamic environment and time delay is introduced into the method, so that the information tracking capability is reduced.
Meanwhile, scholars in academia strive for effective data online noise reduction methods. Document application of digital filter in micromechanical gyroscope systems (sensors and microsystems, 2003,22(9):56-57) the use of conventional digital filters enables to filter out high frequency noise components in signals, whereas conventional digital filters have disadvantages and limitations for non-stationary and narrow bandwidth signals.
The document "real-time filtering technique of random noise of fiber-optic gyroscope" (data acquisition and processing, 2009,24(5):671-675) proposes an online noise reduction technique based on kalman filtering, which can effectively suppress white noise or colored noise, but because the filtering limitation condition is harsh, the prior statistical property of the data needs to be accurately known, so that it has certain limitations.
The document "a real-time wavelet denoising algorithm" (academic report of instruments, 2004,25(6): 781-.
Therefore, aiming at the problems, the invention provides an accelerometer online noise reduction method of a ship strapdown inertial navigation system, which is a method for realizing online noise reduction, analysis and parameter extraction of accelerometer signals by modeling useful signals of an accelerometer and using an adaptive filter to reserve signals with strong correlation with the model in the accelerometer signals.
Disclosure of Invention
The invention aims to provide an accelerometer online noise reduction method of a ship strapdown inertial navigation system, which can solve the problem of high noise of an accelerometer of the ship strapdown inertial navigation system, realize online noise reduction of an accelerometer in the ship strapdown inertial navigation system and greatly improve the information accuracy of the accelerometer.
The purpose of the invention is realized as follows:
the invention discloses an accelerometer online noise reduction method of a ship strapdown inertial navigation system, which comprises the following specific implementation steps of:
(1) establishing a correlation model according to the characteristics of ship line motion, inputting the established model as an input vector into an adaptive filter, taking the output of an accelerometer as an expected signal of the adaptive filter, continuously correcting a coefficient vector of the adaptive filter through a steepest descent algorithm, and taking the product of the output coefficient vector and the input vector of the adaptive filter as a result of noise reduction of the accelerometer;
(2) determining the output frequency of an accelerometer of a ship strapdown inertial navigation system, and setting the dimension of an input vector of an adaptive noise reducer and a convergence factor of a steepest descent algorithm;
(3) inputting output data of an accelerometer of a ship strapdown inertial navigation system into an adaptive noise reducer in real time;
(4) and outputting the result of the adaptive noise reducer in real time as the output of the noise reduction of the accelerometer.
For an accelerometer online noise reduction method of a ship strapdown inertial navigation system, the specific implementation steps of the step (1) comprise:
(1.1) integrating forced movement and autonomous navigation of a ship and determining the frequency range of useful signals output by an accelerometer of a ship strapdown inertial navigation system;
(1.2) modeling useful signals, superposing sine and cosine terms and constant values of some frequency points in the frequency band, taking the sine and cosine terms and the constant values as input vectors x (k) of an adaptive filter, taking actual accelerometer signals as expected signals y (k) of the adaptive filter, and carrying out noise reduction through a noise reduction algorithm of the adaptive filter;
(1.3) continuously correcting the coefficient vector w (k) through a steepest descent algorithm, and continuously enabling the product y' (k) of the coefficient vector and the input vector to approach the expected signal y (k);
(1.4) the product y' (k) of the coefficient vector and the input vector is output after noise reduction.
For the on-line noise reduction method for the accelerometer of the ship strapdown inertial navigation system, the updating process of the noise reduction algorithm of the adaptive filter in the step (1) is as follows:
e(k)＝y(k)-w(k)Tx(k)
w(k+1)＝w(k)+2μe(k)x(k)
y'(k)＝wT(k+1)x(k)
wherein x (k) ═ x1(k),x2(k)…x2M(k)]TIs an input vector of the algorithm, and has dimension of 2M, f1～fM-1Is an equidistant frequency point with a movement frequency range of 0.05 Hz-0.3 Hz, k is the updating frequency of the algorithm, T is the time interval of the data output by the accelerometer, y (k) is the signal output by the accelerometer, and w (k) is [ w [, ]1(k),w2(k)…w2M(k)]TAnd [ mu ] is a convergence factor of the updating process, and y' (k) is the output of the adaptive noise reducer, namely the signal after the noise reduction of the accelerometer.
For the on-line noise reduction method for the accelerometer of the ship strapdown inertial navigation system, the input vector and the product y' (k) of the coefficient vector and the input vector in the step (1) only contain the characteristics of the useful signal, a model related to the useful signal is established, a part related to the model in the accelerometer signal is reserved by using a steepest descent algorithm, and a part with weak correlation is removed.
For the on-line noise reduction method for the accelerometer of the ship strapdown inertial navigation system, the stability condition of the convergence factor mu of the steepest descent algorithm in the step (2) is as follows:
where M is the trace of the autocorrelation matrix of the input signal vector x (k).
For the on-line noise reduction method for the accelerometer of the ship strapdown inertial navigation system, the noise reduction algorithm directly influences the noise reduction effect through the selected parameters, and the parameters in the algorithm are determined by combining the actual conditions, so that the optimal noise reduction effect is obtained.
The invention has the beneficial effects that:
the on-line noise reduction method for the accelerometer of the ship strapdown inertial navigation system can solve the problem that the accelerometer of the ship strapdown inertial navigation system is high in noise, achieves on-line noise reduction of the accelerometer of the ship strapdown inertial navigation system, improves accuracy of the accelerometer of the ship strapdown inertial navigation system, and has the advantages of being good in noise reduction effect, high in real-time performance, moderate in calculated amount and the like, and the development prospect is wide.
Drawings
FIG. 1 is a schematic view of an on-line noise reduction overall process of an accelerometer of a marine strapdown inertial navigation system according to the present invention;
FIG. 2 is a schematic diagram illustrating an on-line noise reduction principle of an accelerometer of a marine strapdown inertial navigation system according to the present invention;
FIG. 3 is a schematic flow chart of an on-line noise reduction algorithm of an accelerometer of the marine strapdown inertial navigation system according to the present invention;
FIG. 4 is a schematic diagram showing comparison of simulation data and real values before and after noise reduction using the present invention;
FIG. 5 is a schematic diagram showing comparison between the real values of the sea test data before denoising and after denoising by using the present invention;
FIG. 6 is a schematic diagram of a frequency spectrum before denoising sea test data in the present invention;
FIG. 7 is a schematic diagram of a spectrum of sea test data after noise reduction by the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
With reference to fig. 1, the invention discloses an accelerometer online noise reduction method of a ship strapdown inertial navigation system, which specifically comprises the following implementation steps:
(1) establishing a correlation model according to the characteristics of ship line motion, inputting the established model as an input vector into an adaptive filter, taking the output of an accelerometer as an expected signal of the adaptive filter, continuously correcting a coefficient vector of the adaptive filter through a steepest descent algorithm, and taking the product of the output coefficient vector and the input vector of the adaptive filter as a result of noise reduction of the accelerometer;
(2) determining the output frequency of an accelerometer of a ship strapdown inertial navigation system, and setting the dimension of an input vector of an adaptive noise reducer and a convergence factor of a steepest descent algorithm;
(3) inputting output data of an accelerometer of a ship strapdown inertial navigation system into an adaptive noise reducer in real time;
(4) and outputting the result of the adaptive noise reducer in real time as the output of the noise reduction of the accelerometer.
For an accelerometer online noise reduction method of a ship strapdown inertial navigation system, the specific implementation steps of the step (1) comprise:
(1.1) integrating forced movement and autonomous navigation of a ship and determining the frequency range of useful signals output by an accelerometer of a ship strapdown inertial navigation system;
(1.2) modeling useful signals, superposing sine and cosine terms and constant values of some frequency points in the frequency band, taking the sine and cosine terms and the constant values as input vectors x (k) of an adaptive filter, taking actual accelerometer signals as expected signals y (k) of the adaptive filter, and carrying out noise reduction through a noise reduction algorithm of the adaptive filter;
(1.3) continuously correcting the coefficient vector w (k) through a steepest descent algorithm, and continuously enabling the product y' (k) of the coefficient vector and the input vector to approach the expected signal y (k);
(1.4) the product y' (k) of the coefficient vector and the input vector is output after noise reduction.
The invention discloses a specific embodiment of an accelerometer online noise reduction method of a ship strapdown inertial navigation system, which comprises the following steps:
(1) under the general condition, under the disturbance of a sea wave environment, the three shafts of the ship move in a forced line, and the acceleration frequency band of the movement is 0.05 Hz-0.3 Hz; because of the large fluid resistance, the speed change of the ship in the autonomous sailing process is slow, so the acceleration of the ship course axis is low frequency quantity or constant, and the acceleration of other axes is zero.
With reference to fig. 2, by integrating forced motion and autonomous navigation of a ship, the frequency of a useful signal output by an accelerometer of a strapdown inertial navigation system for a ship can be considered to be within 0.05Hz to 0.3Hz, the useful signal is modeled as superposition of sine and cosine terms and constant values of some frequency points in the frequency band, the sine and cosine terms and the constant values are used as input vectors x (k) of an adaptive filter, an actual accelerometer signal is used as an expected signal y (k) of the adaptive filter, a coefficient vector w (k) is continuously corrected by a steepest descent algorithm, so that a product y '(k) of the coefficient vector and the input vector approaches to the expected signal, and the product y' (k) of the coefficient vector and the input vector only contains the useful signal part because the input vector only contains the characteristics of the useful signal; from another point of view, the idea of the invention is to establish a model related to a useful signal, reserve a part related to the model in an accelerometer signal by using a steepest descent algorithm, remove a part with weaker correlation, and finally take the product y' (k) of a coefficient vector and an input vector as an output after noise reduction.
The specific contents of the noise reduction algorithm are as follows:
equally dividing frequency points of 0.05 Hz-0.3 Hz of the frequency band of the useful signal, wherein the number of the frequency points is M-1, and the frequency point is f1～fM-1(ii) a To facilitate the selection and analysis of the analysis parameters, the value of the constant term in the input vector is 0.7071, the number of the constant terms is 2, and the dimension of the input vector x (k) of the adaptive filter is 2M, which is in the following form
x(k)＝[x1(k),x2(k)…x2M(k)]T
Wherein
Where k is the number of algorithm updates and T is the time interval for the accelerometer to output data. The coefficient vector is of the form: w (k) ═ w1(k),w2(k)…w2M(k)]TThe error in the updating process is as follows:
e(k)＝y(k)-w(k)Tx(k)
wherein y (k) is the signal output by the accelerometer, and the process of updating the coefficient vector by using the steepest descent algorithm as the expected signal of the adaptive filter is as follows:
in the formula, mu is a convergence factor of the updating process, and the convergence of the updating process can be ensured only by reasonably selecting the convergence factor mu;
is an error gradient vector associated with the coefficient vector w (k), as known from the error expression,
can be obtained by substituting the above formula
w(k+1)＝w(k)+2μe(k)x(k)
And taking the product of the updated coefficient vector and the input vector as the output of the adaptive filter, namely the output signal y' (k) of the accelerometer after noise reduction.
With reference to fig. 3, the update process of the noise reduction algorithm is as follows:
e(k)＝y(k)-w(k)Tx(k)
w(k+1)＝w(k)+2μe(k)x(k)
y'(k)＝wT(k+1)x(k)
as can be seen from the above updating process, the coefficient vector w (k) is updated every time, and the frequency point frDoes not participate in updating; the parameters that need to be reasonably selected in the algorithm are M, mu and T.
(2) In the invention, in order to ensure that the algorithm can be converged, the range of the convergence factor needs to be obtained. In the process of updating by using the steepest descent method, the stability condition of the convergence factor is as follows:
where R is the autocorrelation matrix of the input signal vector x (k) and tr [ R ] represents the traces of matrix R. The autocorrelation matrix R is:
is obtained according to the form of the input signal vector x (k)
Then the autocorrelation matrix R can be reduced to
The above equation indicates that the autocorrelation matrix R of the input vector is fixed, and tr [ R ]]When M is the maximum value of the convergence factor in the steepest descent method, the value of the convergence factor is within the range
This range is only a precondition for the stability of the algorithm and does not ensure the optimal performance of the algorithm.
(3) The noise reduction effect of the invention is closely related to the selection of parameters in the algorithm, and in order to obtain a better noise reduction effect, the parameters in the algorithm need to be selected according to actual conditions.
The data output by the accelerometer is y (k), and the variance of the noise signal contained in y (k) is
The useful data to be extracted is yt(k) Then, then
y(k)＝yt(k)+n(k)
If in the adaptive filter
Then call woIs the optimal coefficient vector. However, in the actual updating process, w (k) and woError in comparison, is recorded as Δ w (k) ═ w (k) — woBy analysis and derivation of the formula, the output mean square error caused by Δ w (k) can be reduced to
Δ ξ (k) can be considered as the noise variance of the denoised output y' (k). To suppress the effects of noise, where the above equation M μ is typically less than 0.1, Δ ξ (k) reduces to:
it can be seen that
The value of (d) is the multiple of the noise attenuation and is denoted as a.
In practical cases, the optimal coefficient vector woIs not fixed, so that the steepest descent algorithm needs to be analyzed for the optimal coefficient vector wo(k) The tracking performance of (2). Due to the optimal coefficient vector wo(k) Is relatively large, so a first order Markov process is used to pair wo(k) Modeling, described as
wo(k+1)＝λwwo(k)+nw(k)
Can be thought of as a vector nw(k) Is a white noise process vector with the optimal coefficient vector change, the ith element is zero mean and the variance is
The white noise process of (2); generally the optimum coefficient wo(k) The rate of change is slower, the factor λwTending to 1, i.e. the change of the optimal coefficient vector is considered to be from the noise vector n of the optimal coefficientw(k) In that respect By analysis and formula derivation, the noise vector n of the optimal coefficientw(k) Induced output lag mean square errorIs composed of
In the formula
Noise vector n for optimal coefficientsw(k) Mean of variance of medium elements, i.e.
Due to the fact that
Is not easy to obtain, so that the qualitative analysis is carried out on the optimal coefficient vector, the sampling time is smaller when the output frequency of the accelerometer of the strapdown inertial navigation system is higher, and the variation of the optimal coefficient vector in each updating process is smaller, namely
The smaller the value of (c); it can be seen from the above formula that the error of the output lag is proportional to the factor M, and therefore, the noise attenuation factor a and the factor M need to be reasonably selected.
In order to effectively model the input vector in a useful signal frequency band, the value of M cannot be too small; the larger the value of M is, the larger the calculation amount is, and the larger the output lag error is caused, so that the value of M cannot be too large; the value range of M is 10-20. If the value of the multiple A of noise attenuation is too small, the noise reduction effect is not obvious; if the value of the noise attenuation factor is too large, the convergence time is long, the output lag error caused by the convergence time is large, and the proper value range of the multiple A of the noise attenuation factor is 10-20. The results of a plurality of experiments show that: in the case where the accelerometer output frequency of the strapdown inertial navigation system is greater than 100Hz and the parameters M and a are within the above ranges, there is substantially no problem of output lag.
The invention discloses a simulation embodiment of an accelerometer online noise reduction method of a ship strapdown inertial navigation system, which comprises the following steps:
in order to enable simulation data to be close to actual data output by an accelerometer of a marine strapdown inertial navigation system, the simulation data are obtained according to a P-M sea wave spectrum, the sampling frequency is 200Hz, the data frequency band is 0.08 Hz-0.3 Hz, the three-average wave height is 2M, and white noise with the variance of 0.01 is added into the data; in the noise reduction algorithm, the modeling frequency range is also 0.08 Hz-0.3 Hz, the parameter M is 10, the convergence factor mu is 0.01, the noise attenuation multiple A is 10, the coefficient vector and the input vector are zero vectors, and other initial variables are zero. With reference to fig. 4, a comparison is made between the curves of the noise reduction and the true value before the noise reduction of the simulation data of the accelerometer, after the noise reduction of the accelerometer is performed by using the method of the present invention, it can be seen that the noise reduction effect is obvious, and the output does not have the problem of hysteresis, and through the analysis of the data, the variance of the noise of the data after the noise reduction is 0.0012, which is basically consistent with the theoretical value of 0.001.
The embodiment of sea test data of the online noise reduction method of the accelerometer of the ship strapdown inertial navigation system disclosed by the invention comprises the following steps:
the course axis accelerometer output of a certain type of marine strapdown inertial navigation system in an offshore test is used as original data, the output frequency of the accelerometer is 100Hz under a low sea condition in a test environment, the modeling frequency range in a noise reduction algorithm is 0.08 Hz-0.3 Hz, a parameter M is 10, a convergence factor mu is 0.005, a coefficient vector and an input vector are zero vectors, and other initial variables are zero. The original data are subjected to offline noise reduction to obtain more accurate accelerometer data which are used as true values, and the curves of the original sea test data, the sea test data subjected to noise reduction by using the method and the true values are compared with each other by combining the graph shown in FIG. 5, so that the noise reduction effect is good, and the output does not have the problem of lag.
In order to better analyze data, the frequency spectrum of the original data is compared with the frequency spectrum of the data subjected to noise reduction by using the method disclosed by the invention in combination with the images in the images.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (5)
1. An accelerometer online noise reduction method of a ship strapdown inertial navigation system is characterized by comprising the following specific implementation steps:
(1) establishing a correlation model according to the characteristics of ship line motion, inputting the established model as an input vector into an adaptive filter, taking the output of an accelerometer as an expected signal of the adaptive filter, continuously correcting a coefficient vector of the adaptive filter through a steepest descent algorithm, and taking the product of the output coefficient vector and the input vector of the adaptive filter as a result of noise reduction of the accelerometer;
(2) determining the output frequency of an accelerometer of a ship strapdown inertial navigation system, and setting the dimension of an input vector of an adaptive noise reducer and a convergence factor of a steepest descent algorithm;
(3) inputting output data of an accelerometer of a ship strapdown inertial navigation system into an adaptive noise reducer in real time;
(4) outputting the result of the adaptive noise reducer in real time as the output of the accelerometer noise reduction;
the concrete implementation steps of the step (1) comprise:
(1.1) integrating forced movement and autonomous navigation of a ship and determining the frequency range of useful signals output by an accelerometer of a ship strapdown inertial navigation system;
(1.2) modeling useful signals, superposing sine and cosine terms and constant values of certain frequency points in the frequency range of the useful signals, taking the sine and cosine terms and the constant values as input vectors x (k) of a self-adaptive filter, taking actual accelerometer signals as expected signals y (k) of the self-adaptive filter, and denoising through a denoising algorithm of the self-adaptive filter;
(1.3) continuously correcting the coefficient vector w (k) through a steepest descent algorithm, and continuously enabling the product y' (k) of the coefficient vector and the input vector to approach the expected signal y (k);
(1.4) the product y' (k) of the coefficient vector and the input vector is output after noise reduction.
2. The on-line noise reduction method for the accelerometer of the ship strapdown inertial navigation system according to claim 1, wherein the updating process of the noise reduction algorithm of the adaptive filter in the step (1) is as follows:
e(k)＝y(k)-w(k)Tx(k)
w(k+1)＝w(k)+2μe(k)x(k)
y'(k)＝wT(k+1)x(k)
wherein x (k) ═ x1(k),x2(k)…x2M(k)]TIs an input vector of the algorithm, and has dimension of 2M, f1～fM-1Is an equidistant frequency point with a movement frequency range of 0.05 Hz-0.3 Hz, k is the updating frequency of the algorithm, T is the time interval of the data output by the accelerometer, y (k) is the signal output by the accelerometer, and w (k) is [ w [, ]1(k),w2(k)…w2M(k)]TAnd [ mu ] is a convergence factor of the updating process, and y' (k) is the output of the adaptive noise reducer, namely the signal after the noise reduction of the accelerometer.
3. The on-line noise reduction method for the accelerometer of the ship strapdown inertial navigation system according to claim 1, wherein the input vector and the product y' (k) of the coefficient vector and the input vector in step (1) only contain the features of the useful signal, a model related to the useful signal is established, a part related to the model in the accelerometer signal is reserved by using a steepest descent algorithm, and a part with weak correlation is removed.
4. The on-line noise reduction method for the accelerometer of the ship strapdown inertial navigation system according to claim 1, wherein the stability condition of the convergence factor μ of the steepest descent algorithm in the step (2) is as follows:
where M is the trace of the autocorrelation matrix of the input signal vector x (k).
5. The on-line noise reduction method for the accelerometer of the ship strapdown inertial navigation system according to claim 1, wherein: the noise reduction algorithm directly influences the noise reduction effect through the selected parameters, and the parameters in the algorithm are determined by combining with the actual situation, so that the optimal noise reduction effect is obtained.
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