CN117555036A - Inertial stabilized platform aviation gravity signal extraction method and device - Google Patents
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Abstract
The invention discloses an inertial stabilized platform aviation gravity signal extraction method and device, and belongs to the technical field of aviation gravity exploration. Wherein the method comprises the following steps: acquiring aviation gravity measurement data of a target area; the aviation gravity measurement data are obtained by measuring the target area through an inertial stabilization platform type gravity meter; inputting the aviation gravity measurement data into a Kalman filter based on a Markov process, and extracting an aviation gravity signal. According to the inertial stabilized platform aviation gravity signal extraction method and device disclosed by the invention, the Kalman filter based on the Markov process is used for processing aviation gravity measurement data of a target area, so that noise can be filtered more effectively, gravity anomaly can be extracted from the aviation gravity measurement data containing strong noise more accurately, useful signal frequency bands are reserved more, the reservation of noise frequency bands is reduced, and the effect of extracting aviation gravity signals can be improved.
Description
Technical Field
The invention relates to the technical field of aviation gravity exploration, in particular to an inertial stabilized platform aviation gravity signal extraction method and device.
Background
Aero gravity measurement is the determination of useful signals on the flight trajectory of an aircraft, aero gravity signals (also known as "gravity anomaly signals" or "gravity anomalies"), using a gravity meter and a global navigation satellite system (Global Navigation Satellite System, GNSS). Gravity data in a larger area can be efficiently and quickly acquired through aviation gravity measurement. However, in the actual dynamic measurement process of the aviation gravity, the measurement result directly output by the gravity meter comprises the motion acceleration and random vibration acceleration of carriers such as an airplane, so that the signal-to-noise ratio of the original signal of the aviation gravity is extremely low and is about 10 -5 -10 -6 The difficulty in extracting the gravity anomaly signal is high.
The gravity anomaly field is a space position function, and the main intensity is concentrated in a low-frequency part, so that in the existing aviation gravity data processing, a frequency domain rate filter is adopted to carry out filtering processing on aviation gravity measurement, and aviation gravity signals are extracted. However, this method has a disadvantage in that only one approximate cutoff frequency can be set according to the experience of the data processor, and the setting of the cutoff frequency does not necessarily meet the actual situation.
Therefore, the existing aviation gravity signal extraction method is imperfect, and the loss of useful signal frequency bands or the reservation of excessive noise frequency bands are easy to cause.
Disclosure of Invention
The invention aims to provide an inertial stabilized platform aviation gravity signal extraction method and device, which can improve the aviation gravity signal extraction effect.
In order to achieve the above purpose, the invention provides an inertial stabilized platform aviation gravity signal extraction method, comprising the following steps:
acquiring aviation gravity measurement data of a target area; the aviation gravity measurement data are obtained by measuring the target area through an inertial stabilization platform type gravity meter;
inputting the aviation gravity measurement data into a Kalman filter based on a Markov process, and extracting an aviation gravity signal.
In one embodiment of the present invention, the inputting the aero gravity measurement data into a kalman filter based on a markov process, extracting an aero gravity signal, includes:
modeling the gravity anomaly of the target area along a flight path according to the aviation gravity measurement data based on a Markov process and an aviation gravity measurement principle, and obtaining a state equation and a measurement equation for estimating the gravity anomaly;
and extracting the aviation gravity signal based on the state equation and the measurement equation of the optimal Kalman smoother.
In one embodiment of the present invention, the Markov process is a third order Gaussian-Markov process.
In one embodiment of the present invention, the method further comprises:
and calculating and extracting the cut-off frequency of the aviation gravity signal based on the transfer function of the optimal Kalman smoother.
In an embodiment of the present invention, before calculating the cutoff frequency for extracting the aviation gravity signal based on the transfer function of the optimal kalman smoother, the method further includes:
and acquiring a transfer function of the optimal Kalman smoother.
In an embodiment of the present invention, the acquiring the transfer function of the kalman filter process includes:
acquiring a transfer function of a forward filtering channel based on forward Kalman filtering, and acquiring a transfer function of a backward filtering channel based on backward Kalman filtering;
and acquiring the transfer function based on the transfer function of the forward filtering channel and the transfer function of the backward filtering channel.
In one embodiment of the present invention, an inertial stabilization platform airborne gravity signal extraction device comprises:
the acquisition module is used for acquiring aviation gravity measurement data of the target area; the aviation gravity measurement data are obtained by measuring the target area through an inertial stabilization platform type gravity meter;
And the extraction module is used for inputting the aviation gravity measurement data into a Kalman filter based on a Markov process to acquire an aviation gravity signal.
In one embodiment of the invention, an electronic device includes a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor implements the steps of the inertial stabilized platform aero gravity signal extraction method as described in any one of the above when executing the program.
In one embodiment of the invention, a non-transitory computer readable storage medium has stored thereon a computer program which, when executed by a processor, implements the steps of the inertial stabilized platform aero gravity signal extraction method as described in any one of the above.
In an embodiment of the invention, a computer program product comprises a computer program which, when executed by a processor, implements the steps of the inertial stabilized platform aero gravity signal extraction method as described in any one of the above.
Compared with the prior art, the method and the device for extracting the aviation gravity signal of the inertial stabilization platform have the beneficial effects that the Kalman filter based on the Markov process is used for processing the aviation gravity measurement data of the target area, so that noise can be filtered more effectively, gravity anomalies can be extracted from the aviation gravity measurement data containing strong noise more accurately, useful signal frequency bands are reserved more, the reservation of the noise frequency bands is reduced, and the effect of extracting the aviation gravity signal can be greatly improved.
Drawings
FIG. 1 is a flow diagram of a method for inertial stabilized platform aero gravity signal extraction in accordance with an embodiment of the present invention;
FIG. 2 is a schematic diagram of power spectral density of a gravity anomaly model in an inertial stabilized platform aerial gravity signal extraction method according to an embodiment of the present invention;
FIG. 3 is a graph showing the comparison of the effects of the inertial stabilized platform aero gravity signal extraction method according to one embodiment of the present invention;
FIG. 4 is a second comparison of the effects of the inertial stabilized platform aero gravity signal extraction method according to an embodiment of the present invention;
FIG. 5 is a schematic structural view of an inertial stabilization platform airborne gravity signal extraction device according to an embodiment of the invention;
fig. 6 is a schematic structural view of an electronic device according to an embodiment of the present invention.
Detailed Description
The following detailed description of embodiments of the invention is, therefore, to be taken in conjunction with the accompanying drawings, and it is to be understood that the scope of the invention is not limited to the specific embodiments.
Throughout the specification and claims, unless explicitly stated otherwise, the term "comprise" or variations thereof such as "comprises" or "comprising", etc. will be understood to include the stated element or component without excluding other elements or components.
As shown in fig. 1 to 6, the inertial stabilization platform aero gravity signal extraction method and apparatus according to the preferred embodiment of the present invention may be implemented as follows.
Fig. 1 is a schematic flow chart of an inertial stabilized platform aero gravity signal extraction method according to an embodiment of the invention. As shown in fig. 1, the method may include the steps of: step 101 and step 102.
Step 101, acquiring aviation gravity measurement data of a target area; the aeronautical gravity measurement data are obtained by measuring the target area through an inertial stabilization platform type gravity meter.
In particular, the airborne gravity measurement data may include data obtained by performing airborne gravity measurement on a target area by an inertial stabilized platform type gravity meter and a global navigation satellite system mounted on a flight carrier such as an airplane. The target area may be any area, and the scope, type, etc. of the target area are not specifically limited in the embodiment of the present invention.
An inertial stabilization platform type gravity meter is an aviation gravity measuring instrument based on a triaxial inertial stabilization platform measurement principle.
After airborne gravity measurement of the target area by the airborne gravity measurement system, airborne gravity measurement data of the target area is obtained.
And 102, inputting the aviation gravity measurement data into a Kalman filter based on a Markov process, and extracting an aviation gravity signal.
Specifically, the process of data acquisition and gravity anomaly signal extraction in the flight measurement of an aircraft can be regarded as a time function, so that the gravity anomaly signal can be solved by using Kalman filtering. For a dynamic measurement system, the Kalman filtering method has stronger robustness, but has the difficulty of constructing a state equation. Although the state equation model can be established according to the physical stress state of the gravity meter in measurement, the state equation during measurement cannot be completely and truly described through a simple mechanical model because the stress state of the aircraft in the flight process is complex, so that it is very important to find a suitable construction method of the state equation. Since kalman filtering is time domain filtering, how to assign spatial significance to signals extracted via this method is also an important point in the current discussion.
In the embodiment of the invention, the state equation is established directly according to the state of gravity anomaly. The Kalman filter based on the Markov process is built in advance, and a state equation and the Kalman filter based on the Markov process can be built in, so that after the aviation gravity measurement data of the target area is input into the Kalman filter based on the Markov process, the Kalman filter can be carried out on the power spectral density described by the state equation, and the aviation gravity signal can be extracted.
Kalman filtering is a method that relies on a dynamic model of the system. Before Kalman filtering, firstly, proper system states are required to be selected, and a system state equation and a measurement equation in a time domain form are given, wherein the system state equation and the measurement equation are shown in formulas (1) and (2) respectively:
X k ＝Φ k,k-1 X k-1 +B k-1 u k-1 +Γ k-1 W k-1 。 (1)
Z k ＝H k X k +V k 。 (2)
wherein X is k Is the state of the system; phi k,k-1 A state one-step transition matrix; b (B) k-1 Is an input coupling matrix; u (u) k-1 Is a control input item; Γ -shaped structure k-1 Driving a matrix for system noise; w (W) k Is a systematic noise sequence with variance Q k ；Z k Is a measurement input; h k To measure the sensitivity matrix, V k To measure noise sequences, the variance is R k 。
Wherein the system noise sequence W k The requirements are as follows:
E[W k ]＝0。 (3)
measuring noise sequence V k The requirements are as follows:
E[V k ]＝0。 (5)
at the same time W k And V k The mutually uncorrelated conditions have to be met:
and the system noise and the measurement noise at any time and the initial value of the system all need to meet the uncorrelated conditions, namely:
let the variance Q of system noise k For non-negative fixed array, the variance R of noise is measured k For positive array, under the condition that the conditions are all satisfied, the state initial value and the predicted mean square error initial value P of the system are given 0 The state estimation value of each moment can be calculated through iteration according to the following flow:
and (3) carrying out one-step prediction of the state:
and (3) performing state estimation:
Calculating Kalman filtering gain:
calculating one-step predictive mean square error
Estimating mean square error
In some embodiments, step 102, inputting the aerial gravity measurement data into a markov process-based kalman filter, extracting the aerial gravity signal may include: based on a Markov process and an aviation gravity measurement principle, modeling the gravity anomaly of the target area along a flight path according to aviation gravity measurement data, and obtaining a state equation and a measurement equation for estimating the gravity anomaly.
In particular, a Markov model may be employed within the target region to describe the distribution of gravity anomalies along the path under assumption of homogeneous, isotropic conditions. This provides a basis for estimating gravity anomalies from strongly noisy airborne gravity measurement data using a time-domain optimal smoothing method.
In some embodiments, the markov process described above is a third order gaussian-markov process.
Markov processes refer to a class of stochastic processes that satisfy markov characteristics. Markov characteristics describe that a random dynamic system has a conditional probability density at the future time of the dynamic process equal to the conditional probability density given only the system state at the present time with a probability of 1 given all past and present time states. It is defined as:
Random process { X ] t t.epsilon.T }, if for any T 1 ＜t 2 K＜t n ＜t,x i I is more than or equal to 1 and less than or equal to nThe method comprises the following steps:
this process is called Markov process (Markov process).
The markov process may be strictly represented by an n-order continuous-time linear autoregressive model (Autoregressive Model), abbreviated as AR model, as shown in equation (15):
x (n) (t)+a 1 x (n-1) (t)+···+a n x(t)＝w(t)。 (15)
in (15), x (n) N-th derivative of x; a, a i (i=1, 2,3 … n) is a constant coefficient; w (t) is white noise, and its covariance is defined as:
where N is the variance of the white noise and δ is the unit impact function.
The gravity anomaly of the target region can be modeled along the track using a third-order Gaussian-Markov process, and its covariance function can be expressed as:
wherein, sigma is the standard deviation of gravity anomaly; d is the distance along the track; the coefficient β is constant.
Depending on the velocity v of the carrier (e.g. aircraft, etc.), d can be converted into time τ, resulting in:
the AR model corresponding to equation (18) is:
wherein, the covariance function of the white noise w (t) is assumed to be:
its power spectrum is
Wherein t is 1 And t 2 Representing two moments, t 1 Before, t 2 After which it is.
The AR model represented by equation (19) is a third-order gaussian-markov gravity anomaly model, which is a time domain mathematical model for gravity anomaly estimation.
After the autoregressive model is obtained, the construction of the state equation is completed.
Specifically, the formula (19) can be rewritten as follows:
wherein delta g0 Abnormal weight, delta g1 And delta g2 The first and second derivatives of the gravity anomaly, respectively.
The three variables are selected as state variables, w (t) is white noise, and variance is
A continuous time state equation as shown in equation (24) can be obtained. The state equation is one for estimating gravity anomalies.
Wherein,
discretizing equation (24) with T as a sampling interval, the following can be obtained:
the first part to the right of the equal sign of equation (25) is the state transition part. Because the gravity anomaly of a region is a slow-varying process, taking the linear part of its taylor expansion term, the state transition matrix is:
the second part to the right of the equal sign of equation (25) is the part related to system noise:
in practical cases, 3. Beta. VT in the above formula 2 The value of/2 is generally small and may be omitted.
Let w k-1 For w (t) in time period [ t ] k-1 ,t k ]The mean value in, namely:
then there is
Obviously, when two integration intervals t l ,t l+1 ]And [ t ] k ,t k+1 ]When coincident, there is t=τ, so when l=k, there is:
and when l is not equal to k, E [ w ] k w l ]=0. Thus there is
This shows that the discretized noise is still white, with a variance of:
Q＝q/T。 (32)
thus, the discretized gravity anomaly system equation can be written as:
X k ＝ΦX k-1 +Γw k-1 。 (33)
wherein,
it will be appreciated that the aero gravity measurement data is discrete and thus equation (33) may be used as an equation of state for estimating gravity anomalies.
In some preferred embodiments, the coefficient β=1/7400 (1/m) may be taken, and the standard deviation σ=30.8 (mGal) of the gravity anomaly, where the relevant distance of the corresponding gravity anomaly is 22km. Substituting Guan Shuzhi into equation (34) can determine the system equation of a specific gravity anomaly, i.e., the state equation for estimating the gravity anomaly.
And combining the state equation, selecting a gravity anomaly signal containing noise as a measurement value, and establishing a measurement equation for estimating gravity anomaly as follows:
Z k ＝H k X k +V k 。 (35)
wherein, the sensitivity matrix is measured
H g ＝[1 0 0]。 (36)
The measurement input can be calculated according to the principle of aviation gravity measurement
Wherein Z is a measurement value, f Z For the vertical acceleration obtained by the gravimeter,the gravity normal field is an earth surface gravity acceleration value determined by an earth gravity model; g h The altitude correction term is an acceleration value of the earth gravity decaying along with the increase of altitude; / >Is the vertical acceleration of the aircraft; δa E The term "erlifs" is a coriolis force applied to an aircraft due to the rotation of the earth.
Wherein, measure noise V k The variance of (c) may be determined empirically with respect.
After the state equation and the measurement equation are acquired, the aviation gravity signal can be extracted based on the optimal Kalman smoother, the state equation and the measurement equation.
Specifically, the kalman filter may be an optimal kalman smoother. The optimal Kalman smoother is based on a standard discrete Kalman filter, and a backward smoothing process is added, so that all measurement data in a smoothing time interval can be utilized by a state estimation value at each moment, and the estimation accuracy of the state is improved. From the point of view of signal processing, this is a processing method that improves the signal-to-noise ratio.
In combination with the application background of gravity measurement, the embodiment of the invention can select a fixed interval smoothing algorithm. The basic principles and implementation of the optimal kalman smoothing algorithm are described below.
The classical implementation method of the fixed interval smoothing algorithm is Three-channel fixed interval smoothing (Three-pass fixed interval smoothing), and the calculation process is divided into Three steps, namely forward Kalman filtering, backward Kalman filtering and optimal smoothing. In order to clearly illustrate the meaning of each link calculation process, in the related formula of the optimal Kalman smoother, subscripts f, b and s are introduced to distinguish related physical quantities in three processes of forward filtering (forward), backward filtering (backward) and optimal smoothing (smoothing).
Wherein the forward filtering process is implemented by a standard kalman filter, and the formulas (9) to (13) are written as shown in formulas (38) to (42). The forward procedure starts with k=1.
P f,k ＝(I-K f,k H k )P f,k/k-1 。 (42)
The backward filtering proceeds in reverse order from time k=n. In order to facilitate the representation under a unified Kalman filtering system, firstly, a state estimation mean square error matrix involved in the inverse filtering process is written into an information matrix form, namely, the following steps:
to avoid ambiguity in writing and expression, it is agreed that an I without a subscript represents a unit matrix and an I with a subscript represents an information matrix.
The backward filtering process can be represented by formulas (45) to (49):
the optimal smooth state estimation value is calculated as follows.
Firstly, writing a state estimation mean square error matrix in forward filtering into an information matrix form, namely:
the state estimation mean square error matrix of the optimal smoothing process is:
P s,m ＝(I f,k +I b,k/k+1 ) -1 。 (51)
the smoothed state estimate is:
from the above formula, the arrangement order of the forward and backward filtering processes is different: the state estimation value output by the forward filtering process is a posterior estimation value after measurement and update, and the prior estimation output after one-step state transfer is obtained by the forward filtering. The design is to ensure that the state estimation value of each moment only uses one measurement value of the current moment in the whole optimal smooth calculation process, so that the forward and backward filtering channels do not depend on the same information, and the forward and backward state estimation value of each discrete moment is truly independent. Under the premise, the optimal weighted fusion can be carried out on the forward and backward estimation results according to the mode determined by the formulas (51) and (52), the mean square uncertainty of the estimation results is reduced, and the estimation performance is improved.
The three-channel fixed interval smoothing algorithm is simple to implement, has clear physical meaning and is a commonly used optimal smoothing algorithm. However, a great amount of matrix inversion operation exists in the backward filtering process of the algorithm, so that the calculation efficiency is affected.
In some embodiments, an RTS smoothing algorithm may be employed. The algorithm omits the link of backward filtering, and results obtained by forward filtering at each momentP f,k 、P f,k/k-1 After the sequential saving, the smoothing algorithm is directly and reversely executed from k=n-1 as shown in formulas (53) to (57):
P s,k ＝P f,k 。 (53)
in some embodiments, extracting the aerial gravity signal based on the optimal kalman smoother, the state equation, and the measurement equation includes: and solving a state equation and a measurement equation based on a transfer function of the optimal Kalman smoother, and extracting an aviation gravity signal.
Specifically, a digital filter can be constructed by using an optimal Kalman smoother, and the gravity anomaly is filtered, so that a state equation and a measurement equation are solved, and an aviation gravity signal is extracted.
In some embodiments, the method further comprises: and calculating and extracting the cut-off frequency of the aviation gravity signal based on the transfer function of the optimal Kalman smoother.
Specifically, an optimal kalman smoother for gravity anomaly estimation may be analyzed from the perspective of frequency domain analysis. Firstly, analyzing the characteristics of a gravity anomaly model adopted in a state equation, and then, according to the state equation and a measurement equation of an optimal Kalman smoother, proving the stability of a smoothing process by means of a linear system correlation theory. On the basis, the transfer function of the optimal Kalman smoother in the fixed interval is deduced, a specific transfer function expression is obtained through calculation, and the characteristics of the transfer functions obtained under different measuring noise levels are compared. And finally, a digital filter can be constructed to filter the gravity anomaly by utilizing the calculated transfer function, and the accuracy of the frequency domain analysis of the optimal Kalman smoother is verified.
The characteristics of the gravity anomaly model adopted in the state equation can be analyzed based on a frequency domain characterization method of the gravity anomaly model.
The power spectral density of the third order gaussian-markov random process is according to equation (18):
wherein f represents frequency; q represents the system noise variance.
Substituting the specific values of the parameters given above (coefficient β, standard deviation σ of gravity anomaly and associated distance of the corresponding gravity anomaly) according to equation (58) yields a graph of the power spectral density of the gravity anomaly model as shown in fig. 2.
As can be seen from fig. 2, the power of the gravity anomaly signal is mainly concentrated in the low frequency band, and the signal power is rapidly attenuated as the frequency increases. The power spectral density of the gravity anomaly model can be obtained through the calculation of the transfer function of an optimal Kalman smoother; based on the power spectral density of the gravity anomaly model, the cut-off frequency of the aviation gravity signal can be extracted. The cut-off frequency can be used for the design of the kalman filter.
The optimal kalman smoother is a model-dependent estimation method, and the estimation result of gravity anomaly is based on the weighted average of the model recursion value and the measurement input value, so that the assumption of the model has an important influence on the final estimation result. Therefore, it can be judged that the low-frequency characteristic of the model affects the power spectrum characteristic of the final estimation result, so that the estimation result has similar low-frequency characteristic.
In some embodiments, before calculating the cutoff frequency for extracting the aviation gravity signal based on the transfer function of the optimal kalman smoother, the method further includes: and acquiring a transfer function of the optimal Kalman smoother.
In some embodiments, obtaining the transfer function of the kalman filter process includes: acquiring a transfer function of a forward filtering channel based on forward Kalman filtering, and acquiring a transfer function of a backward filtering channel based on backward Kalman filtering;
And acquiring the transfer function based on the transfer function of the forward filtering channel and the transfer function of the backward filtering channel.
Specifically, the preconditions derived from the transfer function of the optimal kalman smoother may be analyzed and validated, including discrete kalman filter stability analysis and discrete kalman filter steady state analysis.
Since the optimal kalman smoother is implemented based on a standard kalman filter, the concept of kalman filter stability and sufficient conditions for discriminating stability are described below.
The stability of the kalman filter refers to the stability of the equilibrium state of the system, i.e. the stability in the sense of lyapunov, and in combination with the steady system according to the embodiments of the present invention, the following detailed definitions of the two types of stability are given.
First, let the linear system be:
X k ＝Φ k,k-1 X k-1 +u k-1 。 (59)
is arranged in parallel withAnd->Is that the system corresponds to different initial states +.>And->State at time t.
Definition 1
If any given ε > 0, one can always find δ=δ (ε, t) 0 ) When (when)There is-> The constant is established, the system shown in the formula (59) is said to be stable; if delta is related to epsilon only and t 0 Irrespective, the system is consistently stable. For a steady system, system stability is equivalent to consistent stability.
Definition 2
If the system shown in formula (59) is not only stable but also suitable for any initial stateAnd->The method comprises the following steps:
i.e. any given μ > 0, t=t (μ, T 0 )>0, when t k ≥t 0 In the case of +T,the constant holds, then the system shown in formula (59) is said to be asymptotically stable; if T is related to mu only and T is related to 0 Independently, the system shown in equation (59) is said to be consistently asymptotically stable. For a steady system, asymptotic stability and consistent asymptotic stability are equivalent.
The physical meaning of stability in the above definition is: the ability of a dynamic system to be progressively unaffected by the initial state over time. If the initial state is considered a disturbance, stability is the ability of the system state to return to the equilibrium point.
In combination with the application background of the embodiment of the invention for estimating the gravity anomaly of the target area, the system stability of Kalman filtering mainly focuses on two aspects, namely a state initial value X 0 And estimating a mean square error matrix P 0 Impact on final gravity anomaly estimation. If the filtering time is increased with the increase of the filtering time,and->Each is progressively unaffected by its initial value, indicating that the filter system is stable.
One sufficient condition for discrete kalman filter stability discrimination is given below.
Theorem 1
Let the state equation and the measurement equation of the discrete system be respectively
X k ＝Φ k,k-1 X k-1 +Γ k-1 W k-1 。 (61)
Z k ＝H k X k +V k 。 (62)
In the middle of
If the system is consistently fully randomly controllable and consistently fully randomly observable, and Q k And R is k Is positive, the kalman filter is uniformly progressive stable.
For a steady system, under the condition that Q is positive, the consistency is completely random and controllable, and the consistency can be judged by a formula (64):
rank[Φ n-1 Γ Φ n-2 Γ … Γ]＝n。 (64)
for a steady system, consistent, fully random observability can be determined by equation (65):
in the above formula, n is the dimension of the system.
The noise of the state equation (33) and the measurement equation (35) of the discretized gravity anomaly system is scalar and positive, and meets the requirement of positive determination.
Calculating the identical complete random controllable discriminant, substituting the same into the relevant parameters, and calculating to obtain
Calculating a uniform completely random controllable discriminant, substituting related parameters, and calculating to obtain:
from this, it can be seen that the kalman filter designed according to the state equation (33) and the measurement equation (35) of the gravity anomaly system is consistently and progressively stable. Therefore, in the test process, different initial values have no influence on the estimation result.
For a stationary system, if the filter is filter stable, the mean square error matrix not only asymptotically is independent of the initial value, but also gradually tends to some steady state value. Namely, as time goes by, there are:
P k+1 ＝P k 。 (68)
Recording the steady state value of the one-step prediction mean square error array asAccording to the formula (11) and the formula (12), there are
The steady state kalman gain is:
the steady state estimated mean square error matrix is:
it can be seen that in the standard kalman filter algorithm, when the filter reaches a steady state value, the filter-related parameters are all constant values.
Further, after determining the parameters of the filter, all parameter values, in particular the kalman gain values, can theoretically be obtained by solving equation (69). Moreover, this process is independent of the specific metrology input, i.e., the filter design may be completed prior to the actual filtering operation.
But equation (69) is an algebraic licarpa equation,directly solving it corresponds to solution n 2 A system of quadratic equations of order. Considering the symmetry of the mean square error matrix, the actually solved equations are n (n-1), and the non-negative root of the quadratic equation needs to be taken out, and the calculated amount is still large, so that the equations are not directly solved generally. However, the existence of a steady state solution is strictly theoretical. This provides for the later derivation of the transfer function to solve for the optimal kalman smoother.
The derivation of the optimal kalman smoother transfer function is described below.
Taking the optimal Kalman smoother after reaching a steady state as a system, taking a measured value containing noise as a system input (thus the measured value can be called as a measured input value or a measured input), taking an abnormal gravity optimal estimated value output by the optimal Kalman smoother as a system output, and establishing a transfer function model. The transfer function can reflect the frequency domain characteristic of the system, and the stability and the steady state characteristic of the filter ensure the uniqueness of the transfer function, namely, the characteristics of the filter after reaching the steady state are the same under the condition of giving initial values in different states. And is independent of the input measurement after the filter parameters are given.
The derivation can be performed sequentially from the forward filtering channel, the backward filtering channel and the optimal smoothing channel according to the recursive equation and the implementation process of the optimal Kalman smoother.
The transfer function of the forward filter channel is first derived. According to the basic theory of the optimal Kalman smoother, forward filtering is realized through a standard Kalman filter, and a forward filtering channel obtains a posterior estimated value at the current moment. From equations (38) and (39), the relationship between the posterior estimate and the metrology input can be derived:
In the gravity anomaly model, as can be seen from the equation (26), the state transition matrix is a constant matrix, and therefore, the time is not distinguished. And the measurement sensitivity matrix, as shown in equation (36), is also a constant matrix. Under steady state conditions, the Kalman gain is also a constant matrix, thus rewritten equation (72) as a differential equation form:
to the above Z conversion, there are
The transfer function of the available forward filter channels is:
since the measurement value is a scalar, i.e. Z (k) is a one-dimensional sequence, equation (75) can be written as
Wherein H is f1 (z)、H f2 (z)、H f3 (z) is the transfer function relationship between each of the three states and the metrology input; k (K) f1 K f2 K f3 Three components of the steady state kalman gain of the forward filtering process, respectively.
Substituting the discrete state transition matrix shown in equation (34) and solving equation (76) yields the form of the solution shown in equation (77).
The backward filtering channel outputs a one-step predicted value of the state, namely an a priori estimated value of the state. From formulas (47) and (49), it is possible to obtain:
also, for a steady state system with stable filtering, after entering steady state, the relevant parameters all converge to a constant matrix. Thus, the equation can be written (78) as the differential equation form:
z-transformation is performed on the above, and the following steps are included:
The transfer function of the available backward filtering channel is:
since the measurement value is a scalar, i.e. Z (k) is a one-dimensional sequence, equation (81) can be written as
Wherein H is b1 (z)、H b2 (z)、H b3 (z) is the transfer function relationship between each of the three states and the metrology input. K (K) b1 K b2 K b3 Three components of the steady state kalman gain of the forward filtering process, respectively.
Substituting the discrete state transition matrix shown in equation (34) and solving equation (82) yields the form of the solution shown in equation (83).
The optimal smoothing channel is essentially a weighted average of the forward and backward filtering results, and the weighting coefficients are only related to the forward and backward filtering channel estimation mean square error matrix. After the filter system stabilizes and reaches steady state, the weighting coefficients of the forward and backward filtering results are constant values according to equation (52). Thus, the transfer function between the optimal smoothed output after steady state and the metrology input is, according to equations (52), (75) and (81), readily available:
wherein P is s 、I b And I f Are the corresponding estimated mean square error matrix or information matrix in steady state. Equation (84) represents the transfer function of the optimal Kalman smoother.
In gravity anomaly estimation, the relationship between the output gravity anomaly and the metrology input is of interest. Therefore, only H is ultimately calculated s The first item in (z). The solution form shown in equation (85) can be obtained from equations (75), (81) and (84).
The method has the advantages that the Kalman filter based on the Markov process is used for processing the aviation gravity measurement data of the target area, so that noise can be filtered more effectively, gravity anomalies can be extracted from the aviation gravity measurement data containing strong noise more accurately, useful signal frequency bands are reserved more, the reservation of the noise frequency bands is reduced, and the effect of extracting aviation gravity signals can be greatly improved.
In order to facilitate the explanation of the advantageous effects of the invention, the following description is given by way of example.
Taking aerogravity measurement data of a certain undulating mountain area as an example, as shown in fig. 3 and fig. 4, the processing results of a conventional FIR (Finite Impulse Response ) low-pass filter (with a cutoff frequency set to 0.01Hz according to an empirical value) and the processing results of a kalman filter based on a markov process (with a cutoff frequency of a processed signal being about 0.01 Hz) in the embodiment of the present invention are respectively shown. The aircraft performs 3 measurements on the same test line, resulting in 3 repeated line data. As can be seen by comparing the internal coincidence precision of the 3 repeated line data, the processing result of the Kalman filter based on the Markov process contains less noise than the processing result of the traditional FIR low-pass filter, the internal coincidence precision of the repeated line is 0.523mGAL, and the internal coincidence precision of the repeated line is 0.547mGAL. It can be seen that the use of a kalman filter based on a markov process has a better effect in processing aeronautical gravity measurement data than a conventional FIR low-pass filter at the same cut-off frequency.
The inertial stabilized platform aero gravity signal extraction device provided by the invention is described below, and the inertial stabilized platform aero gravity signal extraction device described below and the inertial stabilized platform aero gravity signal extraction method described above can be correspondingly referred to each other.
Fig. 5 is a schematic structural diagram of an inertial stabilized platform aeronautical gravity signal extraction device provided by the invention. Based on the foregoing content of any of the foregoing embodiments, as shown in fig. 5, the apparatus includes an acquisition module 501 and an extraction module 502, where:
an acquisition module 501, configured to acquire airborne gravity measurement data of a target area; the aviation gravity measurement data are obtained by measuring the target area through an inertial stabilization platform type gravity meter;
the extraction module 502 is configured to input the airborne gravity measurement data into a kalman filter based on a markov process, and obtain an airborne gravity signal.
In particular, the acquisition module 501 and the extraction module 502 may be electrically connected.
Optionally, the extracting module 502 may specifically include:
the equation acquisition unit is used for modeling the gravity anomaly of the target area along the flight path according to the aviation gravity measurement data based on the Markov process and the aviation gravity measurement principle, and acquiring a state equation and a measurement equation for estimating the gravity anomaly;
And the signal extraction unit is used for extracting the aviation gravity signal based on the optimal Kalman smoother, the state equation and the measurement equation.
Alternatively, the markov process is a third order gaussian-markov process.
Optionally, the signal extraction unit may be specifically configured to solve a state equation and a measurement equation based on a transfer function of the optimal kalman smoother, and extract an aviation gravity signal.
Optionally, the extracting module 502 may further include:
and the cut-off frequency extraction unit is used for calculating and extracting the cut-off frequency of the aviation gravity signal based on the transfer function of the optimal Kalman smoother.
Optionally, the extracting module 502 may further include:
and the transfer function acquisition unit is used for acquiring the transfer function of the optimal Kalman smoother.
Alternatively, the transfer function acquiring unit may be specifically configured to:
the transfer function acquisition unit is used for acquiring the transfer function of the forward filtering channel based on forward Kalman filtering and acquiring the transfer function of the backward filtering channel based on backward Kalman filtering; and acquiring a transfer function based on the transfer function of the forward filter channel, the transfer function of the backward filter channel and the optimal smoothing of the fixed interval smoothing.
The inertial stabilized platform aviation gravity signal extraction device provided by the embodiment of the invention is used for executing the inertial stabilized platform aviation gravity signal extraction method provided by the invention, the implementation mode of the inertial stabilized platform aviation gravity signal extraction device is consistent with the implementation mode of the inertial stabilized platform aviation gravity signal extraction method provided by the invention, the same beneficial effects can be achieved, and the detailed description is omitted.
The inertial stabilized platform aviation gravity signal extraction device is used for the inertial stabilized platform aviation gravity signal extraction method of the previous embodiments. Therefore, the description and definition in the inertial stabilization platform aviation gravity signal extraction method in the foregoing embodiments may be used for understanding each execution module in the embodiments of the present invention.
The method has the advantages that the Kalman filter based on the Markov process is used for processing the aviation gravity measurement data of the target area, so that noise can be filtered more effectively, gravity anomalies can be extracted from the aviation gravity measurement data containing strong noise more accurately, useful signal frequency bands are reserved more, the reservation of the noise frequency bands is reduced, and the effect of extracting aviation gravity signals can be greatly improved.
Fig. 6 illustrates a physical schematic diagram of an electronic device, as shown in fig. 6, which may include: processor 610, communication interface (Communications Interface) 620, memory 630, and communication bus 640, wherein processor 610, communication interface 620, and memory 630 communicate with each other via communication bus 640. The processor 610 may invoke logic instructions in the memory 630 to perform an inertial stabilized platform aero gravity signal extraction method comprising: acquiring aviation gravity measurement data of a target area; the aviation gravity measurement data are obtained by measuring a target area through an inertial stabilization platform type gravity meter; the aviation gravity measurement data are input into a Kalman filter based on a Markov process, and an aviation gravity signal is extracted.
Further, the logic instructions in the memory 630 may be implemented in the form of software functional units and stored in a computer-readable storage medium when sold or used as a stand-alone product. Based on this understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution, in the form of a software product stored in a storage medium, comprising several instructions for causing a computer device (which may be a personal computer, a server, a network device, etc.) to perform all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
The processor 610 in the electronic device provided by the embodiment of the present invention may call the logic instruction in the memory 630, and its implementation manner is consistent with the implementation manner of the inertial stabilization platform aviation gravity signal extraction method provided by the present invention, and may achieve the same beneficial effects, which are not described herein again.
In another aspect, the present invention also provides a computer program product comprising a computer program stored on a non-transitory computer readable storage medium, the computer program comprising program instructions which, when executed by a computer, enable the computer to perform the inertial stabilized platform aerogravity signal extraction method provided by the above methods, the method comprising: acquiring aviation gravity measurement data of a target area; the aviation gravity measurement data are obtained by measuring a target area through an inertial stabilization platform type gravity meter; the aviation gravity measurement data are input into a Kalman filter based on a Markov process, and an aviation gravity signal is extracted.
When the computer program product provided by the embodiment of the invention is executed, the method for extracting the inertial stabilization platform aviation gravity signal is realized, the specific implementation mode is consistent with the implementation mode recorded in the embodiment of the method, and the same beneficial effects can be achieved, and the detailed description is omitted here.
In yet another aspect, the present invention further provides a non-transitory computer readable storage medium having stored thereon a computer program which, when executed by a processor, is implemented to perform the inertial stabilized platform aero gravity signal extraction methods provided above, the method comprising: acquiring aviation gravity measurement data of a target area; the aviation gravity measurement data are obtained by measuring a target area through an inertial stabilization platform type gravity meter; the aviation gravity measurement data are input into a Kalman filter based on a Markov process, and an aviation gravity signal is extracted.
When the computer program stored on the non-transitory computer readable storage medium provided by the embodiment of the invention is executed, the method for extracting the inertial stabilization platform aviation gravity signal is realized, and the specific implementation manner is consistent with the implementation manner recorded in the embodiment of the method, and the same beneficial effects can be achieved, and the detailed description is omitted herein.
It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The foregoing descriptions of specific exemplary embodiments of the present invention are presented for purposes of illustration and description. It is not intended to limit the invention to the precise form disclosed, and obviously many modifications and variations are possible in light of the above teaching. The exemplary embodiments were chosen and described in order to explain the specific principles of the invention and its practical application to thereby enable one skilled in the art to make and utilize the invention in various exemplary embodiments and with various modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the claims and their equivalents.
Claims (10)
1. The method for extracting the inertial stabilized platform aviation gravity signal is characterized by comprising the following steps of:
acquiring aviation gravity measurement data of a target area; the aviation gravity measurement data are obtained by measuring the target area through an inertial stabilization platform type gravity meter;
inputting the aviation gravity measurement data into a Kalman filter based on a Markov process, and extracting an aviation gravity signal.
2. The inertial stabilization platform aerial gravity signal extraction method of claim 1, wherein the inputting the aerial gravity measurement data into a markov process based kalman filter extracts an aerial gravity signal comprising:
modeling the gravity anomaly of the target area along a flight path according to the aviation gravity measurement data based on a Markov process and an aviation gravity measurement principle, and obtaining a state equation and a measurement equation for estimating the gravity anomaly;
and extracting the aviation gravity signal based on the optimal Kalman smoother, the state equation and the measurement equation.
3. The inertial stabilized platform aero gravity signal extraction method of claim 2, wherein the markov process is a third order gaussian-markov process.
4. A method of inertial stabilized platform aero gravity signal extraction according to claim 2 or 3, further comprising:
and calculating and extracting the cut-off frequency of the aviation gravity signal based on the transfer function of the optimal Kalman smoother.
5. The inertial stabilization platform aerial gravity signal extraction method of claim 4, wherein before calculating the cutoff frequency for extracting the aerial gravity signal based on the transfer function of the optimal kalman smoother, further comprises:
and acquiring a transfer function of the optimal Kalman smoother.
6. The inertial stabilization platform aerial gravity signal extraction method of claim 5, wherein the obtaining a transfer function of the kalman filtering process comprises:
acquiring a transfer function of a forward filtering channel based on forward Kalman filtering, and acquiring a transfer function of a backward filtering channel based on backward Kalman filtering;
and acquiring the transfer function based on the transfer function of the forward filtering channel and the transfer function of the backward filtering channel.
7. An inertial stabilization platform aviation gravity signal extraction device, which is characterized by comprising:
The acquisition module is used for acquiring aviation gravity measurement data of the target area; the aviation gravity measurement data are obtained by measuring the target area through an inertial stabilization platform type gravity meter;
and the extraction module is used for inputting the aviation gravity measurement data into a Kalman filter based on a Markov process to acquire an aviation gravity signal.
8. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor performs the steps of the inertial stabilized platform aero gravity signal extraction method of any one of claims 1 to 6 when the program is executed.
9. A non-transitory computer readable storage medium having stored thereon a computer program, wherein the computer program when executed by a processor implements the steps of the inertial stabilization platform aero gravity signal extraction method of any one of claims 1 to 6.
10. A computer program product comprising a computer program, characterized in that the computer program when executed by a processor implements the steps of the inertial stabilization platform aero gravity signal extraction method according to any of claims 1 to 6.
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