CN113137975B - Inertial correction method and device for astronomical inertial integrated navigation and electronic equipment - Google Patents
Inertial correction method and device for astronomical inertial integrated navigation and electronic equipment Download PDFInfo
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Abstract
The application provides an inertial correction method, an inertial correction device and electronic equipment for astronomical inertial integrated navigation, and relates to the technical field of astronomical inertial integrated navigation, wherein the method comprises the steps of acquiring an aircraft at t determined by an inertial navigation system k The first position of moment and the acquisition of the position of the aircraft determined by the astronomical navigation system at t k A second position at the moment, performing extended Kalman filtering on the first position and the second position to obtain a third position, and determining t according to a plurality of preset prediction models and the third position k+1 Predicted value of time, finally according to t k+1 The predicted value of the time corrects the fourth position. The technical scheme provided by the application can be at t k+1 Determining in advance that the second position is at t before the moment k+1 The predicted value of the moment ensures that the computer can correct the fourth position in time through the predicted value when obtaining the fourth position, thereby eliminating the influence of time delay in the existing correction technology and improving the correction precision of the correction technology.
Description
Technical Field
The application relates to an astronomical inertial integrated navigation technology, in particular to an inertial correction method and device for astronomical inertial integrated navigation and electronic equipment, and belongs to the technical field of inertial navigation correction.
Background
The prior airborne navigation has developed an astronomical inertial integrated navigation mode, and the inertial navigation has the advantages of high short-time sequence precision, continuous output, strong anti-interference capability and the like, but also has the defect of large accumulated error during long-time working; astronomical navigation has advantages of good concealment, strong autonomy, high precision and the like, but also has the defects of discontinuous output and easy environmental influence. By combining astronomical navigation and inertial navigation, the defects of both parties can be well overcome, and a practical, reliable and high-precision navigation technology is realized.
In astronomical inertial integrated navigation, the error of inertial navigation increases cumulatively with time, so that the inertial navigation needs to be corrected after a period of use to eliminate the error of inertial navigation. The current common scheme is to correct inertial navigation through the position information of astronomical navigation. However, the existing correction technology has a time delay problem, so that the position information of the astronomical navigation is inconsistent with the position information of the inertial navigation to be corrected in terms of generation time, and the correction precision of the inertial navigation is affected, and therefore, the correction precision of the existing correction technology is also greatly improved.
Disclosure of Invention
In view of this, the present application provides an inertial correction method, device and electronic equipment for astronomical inertial integrated navigation, which are used for improving the correction precision of the existing correction technology.
In order to achieve the above object, in a first aspect, an embodiment of the present application provides an inertial correction method for astronomical inertial integrated navigation, applied to an aircraft, where the aircraft includes an inertial navigation system and an astronomical navigation system, the method includes:
acquiring an aircraft determined by an inertial navigation system at t k The first position of the moment is obtained, and the position t of the aircraft determined by the astronomical navigation system is obtained k A second position of the moment;
performing extended Kalman filtering on the first position and the second position to obtain a third position;
determining t according to a preset prediction model and a third position k+1 The prediction model is a diagonal matrix determined according to the output period, the time delay estimated value and a plurality of preset adjusting parameters of the astronomical navigation system;
according to t k+1 Correcting a fourth position by the predicted value of the moment, wherein the fourth position is at t k+1 Position of aircraft obtained by inertial navigation system at moment, t k Time sum t k+1 The time intervals are one output period of the astronomical navigation system.
Optionally, the prediction model is a plurality of;
the formula of the prediction model is:
wherein phi is j (k/k-1) represents a prediction model, j represents a number of the prediction model, T represents an output period of the astronomical navigation system, e, f, g, n, m and q represent adjustment parameters, respectively, and τ represents a delay estimation value of the astronomical navigation system.
Optionally, determining t according to a plurality of preset prediction models and a third position k+1 Predicted values of time instants including:
according to t corresponding to each prediction model k Update weight, third position and t of time k Determining a predicted value of time moment and t corresponding to each predicted model k+1 Updating weight value at moment;
according to each prediction model and t corresponding to each prediction model k+1 The updating weight and the third position of the moment determine the predicted value corresponding to each predicted model;
determining t according to the prediction value corresponding to each prediction model k+1 Predicted value of time.
Optionally, according to t corresponding to each prediction model k Update weight, third position and t of time k Determining a predicted value of time moment and t corresponding to each predicted model k+1 The updating weight of the moment comprises the following steps:
for each prediction model, according to t corresponding to the prediction model k Determining an evaluation value corresponding to the prediction model according to the difference value between the predicted value of the moment and the third position;
determining an update value corresponding to the prediction model according to the evaluation value and the prediction error corresponding to the prediction model;
according to the updated value corresponding to the prediction model and t corresponding to each prediction model k Updating weight of moment to determine t corresponding to predictive model k+1 Updating weight of time.
Optionally, according to t corresponding to the prediction model k The predicting value and the third position of the moment determine the corresponding evaluating value of the predicting model, which comprises the following steps:
and determining an evaluation value corresponding to the prediction model by adopting the following formula:
wherein, representing t corresponding to the jth predictive model k+1 Predicted value of time, Z k Representing t k A third position Z corresponding to the moment k-1 Representing t k-1 Third position corresponding to time->Representing t corresponding to the jth predictive model k Predicted value of moment, v j (k) Representing the evaluation value, t, corresponding to the jth predictive model k Time sum t k-1 The time intervals are one output period of the astronomical navigation system.
Optionally, determining the update value corresponding to the prediction model according to the evaluation value and the prediction error corresponding to the prediction model includes:
the update value corresponding to the prediction model is determined by adopting the following formula:
wherein, r (k) represents white noise of astronomical navigation, < >>Representing the jth predictionError variance matrix corresponding to model S j (k) Representing the prediction error corresponding to the jth prediction model, Λ j (k) Representing the update value, v corresponding to the j-th prediction model j (k) And representing the evaluation value corresponding to the j-th prediction model.
Optionally, according to the updated value corresponding to the prediction model and t corresponding to each prediction model k Updating weight of moment to determine t corresponding to predictive model k+1 The updating weight of the moment comprises the following steps:
determining t corresponding to the prediction model by adopting the following formula k+1 Update weight of time:
wherein c represents an update coefficient, μ j (k) Representing t corresponding to the jth predictive model k+1 Update weight, μ for time instant j (k-1) represents t corresponding to the jth predictive model k Updating weight of time.
In a second aspect, an embodiment of the present application provides an inertial correction device for astronomical inertial integrated navigation, applied to an aircraft, where the aircraft includes an inertial navigation system and an astronomical navigation system, the device includes:
the acquisition module is used for acquiring the aircraft determined by the inertial navigation system at t k The first position of the moment is obtained, and the position t of the aircraft determined by the astronomical navigation system is obtained k A second position of the moment;
the filtering module is used for performing extended Kalman filtering on the first position and the second position to obtain a third position;
the prediction module is used for determining t according to a preset prediction model and a third position k+1 The prediction model is a diagonal matrix determined according to the output period, the time delay estimated value and a plurality of preset adjusting parameters of the astronomical navigation system;
correction module for according to t k+1 Correcting a fourth position by the predicted value of the moment, wherein the fourth position is at t k+1 The moment is obtained by an inertial navigation systemPosition of the aircraft, t k Time sum t k+1 The time intervals are one output period of the astronomical navigation system.
Optionally, the prediction model is a plurality of;
the formula of the prediction model is:
wherein phi is j (k/k-1) represents a prediction model, j represents a number of the prediction model, T represents an output period of the astronomical navigation system, e, f, g, n, m and q represent adjustment parameters, respectively, and τ represents a delay estimation value of the astronomical navigation system.
Optionally, the prediction module is specifically configured to:
according to t corresponding to each prediction model k Update weight, third position and t of time k Determining a predicted value of time moment and t corresponding to each predicted model k+1 Updating weight value at moment;
according to each prediction model and t corresponding to each prediction model k+1 The updating weight and the third position of the moment determine the predicted value corresponding to each predicted model;
determining t according to the prediction value corresponding to each prediction model k+1 Predicted value of time.
Optionally, the prediction module is specifically configured to:
for each prediction model, according to t corresponding to the prediction model k Determining an evaluation value corresponding to the prediction model according to the difference value between the predicted value of the moment and the third position;
determining an update value corresponding to the prediction model according to the evaluation value and the prediction error corresponding to the prediction model;
according to the updated value corresponding to the prediction model and t corresponding to each prediction model k Updating weight of moment to determine t corresponding to predictive model k+1 Updating weight of time.
Optionally, the prediction module is specifically configured to:
and determining an evaluation value corresponding to the prediction model by adopting the following formula:
wherein, representing t corresponding to the jth predictive model k+1 Predicted value of time, Z k Representing t k A third position Z corresponding to the moment k-1 Representing t k-1 Third position corresponding to time->Representing t corresponding to the jth predictive model k Predicted value of moment, v j (k) Representing the evaluation value, t, corresponding to the jth predictive model k Time sum t k-1 The time intervals are one output period of the astronomical navigation system.
Optionally, the prediction module is specifically configured to:
the update value corresponding to the prediction model is determined by adopting the following formula:
wherein, r (k) represents white noise of astronomical navigation, < >>Representing an error variance matrix corresponding to the jth prediction model, S j (k) Representing the prediction error corresponding to the jth prediction model，Λ j (k) Representing the update value, v corresponding to the j-th prediction model j (k) And representing the evaluation value corresponding to the j-th prediction model.
Optionally, the prediction module is specifically configured to:
determining t corresponding to the prediction model by adopting the following formula k+1 Update weight of time:
wherein c represents an update coefficient, μ j (k) Representing t corresponding to the jth predictive model k+1 Update weight, μ for time instant j (k-1) represents t corresponding to the jth predictive model k Updating weight of time.
In a third aspect, an embodiment of the present application provides an electronic device, including: a memory and a processor, the memory for storing a computer program; the processor is adapted to perform the method of the first aspect or any of the embodiments of the first aspect described above when the computer program is invoked.
In a fourth aspect, embodiments of the present application provide a computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the method of the first aspect or any implementation of the first aspect.
The inertial correction method, the device and the electronic equipment for astronomical inertial integrated navigation provided by the embodiment of the application can acquire the t of the aircraft determined by the inertial navigation system k The first position of moment and the acquisition of the position of the aircraft determined by the astronomical navigation system at t k A second position at the moment, performing extended Kalman filtering on the first position and the second position to obtain a third position, and determining t according to a plurality of preset prediction models and the third position k+1 Predicted value of time, finally according to t k+1 Correcting a fourth position by the predicted value of the moment, wherein the fourth position is a position at t k+1 The position of the aircraft is obtained at the moment through an inertial navigation system. The application can be at t k+1 Determining in advance that the second position is at t before the moment k+1 The predicted value of the moment ensures that the computer can correct the fourth position in time through the predicted value when obtaining the fourth position, thereby eliminating the influence of time delay in the existing correction technology and improving the correction precision of the correction technology.
Drawings
Fig. 1 is a schematic flow chart of an inertial correction method for astronomical inertial integrated navigation according to an embodiment of the present application;
FIG. 2 is a diagram of an aircraft flight trajectory provided by an embodiment of the present application;
FIG. 3 is a graph showing the comparison of the positioning error with time before and after inertial correction according to an embodiment of the present application;
FIG. 4 is a graph comparing inertial corrected fore-and-aft heading errors over time provided by embodiments of the present application;
FIG. 5 is a graph showing the comparison of the inertial correction of the velocity error of the attitude with time before and after the inertial correction according to the embodiment of the present application;
FIG. 6 is a schematic structural diagram of an inertial correction device for astronomical inertial integrated navigation according to an embodiment of the present application;
fig. 7 is a schematic structural diagram of an electronic device according to an embodiment of the present application.
Detailed Description
The inertial correction method for astronomical inertial integrated navigation provided by the embodiment of the application can be applied to electronic equipment such as a computer, a workstation or a processing terminal, and the specific type of the electronic equipment is not limited.
In the astronomical inertial integrated navigation system, because the astronomical navigation system has the characteristics of high precision and no time variation of errors, a computer can utilize position information obtained by the astronomical navigation system to carry out error correction on the inertial navigation system so as to eliminate accumulated errors generated by time in the inertial navigation system. However, in practical applications, the astronomical navigation system may correct the inertial navigation system after outputting the position information of the aircraft and performing certain correction and filtering processing on the position information. It is assumed that at 1 st second, the inertial navigation system outputs first position information of the aircraft and the astronomical navigation system outputs second position information of the aircraft. However, after the correction and filtering processing, the computer can output the processed second position information only when the 1.5 th second is needed, and at this time, a time delay of 0.5 second exists between the processed second position information and the first position information. This delay problem can affect the accuracy of the correction of the prior art due to the fast speed of movement of the aircraft.
In order to solve the above-described problems and to improve the correction accuracy of the correction technique, the technical solutions of the present application will be described in detail with specific embodiments. The following embodiments may be combined with each other, and some embodiments may not be repeated for the same or similar concepts or processes.
Fig. 1 is a schematic flow chart of an inertial correction method for astronomical inertial integrated navigation according to an embodiment of the present application, as shown in fig. 1, the method includes the following steps:
s110, acquiring an aircraft determined by an inertial navigation system at t k The first position of the moment is obtained, and the position t of the aircraft determined by the astronomical navigation system is obtained k A second position of the moment.
In the embodiment of the application, the aircraft comprises an inertial navigation system and an astronomical navigation system, and the computer can acquire the position t of the aircraft determined by the inertial navigation system k The first position of moment is obtained simultaneously, and the time t of the aircraft determined by the astronomical navigation system is obtained k A second position of the moment. The first location and the second location may each include longitude data, latitude data, and altitude data of the aircraft.
S120, performing extended Kalman filtering on the first position and the second position to obtain a third position.
Kalman filtering is an algorithm that uses a linear system state equation to optimally estimate the state of a system based on the observed data of the system. Since the observed data includes system noise and interference, the optimal estimate can also be considered a filtering process. Since Kalman filtering is only applicable to linear systems, and in practice, the observed data is typically nonlinear, extended Kalman filtering applicable to nonlinear systems is derived.
Specifically, the extended kalman filter includes a state equation and an observation equation, and the computer may determine the filtered first position according to the first position and the state equation of the extended kalman. And determining a third position according to the filtered first position, the filtered second position and the extended Kalman observation equation.
By way of example, the process of establishing the state equation and the observation equation of the extended kalman filter is explained below.
First, a state equation and an observation equation of the integrated navigation system are established.
Taking an error equation of the inertial navigation system as a state equation of the integrated navigation system, wherein the expression is as follows:
wherein F (t) represents a matrix of the integrated navigation system, G (t) represents a matrix of error coefficients, and an attitude transformation matrix representing an aircraft coordinate system to a combined navigational coordinate system, W (t) represents a systematic error vector, and W (t) = [ W bx ，W by ，W bz ，W ax ，W ay ，W az ] T ；W bx 、W by And W is bz All represent measurement white noise of a gyro sensor in an inertial navigation system; w (W) ax 、W ay And W is az All represent the measured white noise of the acceleration sensor in the inertial navigation system.
Simplifying the drift amount in a gyroscopic sensor measurement system using the first order markov principle, the state equation variables can be expressed as follows:
wherein phi is E ,φ N And phi U All are mathematical platform error angles; δV (delta V) E 、δV N And δV U All are speed errors;a latitude error, δλ is a longitude error, δh is a height error; epsilon bx 、ε by And epsilon bz All are gyro constant drift errors; />And->Are all accelerometer zero offset.
Altitude h output according to observation device of astronomical navigation system p And azimuth angle A p And the altitude angle h calculated by the inertial navigation system c And azimuth angle A c An observed star unit direction vector under a geographic coordinate system is established, and the expression is as follows:
X 1 ＝[cos h p sin A p cos h p cos A p sinh p ]
X 2 ＝[cosh C sin A C cosh C cos A C sinh C ] (3)
wherein X is 1 Indicating the observed star unit direction vector, X of astronomical navigation system 2 Representing the observed sidereal unit direction vector of the inertial navigation system.
Establishing an observation platform coordinate system (p system) of an astronomical navigation system and a resolving coordinate system (C system) of an inertial navigation system, and combining a directional cosine matrix transformation method, wherein the coordinate transformation matrixes of the p system and the C system are as follows:
wherein,represents the coordinate transformation matrix of the p-system and the C-system, δλ represents the longitude error between the p-system and the C-system, δΦ represents the latitude error between the p-system and the C-system.
In the astronomical inertial integrated navigation system, in general, the distance between the observation target star and the earth is considered to be infinity, and the astronomical navigation system observation fixed star unit direction vector and the inertial navigation system observation fixed star unit direction vector can be approximated to the same vector. From the above analysis, the following expression can be obtained from the expression (3) and the expression (4):
further, the following expression can be obtained according to the formula (5):
in practical applications, the values of Δh and Δa are small, so equation (6) can be further converted into the following expression:
the observation equation of the integrated navigation system can be obtained by combining the formula (3), the formula (4), the formula (5) and the formula (7):
wherein V is 1 Representing azimuth angle observation error of astronomical navigation system, V 2 Indicating the altitude angle observation error of the astronomical navigation system.
And then, optimizing and updating a state equation and an observation equation of the integrated navigation system by adopting an extended Kalman filtering algorithm.
A state space model in the form of a random nonlinear system is expressed as follows:
X k ＝f(X k-1 )+Γ k-1 W k-1 (9)
Z k ＝h(X k )+V k (10)
wherein f (X) k-1 ) And h (X) k ) All representing some non-linear function, W k-1 And V k All represent gaussian white noise.
The nonlinear function f (X k-1 ) Surrounding the last filtered valueExpanding into a form of a Taylor series, and performing first-order linearization truncation to obtain an approximate expression of the nonlinear function as follows:
nonlinear function h (X k ) At the position ofThe linearization approximation at this point is as follows:
after the linearization treatment, the equation (9) and the equation (10) can obtain a first-order linearized state equation and an observation equation, as follows:
to simplify the above expression, the following relationships can be assumed, respectively:
bringing equations (15), (16), (17) and (18) into equations (13) and (14) yields simplified state and observation equations as follows:
X k ＝ξ(k|k-1)X k-1 +M(k-1)+Γ k-1 W k-1 (19)
Z k ＝H(k)X(k)+N(k)+V k (20)
according to the Kalman filtering principle, five basic expressions of the discrete extended Kalman filtering equation can be obtained as follows:
state one-step prediction equation:
state estimation equation:
filter gain equation:
K k ＝P k|k-1 H k T (H k P k|k-1 H k T +R k ) -1 (23)
one-step predictive mean square error equation:
P k|k-1 ＝ξ k,k-1 P k-1 ξ k,k-1 T +Γ k-1 Q k-1 Γ k-1 T (24)
the estimated mean square error equation can be expressed in two forms:
P k|k ＝(I-K k H k )P k/k-1 (I-K k H k ) T +K k R k K k T (25)
P k|k ＝(I-K k H k )P k/k-1 (26)
s130, determining t according to a preset prediction model and a third position k+1 Predicted value of time.
In order to solve the time delay problem, the computer can use the predicted value to replace the actual measured value to correct the inertial navigation system. For example, in order to correct the first position information output by the inertial navigation system at the 2 nd second, the computer may output a predicted value for the second position information output by the astronomical navigation system at the 2 nd second in advance at the 1.8 th second. And then correcting the first position information by using the predicted value, wherein no time delay exists between the predicted value and the first position information, so that the influence of the time delay in the existing correction technology can be eliminated, and the correction precision of the correction technology is improved.
Since the predicted value is not exactly equal to the measured value, the computer can determine t according to a plurality of preset predicted models and the third position in order to ensure that the predicted value is as identical to the measured value as possible k+1 Predicted value of time. The prediction model is a diagonal matrix determined according to an output period, a time delay estimated value and a plurality of preset adjusting parameters of the astronomical navigation system, and the specific formula is as follows:
wherein j represents the number of the prediction model, Φ j (k/k-1) represents a predictive model, representing t corresponding to the jth predictive model k+1 Predicted value of time, Z k Representing t k And a third position corresponding to the moment, wherein T represents an output period of the astronomical navigation system, e, f, g, n, m and q respectively represent adjustment parameters, and tau represents a time delay estimated value of the astronomical navigation system. It should be noted that e, f, g, n, m, q and τ can be determined by experiment to specific values, t k Time sum t k+1 The time intervals are one output period of the astronomical navigation system.
After determining the predicted values corresponding to the plurality of different prediction models according to equation (27), the computer may determine an average of the plurality of predicted values as the final t k+1 The predicted value of the time may be determined as the final t by a weighted average of a plurality of predicted values k+1 Predicted value of time.
In order to further ensure the accuracy of the predicted value, the computer can also improve the accuracy of the predicted value by adding a method for updating the weight. Specifically, the computer may determine t by the following steps k+1 Predicted value of time:
s131, according to t corresponding to the prediction model k Update weight, third position and t of time k Determining a t corresponding to a predictive model according to a predicted value of time k+1 Updating weight of time.
For each prediction model, first, the computer may calculate the corresponding t according to the prediction model k Determining the difference between the predicted value of the moment and the third position, and determining the correspondence of the prediction modelIs a target of the evaluation value of (a).
Specifically, the computer may determine the evaluation value corresponding to the prediction model using the following formula:
wherein,representing t corresponding to the jth predictive model k Predicted value of moment, v j (k) Representing the evaluation value, t, corresponding to the jth predictive model k Time sum t k-1 The time intervals are one output period of the astronomical navigation system.
And secondly, the computer can determine an updated value corresponding to the prediction model according to the evaluation value and the prediction error corresponding to the prediction model.
Specifically, the computer may determine the updated value corresponding to the prediction model using the following formula:
wherein, r (k) represents white noise of astronomical navigation, < >>Representing an error variance matrix corresponding to the jth prediction model, S j (k) Representing the prediction error corresponding to the jth prediction model, Λ j (k) Representing the update value, v corresponding to the j-th prediction model j (k) And representing the evaluation value corresponding to the j-th prediction model.
Finally, the computer can calculate the corresponding updated value of the prediction model and the prediction modelCorresponding t k Updating weight of moment to determine t corresponding to the prediction model k+1 Updating weight of time.
Specifically, the computer may determine t corresponding to the prediction model using the following formula k+1 Update weight of time:
wherein c represents an update coefficient, μ j (k) Representing t corresponding to the jth predictive model k+1 Update weight, μ for time instant j (k-1) represents t corresponding to the jth predictive model k Updating weight of time.
S132, according to each prediction model and t corresponding to each prediction model k+1 And determining a predicted value corresponding to each prediction model by the updated weight value and the third position of the moment.
The following formula can be obtained from the formula (30) and the formula (27):
specifically, the computer may determine a prediction value corresponding to each prediction model according to equation (31).
S133, determining t according to the prediction values corresponding to the prediction models k+1 Predicted value of time.
In the embodiment of the present application, the computer may sum the prediction values corresponding to the prediction models, determine an average value according to the sum value, and determine the average value as t k+1 Predicted value of time.
Specifically, the computer may determine t using the following formula k+1 The sum of the predicted values of the moments.
Wherein,the sum of the prediction values corresponding to the respective prediction models is represented, and r represents the total number of the prediction models.
S140, according to t k+1 The predicted value of the time corrects the fourth position.
After the processing of the steps, the computer can at t k+1 Get t before the moment k+1 Predicted value of time and at t k+1 According to time t k+1 Correcting a fourth position by the predicted value of the moment, wherein the fourth position is the position of the computer at t k+1 The position of the aircraft is obtained at the moment through an inertial navigation system.
Simulation experiment verification is carried out on an inertial correction method of astronomical inertial integrated navigation. In the simulation system, the initial position of the aircraft may be set to be 1Km from the ground in the air, and referring to fig. 2, fig. 2 is a flight trajectory diagram of the aircraft provided in the embodiment of the present application. Fig. 3 can be obtained through system analysis, and fig. 3 is a comparison chart of the time-dependent positioning error before and after inertial correction according to the embodiment of the present application. As can be seen from fig. 3, the accuracy of longitude, latitude and altitude before inertial correction is 50m, 50m and 20m, respectively, while the accuracy of longitude, latitude and altitude after inertial correction is 10m, 10m and 20m, respectively. Therefore, after compensation using inertial correction, the accuracy of longitude and latitude increases from 50m to 10m. From this it can be concluded that: the inertial correction method can effectively improve the accuracy of longitude and latitude in navigation information with little effect on the accuracy of altitude location because the inertial navigation system does not provide altitude location, so in the inertial correction method, altitude information is not compensated. The conclusion is consistent with the theoretical analysis, and the fact that the inertial correction method provided by the embodiment of the application can effectively improve the navigation precision of the astronomical inertial integrated navigation system is verified.
Further, by simulating the heading accuracy of the aircraft before and after the inertial correction, fig. 4 may be obtained, and fig. 4 is a comparison chart of the heading error before and after the inertial correction with time provided in the embodiment of the present application. As can be seen from fig. 4, the heading angle accuracy of the aircraft is 8' before the inertial correction; after inertial correction, the heading angle accuracy of the aircraft is improved to 0.5'. Simulation results show that: the inertial correction method has obvious effect on improving the heading angle accuracy of the aircraft.
Further, by simulating the attitude speed accuracy of the aircraft before and after the inertial correction, fig. 5 may be obtained, and fig. 5 is a comparison chart of the inertial correction before and after the inertial correction with time change. As can be seen from FIG. 5, the forward east, north and sky attitude speed accuracies were 0.01m/s, 0.1m/s and 0.01m/s, respectively, while the forward east, north and sky attitude speed accuracies were 0.3m/s, 1.5m/s and 0.03m/s, respectively, after inertial correction. Therefore, after inertial correction, the east and north direction gesture speed accuracy is improved by one order of magnitude, and the sky direction gesture speed accuracy is basically unchanged. From this it can be concluded that: the inertial correction method can effectively improve the east and north direction gesture speed accuracy in the navigation information, and has almost no influence on the sky direction gesture speed, for the same reason as the positioning accuracy influence in fig. 3. The conclusion is consistent with the theoretical analysis, and the fact that the inertial correction method provided by the invention can effectively improve the gesture speed precision of the astronomical inertial integrated navigation system is verified.
In an embodiment of the present application, the computer obtains the determined aircraft at t by the inertial navigation system k The first position of moment and the acquisition of the position of the aircraft determined by the astronomical navigation system at t k A second position at the moment, performing extended Kalman filtering on the first position and the second position to obtain a third position, and determining t according to a plurality of preset prediction models and the third position k+1 Predicted value of time, finally according to t k+1 Correcting a fourth position by the predicted value of the moment, wherein the fourth position is a position at t k+1 The position of the aircraft is obtained at the moment through an inertial navigation system. Through the technical scheme, the application can be at t k+1 Determining in advance that the second position is at t before the moment k+1 The predicted value of the moment ensures that the computer can correct the fourth position in time through the predicted value when obtaining the fourth position, thereby eliminating the influence of time delay in the existing correction technology and improving the correction precision of the correction technology.
Based on the same inventive concept, as an implementation of the above method, the embodiment of the present application provides an inertial correction device for astronomical inertial integrated navigation, where the embodiment of the device corresponds to the embodiment of the foregoing method, for convenience of reading, the embodiment of the present device does not describe details in the embodiment of the foregoing method one by one, but it should be clear that the device in the embodiment can correspondingly implement all the details in the embodiment of the foregoing method.
Fig. 6 is a schematic structural diagram of an inertial correction device for astronomical inertial integrated navigation according to an embodiment of the present application, where, as shown in fig. 6, the device provided in this embodiment is applied to an aircraft, and the aircraft includes an inertial navigation system and an astronomical navigation system, and the device provided in this embodiment includes:
an acquisition module 110 for acquiring the determined aircraft at t by the inertial navigation system k The first position of the moment is obtained, and the position t of the aircraft determined by the astronomical navigation system is obtained k A second position of the moment;
the filtering module 120 is configured to perform extended kalman filtering on the first location and the second location to obtain a third location;
a prediction module 130 for determining t according to a preset prediction model and a third position k+1 The prediction model is a diagonal matrix determined according to the output period, the time delay estimated value and a plurality of preset adjusting parameters of the astronomical navigation system;
a correction module 140 for correcting the data according to t k+1 Correcting a fourth position by the predicted value of the moment, wherein the fourth position is at t k+1 Position of aircraft obtained by inertial navigation system at moment, t k Time sum t k+1 The time intervals are one output period of the astronomical navigation system.
Optionally, the prediction model is a plurality of;
the formula of the prediction model is:
wherein phi is j (k/k-1) represents a prediction model, j represents a number of the prediction model, T represents an output period of the astronomical navigation system, e, f, g, n, m and q represent adjustment parameters, respectively, and τ represents a delay estimation value of the astronomical navigation system.
Optionally, the prediction module 130 is specifically configured to:
according to t corresponding to each prediction model k Update weight, third position and t of time k Determining a predicted value of time moment and t corresponding to each predicted model k+1 Updating weight value at moment;
according to each prediction model and t corresponding to each prediction model k+1 The updating weight and the third position of the moment determine the predicted value corresponding to each predicted model;
determining t according to the prediction value corresponding to each prediction model k+1 Predicted value of time.
Optionally, the prediction module 130 is specifically configured to:
for each prediction model, according to t corresponding to the prediction model k Determining an evaluation value corresponding to the prediction model according to the difference value between the predicted value of the moment and the third position;
determining an update value corresponding to the prediction model according to the evaluation value and the prediction error corresponding to the prediction model;
according to the updated value corresponding to the prediction model and t corresponding to each prediction model k Updating weight of moment to determine t corresponding to predictive model k+1 Updating weight of time.
Optionally, the prediction module 130 is specifically configured to:
and determining an evaluation value corresponding to the prediction model by adopting the following formula:
wherein, representing t corresponding to the jth predictive model k+1 Predicted value of time, Z k Representing t k A third position Z corresponding to the moment k-1 Representing t k-1 Third position corresponding to time->Representing t corresponding to the jth predictive model k Predicted value of moment, v j (k) Representing the evaluation value, t, corresponding to the jth predictive model k Time sum t k-1 The time intervals are one output period of the astronomical navigation system.
Optionally, the prediction module 130 is specifically configured to:
the update value corresponding to the prediction model is determined by adopting the following formula:
wherein, r (k) represents white noise of astronomical navigation, < >>Representing an error variance matrix corresponding to the jth prediction model, S j (k) Representing the prediction error corresponding to the jth prediction model, Λ j (k) Representing the update value, v corresponding to the j-th prediction model j (k) And representing the evaluation value corresponding to the j-th prediction model.
Optionally, the prediction module 130 is specifically configured to:
determining t corresponding to the prediction model by adopting the following formula k+1 Update weight of time:
wherein c represents an update coefficient, μ j (k) Representing t corresponding to the jth predictive model k+1 Update weight, μ for time instant j (k-1) represents t corresponding to the jth predictive model k Updating weight of time.
It will be apparent to those skilled in the art that, for convenience and brevity of description, only the above-described division of the functional units and modules is illustrated, and in practical application, the above-described functional distribution may be performed by different functional units and modules according to needs, i.e. the internal structure of the apparatus is divided into different functional units or modules to perform all or part of the above-described functions. The functional units and modules in the embodiment may be integrated in one processing unit, or each unit may exist alone physically, or two or more units may be integrated in one unit, where the integrated units may be implemented in a form of hardware or a form of a software functional unit. In addition, specific names of the functional units and modules are only for convenience of distinguishing from each other, and are not used for limiting the protection scope of the present application. The specific working process of the units and modules in the above system may refer to the corresponding process in the foregoing method embodiment, which is not described herein again.
Based on the same inventive concept, the embodiment of the application also provides electronic equipment. Fig. 7 is a schematic structural diagram of an electronic device provided in an embodiment of the present application, and as shown in fig. 7, the electronic device provided in the embodiment includes: at least one processor 20 (only one shown in fig. 7), a memory 21, and a computer program 22 stored in the memory 21 and executable on the at least one processor 20, the processor 20 implementing the steps in any of the various computer control method embodiments described above when executing the computer program 22.
The processor 20 may be a central processing unit (Central Processing Unit, CPU), and the processor 20 may also be other general purpose processors, digital signal processors (Digital Signal Processor, DSP), application specific integrated circuits (Application Specific Integrated Circuit, ASIC), off-the-shelf programmable gate arrays (Field-Programmable Gate Array, FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, or the like. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The memory 21 may in some embodiments be an internal storage unit of a computer, such as a hard disk or a memory of the computer. The memory 21 may also be an external storage device of the computer in other embodiments, such as a plug-in hard disk provided on the computer, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash Card (Flash Card), etc. Further, the memory 21 may also include both an internal storage unit and an external storage device of the computer. The memory 21 is used to store an operating system, application programs, boot loader (BootLoader), data, and other programs and the like, such as program codes of computer programs and the like. The memory 21 may also be used to temporarily store data that has been output or is to be output.
The embodiment of the application also provides a computer readable storage medium, on which a computer program is stored, which when executed by a processor, implements the method described in the above method embodiment.
In the foregoing embodiments, the descriptions of the embodiments are emphasized, and in part, not described or illustrated in any particular embodiment, reference is made to the related descriptions of other embodiments.
Those of ordinary skill in the art will appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, or combinations of computer software and electronic hardware. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present application.
In the embodiments provided in the present application, it should be understood that the disclosed apparatus/device and method may be implemented in other manners. For example, the apparatus/device embodiments described above are merely illustrative, e.g., the division of the modules or units is merely a logical functional division, and there may be additional divisions when actually implemented, e.g., multiple units or components may be combined or integrated into another system, or some features may be omitted or not performed. Alternatively, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection via interfaces, devices or units, which may be in electrical, mechanical or other forms.
It should also be understood that the term "and/or" as used in this specification and the appended claims refers to any and all possible combinations of one or more of the associated listed items, and includes such combinations.
In addition, in the description of the present application and the appended claims, the terms "first," "second," "third," and the like are used merely to distinguish between descriptions and are not to be construed as indicating or implying relative importance.
Reference in the specification to "one embodiment" or "some embodiments" or the like means that a particular feature, structure, or characteristic described in connection with the embodiment is included in one or more embodiments of the application. Thus, appearances of the phrases "in one embodiment," "in some embodiments," "in other embodiments," and the like in the specification are not necessarily all referring to the same embodiment, but mean "one or more but not all embodiments" unless expressly specified otherwise. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless expressly specified otherwise.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present application, and not for limiting the same; although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present application.
Claims (9)
1. An inertial correction method for astronomical inertial integrated navigation, applied to an aircraft, characterized in that the aircraft comprises an inertial navigation system and an astronomical navigation system, the method comprising:
acquiring the determined t of the inertial navigation system at the aircraft k The first position of the moment is obtained, and the position t of the aircraft determined by the astronomical navigation system is obtained k A second position of the moment;
performing extended Kalman filtering on the first position and the second position to obtain a third position;
determining t according to a preset prediction model and the third position k+1 The prediction model is a diagonal matrix determined according to the output period, the time delay estimated value and a plurality of preset adjusting parameters of the astronomical navigation system;
according to t k+1 Correcting a fourth position by a predicted value of time, wherein the fourth position is at t k+1 The position of the aircraft obtained by the inertial navigation system at the moment, the t k Time of day and t k+1 The output period of the astronomical navigation system is spaced between the moments;
the number of the prediction models is multiple;
the formula of the prediction model is as follows:
wherein phi is j (k/k-1) represents the prediction model, j represents the number of the prediction model, T represents the output period of the astronomical navigation system, e, f, g, n, m and q represent adjustment parameters, respectively, and τ represents the delay estimation of the astronomical navigation systemAnd (5) calculating.
2. The method of claim 1, wherein t is determined based on a predetermined plurality of predictive models and the third location k+1 Predicted values of time instants including:
according to t corresponding to each prediction model k Update weight of time, the third position and t k Determining a predicted value of time moment, and determining t corresponding to each prediction model k+1 Updating weight value at moment;
according to each prediction model and t corresponding to each prediction model k+1 The updated weight value of the moment and the third position determine a predicted value corresponding to each predicted model;
determining the t according to the prediction value corresponding to each prediction model k+1 Predicted value of time.
3. The method according to claim 2, wherein said t corresponds to each of said predictive models k Update weight of time, the third position and t k Determining a predicted value of time moment, and determining t corresponding to each prediction model k+1 The updating weight of the moment comprises the following steps:
for each prediction model, according to t corresponding to the prediction model k Determining an evaluation value corresponding to the prediction model according to the difference value between the predicted value of the moment and the third position;
determining an update value corresponding to the prediction model according to the evaluation value and the prediction error corresponding to the prediction model;
according to the updated value corresponding to the prediction model and t corresponding to the prediction model k Determining t corresponding to the prediction model according to the updated weight of the moment k+1 Updating weight of time.
4. A method according to claim 3, wherein said t corresponds to said predictive model k Determining the predicted value of the moment and the third position, and determining the evaluation corresponding to the prediction modelValue, including:
and determining an evaluation value corresponding to the prediction model by adopting the following formula:
wherein, representing t corresponding to the jth predictive model k+1 Predicted value of time, Z k Representing t k The third position Z corresponding to the moment k-1 Representing t k-1 Third position corresponding to time->Representing t corresponding to the jth predictive model k Predicted value of moment, v j (k) Representing the evaluation value corresponding to the jth predictive model, t k Time of day and t k-1 The time intervals are one output period of the astronomical navigation system.
5. The method of claim 4, wherein determining the updated value corresponding to the prediction model based on the evaluation value and the prediction error corresponding to the prediction model comprises:
and determining an update value corresponding to the prediction model by adopting the following formula:
wherein, r (k) represents white noise of the astronomical navigation,>representing an error variance matrix corresponding to the jth prediction model, S j (k) Representing the prediction error corresponding to the jth prediction model, Λ j (k) Representing the update value, v, corresponding to the jth predictive model j (k) And representing the evaluation value corresponding to the j-th prediction model.
6. The method of claim 5, wherein the updating value corresponding to the prediction model and the t corresponding to the prediction model are based on the updating value corresponding to the prediction model k Determining t corresponding to the prediction model according to the updated weight of the moment k+1 The updating weight of the moment comprises the following steps:
determining t corresponding to the prediction model by adopting the following formula k+1 Update weight of time:
wherein c represents an update coefficient, μ j (k) Representing t corresponding to the jth predictive model k+1 Update weight, μ for time instant j (k-1) represents t corresponding to the jth predictive model k Updating weight of time.
7. An inertial correction device for astronomical inertial integrated navigation applied to an aircraft, characterized in that it comprises an inertial navigation system and an astronomical navigation system, said device comprising:
an acquisition module for acquiring the determined aircraft at t by the inertial navigation system k The first position of the moment is obtained, and the position t of the aircraft determined by the astronomical navigation system is obtained k A second position of the moment;
the filtering module is used for performing extended Kalman filtering on the first position and the second position to obtain a third position;
a prediction module for determining t according to a preset prediction model and the third position k+1 The prediction model is a diagonal matrix determined according to the output period, the time delay estimated value and a plurality of preset adjusting parameters of the astronomical navigation system;
a correction module for correcting the T k+1 Correcting a fourth position by a predicted value of time, wherein the fourth position is at t k+1 The position of the aircraft obtained by the inertial navigation system at the moment, the t k Time of day and t k+1 The output period of the astronomical navigation system is spaced between the moments;
the number of the prediction models is multiple;
the formula of the prediction model is as follows:
wherein phi is j (k/k-1) represents the prediction model, j represents the number of the prediction model, T represents the output period of the astronomical navigation system, e, f, g, n, m and q represent adjustment parameters respectively, and τ represents the time delay estimated value of the astronomical navigation system.
8. An electronic device, comprising: a memory and a processor, the memory for storing a computer program; the processor is configured to perform the method of any of claims 1-6 when the computer program is invoked.
9. A computer readable storage medium, on which a computer program is stored, which computer program, when being executed by a processor, implements the method according to any of claims 1-6.
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