CN114136310B - Autonomous error suppression system and method for inertial navigation system - Google Patents
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Abstract
The invention provides an inertial navigation system error autonomous suppression system and method, comprising the steps of establishing an inertial navigation error autonomous suppression state equation, establishing an inertial navigation error autonomous suppression observation equation, kalman filtering and the like. Under the condition that auxiliary information such as satellites and odometers is invalid, the method can utilize the lateral displacement and the lateral speed obtained by the calculation of the inertial navigation system in the rapid running process of the track detection vehicle to make differences with the actual lateral displacement and the lateral speed, and utilize the characteristic that the lateral displacement is zero to carry out filtering calculation, so that the accurate estimation and correction of the error of the inertial navigation system are realized, and the inertial measurement precision is improved.
Description
Technical Field
The invention relates to an inertial navigation system error autonomous suppression system and method, in particular to an inertial navigation system error autonomous suppression system and method for a track detection system, and belongs to the technical field of track detection application. Belongs to the technical field.
Background
Along with the continuous development of railway construction in China, existing lines are increasingly reconstructed, expanded and newly built projects, and line mapping plays a decisive role in engineering construction, and directly influences the quality, cost and construction period of engineering. In order to ensure the operation safety of rail transit, in recent years, a rail precision detection technology is rapidly developed, and a large amount of manpower and material resources are invested in a plurality of countries to develop and update various rail detection methods so as to meet the requirements of high speed and heavy load of the current railway. The vehicle-mounted dynamic detection mode has small influence on normal operation, high efficiency and high speed, truly reflects the infrastructure state under the train operation condition, and becomes one of main detection means of the safety states of railway and urban rail transit infrastructures.
The vehicle-mounted orbit detection system realizes high-precision measurement of orbit geometric parameters through information fusion of a plurality of sensors such as inertia, an odometer, a satellite, laser ranging and the like by using an inertia measurement core. The inertial navigation system can continuously provide high-precision information such as position, speed, attitude and the like, and is an indispensable measuring device, but errors of the inertial navigation system accumulate with time, and the error growth of the inertial navigation system needs to be restrained by aid of auxiliary information such as an odometer, satellite positioning and the like.
Satellite signals are easy to interfere, and satellite information is not available in environments where satellite signals are rejected, such as tunnels, jungles and the like. The running speed of the rail detection vehicle is high, and the odometer is damaged due to vibration, abrasion and the like, so that the inertial navigation system has no auxiliary information available, and therefore, how to realize autonomous suppression of errors of the inertial navigation system is particularly important.
Disclosure of Invention
The invention aims to overcome one of the defects in the prior art and provides an inertial navigation system error autonomous suppression system and an inertial navigation system error autonomous suppression method.
The technical solution of the invention is as follows: an inertial navigation system error autonomous suppression method comprises the following steps:
an inertial navigation error autonomous suppression state equation is established,
wherein X (t) is a state variable at time t, and the state variable is represented by a lateral position error delta S of the inertial navigation system pz Lateral velocity error δV pz Three axial misalignment angles phi of the carrier coordinate system X, Y, Z px 、φ py 、φ pz X, Y, Z three-axis gyro drift ε x 、ε y 、ε z Is a filtering state variable, F isA state transition matrix of a continuous state equation corresponding to a state variable at the moment t, wherein w (t) is a random noise vector of the system at the moment t;
an inertial navigation error autonomous suppression observation equation is established,
Z k ＝H·X k +V k
wherein ,Zk At t k The filtering observed quantity of moment is selected, and the lateral displacement error delta S of the inertial navigation system under the running coordinate system of the track detection vehicle is selected pz And lateral velocity error δV pz As a filtering observational quantity, X k At t k Time state variable, H is the observation matrix, V k At t k Observing the amount of noise at the moment;
setting Kalman filtering adaptive factor alpha i ，
wherein ,to normalize the prediction residual, c 0 and c1 Is->A threshold range;
kalman filtering, self-adapting factor alpha according to Kalman filtering i The updating of Kalman filtering parameters is adjusted to realize the estimation of the error of the inertial navigation system.
An inertial navigation system error autonomous suppression system comprises a memory and a processor, wherein the memory stores a computer program, and the processor realizes an inertial navigation system error autonomous suppression method when executing the computer program.
Compared with the prior art, the invention has the beneficial effects that:
(1) Under the condition that auxiliary information such as satellites and odometers are invalid, the method can utilize the lateral displacement and the lateral speed obtained by the calculation of the inertial navigation system in the rapid running process of the track detection vehicle to make differences with the actual lateral displacement and the lateral speed, and utilize the characteristic that the lateral displacement is zero to carry out filtering calculation so as to realize accurate estimation and correction of errors of the inertial navigation system and improve the inertial measurement precision;
(2) The invention determines the self-adaptive factor of Kalman filtering, adjusts the parameters of the filter through the self-adaptive factor, and improves the filtering precision.
Drawings
FIG. 1 is a flow chart of the present invention.
Detailed Description
The present invention will be described in detail with reference to specific examples and drawings.
The invention provides an inertial navigation system error autonomous suppression method, as shown in fig. 1, which comprises the following steps:
an inertial navigation error autonomous suppression state equation is established,
wherein X (t) is a state variable at time t, and the state variable is represented by a lateral position error delta S of the inertial navigation system pz Lateral velocity error δV pz Three axial misalignment angles phi of the carrier coordinate system X, Y, Z px 、φ py 、φ pz X, Y, Z three-axis gyro drift ε x 、ε y 、ε z Is a filter state variable;
f is a state transition matrix of a continuous state equation corresponding to the state variable at the moment t;
w (t) is the system random noise vector at time t.
In the running process of the track detection vehicle, the track detection vehicle is constrained by the railway track, the course change is small, the course of the track detection vehicle can be considered unchanged in a short time, and only the longitudinal speed and the longitudinal displacement along the railway track are zero, and the lateral speed and the lateral displacement along the railway track are zero. Therefore, the invention utilizes the lateral displacement and the lateral speed obtained by the calculation of the inertial navigation system in the running process of the track detection vehicle to make a difference with the actual lateral displacement and the lateral speed, and utilizes the characteristic that the lateral displacement is zero to carry out filtering calculation, thereby realizing the accurate estimation and correction of the error of the inertial navigation system and improving the inertial measurement precision.
The method comprises the following steps:
1. lateral position error δS using inertial navigation system pz Lateral velocity error δV pz Misalignment angle phi of three axial directions px 、φ py 、φ pz Three axial gyro drift ε x 、ε y 、ε z To filter the state variables, the system state variables X, x= [ δs ] are obtained pz δV pz φ px φ py φ pz ε x ε y ε z ] T 。
Lateral position error equation:
lateral velocity error equation:
misalignment angle error equation:
in the formula ,for the state transition matrix from the inertial navigation system carrier coordinate system to the navigation coordinate system,/for the inertial navigation system carrier coordinate system>For the state transition matrix from the navigation coordinate system to the track inspection vehicle running coordinate system, f n 、f u 、f e Respectively represent the north, the sky and the east accelerations, p 21 、p 22 、p 23 、p 11 、p 12 、p 13 Respectively->Is an element of (a).
wherein ,ψ0 For the initial heading angle of the rail test car,λ 0 respectively representing the latitude, longitude and +.>λ represents the latitude and longitude, respectively, of the track inspection vehicle currently located.
2. Establishing a state equation of autonomous error suppression filtering of the inertial navigation system:
wherein X (t) is a state variable at the time t, F is a state transition matrix of a continuous state equation corresponding to the state variable at the time t, and w (t) is a random noise vector of the system at the time t.
The values of the elements in the system state matrix F can be obtained according to the above-derived lateral position error equation, lateral velocity error equation, and misalignment angle error equation.
Discretization can be achieved:
X k ＝Φ k,k-1 X k-1 +Γ k-1 W k-1
wherein ,Xk Is t k The time of day state variable is a function of,at t k-1 From time to t k A system one-step state transition matrix of time, wherein ∈>T is the filtering period, T n For discrete periods, F i Is a system matrix; Γ -shaped structure k-1 =i is the noise driving matrix of the system; w (W) k For excitation noise sequence of system, it satisfies E W k ]＝0，/>Wherein when k=j, δ k,j =1, otherwise 0, q k Is W k Is assumed to be non-negative.
An inertial navigation error autonomous suppression observation equation is established,
Z k ＝H·X k +V k
wherein ,Zk At t k Time-of-day filtering observance, X k At t k The time of day state variable is a function of,to observe the matrix, V k At t k The time observation is noisy.
The method comprises the following steps:
1. selecting lateral displacement error delta S of inertial navigation system under running coordinate system of track detection vehicle pz And lateral velocity error δV pz As the filtering observed quantity, a filtering observed quantity Z is obtained.
2. And establishing an inertial navigation error autonomous suppression observation equation.
The system observation equation may be expressed as follows:
Z k ＝H·X k +V k
in the formula ,to observe the matrix, V k To observe the noise.
Setting Kalman filtering adaptive factor alpha i ，
wherein ,representing the accuracy of the filtered observables for the standardized prediction residual; c 0 and c1 Is->Threshold range, typically 0 < c, determined empirically 0 ＜1.5，3.0＜c 1 ＜4.5，c 0 The smaller the value is, the more strict the condition is, c 1 The smaller the value, the more stringent the condition.
Normalized prediction residualσ R Is the standard deviation of observed noise, +.>One-step prediction of the state.
Kalman filtering is adopted to realize the estimation of the inertial navigation system error.
The Kalman filtering in this step adapts the factor alpha according to the Kalman filtering i To adjust the updating of the Kalman filtering parameters when alpha i Observations all participate in the updating of the filter when =1, when α i When the observed value is approximately equal to 0, the observed value does not participate in updating the filter, and when 0 is less than alpha i < 1, the observed value participates in the specific gravity reduction of the filter update.
According to the calculated Kalman filtering adaptive factor alpha i The equivalent covariance of Kalman filtering can be obtainedBy->The observed noise covariance R in the kalman filter is updated.
R is the observed noise covariance.
The invention adjusts the parameters of the filter by determining the adaptive factor according to the adaptive factor alpha i Can be obtained, when the observed quantity error is small, alpha i The observation values =1 all participate in the updating of the filter; when the observed quantity contains an observed error other than a small predicted value, i.e. 0 < alpha i < 1, the observed value participates in the proportion reduction of the filter update; when the observed quantity contains an observed error other than a large predicted value, alpha i And (4) the observation value does not participate in the updating of the filter.
Let t be k The estimated state of the moment is subject to the system noise sequence W k-1 Driven, the equation of state is described by:
X k ＝Φ k,k-1 X k-1 +Γ k-1 W k-1
for X k The observation equation of (2) satisfies the following relationship
Z k ＝H k X k +V k
in the formula ,Φk,k-1 At t k-1 From time to t k Time-of-day system one-step state transition matrix Γ k-1 Is the noise of the systemDrive matrix, W k H is the excitation noise sequence of the system k Is t k Observation matrix of time system, V k Is t k The time of day system observes a sequence of noise.
At the same time W k and Vk Satisfies the following relationship
E[W k ]＝0，
E[V k ]＝0，
in the formula ,Qk Is W k Is determined by a variance matrix of (1), assuming a non-negative determination,is V k Is assumed to be positive.
Corresponding filtering algorithm can be obtained
State one-step prediction
One-step prediction mean square error array
Filtering gain
State estimation
Estimating a mean square error matrix
Specific Kalman filtering in this step is well known in the art.
The invention further provides a system for realizing the inertial navigation system error autonomous suppression method, which comprises a memory and a processor, wherein the memory stores a computer program, and the processor realizes the inertial navigation system error autonomous suppression when executing the computer program.
The invention is not described in detail in a manner known to those skilled in the art.
Claims (10)
1. An inertial navigation system error autonomous suppression method is characterized by comprising the following steps:
an inertial navigation error autonomous suppression state equation is established,
wherein X (t) is a state variable at time t, and the state variable is represented by a lateral position error delta S of the inertial navigation system pz Lateral velocity error δV pz Three axial misalignment angles phi of the carrier coordinate system X, Y, Z px 、φ py 、φ pz X, Y, Z three-axis gyro drift ε x 、ε y 、ε z For the filtering state variable, F is a state transition matrix of a continuous state equation corresponding to the state variable at the moment t, and w (t) is a random noise vector of the system at the moment t;
an inertial navigation error autonomous suppression observation equation is established,
Z k ＝H·X k +V k
wherein ,Zk At t k The filtering observed quantity of moment is selected, and the lateral displacement error delta S of the inertial navigation system under the running coordinate system of the track detection vehicle is selected pz And lateral velocity error δV pz As a filtering observational quantity, X k At t k Time state variable, H is the observation matrix, V k At t k Observing the amount of noise at the moment;
setting Kalman filtering adaptive factor alpha i ，
wherein ,to normalize the prediction residual, c 0 and c1 Is->A threshold range;
kalman filtering, self-adapting factor alpha according to Kalman filtering i The updating of Kalman filtering parameters is adjusted to realize the estimation of the error of the inertial navigation system;
the Kalman filtering is performed when alpha i Observations all participate in the updating of the filter when =1, when α i When the observed value is approximately equal to 0, the observed value does not participate in updating the filter, and when 0 is less than alpha i < 1, use of equivalent covarianceThe observed noise covariance R in the kalman filter is updated.
2. The inertial navigation system error autonomous suppression method according to claim 1, wherein: the equivalent covariance
3. The inertial navigation system error autonomous suppression method according to claim 1, wherein: the normalized prediction residual wherein σR Is the standard deviation of observed noise, +.>For one-step prediction of state, H k Is t k An observation matrix of the time-of-day system.
4. The inertial navigation system error autonomous suppression method according to claim 1, wherein: the saidThreshold range, 0 < c 0 ＜1.5，3.0＜c 1 ＜4.5。
5. The inertial navigation system error autonomous suppression method according to claim 1, wherein: the inertial navigation error autonomous suppression state equation is established as follows,
step 1, adopting lateral position error delta S of inertial navigation system pz Lateral velocity error δV pz Misalignment angle phi of three axial directions px 、φ py 、φ pz Three axial gyro drift ε x 、ε y 、ε z To filter the state variables, the system state variables X, x= [ δs ] are obtained pz δV pz φ px φ py φ pz ε x ε y ε z ] T ；
And 2, establishing a state equation of autonomous error suppression filtering of the inertial navigation system.
6. The inertial navigation system error autonomous suppression method according to claim 5, wherein: in the step (1) of the above-mentioned process,
lateral position error equation:
lateral velocity error equation:
misalignment angle error equation:
in the formula ,for the state transition matrix from the inertial navigation system carrier coordinate system to the navigation coordinate system,/for the inertial navigation system carrier coordinate system>For the state transition matrix from the navigation coordinate system to the track inspection vehicle running coordinate system, f n 、f u 、f e Respectively represent the north, the sky and the east accelerations, p 21 、p 22 、p 23 、p 11 、p 12 、p 13 Respectively->Is an element of (2);
wherein ,ψ0 For the initial heading angle of the rail test car,λ 0 respectively representing the latitude, longitude and +.>λ represents the latitude and longitude, respectively, of the track inspection vehicle currently located.
7. The inertial navigation system error autonomous suppression method according to claim 6, wherein: the lateral position error equation, the lateral speed error equation and the misalignment angle error equation obtain the values of the elements in the system state matrix F,
discretizing to obtain:
X k ＝Φ k,k-1 X k-1 +Γ k-1 W k-1
wherein ,Xk Is t k The time of day state variable is a function of,at t k-1 From time to t k A system one-step state transition matrix of time, wherein ∈>T is the filtering period, T n For discrete periods, F i Is a system matrix; Γ -shaped structure k-1 =i is the noise driving matrix of the system; w (W) k For excitation noise sequence of system, it satisfies E W k ]＝0，/>Wherein when k=j, δ k,j =1, otherwise 0, q k Is W k Is assumed to be non-negative.
8. The inertial navigation system error autonomous suppression method according to claim 1, wherein: the inertial navigation error autonomous suppression observation equation is established as follows,
step 1, selecting a lateral displacement error delta S of an inertial navigation system under a track detection vehicle running coordinate system pz And lateral velocity error δV pz As the filtering observed quantity, a filtering observed quantity Z is obtained,
step 2, establishing an inertial navigation error autonomous suppression observation equation Z k ＝H·X k +V k 。
9. The inertial navigation system error autonomous suppression method according to claim 1, wherein: the described kalman filtering is performed by means of a filter,
step 1, let t k The estimated state of the moment is subject to the system noise sequence W k-1 The driving, state equation is described by the following equation,
X k ＝Φ k,k-1 X k-1 +Γ k-1 W k-1
for X k The observation equation of (2) satisfies the following relationship
Z k ＝H k X k +V k
in the formula ,Φk,k-1 At t k-1 From time to t k Time-of-day system one-step state transition matrix Γ k-1 For driving matrix for noise of system, W k H is the excitation noise sequence of the system k Is t k Observation matrix of time system, V k Is t k Observing a noise sequence by a time system;
at the same time W k and Vk Satisfies the following relationship
E[W k ]＝0，
E[V k ]＝0，
in the formula ,Qk Is W k Is determined by a variance matrix of (1), assuming a non-negative determination,is V k Is assumed to be positive;
step 2, kalman filtering,
state one-step prediction
One-step prediction mean square error array
Filtering gain
State estimation
Estimating a mean square error matrix
10. An inertial navigation system error autonomous suppression system, characterized by: the inertial navigation system error autonomous suppression method comprises a memory and a processor, wherein the memory stores a computer program, and the processor realizes the inertial navigation system error autonomous suppression method according to any one of claims 1-9 when executing the computer program.
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