CN103438899A - Method and system for compensating errors generated by inertia measurement system during moving - Google Patents
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Abstract
The invention relates to a method and system for compensating errors generated by an inertia measurement system during moving. The method comprises the following steps: setting a function a (t) for representing a actual truth value of sensor offset or object motion physical quantity; receiving sending data, output by a sensor, of the inertia measurement system in a moving state at a preset time interval delta t, and processing the sensing data to obtain a plurality of data Aj, wherein j is equal to 1, 2, 3,...n; aiming at least one time point tj=delta t*j, carrying out low-order start counting on the plurality of functions by using a primary function according to experience or reasonable guess to be used as a limit condition of curve fitting and/or using boundary, and obtaining a limit condition of at least one group of (Aj-a (t)) and a (t) through processing; solving an expression of the function a (t) according to the limit condition of the at least one group of (Aj-a (t)) and a (t) and a static condition; and obtaining a fitting function of the (Aj-a (t)) and Aj according to the expression of the function a (t), thereby realizing offset elimination. By implementing the invention, the errors can be effectively eliminated, and the measurement data precision is improved.
Description
Technical field
The present invention relates to inertial measurement system, more particularly, relate to a kind of method and system that compensate the error that inertial measurement system produces at the volley.
Background technology
The current problem due to technique, most inertial sensors can not reach the requirement of desirable device, also there are in actual use some intrinsic errors own, as attitude error, acceleration error or velocity error, or due to internal noise, skew, the caused error of rotation, some can measure these errors, some can not be measured, no matter whether can detect, it all can display in actual applications in some way, cause huge injury to system, even cause system crash.
To sensor accelerometer for example, gyroscope, the Data processing of geomagnetic sensor etc. is found, sensor is owing to there being internal noise, or be that under stationary state, output valve has deviation zero point, perhaps because multi-axial sensor add owing to rotatablely moving that each axle central point differs and cause original output data (acceleration, angular velocity, magnetism intensity etc.) deviation between appearance and actual value, perhaps raw data is through an integration, also can produce deviation after quadratic integral, if such deviation is not proofreaied and correct effectively, will greatly affect the precision of data, even cause data disperse and lost efficacy.
If side-play amount is eliminated and will effectively be improved data precision, and all there are such side-play amount problem in accelerometer, gyroscope, geomagnetic sensor data, and the error no matter which kind of factor produces finally can embody with certain side-play amount.Therefore be necessary to develop a kind of method and system of eliminating side-play amount, to reach the elimination error, the purpose of systems stabilisation.
Summary of the invention
The technical problem to be solved in the present invention is, has in actual use the problem of error for existing inertial sensor, and a kind of method and system that compensate the error that inertial measurement system produces at the volley are provided.
The technical solution adopted for the present invention to solve the technical problems is: a kind of method that compensates the error that inertial measurement system produces at the volley is provided, comprises:
A, function a (t) is set, in order to the true value of the physical quantity reality that represents the object of which movement that sensor offset amount in described inertial measurement system or sensor will measure, wherein t means the time;
B, with the sense data of inertial measurement system under motion state of predetermined time interval of delta t receiving sensor output, and described sense data is processed, to obtain a plurality of data A
j, j=1,2,3 ... n;
C, at least one time point t
j=Δ t*j, use curve matching and/or use the qualifications on border, treatedly draw at least one group of (A
j-a (t)), the qualifications of a (t); Wherein, when function a (t) representative sensor side-play amount, (A
j-a (t)) representative does not truly have the exercise data of skew; During the true value of the physical quantity reality of the object of which movement that will measure when function a (t) representative sensor, (A
j-a (t)) represent side-play amount;
D, according to described at least one group of (A
j-a (t)), qualifications and the quiescent conditions of a (t), obtain the expression formula of function a (t);
E, according to the expression formula of function a (t), obtain (A
j-a (t)), A
jfitting function, thereby realize that side-play amount eliminates.
In the method for the error produced at the volley at compensation inertial measurement system of the present invention, step C comprises:
C1, to (A
j-a (t)) and a (t), use curve matching and/or use the qualifications on border, draw first group of (A
j-a (t)), the qualifications of a (t);
C2, to A
j, a (t) and (A
j-a (t)) once and/or quadratic integral, use curve matching and/or use the qualifications on border, draw second group of (A
j-a (t)), the qualifications of a (t); And/or
C3, to (A
j-a (t)) and/or a (t) once and/or quadratic integral, use quiescent conditions, draw the 3rd group of (A
j-a (t)), the qualifications of a (t).
In the method for the error produced at the volley at compensation inertial measurement system of the present invention, described function a (t) means by following form:
The k rank polynomial expression of time t, k=0 wherein, 1,2 ... n, or
The linear combination a0+ Σ (a of sine and cosine function
ksin (kt)+b
kcos (kt)), wherein, a0, a
k, b
kfor undetermined coefficient, k=1,2 ... n, or
Any linear combination of front m function of denumerable interval orthogonal function base on mathematics, wherein m is predetermined positive integer.
In the method for the error produced at the volley at compensation inertial measurement system of the present invention, described sense data is one or more in acceleration, speed, angular velocity, angular acceleration, and described function a (t) is correspondingly one or more in acceleration, speed, angular velocity, angular acceleration.
In the method for the error produced at the volley at compensation inertial measurement system of the present invention, described step D comprises that the method processing of using method of Lagrange multipliers or differential and qualifications and limited boundary condition calculates all coefficients in function a (t), to obtain the expression formula of function a (t).
In the method for the error produced at the volley at compensation inertial measurement system of the present invention, in described step B, described sense data is processed and comprised, sense data is carried out to following at least one processing: filtering algorithm, rotation, through continuous function conversion and integration.
In the method for the error produced at the volley at compensation inertial measurement system of the present invention, described steps A comprise by the test or empirical value function a (t) is set.
The present invention solves another technical scheme that its technical matters adopts: construct a kind of system that compensates the error that inertial measurement system produces at the volley, comprising:
The function setup module, for function a (t) is set, in order to the true value of the physical quantity reality that represents the object of which movement that sensor offset amount in described inertial measurement system or sensor will measure, wherein t means the time;
The sense data processing module, for the sense data of inertial measurement system under motion state with predetermined time interval of delta t receiving sensor output, and processed described sense data, to obtain a plurality of data A
j, j=1,2,3 ... n;
Qualifications is confirmed module, for at least one time point t
j=Δ t*j, use curve matching and/or use the qualifications on border, treatedly draw at least one group of (A
j-a (t)), the qualifications of a (t); Wherein, when function a (t) representative sensor side-play amount, (A
j-a (t)) representative does not truly have the exercise data of skew; During the true value of the physical quantity reality of the object of which movement that will measure when function a (t) representative sensor, (A
j-a (t)) represent side-play amount;
Function solves module, for according to described at least one group of (A
j-a (t)), qualifications and the quiescent conditions of a (t), solve the expression formula of function a (t);
Fitting module, the expression formula for according to function a (t), obtain (A
j-a (t)), A
jfitting function, thereby realize that side-play amount eliminates.
In the system of the error produced at the volley at compensation inertial measurement system of the present invention, qualifications confirms that module comprises:
First confirms module, for to (A
j-a (t)) and a (t), use curve matching and/or use the qualifications on border, draw first group of (A
j-a (t)), the qualifications of a (t);
Second confirms module, for to A
j, a (t) and (A
j-a (t)) once and/or quadratic integral, use curve matching and/or use the qualifications on border, draw second group of (A
j-a (t)), the qualifications of a (t); And/or
The 3rd confirms module, for to (A
j-a (t)) and/or a (t) once and/or quadratic integral, use quiescent conditions, draw the 3rd group of (A
j-a (t)), the qualifications of a (t).
In the system of the error produced at the volley at compensation inertial measurement system of the present invention, described function a (t) means by following form:
The k rank polynomial expression of time t, k=0 wherein, 1,2 ... n, or
The linear combination a0+ Σ (a of sine and cosine function
ksin (kt)+b
kcos (kt)), wherein, a0, a
k, b
kfor undetermined coefficient, k=1,2 ... n, or
Any linear combination of front m function of denumerable interval orthogonal function base on mathematics, wherein m is predetermined positive integer.
In the system of the error produced at the volley at compensation inertial measurement system of the present invention, described sense data is one or more in acceleration, speed, angular velocity, angular acceleration, and described function a (t) is correspondingly one or more in acceleration, speed, angular velocity, angular acceleration.
In the system of the error produced at the volley at compensation inertial measurement system of the present invention, described function solves module and uses the method processing of method of Lagrange multipliers or differential and qualifications and limited boundary condition to calculate all coefficients in function a (t), to solve the expression formula of function a (t).
In the system of the error produced at the volley at compensation inertial measurement system of the present invention, described sense data processing module is processed and is comprised described sense data, and sense data is carried out to following at least one processing: filtering algorithm, rotation, through continuous function conversion and integration.
In the system of the error produced at the volley at compensation inertial measurement system of the present invention, described function setup module is by test or empirical value hypothesis function a (t).
Implement the present invention, can effectively eliminate error, improve measure data precision.The parameter under static state by detecting sensor, utilize this parameter to revise the error that inertial measurement system produces at the volley, thereby reached the motion state of rediscover and the purpose of systems stabilisation.
The accompanying drawing explanation
Fig. 1 is the logic diagram that the present invention compensates the system of the error that inertial measurement system produces at the volley;
Fig. 2 is the process flow diagram that the present invention compensates the method for the error that inertial measurement system produces at the volley.
Embodiment
The present invention conceives use zero point or central point information (being exactly the measuring value remained static in theory) compensates the error that inertial measurement system produces at the volley.Wherein, utilize sensor in part has moved or the data that sense in the total movement process and process after information, effectively correct the error produced due to factors such as noise, skew, rotations, make system approach real motion state and systems stabilisation effectively.
Particularly, in technical scheme of the present invention, at first suppose a function a (t), the actual value curve of approximation of the physical quantity of moving in order to representative sensor side-play amount curve of approximation or testee.Wherein the physical quantity of sensor sensing value or testee motion can be one or more in acceleration, speed, angular velocity, displacement, angular displacement, magnetism intensity etc.Function a (t) is definite value not necessarily, can be the k rank polynomial expression of time t, and wherein k can equal 0,1,2 ... n; Or the linear combination a0+ Σ (a of sine and cosine function
ksin (kt)+b
kcos (kt)), k=1,2 wherein ... n; Or any linear combination of front n function of denumerable interval orthogonal function base on mathematics, n selectes, and the numerical value of n is larger, and the degrees of freedom of curve are just higher, and the approximate value obtained just more approaches actual value.
In the object of which movement process, for certain section moved or total movement in the data that sense and process after information, this processing comprises the sense data that sensor is obtained with object of which movement, after filtering algorithm, rotation, through continuous function conversion, one or more once and/or in quadratic integral, with the information after being processed.Wherein, sense data can be one or more in acceleration, speed, angular velocity, angular acceleration, displacement, angular displacement, magnetic force.
If central point has skew, utilize the setting idea of central point side-play amount and quiescent conditions, add the method for curve or once and/or the qualifications on the curve-fitting method after quadratic integral or border or once and/or the setting of the qualifications on the border after quadratic integral or quiescent conditions or once and/or the setting of the quiescent conditions after quadratic integral, obtain the qualifications of many groups, thereby obtain a plurality of equations.These equations are solved, can be in the hope of each coefficient in function a (t), thus obtain the information of side-play amount, calculate side-play amount.As selection, can use method of Lagrange multipliers in mathematics to process the implicit function condition, or implicit function is localised in enough little scope to the generic function condition that draws.Select as another, can use the method processing of differential and limited boundary condition to calculate all coefficients in function a (t), to solve the expression formula of function a (t).
In technical scheme of the present invention, curve can adopt least square method, least absolute value area, be multiplied by the proportion partition function (density function) least square method or be multiplied by the least absolute value area scheduling algorithm of proportion partition function.It should be noted that, in the present invention, the adoptable algorithm of curve is not limited to above-mentioned algorithm, as long as can in the interval function space, define one apart from idea (apart from idea Norm, be the specific term in mathematical theory, in space, define exactly one can digitized generalized distance concept) fitting algorithm all can be suitable for the present invention.As long as enough qualificationss are arranged, the matching of function not necessarily needs to accomplish matching the most applicable or the lowest difference distance, and sensing value true value curve of approximation is the matching curve of approximation of the suitableeest or lowest difference distance not necessarily.
Below in conjunction with accompanying drawing, the present invention will be further described.
As is known to the person skilled in the art, inertial measurement system is arranged on testee usually, in order to measure the motion state of object.As shown in Figure 1, inertial measurement system comprises processing unit 10 and communicates with sensor 30 and the storer 20 of connection, and the electric supply installation (not shown).The system that the present invention compensates the error that inertial measurement system produces at the volley comprises that the function setup module 11, sense data processing module 13, the qualifications that are arranged in processing unit 10 confirm that module 15, function solve module 17 and fitting module 19.Wherein,
Function setup module 11, for function a (t) is set, this function a (t) is used for representing the true value of the physical quantity reality of the object of which movement that sensor offset amount in inertial measurement system or sensor will measure, wherein t means the time.In each embodiment of the present invention, the function setup module is by test or empirical value hypothesis function a (t).In one embodiment of this invention, the k rank polynomial repressentation of time t for function a (t), k=0 wherein, 1,2 ... n.In another embodiment, the linear combination a0+ Σ (a of sine and cosine function for function a (t)
ksin (kt)+b
kcos (kt)) mean, wherein, a0, a
k, b
kfor undetermined coefficient, k=1,2 ... n.In another embodiment, function a (t) shows by any linear combination table of front m function of interval orthogonal function base denumerable on mathematics, and wherein m is predetermined positive integer.
Sense data processing module 13, it is with the sense data of inertial measurement system under motion state of predetermined time interval of delta t receiving sensor 30 output, and sense data is processed, to obtain a plurality of data A
j, j=1,2,3 ... n.In the present invention, the sense data processing module is processed and is comprised described sense data, and sense data is carried out to following at least one processing: filtering algorithm, rotation, through continuous function conversion and integration.
In each embodiment of the present invention, sense data is one or more in acceleration, speed, angular velocity, angular acceleration, and function a (t) is correspondingly one or more in acceleration, speed, angular velocity, angular acceleration.
Qualifications is confirmed module 15, for at least one time point t
j=Δ t*j, rule of thumb or Rational Conjecture use the basis function low order to start at several functions of front to do curve and/or use the qualifications on border, treatedly draw at least one group of (A
j-a (t)), the qualifications of a (t).It should be noted that, when function a (t) representative sensor side-play amount, (A
j-a (t)) representative does not truly have the exercise data of skew; During the true value of the physical quantity reality of the object of which movement that will measure when function a (t) representative sensor, (A
j-a (t)) represent side-play amount.
Function solves module 17, for according to above-mentioned at least one group of (A
j-a (t)), qualifications and the quiescent conditions of a (t), solve the expression formula of function a (t).For example, in one embodiment of this invention, function solves module and uses the method for Lagrange multipliers processing to calculate all coefficients in function a (t), to solve the expression formula of function a (t).In another embodiment of the present invention, function solves module and uses the method processing of differential and limited boundary condition to calculate all coefficients in function a (t), to solve the expression formula of function a (t).
Fitting module 19, the expression formula for according to function a (t), obtain the fitting function of (Aj-a (t)), Aj, thereby realize the side-play amount elimination.
Further, qualifications confirms that module comprises: first confirms module, the second confirmation module and or the 3rd confirmation module.Wherein, first confirms that module is used for (A
j-a (t)) and a (t), use curve matching and/or use the qualifications on border, draw first group of (A
j-a (t)), the qualifications of a (t).Second confirms that module is used for A
j, a (t) and (A
j-a (t)) once and/or quadratic integral, use curve matching and/or use the qualifications on border, draw second group of (A
j-a (t)), the qualifications of a (t).The 3rd confirms that module is used for (A
j-a (t)) and/or a (t) once and/or quadratic integral, use quiescent conditions, draw the 3rd group of (A
j-a (t)), the qualifications of a (t).
In each embodiment of the present invention, quiescent conditions is in continuous data, obtains wherein certain feature, static in order to judge whether.Correspondingly, be judged to be speed when static, acceleration, displacement, angular velocity, angular acceleration, angular displacement is information at zero point.As a N continuous data fall near and comprise 0 interval (N and interval size can be calmly own, but the accuracy of judgement has fine or not difference), or the continuous N number has N to fall near and comprise 0 interval (M and N will reach greatly), or the standard deviation estimator of a N continuous data is less than certain value, or the difference of former and later two adjacent datas falls near and comprises 0 interval (N and interval size can be calmly own continuously, but the accuracy of judgement has fine or not difference), or the poor M number of former and later two adjacent datas has N to fall near and comprise 0 interval (M and N will reach greatly) continuously.For example, A
jwhile being acceleration, certain quiescent conditions generation speed should be 0, but A
jan integration (Σ A
jΔ T, i.e. speed) not but 0, thus just contain the information of acceleration side-play amount here, and can calculate, so can obtain (A
j-a (t)), the qualifications of a (t).
As shown in Figure 2, the method that the present invention compensates the error that inertial measurement system produces at the volley comprises:
At first, in steps A, function a (t) is set, in order to the true value of the physical quantity reality that represents the object of which movement that sensor offset amount in described inertial measurement system or sensor will measure, wherein t means the time.
Then, in step B, with the sense data of inertial measurement system under motion state of predetermined time interval of delta t receiving sensor output, and described sense data is processed, to obtain a plurality of data A
j, j=1,2,3 ... n.
In step C, at least one time point t
j=Δ t*j, rule of thumb or Rational Conjecture use the basis function low order to start at several functions of front to do curve and/or use the qualifications on border, treatedly draw at least one group of (A
j-a (t)), the qualifications of a (t); Wherein, when function a (t) representative sensor side-play amount, (A
j-a (t)) representative does not truly have the exercise data of skew; During the true value of the physical quantity reality of the object of which movement that will measure when function a (t) representative sensor, (A
j-a (t)) represent side-play amount;
In step D, according to described at least one group of (A
j-a (t)), qualifications and the quiescent conditions of a (t), obtain the expression formula of function a (t);
In step e, the expression formula according to function a (t), obtain (A
j-a (t)), A
jfitting function, thereby realize that side-play amount eliminates.
Further, step C comprises:
Step C1, to (Aj-a (t)) and a (t), use curve matching and/or use the qualifications on border, draw the qualifications of first group (Aj-a (t)), a (t);
Step C2, to Aj, a (t) and (Aj-a (t)) once and/or quadratic integral, use curve matching and/or use the qualifications on border, draw the qualifications of second group (Aj-a (t)), a (t); And/or
Step C3, to (Aj-a (t)) and/or a (t) once and/or quadratic integral, use quiescent conditions, draw the qualifications of the 3rd group (Aj-a (t)), a (t).
In order to understand better the present invention, below the present invention is compensated to the method for the error that inertial measurement system produces at the volley two kinds of embodiments be described respectively.
One, embodiment one, comprises the steps:
1) by test or empirical value, the side-play amount of supposing sensor is function a (t);
2) side-play amount a (t) can be acceleration, speed, angular velocity etc.; A (t) is definite value not necessarily, can use k rank polynomial expression k can equal=0,1,2 ... n; The linear combination a0+ Σ (a of sine and cosine function
ksin (kt)+b
kcos (kt)) k=1,2 ... n; N any linear combination containing number before denumerable interval function substrate also or on any mathematics.N selectes.
3) sense data that detecting sensor motion obtains, algorithm or not after filtering after filtering, rotation or not rotation, through the continuous function conversion or do not change, integration or integration not, obtain data A
j, j=1,2,3 ... n; Wherein data are one or more in acceleration, speed, angular velocity, angular acceleration;
4) because a (t) is A
jside-play amount, identical physical quantity, consider (A
j-a (t));
5) suppose now (A
j-a (t)) be truly there is no the exercise data of skew, a (t) is A
jside-play amount, use curve fitting algorithm (least square method, least absolute value area, be multiplied by least square that proportion distributes, be multiplied by the least absolute value area scheduling algorithm that proportion distributes), and/or use the qualifications on border, obtain first group of (A
j-a (t)), the qualifications of a (t).
6) if A
jonce and/or the integration of secondary be also the data that need, so, be A
j, a (t), (A
j-a (t)) once and/or quadratic integral, if once and/or secondary also exist the qualifications of border qualifications, matched curve, so, can obtain second group of (A
j-a (t)), the qualifications of a (t).
7) utilize quiescent conditions, observe (A
j-a (t)) and/or an integration, the quadratic integral of a (t), whether also produce qualifications, so, can obtain the 3rd group of (A
j-a (t)) and/or the qualifications of a (t).
8) qualifications of comprehensive the one two three group, wherein the implicit function condition can be used method of Lagrange multipliers in mathematics to process, and can calculate all coefficients in a (t), obtains (A
j-a (t)), A
jfitting function, realize and can be used as side-play amount eliminating.
Two, embodiment two, comprise the steps:
1), by test or empirical value, suppose to obtain the function a (t) of sensor;
2) a (t) can be acceleration, speed, angular velocity etc.; A (t) is definite value not necessarily, can use k rank polynomial expression k can equal=0,1,2 ... n, the linear combination a0+ Σ (a of sine and cosine function
ksin (kt)+b
kcos (kt)) k=1,2 ... n, n any linear combination containing number before denumerable interval function substrate also or on any mathematics.N selectes.
3) sense data that detecting sensor motion obtains, algorithm or not after filtering after filtering, rotation or not rotation, through the continuous function conversion or do not change, integration or integration not, obtain data A
j, j=1,2,3 ... n; Data are one or more in acceleration, speed, angular velocity, angular acceleration.
4) a (t) can represent 3) middle A
jnumerical approximation performance.
5) because a (t) is A
jnumerical approximation, identical physical quantity, consider (A
j-a (t))
6) supposition (A
j-a (t)) be side-play amount, the idea of use curve matching (least square method, least absolute value area, be multiplied by the least square that proportion distributes, be multiplied by the least absolute value area that proportion distributes, etc. idea), and/or use the qualifications on border, obtain first group of (A
j-a (t)), the qualifications of a (t).
7) if A
jonce and/or the integration of secondary be also the data that need, so, just be A
j, a (t), (A
j-a (t)) once and/or quadratic integral, if once and/or secondary also exist the border qualifications, the qualifications of matched curve, so, can obtain second group of (A
j-a (t)), the qualifications of a (t).
8) utilize quiescent conditions, observe (A
j-a (t)) and/or an integration, the quadratic integral of a (t), whether also produce qualifications, so, can obtain the 3rd group of (A
j-a (t)) and/or the qualifications of a (t).
9) the comprehensive qualifications of first, second and third group, wherein the implicit function condition can be used method of Lagrange multipliers in mathematics to process, can calculate all coefficients in a (t), obtain the fitting function of (Aj-a (t)), Aj, and can be used as and realize that side-play amount eliminates.
Below provide several examples, to help understanding the present invention.
Example 1
A, establish function a (t) for representing the sensor offset amount of inertial measurement system, the acceleration of motion of sensor sensing testee, sensor offset amount a (t) is assumed to be constant, with the zero degree polynomial expression namely constant k carry out matching, therefore use an order polynomial (k*t-h) to mean speed sensitive offset Δ V (t).
B, in the inertia measurement process, with predetermined time interval of delta t receiving sensor output sensing data, and described sense data is processed, to obtain a plurality of speed data V
j, j=1,2,3 ... n.Wherein at t=T constantly, the speed measuring value is Ve (having met quiescent conditions when t=T).
C, for t=and t=T (having met quiescent conditions when t=0 and the T) these two moment, system is judged these two moment and is remained static, actual speed should be zero.Wherein, t=0 is the exercise duration of testee, speed V now
0=0, the sensor offset amount is also zero.Obtain like this two qualificationss: 1) t=0, V
0=0; 2) during t=T, V
t=0, and the speed measuring value is Ve (Σ A
jΔ T calculates).
D, utilize least square fitting acceleration off-set value (because condition is more than enough, in this example without the least square method condition enough, become the dihydric phenol simultaneous equations) and above-mentioned two qualificationss, can obtain coefficient a and b in function a (t)=(a*t-b), as follows:
1) t=0 is constantly: V=(k*t-h)=-h=0, h=0;
2) t=T is constantly: V=(k*t-h)=-k*T-h=Ve, by the h=0 substitution, obtain k=Ve/T;
Can obtain thus function Δ V (t)=-Ve/T*t.
The error in measurement of E so acceleration (being bias) is-Ve/T that speed is at t
hmodified value constantly is-(Ve/T) * t
h, the modified value of displacement is-1/2* (Ve/T) * t
h 2.
Example 2
A, in a simple single moving process, if function a (t) is for representing the acceleration of motion of inertial measurement system object sensing, rule of thumb or Rational Conjecture, the function a (t) of the actual true value of acceleration is used 1 order polynomial (k*t+h) to carry out matching, therefore uses 2 order polynomials (k/2*t^2+h*t+l) to mean speed amount V (t).
B, in the inertia measurement process, with predetermined time interval of delta t receiving sensor output sensing data, and described sense data is processed, to obtain a plurality of speed data V
j, j=1,2,3 ... n.Wherein at t=T constantly, the speed measuring value is Ve (having met quiescent conditions when t=T).。
C, for t=and t=T (having met quiescent conditions when t=0 and the T) these two moment, system is judged these two moment and is remained static, actual speed should be zero.Wherein, t=0 is the exercise duration of testee, speed V now
0=0, the sensor offset amount is also zero.Obtain like this two qualificationss: 1) t=0, V
0=0; 2) during t=T, V
t=0, and the speed measuring value be Ve (Σ Aj Δ T calculate skew obviously arranged, need to revise).
D, above-mentioned two border qualificationss, can obtain coefficient k, h and l in function V (t)=(k/2*t^2+h*t+l), as follows:
1) t=0 constantly: V=(k/2*t^2+h*t+l)=l=0, l=0;
2) t=T constantly: V=(k/2*t^2+h*t+l)=k/2*t^2+h*t+l=0, by the l=0 substitution, obtains the condition of k/2*t^2+h*t=0;
3) under the condition of k/2*t^2+h*t=0, utilize the least square fitting accekeration, use (k*t+h) fitting data A
j.
E, thus, problem just becomes under the k/2*t^2+h*t=0 condition; (k*t+h) fitting data A
jthe least square fitting problem, can use method of Lagrange multipliers to process and calculate k and h.This example is due to the measured value A that involves the every bit acceleration
jso the formula of k and h performance is not listed, but obviously can calculate and solution arranged.
Example 3
A, in a simple single moving process, establish function a (t) for representing the acceleration of motion of inertial measurement system object sensing, rule of thumb or Rational Conjecture, the function a (t) of the actual true value of acceleration is used Σ a0+ Σ (a
ksin (kt)+b
kcos (kt)), k=1 ... m carrys out matching, therefore uses Σ a0*t+ Σ (a
k/ k*cos (kt)+b
k/ k*sin (kt)) mean speed amount V (t), k=1 ... m.
B, in the inertia measurement process, with predetermined time interval of delta t receiving sensor output sensing data, and described sense data is processed, to obtain a plurality of speed data V
j, j=1,2,3 ... n.Wherein at t=T constantly, the speed measuring value is Ve (having met quiescent conditions when t=T).。
C, convergent-divergent time shaft again, make t=T become t=π (circular constant) for t=and t=π (having met quiescent conditions when t=0 and the π) these two moment, and system is judged these two moment and remained static, and actual speed should be zero.Wherein, t=0 is the exercise duration of testee, speed V now
0=0, the sensor offset amount is also zero.Obtain like this two qualificationss: 1) t=0, V
0=0; 2) during t=π, V
π=0, and the speed measuring value is Ve (Σ A
jΔ T calculates obviously skew, needs to revise).
D, above-mentioned two border qualificationss, can obtain coefficient k, h and l in function V (t)=(k/2*t^2+h*t+l), as follows:
1) t=0 constantly: V=Σ a0*t+ Σ (a
k/ k*cos (kt)+b
k/ k*sin (kt))=0, k=1 ... m,
2) t=π constantly: V=Σ a0*t+ Σ (a
k/ k*cos (kt)+b
k/ k*sin (kt))=0, k=1 ... m, condition;
3) under above-mentioned two conditions, utilize the least square fitting accekeration, use Σ a0+ Σ (a
ksin (kt)+b
kcos (kt))=0, k=1 ... m fitting data A
j.
E, thus, problem just becomes 1) and 2) under the simultaneous condition; Σ a0+ Σ (a
ksin (kt)+b
kcos (kt))=0, k=1 ... m fitting data A
jthe least square fitting problem, can use method of Lagrange multipliers to process and calculate k and h.This example is due to the measured value A that involves the every bit acceleration
jso, Σ a0+ Σ (a
ksin (kt)+b
kcos (kt))=0, k=1 ... the formula of m performance is not listed, but obviously can calculate and solution arranged.
To sum up, the present invention utilizes the due sensor under quiescent conditions to measure the zero data judgement, reach under a quiescent conditions after quadratic integral and should produce the zero data judgement, add curve-fitting method (least square method for example, the least absolute value area, be multiplied by the least square that proportion distributes, or be multiplied by least absolute value area that proportion distributes etc.), curve-fitting method after quadratic integral (least square method for example, the least absolute value area, be multiplied by the least square that proportion distributes, or be multiplied by the least absolute value area scheduling algorithm that proportion distributes), and one or more data in the qualifications on border are eliminated the error that zero point offset amount produces, and as often as possible get rid of the open country value produced at each operation link by multiple condition restriction, realize the stability of system.
Claims (14)
1. a method that compensates the error that inertial measurement system produces at the volley, is characterized in that, comprising:
A, function a (t) is set, in order to the true value of the physical quantity reality that represents the object of which movement that sensor offset amount in described inertial measurement system or sensor will measure, wherein t means the time;
B, with the sense data of inertial measurement system under motion state of predetermined time interval of delta t receiving sensor output, and described sense data is processed, to obtain a plurality of data A
j, j=1,2,3 ... n;
C, at least one time point t
j=Δ t*j, use curve matching and/or use the qualifications on border, treatedly draw at least one group of (A
j-a (t)), the qualifications of a (t); Wherein, when function a (t) representative sensor side-play amount, (A
j-a (t)) representative does not truly have the exercise data of skew; During the true value of the physical quantity reality of the object of which movement that will measure when function a (t) representative sensor, (A
j-a (t)) represent side-play amount;
D, according to described at least one group of (A
j-a (t)), qualifications and the quiescent conditions of a (t), obtain the expression formula of function a (t);
E, according to the expression formula of function a (t), obtain (A
j-a (t)), A
jfitting function, thereby realize that side-play amount eliminates.
2. the method for the error that compensation inertial measurement system according to claim 1 produces at the volley, is characterized in that, step C comprises:
C1, to (A
j-a (t)) and a (t), use curve matching and/or use the qualifications on border, draw first group of (A
j-a (t)), the qualifications of a (t);
C2, to A
j, a (t) and (A
j-a (t)) once and/or quadratic integral, use curve matching and/or use the qualifications on border, draw second group of (A
j-a (t)), the qualifications of a (t); And/or
C3, to (A
j-a (t)) and/or a (t) once and/or quadratic integral, use quiescent conditions, draw the 3rd group of (A
j-a (t)), the qualifications of a (t).
3. the method for the error that compensation inertial measurement system according to claim 2 produces at the volley, is characterized in that, described function a (t) means by following form:
The k rank polynomial expression of time t, k=0 wherein, 1,2 ... n, or
The linear combination a0+ Σ (a of sine and cosine function
ksin (kt)+b
kcos (kt)), wherein, a0, a
k, b
kfor undetermined coefficient, k=1,2 ... n, or
Any linear combination of front m function of denumerable interval orthogonal function base on mathematics, wherein m is predetermined positive integer.
4. the method for the error that compensation inertial measurement system according to claim 3 produces at the volley, it is characterized in that, described sense data is one or more in acceleration, speed, angular velocity, angular acceleration, and described function a (t) is correspondingly one or more in acceleration, speed, angular velocity, angular acceleration.
5. the method for the error that compensation inertial measurement system according to claim 3 produces at the volley, it is characterized in that, described step D comprises that the method processing of using method of Lagrange multipliers or differential and qualifications and limited boundary condition calculates all coefficients in function a (t), to obtain the expression formula of function a (t).
6. the method for the error produced at the volley according to the described compensation inertial measurement system of any one in claim 1 to 5, it is characterized in that, in described step B, described sense data is processed and comprised, sense data is carried out to following at least one processing: filtering algorithm, rotation, through continuous function conversion and integration.
7. the method for the error that compensation inertial measurement system according to claim 6 produces at the volley, is characterized in that, described steps A comprise by the test or empirical value function a (t) is set.
8. a system that compensates the error that inertial measurement system produces at the volley, is characterized in that, comprising:
The function setup module, for function a (t) is set, in order to the true value of the physical quantity reality that represents the object of which movement that sensor offset amount in described inertial measurement system or sensor will measure, wherein t means the time;
The sense data processing module, for the sense data of inertial measurement system under motion state with predetermined time interval of delta t receiving sensor output, and processed described sense data, to obtain a plurality of data A
j, j=1,2,3 ... n;
Qualifications is confirmed module, for at least one time point t
j=Δ t*j, use curve matching and/or use the qualifications on border, treatedly draw at least one group of (A
j-a (t)), the qualifications of a (t); Wherein, when function a (t) representative sensor side-play amount, (A
j-a (t)) representative does not truly have the exercise data of skew; During the true value of the physical quantity reality of the object of which movement that will measure when function a (t) representative sensor, (A
j-a (t)) represent side-play amount;
Function solves module, for according to described at least one group of (A
j-a (t)), qualifications and the quiescent conditions of a (t), solve the expression formula of function a (t);
Fitting module, the expression formula for according to function a (t), obtain (A
j-a (t)), A
jfitting function, thereby realize that side-play amount eliminates.
9. the system of the error that compensation inertial measurement system according to claim 8 produces at the volley, is characterized in that, qualifications confirms that module comprises:
First confirms module, for to (A
j-a (t)) and a (t), use curve matching and/or use the qualifications on border, draw first group of (A
j-a (t)), the qualifications of a (t);
Second confirms module, for to A
j, a (t) and (A
j-a (t)) once and/or quadratic integral, use curve matching and/or use the qualifications on border, draw second group of (A
j-a (t)), the qualifications of a (t); And/or
The 3rd confirms module, for to (A
j-a (t)) and/or a (t) once and/or quadratic integral, use quiescent conditions, draw the 3rd group of (A
j-a (t)), the qualifications of a (t).
10. the system of the error that compensation inertial measurement system according to claim 9 produces at the volley, is characterized in that, described function a (t) means by following form:
The k rank polynomial expression of time t, k=0 wherein, 1,2 ... n, or
The linear combination a0+ Σ (a of sine and cosine function
ksin (kt)+b
kcos (kt)), wherein, a0, a
k, b
kfor undetermined coefficient, k=1,2 ... n, or
Any linear combination of front m function of denumerable interval orthogonal function base on mathematics, wherein m is predetermined positive integer.
11. the system of the error that compensation inertial measurement system according to claim 10 produces at the volley, it is characterized in that, described sense data is one or more in acceleration, speed, angular velocity, angular acceleration, and described function a (t) is correspondingly one or more in acceleration, speed, angular velocity, angular acceleration.
12. the system of the error that compensation inertial measurement system according to claim 10 produces at the volley, it is characterized in that, described function solves module and uses the method processing of method of Lagrange multipliers or differential and qualifications and limited boundary condition to calculate all coefficients in function a (t), to solve the expression formula of function a (t).
13. the system of the error that according to Claim 8 to 12, the described compensation inertial measurement system of any one produces at the volley, it is characterized in that, described sense data processing module is processed and is comprised described sense data, and sense data is carried out to following at least one processing: filtering algorithm, rotation, through continuous function conversion and integration.
14. the system of the error that compensation inertial measurement system according to claim 13 produces at the volley, is characterized in that, described function setup module is by test or empirical value hypothesis function a (t).
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