CN109029499A - A kind of accelerometer bias iteration optimizing estimation method based on gravity apparent motion model - Google Patents
A kind of accelerometer bias iteration optimizing estimation method based on gravity apparent motion model Download PDFInfo
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Abstract
The accelerometer bias iteration optimizing estimation method based on gravity apparent motion model that the invention discloses a kind of includes the following steps: that (1) building includes the gravity apparent motion model including accelerometer bias；(2) design weight apparent motion/accelerometer bias parameter optimization objective function；(3) design is based on Newton iteration optimizing gravity apparent motion parameter, accelerometer bias algorithm for estimating.The present invention provides a kind of accelerometer bias iteration optimizing estimation method based on gravity apparent motion model, propose introducing acceleration constant value zero bias in a model, by constructing objective function, the identification of gravity apparent motion model parameter and the estimation of accelerometer bias are realized in the method for parameter optimization, are completed SINS and are initially aligned.
Description
Technical field
The present invention relates to navigation algorithm technical field, especially a kind of accelerometer bias based on gravity apparent motion model
Iteration optimizing estimation method.
Background technique
System-level calibration is to guarantee the important measures of strap-down inertial navigation system (SINS) operating accuracy, system-level calibration
Refer generally to live calibration, i.e., system before work, external auxiliary reference information is utilized in the course of work, carry out including instrument error
Various alignments, calibration inside.Zero-velocity curve based on velocity composition is a kind of common system-level calibration mode.
Zero-velocity curve substantially belongs to one kind of speeds match combination.In velocity composition, horizontal misalignment and acceleration
It counts zero bias and there is coupling, can both bring horizontal velocity error, idol can not be solved between the two.It is generally acknowledged that horizontal accelerometer
Zero bias can not estimate that horizontal misalignment alignment precision is decided by accelerometer bias.
For instrument error problem, scholar thinks that gyroscope noise can be in the integral process of tracking carrier system variation in the industry
In be smoothed, thus its negative effect can be ignored；But acceleration measuring magnitude directly participates in parsing alignment, and acceleration analysis is made an uproar
Sound is affected to alignment result.For acceleration analysis noise, scholar proposes many analytic methods in the industry, as integration method,
Many algorithms such as low pass filtering method, parameter identification method, it is a degree of to improve alignment precision.Wherein utilize the ginseng after identification
Number reconstruct gravity apparent motion carries out parsing alignment, the ultimate precision that precision programmable single-chip system instrument error determines.But the above method rarely has
The constant value problem in instrument error is paid close attention to, thus alignment precision can not still break through the ultimate precision that accuracy of instrument is determined.
Summary of the invention
Technical problem to be solved by the present invention lies in provide a kind of accelerometer bias based on gravity apparent motion model
Iteration optimizing estimation method proposes introducing acceleration constant value zero bias in a model, by constructing objective function, with parameter optimization
Method realize gravity apparent motion model parameter identification and accelerometer bias estimation, complete SINS be initially aligned.
In order to solve the above technical problems, the present invention provides a kind of accelerometer bias iteration based on gravity apparent motion model
Optimizing estimation method, includes the following steps:
(1) building includes the gravity apparent motion model including accelerometer bias；
(2) design weight apparent motion/accelerometer bias parameter optimization objective function；
(3) design is based on Newton iteration optimizing gravity apparent motion parameter, accelerometer bias algorithm for estimating.
Preferably, in step (1), building includes the gravity apparent motion model including accelerometer bias specifically:
Under the conditions of zero-speed, gravity apparent motion model can be quoted from as follows:
E in formula0It is respectively the terrestrial coordinate system at initial time and current time, g with enFor the acceleration of gravity in navigation system
Theoretical value, whereinCan according to earth rotation be aligned the time accurately solve,For a unknown constant value,In longitude and latitude
It is constant value known to one when degree is known；To which formula (1) is rewritable as follows:
In formula (2), A11~33For gravity apparent motion model parameter, ωieFor rotational-angular velocity of the earth, t is the alignment time；
Gravity apparent motion calculated value are as follows:
In formula,For acceleration measuring magnitude；For gravity apparent motion calculated value in inertial system；Initial time is defined to carry
System b0For inertial system i；
Consider that accelerometer constant value zero bias and random error, accelerometer error model can construct as follows:
F in formula (4)bAcceleration theoretical value,It is the constant value zero bias of accelerometer in carrier system, η is
The random noise of accelerometer；
According to formula (4), gravity apparent motion be can be expressed as:
In formulaIt is still random noise；Do not considering random noise
In the case where, (5) formula can be simplified to following formula:
To improve SINS horizontal aligument precision, then need to extract b from formula (6)a。
Preferably, in step (2), design weight apparent motion/accelerometer bias parameter optimization objective function, specifically:
For separation gravity apparent motion and accelerometer bias, rewrites formula (6) and to substitute into formula (5) as follows:
L is theoretically a zero three-dimensional column vector in formula, and matrix A is theoretically a constant value matrix, Ai1、Ai2、Ai3It is square
The corresponding column vector of battle array A；12 location parameter A in formula (7) are solved according to iteration optimization method11~33WithIt can structure
Build following objective function:
F (X)=LT(t)L(t) (8)
In formula,For quantity of state, work as A11~33WithWhen taking true value, have
A at this time11~33WithSolve problems can be converted into optimization problem；To make full use of observation data, more accurately to estimate
A11~33WithValue, by M L in 0~t periodT(t) the cumulative summation of L (t), constructs following objective function:
Preferably, in step (3), design is estimated based on Newton iteration optimizing gravity apparent motion parameter, accelerometer bias
Algorithm, specifically:
Newton method is a kind of linearization technique, and basic idea is that nonlinear equation F (x)=0 is gradually attributed to certain
Linear equation is planted to solve, x is the newton iteration formula of one-dimensional vector are as follows:
Formula (10) shows that the key for solving formula (9) using Newton iteration method is to solve the single order and second-order partial differential coefficient of F (X)
Matrix, i.e. function F (X) its first-order partial derivative and second-order partial differential coefficient can pass through Jacobian matrix and Hessian matrix；
It is as follows that Jacobian matrix is solved to F (X):
To indicate convenient, enableWherein corresponding element can be expressed as follows:
It is as follows that Hessian matrix is solved to F (X):
Specific element may be expressed as:
Following iterative model is constructed according to formula (11)~(14):
Xk+1=Xk+ΔX (16)。
Preferably, in step (3), for formula (10)-(16), specific process of solution is as follows: for current time t,
(31) value of β and α is calculated；
(32) k=1 is set, and the X obtained at the end of the above iteration cycle is initial value；
(33) first-order partial derivative of F (X) is calculated according to formula (11-14)With second-order partial differential coefficientValue；
(34) Δ X is calculated according to formula (15)；
(35) X is updated according to formula (16)；
(36) k=k+1 is set, jumps to third step and restarts to recycle, until X reaches convergence precision or greatest iteration step
Number；
(37) accelerometer bias error is obtained according to iteration result, and weight is carried out to the acceleration of gravity at two moment
Structure, and carry out initial alignment clearing；
In iterative process, iteration is carried out on the basis of upper primary iteration each time, thus only need to be in entire iteration
X initial value is arranged in start time；In iterative process, select greatest iteration step number for iteration end mark.
The invention has the benefit that motivated in (1) initial alignment process merely with zero-speed constraint and the shaking of carrier,
Complete the estimation of acceleration zero bias；(2) it is based on gravity apparent motion model, building regards fortune comprising the gravity including accelerometer bias
Movable model；(3) when constructing objective function, observable data are made full use of, improve the accuracy for solving parameter matrix；(4)
In alignment procedures, accelerometer constant value zero bias can be demarcated, the navigation calculation or other equipment for SINS use.
Detailed description of the invention
Fig. 1 is the gravity apparent motion schematic diagram that the present invention uses.
Fig. 2 is the alignment result figure under the conditions of swaying base of the present invention.
Fig. 3 is accelerometer bias estimated result figure under the conditions of swaying base of the present invention.
Specific embodiment
As shown in Figure 1, a kind of accelerometer bias iteration optimizing estimation method based on gravity apparent motion model, including such as
Lower step:
(1) building includes the gravity apparent motion model including accelerometer bias；
(2) design weight apparent motion/accelerometer bias parameter optimization objective function；
(3) design is based on Newton iteration optimizing gravity apparent motion parameter, accelerometer bias algorithm for estimating.
The cone that the present invention is constituted for gravity apparent motion in inertial system, building include the weight including accelerometer bias
Power apparent motion model, design weight apparent motion/accelerometer bias parameter optimization objective function, and design and sought based on Newton iteration
Excellent gravity apparent motion parameter, accelerometer bias algorithm for estimating.Finally joined using the gravity apparent motion after separation accelerometer zero bias
Digital reconstruction gravity apparent motion, and complete alignment and resolve.
The variation that the acceleration of gravity direction and size with certain point of earth rotation are observed in inertial system, constitutes the circle
Cone.Using the corresponding gravity apparent motion model comprising including accelerometer bias of gyroscope and accelerometer structure figures 1, specifically
Include the following steps:
Under the conditions of zero-speed, gravity apparent motion model can be quoted from as follows:
E in formula0It is respectively the terrestrial coordinate system at initial time and current time, g with enFor the acceleration of gravity in navigation system
Theoretical value, whereinCan according to earth rotation be aligned the time accurately solve,For a unknown constant value,In longitude and latitude
It is constant value known to one when degree is known.To which formula (1) is rewritable as follows:
In formula (2), A11~33For gravity apparent motion model parameter, ωieFor rotational-angular velocity of the earth, t is the alignment time.
Gravity apparent motion calculated value are as follows:
In formula,For acceleration measuring magnitude；For gravity apparent motion calculated value in inertial system；Initial time is defined to carry
System b0For inertial system i.
Consider that accelerometer constant value zero bias and random error, accelerometer error model can construct as follows:
F in formula (4)bAcceleration theoretical value,It is the constant value zero bias of accelerometer in carrier system, η
It is the random noise of accelerometer.
According to formula (4), gravity apparent motion be can be expressed as:
In formulaIt is still random noise.Do not considering random noise
In the case where, (5) formula can be simplified to following formula:
To improve SINS horizontal aligument precision, then need to extract b from formula (6)a。
Design weight apparent motion/accelerometer bias parameter optimization objective function, specifically includes:
For separation gravity apparent motion and accelerometer bias, rewrites formula (6) and to substitute into formula (5) as follows:
L is theoretically a zero three-dimensional column vector in formula, and matrix A is theoretically a constant value matrix, Ai1、Ai2、Ai3It is square
The corresponding column vector of battle array A, such as Ai1=[A11 A21 A31]T.12 positions in formula (7) are solved according to iteration optimization method
Set parameter A11~33WithFollowing objective function can be constructed:
F (X)=LT(t)L(t) (8)
In formula,For quantity of state.Work as A11~33WithWhen taking true value, haveThis
When A11~33WithSolve problems can be converted into optimization problem.To make full use of observation data, more accurately to estimate A11~33
WithValue, the present invention is by M L in 0~t periodT(t) the cumulative summation of L (t), constructs following objective function:
Design is based on Newton iteration optimizing gravity apparent motion parameter, accelerometer bias algorithm for estimating, specifically includes:
Newton method is a kind of linearization technique, and basic idea is that nonlinear equation F (x)=0 is gradually attributed to certain
Linear equation is planted to solve.X is the newton iteration formula of one-dimensional vector are as follows:
Formula (10) shows that the key for solving formula (9) using Newton iteration method is to solve the single order and second-order partial differential coefficient of F (X)
Matrix, i.e. function F (X) its first-order partial derivative and second-order partial differential coefficient can pass through Jacobian matrix and Hessian matrix.
It is as follows that Jacobian matrix is solved to F (X):
To indicate convenient, enableWherein corresponding element can be expressed as follows:
It is as follows that Hessian matrix is solved to F (X):
Specific element may be expressed as:
Following iterative model is constructed according to formula (11)~(14):
Xk+1=Xk+ΔX (16)
Specific process of solution is as follows: for current time t,
Step 1: the value of β and α is calculated；
Step 2: setting k=1, and the X obtained at the end of the above iteration cycle is initial value；
Step 3: the first-order partial derivative of F (X) is calculated according to formula (11-14)With second-order partial differential coefficient
Value；
Step 4: Δ X is calculated according to formula (15)；
Step 5: X is updated according to formula (16)；
Step 6: setting k=k+1 jumps to third step and restarts to recycle, until X reaches convergence precision or greatest iteration
Step number；
Step 7: accelerometer bias error is obtained according to iteration result, and the acceleration of gravity at two moment is carried out
Reconstruct, and carry out initial alignment clearing.
In iterative process, iteration is carried out on the basis of upper primary iteration each time, thus only need to be in entire iteration
X initial value is arranged in start time；In iterative process, select greatest iteration step number for iteration end mark.
Beneficial effects of the present invention are verified by emulation as follows:
Matlab simulates inertia type instrument data
Swinging condition is by taking the naval vessel under the conditions of mooring as an example, it is assumed that under the influence of stormy waves, naval vessel shakes across the sea
Cyclically-varying is done in movement, pitching, roll and course, and mathematical model is as follows:
A in formulaP、AR、AHFor the rocking tendency in pitching, rolling and course, fP、fR、fHFor corresponding wobble frequency, θP、θR、
θHFor starting phase angle, P0、R0、H0For initial attitude angle.Under swaying base, the velocity and acceleration on naval vessel is all zero.If used
Property instrument be medium accuracy device,
Sub- inertia type instrument gross data is obtained by above-mentioned emulation digital simulation, and is superimposed corresponding instrument error on it
As instrument actual acquired data, sub- inertial navigation samples the instrument actual acquired data, is used for navigation calculation, sampling week
Phase is 10ms.
The relevant parameter of emulation:
Naval vessel initial position: 118 ° of east longitude, 32 ° of north latitude；
Ship speed: 0m/s；
Ship sway amplitude: 10 ° of pitching, 7 ° of rolling, boat shake 8 °；
The ship sway period: pitching 12s, rolling 8s, boat shake 12s；
Ship sway initial phase: being 0；
Naval vessel initial heading: being 0 °；
Equatorial radius: 6378165m；
Earth ellipsoid degree: 1/298.3；
Earth surface acceleration of gravity: 9.8m/s2；
Rotational-angular velocity of the earth: 15.04088 °/h；
Gyroscope constant value error: 0.01 °/h；
Gyroscopic drift error: 0.005 °/h；
Accelerometer bias: x, y, z-axis are respectively 80ug, 100ug, 120ug；
Accelerometer Random Drift Error: being 50ug；
The verifying that alignment is calculated with accelerometer constant value zero bias
Proof of algorithm is carried out in ordinary PC.Simulation time 2500s, during simulation process, (1) generates instrumented data；
(2) according to instrumented data and accelerometer bias error, gravity apparent motion model is rebuild；(3) Optimization goal function is designed；(4)
It introduces Newton iteration method and carries out parameter optimization (5) using the gravity apparent motion parameter value reconstruct gravity after separation accelerometer zero bias
Apparent motion simultaneously participates in alignment resolving；(6) it repeats the above steps.Fig. 2 and 3 is respectively alignment result and accelerometer constant value zero bias
Error.
Zero indicates that zero curve, ideal eH, ideal eP, ideal eR respectively indicate course angle, pitch angle and cross in Fig. 2
The limit alignment precision of roll angle.Each curve shows under swaying base in figure, and the method (method 2) that the present invention designs is effective
Complete initial alignment, and to be superior to the strapdown compass based on inertial system gravity apparent motion initial for horizontal aligument accuracy and speed
The horizontal aligument precision of alignment methods (method 1)
Dotted line indicates to add table zero bias theoretical value in curve in Fig. 3, and it is attached that 3 axis add table zero bias that can quickly converge on right value
Closely, show under swaying base, the method that the present invention designs can efficiently accomplish the calibration of three axis accelerometer.
Claims (5)
1. a kind of accelerometer bias iteration optimizing estimation method based on gravity apparent motion model, which is characterized in that including such as
Lower step:
(1) building includes the gravity apparent motion model including accelerometer bias；
(2) design weight apparent motion/accelerometer bias parameter optimization objective function；
(3) design is based on Newton iteration optimizing gravity apparent motion parameter, accelerometer bias algorithm for estimating.
2. the accelerometer bias iteration optimizing estimation method based on gravity apparent motion model as described in claim 1, special
Sign is, in step (1), building includes the gravity apparent motion model including accelerometer bias specifically:
Under the conditions of zero-speed, gravity apparent motion model can be quoted from as follows:
E in formula0It is respectively the terrestrial coordinate system at initial time and current time, g with enIt is theoretical for the acceleration of gravity in navigation system
Value, whereinCan according to earth rotation be aligned the time accurately solve,For a unknown constant value,Longitude and latitude
Know constant value known to Shi Weiyi；To which formula (1) is rewritable as follows:
In formula (2), A11~33For gravity apparent motion model parameter, ωieFor rotational-angular velocity of the earth, t is the alignment time；
Gravity apparent motion calculated value are as follows:
In formula,For acceleration measuring magnitude；For gravity apparent motion calculated value in inertial system；Define initial time carrier system b0
For inertial system i；
Consider that accelerometer constant value zero bias and random error, accelerometer error model can construct as follows:
F in formula (4)bAcceleration theoretical value,It is the constant value zero bias of accelerometer in carrier system, η is to accelerate
Spend the random noise of meter；
According to formula (4), gravity apparent motion be can be expressed as:
In formula It is still random noise；In the feelings for not considering random noise
Under condition, (5) formula can be simplified to following formula:
To improve SINS horizontal aligument precision, then need to extract b from formula (6)a。
3. the accelerometer bias iteration optimizing estimation method based on gravity apparent motion model as described in claim 1, special
Sign is, in step (2), design weight apparent motion/accelerometer bias parameter optimization objective function, specifically:
For separation gravity apparent motion and accelerometer bias, rewrites formula (6) and to substitute into formula (5) as follows:
L is theoretically a zero three-dimensional column vector in formula, and matrix A is theoretically a constant value matrix, Ai1、Ai2、Ai3It is matrix A
Corresponding column vector；12 location parameter A in formula (7) are solved according to iteration optimization method11~33WithIt can construct
Following objective function:
F (X)=LT(t)L(t) (8)
In formula,For quantity of state, work as A11~33WithWhen taking true value, haveAt this time
A11~33WithSolve problems can be converted into optimization problem；To make full use of observation data, more accurately to estimate A11~33
WithValue, by M L in 0~t periodT(t) the cumulative summation of L (t), constructs following objective function:
4. the accelerometer bias iteration optimizing estimation method based on gravity apparent motion model as described in claim 1, special
Sign is, in step (3), design is based on Newton iteration optimizing gravity apparent motion parameter, accelerometer bias algorithm for estimating, specifically
Are as follows:
Newton method is a kind of linearization technique, and basic idea is that nonlinear equation F (x)=0 is gradually attributed to certain line
Property equation solve, x is the newton iteration formula of one-dimensional vector are as follows:
Formula (10) shows that the key for solving formula (9) using Newton iteration method is to solve the single order and second-order partial differential coefficient square of F (X)
Battle array, i.e. function F (X) its first-order partial derivative and second-order partial differential coefficient can pass through Jacobian matrix and Hessian matrix；
It is as follows that Jacobian matrix is solved to F (X):
To indicate convenient, enableWherein corresponding element can be expressed as follows:
It is as follows that Hessian matrix is solved to F (X):
Specific element may be expressed as:
Following iterative model is constructed according to formula (11)~(14):
Xk+1=Xk+ΔX (16)。
5. the accelerometer bias iteration optimizing estimation method based on gravity apparent motion model as claimed in claim 4, special
Sign is, in step (3), for formula (10)-(16), specific process of solution is as follows: for current time t,
(31) value of β and α is calculated；
(32) k=1 is set, and the X obtained at the end of the above iteration cycle is initial value；
(33) first-order partial derivative of F (X) is calculated according to formula (11-14)With second-order partial differential coefficientValue；
(34) Δ X is calculated according to formula (15)；
(35) X is updated according to formula (16)；
(36) k=k+1 is set, jumps to third step and restarts to recycle, until X reaches convergence precision or greatest iteration step number；
(37) accelerometer bias error is obtained according to iteration result, and the acceleration of gravity at two moment is reconstructed, and
Carry out initial alignment clearing；
In iterative process, iteration is all to carry out on the basis of upper primary iteration, thus need to only start in entire iteration each time
X initial value is arranged in moment；In iterative process, select greatest iteration step number for iteration end mark.
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