CN110487268A - A kind of three increment sculling Error Compensation Algorithm of interpolation inputted based on angular speed and specific force - Google Patents
A kind of three increment sculling Error Compensation Algorithm of interpolation inputted based on angular speed and specific force Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
- G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
- G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/20—Instruments for performing navigational calculations
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Abstract
The present invention provides a kind of three increment sculling Error Compensation Algorithms of interpolation inputted based on angular speed and specific force, belong to navigation algorithm field.The present invention based on three increment sculling Error Compensation Algorithms, devises three increment sculling Error Compensation Algorithm of interpolation under conditions of the input that the input of gyroscope is angular speed and accelerometer is than force information.Pass through angular speed and the specific force matched curve with first three moment and current time, two input angle speeds of interpolation and two input specific forces are distinguished among the input angle speed and input specific force at current time and the input angle speed of previous moment and input specific force, complete three increment sculling error compensation of interpolation.Speed renewal frequency of the invention improves three times compared with the speed renewal frequency of three traditional increment sculling Error Compensation Algorithms, it is identical as the speed renewal frequency of list sample sculling Error Compensation Algorithm, and velocity error is significantly less than list sample sculling Error Compensation Algorithm.
Description
Technical field
The present invention relates to a kind of three increment sculling error compensation of interpolation calculations inputted based on angular speed and specific force
Method belongs to navigation algorithm field.
Background technique
When carrier does linearly coupled and angular oscillation of the same frequency with phase simultaneously, the rectification of speed can be generated on the second axis
Amount, here it is paddle campaigns.Paddle is a kind of high dynamic movement, is occurred if dealing with improperly and updating the speed for the system that will lead to
Error.Therefore, it needs to compensate sculling error in speed renewal process.
Summary of the invention
It is the defeated of angular speed and accelerometer the technical problem to be solved in the present invention is to provide a kind of input in gyroscope
Enter not lose speed renewal frequency, to pass through fast with the angle at first three moment and current time under conditions of than force information
Rate and specific force matched curve, in the input angle speed at current time and the input angle speed and input of input specific force and previous moment
Difference two input angle speeds of interpolation and two input specific forces among specific force, complete the calculation of three increment Compensation for Coning Error of interpolation
Method.
In order to solve the above technical problems, the present invention provides a kind of three increments of interpolation inputted based on angular speed and specific force to draw
Paddle effect errors backoff algorithm, comprising the following steps:
Step 1: the sculling Error Compensation Algorithm based on input for angular speed and specific force is analyzed；
Step 2: the sculling error compensation optimization algorithm based on input for angular speed and specific force is analyzed；
Step 3: design input is the three increment sculling Error Compensation Algorithm of interpolation of angular speed and specific force.
The invention also includes:
1. step 1 detailed process are as follows: analyze the sculling Error Compensation Algorithm based on input for angular speed and specific force.
Taking geographic coordinate system is navigational coordinate system, and the velocity error equation of inertial navigation system is
In formula (1),For strap-down matrix, fbIt is specific force in the projection of carrier system, V is velocity vector, and g is acceleration of gravity
Vector,For earth rotation angular speed navigational coordinate system projection,For position rate navigational coordinate system projection.
If the update cycle of speed is T, in [tk-1,tk] in this period of time, integral operation is carried out to formula (1), obtains tkWhen
The speed that carrier is carved in navigational coordinate system simplifies are as follows:
In formula (2), VkAnd Vk-1Respectively carrier is in tkAnd tk-1The speed at moment, Ck-1For tk-1The strap-down matrix at moment, Δ
θ is angle increment.
Note
Formula (4) is the velocity compensation amount as caused by harmful acceleration, and formula (3) is the velocity compensation amount as caused by specific force, under
Detailed analysis is done in face of formula (3).
In formula (5),It is accelerometer in [tk-1,tk] the period interior speed increment exported.Note
Due to
So
Formula (9) are substituted into formula (5), are had
Formula (10) right end Section 3 is denoted as
The referred to as sculling error compensation item of speed.I.e. when there is angular oscillation and linearly coupled of the same frequency with phase, it can produce
Raw sculling error.
In [tk-1,tk] in this period of time, the angular speed of carrier and specific force are intended respectively with cubic parabola formula
It closes, can obtain
ω(tk-1+ τ)=a+2b τ+3c τ2+4dτ3,0≤τ≤Δt (12)
f(tk-1+ τ)=A+2B τ+3C τ2+4Dτ3,0≤τ≤Δt (13)
Then, angle increment and speed increment may be expressed as:
Δ θ (τ)=a τ+b τ2+cτ3+dτ4 (14)
Δ ν (τ)=A τ+B τ2+Cτ3+Dτ4 (15)
Angular speed and specific force sampling instant are selected asAnd adopted angular speed and specific force are denoted as ω respectively1、
ω2、ω3And f1、f2、f3, and remember tkMoment angular speed and specific force are respectively ω0And f0, it is brought into angular speed and specific force respectively
In expression formula (12) (13), it can obtain
Above formula is solved, can be obtained
So three increment algorithms of sculling error compensation item are as follows:
2. step 2 detailed process are as follows: analyze and calculated based on the sculling error compensation optimization that input is angular speed and specific force
Method.
Assuming that carrier does paddle campaign, angular speed and specific force are respectively
ω (t)=iB Ω cos Ω t (21)
F (t)=jCsin Ω t (22)
Wherein, i and j is the unit vector along the corresponding axis of carrier coordinate system.
Remember ωkAnd fk+lIt is speed update cycle [tk-1,tk] in a angular speed sampled value of kth (k=0 ..., N-1) and
K+l (l >=1, k+l≤N) a specific force sampled value, wherein N is number of samples in the period.Δ t is enabled to indicate tk-tk-1, then have:
Then, have
Wherein, k is along the unit vector orthogonal with i and j axis.
Consider further that another situation.Remember fkAnd ωk+lIt is speed update cycle [tk-1,tk] in kth (k=0 ..., N-1)
A specific force sampled value and kth+l (l >=1, k+l≤N) a angular speed sampled value, then have:
Then, have
Formula (25) is added with formula (28), is had
As can be seen that when carrier does the paddle campaign of the form as shown in formula (21), (22), ωk×fk+l+fk×ωk+l's
Value is unrelated with k, only related with l.At this point, having
ω0×f1+f0×ω1=ω1×f2+f1×ω2=ω2×f3+f2×ω3 (30)
ω0×f2+f0×ω2=ω1×f3+f1×ω3 (31)
It is following form by three increment algorithmic notations of sculling compensation term based on formula (30) and formula (31):
It brings formula (29) into (32), has
The angular speed formula (21) and specific force formula (22) that paddle campaign is done according to carrier, have:
So the paddle compensation term accurately calculated is answered are as follows:
Then, error caused by three increment algorithms (32) may be expressed as:
Since the frequency omega of carrier vibration will not be too high, sampling time interval Δ t is ms grades, so having under normal circumstances
Ω Δ t < 1.In order to minimize Algorithm ErrorIt is ensured that the low order power item of Ω Δ t is 0 as far as possible, take thus
Formula (38) are solved, k can be obtained1=291/2240, k2=3/56, k3=29/6720.Then, three sons of paddle campaign
Sample optimization algorithm are as follows:
3. step 3 detailed process are as follows:
Traditional sculling Error Compensation Algorithm improves sculling error compensation precision by increasing sample number, but
The output frequency of system can be reduced simultaneously.For this problem, the present invention devises a kind of stroke based on angular speed and specific force interpolation
Paddle effect errors backoff algorithm, the algorithm can reach system output frequency and be under the conditions of certain system output accuracy
The system input consistent requirement of frequency.
As shown in Fig. 1, it is assumed that in tk、tk+h/3、tk+ 2h/3 and tk+ h moment collected angular speed and specific force difference
For ω0、ω1、ω2、ω3And f0、f1、f2、f3, by formula (12) (13) it is found that utilizing this four angular speeds and the available ω of specific force
(tk+ τ) and f (tk+ τ) expression formula.Utilize ω (tk+ τ) and f (tk+ τ) expression formula can find out in tkTo tkWhen any in+h
The angular speed at quarter and the value of specific force.
It at this time can be in [tk+2h/3,tk+ h] period in be inserted into the value of two angular speeds and the value of specific force respectivelyWithThen with ω2、ω3And f2、f3Four angular speeds and specific force calculate [tk+
2h/3,tk+ h] sculling error compensation item Δ V in the periodsculk, finally according to tk+ 2h/3 moment corresponding speed is more
New tkThe speed at+h moment.[t can similarly be found outk+h,tk+ 4h/3] sculling error compensation item Δ V in the periodsculk, root
According to tkThe speed at+h moment updates tkThe speed at+4h/3 moment, and so on.The every h/3 of this method carries out a speed and updates,
Speed renewal frequency is identical as the speed renewal frequency of list sample algorithm, is the 1/3 of traditional three increment algorithm speed renewal frequencies.
Detailed derivation process is given below.
ω (t is determined by formula (12) and formula (13)k+ τ) and f (tk+ τ) expression formula.
Output angular speed and output specific force in τ=2h/3 are respectively as follows:
Interpolation angular speed and interpolation specific force in τ=7h/9 are respectively as follows:
Interpolation angular speed and interpolation specific force in τ=8h/9 are respectively as follows:
Output angular speed and output specific force in τ=h are respectively as follows:
Acquiring every multiplication cross by formula (40), (41), (42), (43), (44), (45), (46), (47) is
Formula (48), (49), (50) are substituted into formula (39), can be found out after merging similar terms in [tk+2h/3,tk+1+ h] in
Sculling compensation term are as follows:
The beneficial effects of the present invention are:
It is specific force in the input that the input of gyroscope is angular speed and accelerometer in Strapdown Inertial Navigation System velocity calculated
Under conditions of information, not lose speed renewal frequency, the present invention based on three increment sculling Error Compensation Algorithms, if
Three increment sculling Error Compensation Algorithm of interpolation is counted.Pass through the angular speed and specific force with first three moment and current time
Matched curve, among the input angle speed and input specific force at current time and the input angle speed of previous moment and input specific force
Two input angle speeds of interpolation and two input specific forces respectively complete three increment sculling error compensation of interpolation.
The speed renewal frequency for the three increment sculling Error Compensation Algorithm of angular speed and specific force interpolation that the present invention designs
Three times are improved compared with the speed renewal frequency of three traditional increment sculling Error Compensation Algorithms, with list sample sculling
The speed renewal frequency of Error Compensation Algorithm is identical, and velocity error is significantly less than list sample sculling Error Compensation Algorithm.
Detailed description of the invention
Fig. 1 is angular speed and specific force interpolation schematic diagram；
Fig. 2 is paddle campaign schematic diagram；
Fig. 3 is sky orientation speed error comparison diagram；
Fig. 4 is north orientation speed error comparison diagram；
Fig. 5 is whole design program flow chart.
Specific embodiment
Present invention is further described in detail with specific embodiment with reference to the accompanying drawing.
In conjunction with Fig. 1 to Fig. 4, in the present invention, the sculling error based on input for angular speed and specific force is analyzed first
Then backoff algorithm is analyzed the sculling error compensation optimization algorithm based on input for angular speed and specific force, is finally designed defeated
Enter the three increment sculling Error Compensation Algorithm of interpolation for angular speed and specific force.The angular speed and specific force interpolation that the present invention designs
The speed renewal frequency of three increment sculling Error Compensation Algorithms and three traditional increment sculling Error Compensation Algorithms
Speed renewal frequency compares three times of raising, identical as the speed renewal frequency of list sample sculling Error Compensation Algorithm, and fast
Degree error is significantly less than list sample sculling Error Compensation Algorithm.
Specific implementation step of the invention is as follows:
Step 1: the sculling Error Compensation Algorithm based on input for angular speed and specific force is analyzed.
Step 2: the sculling error compensation optimization algorithm based on input for angular speed and specific force is analyzed.
Step 3: design input is the three increment sculling Error Compensation Algorithm of interpolation of angular speed and specific force.
Specific steps are described as follows:
(1) inertia device gyroscope output angle rate acceleration meter exports specific force；
(2) angular speed and specific force matched curve；
(3) two angular speed values are inserted into respectively in the matched curve of angular speed and specific force and two are compared force value；
(4) sculling compensation term Δ V is calculatedsculk；
(5) renewal speed V；
Compare the velocity error of the identical two methods of speed renewal frequency, by emulation experiment to verify set by the present invention
The superiority of calculating method.
Experiment condition of the invention is as follows: paddle campaign schematic diagram is as shown in Fig. 2, wherein the angle in paddle movement environment
Amplitude is 10 °, and line amplitude is 1g, paddle motion frequency 1Hz, inertia device sample frequency 100Hz, simulation time 6s.Error pair
Than figure such as attached drawing 3, shown in 4.
The three increment sculling error compensation of angular speed and specific force interpolation that the present invention designs it can be seen from simulation result
Algorithm is identical as the speed renewal frequency of list sample sculling Error Compensation Algorithm, and velocity error is significantly less than list sample and draws
Paddle effect errors backoff algorithm.
Claims (4)
1. a kind of three increment sculling Error Compensation Algorithm of interpolation inputted based on angular speed and specific force, it is characterised in that: packet
Include following steps:
Step 1: the sculling Error Compensation Algorithm based on input for angular speed and specific force is analyzed；
Step 2: the sculling error compensation optimization algorithm based on input for angular speed and specific force is analyzed；
Step 3: design input is the three increment sculling Error Compensation Algorithm of interpolation of angular speed and specific force.
2. a kind of three increment sculling error compensation of interpolation inputted based on angular speed and specific force according to claim 1
Algorithm, it is characterised in that: step 1 detailed process are as follows: analyze the sculling error compensation based on input for angular speed and specific force
Algorithm；
Taking geographic coordinate system is navigational coordinate system, and the velocity error equation of inertial navigation system is
In formula,For strap-down matrix, fbIt is specific force in the projection of carrier system, V is velocity vector, and g is gravity acceleration,For earth rotation angular speed navigational coordinate system projection,For position rate navigational coordinate system projection；
If the update cycle of speed is T, in [tk-1,tk] in this period of time, the velocity error equation of inertial navigation system is accumulated
Partite transport is calculated, and t is obtainedkMoment carrier simplifies in the speed of navigational coordinate system are as follows:
In formula, VkAnd Vk-1Respectively carrier is in tkAnd tk-1The speed at moment, Ck-1For tk-1The strap-down matrix at moment, Δ θ are angle increasing
Amount；
Note
ΔVg/corkIt is the velocity compensation amount as caused by harmful acceleration, Δ VsfkIt is the velocity compensation amount as caused by specific force, below
To Δ VsfkDo detailed analysis；
In above formula,It is accelerometer in [tk-1,tk] the period interior speed increment exported；Note
Due to
So
Δ θ (t) × f (t) is substituted into Δ Vsfk, have
Above formula right end Section 3 is denoted as
This is known as the sculling error compensation item of speed；
In [tk-1,tk] in this period of time, the angular speed of carrier and specific force are fitted respectively with cubic parabola formula, it can
ω(tk-1+ τ)=a+2b τ+3c τ2+4dτ3,0≤τ≤Δt
f(tk-1+ τ)=A+2B τ+3C τ2+4Dτ3,0≤τ≤Δt
Then, angle increment and speed increment may be expressed as:
Δ θ (τ)=a τ+b τ2+cτ3+dτ4
Δ ν (τ)=A τ+B τ2+Cτ3+Dτ4
Angular speed and specific force sampling instant are selected asAnd adopted angular speed and specific force are denoted as ω respectively1、ω2、
ω3And f1、f2、f3, and remember tkMoment angular speed and specific force are respectively ω0And f0, it is brought into angular velocity omega (t respectivelyk-1+ τ) and
Specific force f (tk-1+ τ) in, it can obtain
Above formula is solved, can be obtained
So three increment algorithms of sculling error compensation item are as follows:
3. a kind of three increment sculling error compensation of interpolation inputted based on angular speed and specific force according to claim 1
Algorithm, it is characterised in that: step 2 detailed process are as follows: analyze the sculling error compensation based on input for angular speed and specific force
Optimization algorithm；
Assuming that carrier does paddle campaign, angular speed and specific force are respectively ω (t)=iB Ω cos Ω t
F (t)=jCsin Ω t
Wherein, i and j is the unit vector along the corresponding axis of carrier coordinate system；
Remember ωkAnd fk+lIt is speed update cycle [tk-1,tk] in a angular speed sampled value of kth (k=0 ..., N-1) and kth+l
(l >=1, k+l≤N) a specific force sampled value, wherein N is number of samples in the period, and Δ t is enabled to indicate tk-tk-1, then have:
Then, have
Wherein, k is along the unit vector orthogonal with i and j axis；
Another situation: note fkAnd ωk+lIt is speed update cycle [tk-1,tk] in a specific force of kth (k=0 ..., N-1) adopt
Sample value and kth+l (l >=1, k+l≤N) a angular speed sampled value, then have:
Then, have
ωk×fk+1With fk×ωk+1It is added, has
As can be seen that when carrier does the paddle campaign of the form as shown in ω (t)=iB Ω cos Ω t, f (t)=jCsin Ω t,
ωk×fk+l+fk×ωk+lValue it is unrelated with k, it is only related with l；At this point, having
ω0×f1+f0×ω1=ω1×f2+f1×ω2=ω2×f3+f2×ω3
ω0×f2+f0×ω2=ω1×f3+f1×ω3
It is following form by three increment algorithmic notations of sculling compensation term based on both the above equation:
By ωk×fk+l+fk×ωk+lIt brings intoHave
The angular speed formula and specific force formula that paddle campaign is done according to carrier, have:
So the paddle compensation term accurately calculated is answered are as follows:
Then, three increment algorithmCaused error may be expressed as:
Since the frequency omega of carrier vibration will not be too high, sampling time interval Δ t is ms grades, so there is Ω Δ under normal circumstances
T < 1, in order to minimize Algorithm ErrorIt is ensured that the low order power item of Ω Δ t is 0 as far as possible, take thus
Above formula is solved, k can be obtained1=291/2240, k2=3/56, k3=29/6720, then, three increments of paddle campaign optimize
Algorithm are as follows:
4. a kind of three increment sculling error compensation of interpolation inputted based on angular speed and specific force according to claim 1
Algorithm, it is characterised in that: step 3 detailed process are as follows:
Assuming that in tk、tk+h/3、tk+ 2h/3 and tk+ h moment collected angular speed and specific force are respectively ω0、ω1、ω2、ω3With
f0、f1、f2、f3, by formula
ω(tk-1+ τ)=a+2b τ+3c τ2+4dτ3,0≤τ≤Δt
f(tk-1+ τ)=A+2B τ+3C τ2+4Dτ3,0≤τ≤Δt
It is found that utilizing this four angular speeds and the available ω (t of specific forcek+ τ) and f (tk+ τ) expression formula；Utilize ω (tk+τ)
With f (tk+ τ) expression formula can find out in tkTo tkThe value of the angular speed and specific force of any time in+h；
It at this time can be in [tk+2h/3,tk+ h] period in be inserted into the value of two angular speeds and the value of specific force respectively
WithThen with ω2、ω3And f2、f3Four angular speeds and specific force calculate [tk+2h/3,tk+
H] sculling error compensation item Δ V in the periodsculk, finally according to tk+ 2h/3 the moment, corresponding speed updated tkWhen+h
The speed at quarter；
[t can similarly be found outk+h,tk+ 4h/3] sculling error compensation item Δ V in the periodsculk, according to tk+ h the moment
Speed updates tkThe speed at+4h/3 moment, and so on；
Detailed process is as follows:
By formula
ω(tk-1+ τ)=a+2b τ+3c τ2+4dτ3,0≤τ≤Δt
f(tk-1+ τ)=A+2B τ+3C τ2+4Dτ3,0≤τ≤Δt
Determine ω (tk+ τ) and f (tk+ τ) expression formula；
Output angular speed and output specific force in τ=2h/3 are respectively as follows:
Interpolation angular speed and interpolation specific force in τ=7h/9 are respectively as follows:
Interpolation angular speed and interpolation specific force in τ=8h/9 are respectively as follows:
Output angular speed and output specific force in τ=h are respectively as follows:
Pass through formulaAcquiring every multiplication cross is
Every multiplication cross equation, which is acquired, by three above substitutes into following formula
It can find out after merging similar terms in [tk+2h/3,tk+1+ h] in sculling compensation term are as follows:
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