CN104075711B - A kind of IMU/Wi Fi signal tight integration indoor navigation methods based on CKF - Google Patents
A kind of IMU/Wi Fi signal tight integration indoor navigation methods based on CKF Download PDFInfo
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- 238000005259 measurement Methods 0.000 claims abstract description 70
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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
- G01C21/165—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 combined with non-inertial navigation instruments
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Abstract
The invention discloses a kind of IMU/Wi Fi signal tight integration indoor navigation methods based on CKF, this method includes：Establish the RSS fingerprinting of Wi Fi signals database；Positioned using IMU, obtain pedestrian position PoIMUAnd the information such as speed, acceleration, posture；The drift of IMU accelerometers is corrected by zero-speed correction, and the speed after being corrected；Positioned using Wi Fi signals, obtain pedestrian position PoWi‑Fi；Found respectively in database and PoIMUN nearer reference point and and PoWi‑FiN nearer reference point, and the distance d between measurement point and reference point is obtained according to the position of known reference point respectivelyi IMU、di Wi‑Fi, so as to obtain range difference Δ d；Information fusion is carried out using volume Kalman filtering, finally gives the position of pedestrian, acceleration, speed, attitude information.The inventive method fully utilizes indoor Wi Fi signals and IMU information, carries out information fusion by CKF algorithms, filtering accuracy is high, fast convergence rate, and strong robustness, navigation accuracy are higher.
Description
Technical field
The invention belongs to field of navigation technology, more particularly to one kind to be based on volume Kalman filtering (Cubature Kalman
Filter, CKF) IMU/Wi-Fi signal tight integration indoor navigation methods.
Background technology
Existing pedestrian navigation positioning relies primarily on global position system (Global Position System, GPS) realization.
However, GPS location there is bad dynamic performance, it is non-autonomous the shortcomings of.Particularly indoors, avenue, tunnel etc. easily cover
In the environment of satellite navigation signals, dropout can be produced, even results in positioning failure.
For indoor navigation, the solution method of generally use is to utilize MEMS (Micro-
Electromechanical System, MEMS) inertia device progress indoor navigation.And the pedestrian based on MEMS inertia devices leads
Navigate freedom positioning system, and its device error can rapidly dissipate.In navigation stage, if MEMS inertia devices can not be effectively compensated for
Error, site error can be dissipated with time cube, ultimately result in the failure of system navigation feature.It follows that it is based on MEMS systems
System inertia computation is effective amendment of error applied to the maximum difficult point of pedestrian navigation system.
The error correction and information fusion of usual MEMS system are realized with filtered version.Due to being related to nonlinear model,
When wave filter selects, generally from nonlinear filterings such as EKFs.EKF is a kind of typical
Non-linear filtering method, it is distributed by carrying out the linear expansion of first order Taylor series to nonlinear equation with the state of approaching to reality,
But the Approaching Results only produce in small neighbourhood, otherwise can bring larger error, cause filter result unstable or even dissipate.
In summary, existing indoor pedestrian's integrated navigation system stability is poor, and filtering accuracy is poor, convergence rate
Slowly, robustness is weak, causes pedestrian navigation accuracy poor.
The content of the invention
It is an object of the invention to provide a kind of IMU/Wi-Fi signal tight integration indoor navigation methods based on CKF, it is intended to
Solves the problem of stability existing for existing indoor pedestrian's Combinated navigation method is poor, and filter effect is undesirable.
The realization of the present invention comprises the following steps：
Step 1：The reference point of certain density is chosen indoors, is measured and is recorded each reference point from access point APs receptions
The signal intensity arrived and corresponding positional information PoDB, establish RSS Fingerprint databases；
Step 2：Inertial Measurement Unit is fixed on pedestrian's pin, movable information when being advanced using IMU measurement pedestrians is added
Speed a and rotational speed omega, and the speed Ve of pedestrian is obtained by inertial reference calculationIMU, position PoIMU, posture AtIMU；
Step 3：Zero-speed correction is carried out to accelerometer using the acceleration a that step 2 obtains, and to the motion after correction
Information carries out inertial reference calculation, is filtered by extended filtering device, the position and speed Ve after being correctedZUPT, and with being obtained in step 2
The speed Ve arrivedIMUMake the difference to obtain velocity error △ Ve；
Step 4：The positional information Po obtained using step 2IMUWith reference point in RSS Fingerprint databases
Positional information PoDBIt is compared, filters out and nearer n point Po of the measurement pointi DB(i=1,2 ..., n), then respectively with
The position Po that IMU is measuredIMUMake the difference to obtain the distance between pedestrian and reference point
InvolvedExpression formula is：
Wherein, XIMUAnd YIMUIt is that position coordinates Po is measured by IMUIMUComponent, and have PoIMU={ XIMU, YIMU}；With
Yi DBIt is the coordinate Po of selected reference pointi DBComponent, and have
Step 5：The Wi-Fi antennas carried using pedestrian receive Wi-Fi signal, and measure the signal intensity received, root
The distance d of measurement point and access point APs is calculated according to the mathematical modeling of signal intensity and distance, so as to utilize trilateration solution
Calculate the position Po of measurement pointWi-FiAnd the position measured with IMU makes the difference, site error △ Po are obtained；
Mathematical modeling between involved Wi-Fi signal strength RSS and distance d is：
In formula, d0For known reference distance, RSS0For in reference distance d0The average signal strength at place, p are signal attenuation
Index；
Step 6：The positional information Po arrived using step 5Wi-FiWith the position of reference point in RSS Fingerprint databases
Confidence ceases PoDBIt is compared, filters out and nearer n point Po of the measurement pointi DB(i=1,2 ..., n) then respectively with Wi-Fi
Position obtained position PoWi-FiMake the difference to obtain the distance between pedestrian and reference pointI.e.：
InvolvedExpression formula is：
Wherein, XWi-FiAnd YWi-FiIt is that obtained position coordinates Po is positioned by Wi-FiWi-FiComponent, and have PoWi-Fi=
{XWi-Fi, YWi-Fi}；And Yi DBIt is selected reference point coordinates Poi DBComponent, and have
Step 7：The distance that will be obtained in step 4 and step 6Make the difference, obtain range difference Δ di；
Step 8：The site error △ Po that the velocity error △ Ve and step 5 obtained using step 3 is tried to achieve, as appearance
The quantity of state X=[△ Ve, △ Po] of G-card Kalman Filtering, the range difference Δ d obtained using step 7iFiltered as volume Kalman
Measurement Z=[the Δ d of ripplei], it is filtered resolving using volume Kalman filtering；
Step 9：IMU is measured using filtered velocity error △ Ve, the site error △ Po that are obtained in step 8
Speed Ve, position Po are corrected, so as to obtain final indoor pedestrian navigation information.
In step 1, when choosing reference point, every 5 meters take a reference point, and every 10 meters take a reference point, and each
Four direction at reference point, each 5 groups of data of orientation measurement, measures 40 groups of data and is handled, determine the Wi- of the reference point altogether
Fi signal intensities.
The beneficial effects of the present invention are：
This method filtering accuracy is high, fast convergence rate, and strong robustness, therefore this method can effectively improve navigation essence
Degree.
Brief description of the drawings
Fig. 1 is the flow chart of the IMU/Wi-Fi signal tight integration indoor navigation methods provided by the invention based on CKF.
Fig. 2 is the IMU/Wi-Fi signal tight integration indoor navigation system block diagrams provided by the invention based on CKF.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to embodiments, to the present invention
It is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to
Limit the present invention.
The invention discloses a kind of IMU/Wi-Fi signal tight integration indoor navigation methods based on CKF, this method includes：
Establish the RSS fingerprinting of Wi-Fi signal database；Positioned using IMU, obtain pedestrian position
PoIMUAnd speed, acceleration, the information such as posture；The drift of IMU accelerometers is corrected by zero-speed correction, and corrected
Speed afterwards；Positioned using Wi-Fi signal, obtain pedestrian position PoWi-Fi；Found respectively in the database built up
With PoIMUN nearer reference point and and PoWi-FiN nearer reference point, and obtained respectively according to the position of known reference point
Distance d between measurement point and reference pointi IMU、di Wi-Fi(n=1,2 ..., n), so as to obtain range difference Δ d；Utilize volume karr
Graceful filtering (CKF) carries out information fusion, finally gives the position of pedestrian, acceleration, speed, attitude information.The present invention utilizes CKF
Information fusion is carried out to indoor Wi-Fi signal and the pedestrian navigation system of IMU tight integrations, Wi-Fi is widely used indoors and Wi-
Fi signals are relatively stable, effectively pedestrian's aided inertial navigation system can be navigated.The filtering such as CKF algorithms and EKF and UKF is calculated
Method is compared, and its filtering accuracy is high, fast convergence rate, and strong robustness, therefore this method can effectively improve navigation accuracy.
The IMU/Wi-Fi signal tight integration indoor navigation methods based on CKF comprise the following steps：
Step 1：The reference point of certain density is chosen indoors, is measured and is recorded each reference point from access point (Access
Points APs) signal intensity (Received Signal Strength RSS) that receives and corresponding positional information
PoDB, establish RSS Fingerprint databases；
Step 2：Inertial Measurement Unit (IMU) is tied up on the pin of pedestrian, when being advanced using IMU measurement pedestrians
Movable information acceleration a and rotational speed omega simultaneously obtain the speed Ve of pedestrian, position Po, posture At by inertial reference calculation；
Step 3：Using the acceleration a that step 2 obtains to accelerometer carry out zero-speed correction (ZUPT), and to correction after
Movable information carry out inertial reference calculation, by extended filtering device (Extended Kalman Filter EKF) filter, obtain school
Position and speed Ve after justZUPTAnd the speed with being obtained in step 2 makes the difference to obtain velocity error △ Ve；
Step 4：The positional information Po that step 2 obtainsIMUWith the position of reference point in RSS Fingerprint databases
Information is compared, and is filtered out and nearer n point Po of the measurement pointi DB(i=1,2 ..., n), is then measured with IMU respectively
Position PoIMUMake the difference to obtain the distance between pedestrian and reference pointI.e.：
Wherein XIMUAnd YIMUIt is the position coordinates Po obtained by IMUIMU={ XIMU, YIMU}；And Yi DBIt is selected reference
The coordinate of point
Step 5：The signal intensity RSS that receives of Wi-Fi antenna measurements carried using pedestrian, according to signal intensity with
The mathematical modeling of distance calculates measurement point and APs distance d, so as to resolve the position Po of measurement point using trilaterationWi -FiAnd the position measured with IMU makes the difference to obtain site error △ Po；
Step 6：The positional information Po arrived using step 5Wi-FiWith the position of reference point in RSS Fingerprint databases
Confidence breath is compared, and is filtered out and nearer n point Po of the measurement pointi DB(i=1,2 ..., n) and then determine respectively with Wi-Fi
The position Po that position obtainsWi-FiMake the difference to obtain the distance d between pedestrian and reference pointi Wi-Fi(i=1,2 ..., n) i.e.：
Wherein XWi-FiAnd YWi-FiIt is that obtained position coordinates Po is positioned by Wi-FiWi-Fi={ XWi-Fi, YWi-Fi}；With
Yi DBIt is the coordinate of selected reference point
Step 7：The distance d that will be obtained in step 4 and step 6i IMU、di Wi-FiMake the difference, obtain range difference Δ di；
Step 8：Velocity error △ Ve, the site error △ Po tried to achieve using step 3 and step 5 is used as volume karr
The quantity of state X=[△ Ve △ Po] of graceful filtering, the measurement using the range difference Δ d that step 7 obtains as volume Kalman filtering
Z=[Δ d] is measured, is filtered using volume Kalman filtering；
Step 9：IMU is measured using filtered velocity error △ Ve, the site error △ Po that are obtained in step 8
Speed Ve, position Po are corrected, so as to obtain final pedestrian navigation information.
In step 1, when choosing reference point, the place more than barrier (such as in room) every 5 step take a reference
Point, the few place of barrier (such as corridor, hall) every 10 step take a reference point, and the four direction at each reference point, often
Individual 5 groups of data of orientation measurement, measure 40 groups of data and are handled, finally determine the Wi-Fi signal strength of the reference point altogether.In order to
Make RSS Fingerprint databases more accurate, reference point is measured twice, when once someone walks about indoors,
Once indoors nobody when.
In step 5, pass through formula：
The mathematical modeling established between Wi-Fi signal strength RSS and distance d, in formula, d0For known reference distance, RSS0For
In reference distance d0The average signal strength at place, p are signal attenuation index, and v is the stochastic variable of Gaussian Profile, and its average is 0,
MeansquaredeviationσRSSIt is relevant with indoor barrier.Maximum-likelihood estimation is carried out to above formula, obtains Wi-Fi signal strength RSS and distance d
Between mathematical modeling be：
Measurement point and APs distance d are arrived as available from the above equation, so as to resolve the position Po of measurement point using trilaterationWi -FiAnd the position measured with IMU makes the difference to obtain site error △ Po；
In step 8, it is filtered using volume Kalman filtering (CKF), the speed tried to achieve using step 3 and step 5
Spend error delta Ve, quantity of state X=s [△ Ve △ Po] of the site error △ Po as volume Kalman filtering, step 7 obtain away from
Measurement Z=s [Δ d] of the deviation Δ d as volume Kalman filtering, CKF algorithm process flows are as follows：
1) time updates
State volume point:
Wherein Sk-1=chol { Pk-1, it is matrix Pk-1Cholesky decompose, i.e. error co-variance matrix Pk-1=Sk- 1Sk-1 T(T represents transposition).
The state volume point propagated by state equation:
Status predication:
Error covariance is predicted:
2) measurement updaue
State volume point:
Wherein,
Measure volume point:
Zj,k=h (Xj,k)
Measurement prediction:
The new breath variance of estimation:
Estimate covariance:
Kalman gains:
State updates:
Evaluated error covariance:
Fig. 1 shows the IMU/Wi-Fi signal tight integration indoor navigation method flows provided by the invention based on CKF.For
It is easy to illustrate, illustrate only part related to the present invention.
The IMU/Wi-Fi signal tight integration indoor navigation methods based on CKF of the embodiment of the present invention, should be based on CKF's
IMU/Wi-Fi signal tight integration indoor navigation methods comprise the following steps：
Step 1：The reference point of certain density is chosen indoors, is measured and is recorded each reference point from access point (Access
Points APs) signal intensity (Received Signal Strength RSS) that receives and corresponding positional information
PoDB, establish RSS Fingerprint databases；
Step 2：Inertial Measurement Unit (IMU) is tied up on the pin of pedestrian, when being advanced using IMU measurement pedestrians
Movable information acceleration a and rotational speed omega simultaneously obtain the speed Ve of pedestrian, position Po, posture At by inertial reference calculation；
Step 3：Using the acceleration a that step 2 obtains to accelerometer carry out zero-speed correction (ZUPT), and to correction after
Movable information carry out inertial reference calculation, by extended filtering device (Extended Kalman Filter EKF) filter, obtain school
Position and speed Ve after justZUPTAnd the speed with being obtained in step 2 makes the difference to obtain velocity error △ Ve；
Step 4：The positional information Po that step 2 obtainsIMUWith the position of reference point in RSS Fingerprint databases
Information is compared, and is filtered out and nearer n point Po of the measurement pointi DB(i=1,2 ..., n) and then measured respectively with IMU
Position PoIMUMake the difference to obtain the distance between pedestrian and reference pointI.e.：
Wherein XIMUAnd YIMUIt is the position coordinates Po obtained by IMUIMU={ XIMU, YIMU}；And Yi DBIt is selected reference
The coordinate of point
Step 5：The signal intensity RSS that receives of Wi-Fi antenna measurements carried using pedestrian, according to signal intensity with
The mathematical modeling of distance calculates measurement point and APs distance d, so as to resolve the position Po of measurement point using trilaterationWi -FiAnd the position measured with IMU makes the difference to obtain site error △ Po；
Step 6：The positional information Po arrived using step 5Wi-FiWith the position of reference point in RSS Fingerprint databases
Confidence breath is compared, and is filtered out and nearer n point Po of the measurement pointi DB(i=1,2 ..., n) and then determine respectively with Wi-Fi
The position Po that position obtainsWi-FiMake the difference to obtain the distance d between pedestrian and reference pointi Wi-Fi(i=1,2 ..., n) i.e.：
Wherein XWi-FiAnd YWi-FiIt is the position coordinates Po obtained by IMUWi-Fi={ XWi-Fi, YWi-Fi}；And Yi DBIt is institute
Select the coordinate of reference point
Step 7：The distance d that will be obtained in step 4 and step 6i IMU、di Wi-FiMake the difference, obtain range difference Δ di；
Step 8：Velocity error △ Ve, the site error △ Po tried to achieve using step 3 and step 5 is used as volume karr
The quantity of state X=[△ Ve △ Po] of graceful filtering, the measurement using the range difference Δ d that step 7 obtains as volume Kalman filtering
Z=[Δ d] is measured, is filtered using volume Kalman filtering；
Step 9：IMU is measured using filtered velocity error △ Ve, the site error △ Po that are obtained in step 8
Speed Ve, position Po are corrected, so as to obtain final pedestrian navigation information.
As a prioritization scheme of the embodiment of the present invention, in step 1, when choosing reference point, on the ground more than barrier
Side's 5 step every (such as in room) takes a reference point, and the few place of barrier (such as corridor, hall) every 10 step takes a reference point,
And the four direction at each reference point, each 5 groups of data of orientation measurement, 40 groups of data are measured altogether and are handled, it is final to determine
The Wi-Fi signal strength of the reference point.In order that RSS Fingerprint databases are more accurate, reference point is surveyed twice
Amount, when once someone walks about indoors, once indoors nobody when.
As a prioritization scheme of the embodiment of the present invention, in step 5, pass through formula：
The mathematical modeling established between Wi-Fi signal strength RSS and distance d, in formula, d0For known reference distance, RSS0For
In reference distance d0The average signal strength at place, p are signal attenuation index, and v is the stochastic variable of Gaussian Profile, and its average is 0,
MeansquaredeviationσRSSIt is relevant with indoor barrier.Maximum-likelihood estimation is carried out to above formula, obtains Wi-Fi signal strength RSS and distance d
Between mathematical modeling be：
Measurement point and APs distance d are arrived as available from the above equation, so as to resolve the position Po of measurement point using trilaterationWi -FiAnd the position measured with IMU makes the difference to obtain site error △ Po；
As a prioritization scheme of the embodiment of the present invention, in step 8, filtered using volume Kalman filtering (CKF)
Ripple, the state of velocity error △ Ve tried to achieve by the use of step 3 and step 5, site error △ Po as volume Kalman filtering
Measure X=[△ Ve △ Po], the range difference Δ d that step 7 the obtains measurement Z=[Δ d] as volume Kalman filtering, CKF calculations
Method handling process is as follows：
1) time updates
State volume point:
Wherein Sk-1=chol { Pk-1, it is matrix Pk-1Cholesky decompose, i.e. error co-variance matrix Pk-1=Sk- 1Sk-1 T(T represents transposition).
The state volume point propagated by state equation:
Status predication:
Error covariance is predicted:
2) measurement updaue
State volume point:
Wherein,
Measure volume point:
Zj,k=h (Xj,k)
Measurement prediction:
The new breath variance of estimation:
Estimate covariance:
Kalman gains:
State updates:
Evaluated error covariance:
As shown in figure 1, the IMU/Wi-Fi signal tight integration indoor navigation methods based on CKF of the embodiment of the present invention include
Following steps：
S101：Establish the RSS fingerprinting of Wi-Fi signal database；
S102：Inertial Measurement Unit (IMU) is tied up on the pin of pedestrian, fortune when being advanced using IMU measurement pedestrians
Dynamic Information acceleration a and rotational speed omega simultaneously obtain the speed Ve of pedestrian, position Po, posture At by inertial reference calculation；
S103：Zero-speed correction (ZUPT) is carried out to accelerometer using the acceleration a measured, and the motion after correction is believed
Breath carries out inertial reference calculation, is filtered by extended filtering device (Extended Kalman Filter EKF), the position after being corrected
Put speed VeZUPTAnd the speed with being obtained in step 2 makes the difference to obtain velocity error △ Ve；
S104：The positional information Po obtained using step 2IMUWith the position of reference point in RSS Fingerprint databases
Confidence breath is compared, and filters out the point nearer with the measurement point, the position Po then measured respectively with IMUIMUMake the difference and gone
Distance between people and reference point；
S105：The signal intensity RSS that receives of Wi-Fi antenna measurements carried using pedestrian, according to signal intensity with away from
From mathematical modeling calculate measurement point and APs distance d, so as to using trilateration resolve measurement point position PoWi-Fi
And the position measured with IMU makes the difference to obtain site error △ Po；
S106:The positional information Po arrived using step 5Wi-FiWith the position of reference point in RSS Fingerprint databases
Information is compared, and filters out the point nearer with the measurement point, then positions with Wi-Fi obtained position Po respectivelyWi-FiMake the difference
Obtain the distance between pedestrian and reference point；
S107：The distance d that will be obtained in step 4 and step 6i IMU、di Wi-FiMake the difference, obtain range difference；
S108：Using velocity error △ Ve, site error △ Po as quantity of state, range difference Δ d as volume card measurement,
It is filtered using volume Kalman filtering (CKF)；
S109：Speed Ve, the position Po that velocity error △ Ve, the site error △ Po obtained using filtering is measured to IMU
It is corrected, so as to obtain final pedestrian navigation information；
The present invention's concretely comprises the following steps：
Step 1：The reference point of certain density is chosen indoors, is measured and is recorded each reference point from access point (Access
Points APs) signal intensity (Received Signal Strength RSS) that receives and corresponding positional information
PoDB, establish RSS Fingerprint databases；
When choosing reference point, the place more than barrier (such as in room) every 5 step take a reference point, barrier is few
Local (such as corridor, hall) every 10 step takes a reference point, and the four direction at each reference point, each 5 groups of orientation measurement
Data, 40 groups of data are measured altogether and are handled, finally determine the Wi-Fi signal strength of the reference point.In order that RSS
Fingerprint databases are more accurate, and reference point is measured twice, when once someone walks about indoors, once existed
When indoor nobody.
Step 2：Inertial Measurement Unit (IMU) is tied up on the pin of pedestrian, when being advanced using IMU measurement pedestrians
Movable information acceleration a and rotational speed omega simultaneously obtain the speed Ve of pedestrian, position Po, posture At by inertial reference calculation；
Step 3：Using the acceleration a that step 2 obtains to accelerometer carry out zero-speed correction (ZUPT), and to correction after
Movable information carry out inertial reference calculation, by extended filtering device (Extended Kalman Filter EKF) filter, obtain school
Position and speed Ve after justZUPTAnd the speed with being obtained in step 2 makes the difference to obtain velocity error △ Ve；
Step 4：The positional information Po that step 2 obtainsIMUWith the position of reference point in RSS Fingerprint databases
Information is compared, and is filtered out and nearer n point Po of the measurement pointi DB(i=1,2 ..., n) and then measured respectively with IMU
Position PoIMUMake the difference to obtain the distance between pedestrian and reference pointI.e.：
Wherein XIMUAnd YIMUIt is the position coordinates Po obtained by IMUIMU={ XIMU, YIMU}；And Yi DBIt is selected reference
The coordinate of point
Step 5：The signal intensity RSS that receives of Wi-Fi antenna measurements carried using pedestrian, according to signal intensity with
The mathematical modeling of distance calculates measurement point and APs distance d, that is, passes through formula：
The mathematical modeling established between Wi-Fi signal strength RSS and distance d, in formula, d0For known reference distance, RSS0For
In reference distance d0The average signal strength at place, p are signal attenuation index, and v is the stochastic variable of Gaussian Profile, and its average is 0,
MeansquaredeviationσRSSIt is relevant with indoor barrier.Maximum-likelihood estimation is carried out to above formula, obtains Wi-Fi signal strength RSS and distance d
Between mathematical modeling be：
Measurement point and APs distance d are arrived as available from the above equation, so as to resolve the position of measurement point using trilateration
PoWi-Fi and the position measured with IMU make the difference to obtain site error △ Po；
Step 6：The positional information Po arrived using step 5Wi-FiWith the position of reference point in RSS Fingerprint databases
Confidence breath is compared, and is filtered out and nearer n point Po of the measurement pointi DB(i=1,2 ..., n) and then determine respectively with Wi-Fi
The position Po that position obtainsWi-FiMake the difference to obtain the distance d between pedestrian and reference pointi Wi-Fi(i=1,2 ..., n) i.e.：
Wherein XWi-FiAnd YWi-FiIt is the position coordinates Po obtained by IMUWi-Fi={ XWi-Fi, YWi-Fi}；And Yi DBIt is institute
Select the coordinate of reference point
Step 7：The distance d that will be obtained in step 4 and step 6i IMU、di Wi-FiMake the difference, obtain range difference Δ di；
Step 8：It is filtered using volume Kalman filtering (CKF), the speed tried to achieve using step 3 and step 5 is missed
The quantity of state X=[△ Ve △ Po] of poor △ Ve, site error △ Po as volume Kalman filtering, the range difference that step 7 obtains
Measurement Z=s [Δ d] of the Δ d as volume Kalman filtering, CKF algorithm process flows are as follows：
1) time updates
State volume point:
Wherein Sk-1=chol { Pk-1, it is matrix Pk-1Cholesky decompose, i.e. error co-variance matrix Pk-1=Sk- 1Sk-1 T(T represents transposition).
The state volume point propagated by state equation:
Status predication:
Error covariance is predicted:
2) measurement updaue
State volume point:
Wherein,
Measure volume point:
Zj,k=h (Xj,k)
Measurement prediction:
The new breath variance of estimation:
Estimate covariance:
Kalman gains:
State updates:
Evaluated error covariance:
Step 9：IMU is measured using filtered velocity error △ Ve, the site error △ Po that are obtained in step 8
Speed Ve, position Po are corrected, so as to obtain final pedestrian navigation information.
Claims (1)
1. a kind of IMU/Wi-Fi signal tight integration indoor navigation methods based on CKF, it is characterised in that comprise the following steps：
Step 1：The reference point of certain density is chosen indoors, is measured and is recorded what each reference point received from access point APs
Signal intensity and corresponding positional information PoDB, establish RSS Fingerprint databases；
Step 2：Inertial Measurement Unit is fixed on pedestrian's pin, movable information acceleration when being advanced using IMU measurement pedestrians
A and rotational speed omega, and the speed Ve of pedestrian is obtained by inertial reference calculationIMU, position PoIMU, posture AtIMU；
Step 3：Zero-speed correction is carried out to accelerometer using the acceleration a that step 2 obtains, and to the movable information after correction
Inertial reference calculation is carried out, is filtered by extended filtering device, the position and speed Ve after being correctedZUPT, and with obtaining in step 2
Speed VeIMUMake the difference to obtain velocity error △ Ve；
Step 4：The positional information Po obtained using step 2IMUWith the position of reference point in RSS Fingerprint databases
Information PoDBIt is compared, filters out and nearer n point Po of measurement pointi DB, i=1,2 ..., n, then measured respectively with IMU
Position PoIMUMake the difference to obtain the distance between pedestrian and reference pointI=1,2 ..., n；
InvolvedExpression formula is：
<mrow>
<msubsup>
<mi>d</mi>
<mi>i</mi>
<mrow>
<mi>I</mi>
<mi>M</mi>
<mi>U</mi>
</mrow>
</msubsup>
<mo>=</mo>
<msqrt>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<msup>
<mi>X</mi>
<mrow>
<mi>I</mi>
<mi>M</mi>
<mi>U</mi>
</mrow>
</msup>
<mo>-</mo>
<msubsup>
<mi>X</mi>
<mi>i</mi>
<mrow>
<mi>D</mi>
<mi>B</mi>
</mrow>
</msubsup>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<msup>
<mi>Y</mi>
<mrow>
<mi>I</mi>
<mi>M</mi>
<mi>U</mi>
</mrow>
</msup>
<mo>-</mo>
<msubsup>
<mi>Y</mi>
<mi>i</mi>
<mrow>
<mi>D</mi>
<mi>B</mi>
</mrow>
</msubsup>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</mrow>
Wherein, XIMUAnd YIMUIt is that position coordinates Po is measured by IMUIMUComponent, and have PoIMU={ XIMU, YIMU}；And Yi DBIt is
The coordinate Po of selected reference pointi DBComponent, and have
Step 5：The Wi-Fi antennas carried using pedestrian receive Wi-Fi signal, and measure the signal intensity received, according to letter
The mathematical modeling of number intensity and distance calculates the distance d of measurement point and access point APs, is surveyed so as to be resolved using trilateration
Measure the position Po of pointWi-FiAnd the position measured with IMU makes the difference, site error △ Po are obtained；
Mathematical modeling between involved Wi-Fi signal strength RSS and distance d is：
<mrow>
<mi>d</mi>
<mo>=</mo>
<msub>
<mi>d</mi>
<mn>0</mn>
</msub>
<mo>&CenterDot;</mo>
<msup>
<mn>10</mn>
<mfrac>
<mrow>
<msub>
<mi>RSS</mi>
<mn>0</mn>
</msub>
<mo>-</mo>
<mi>R</mi>
<mi>S</mi>
<mi>S</mi>
</mrow>
<mrow>
<mn>10</mn>
<mo>&CenterDot;</mo>
<mi>p</mi>
</mrow>
</mfrac>
</msup>
</mrow>
In formula, d0For known reference distance, RSS0For in reference distance d0The average signal strength at place, p refer to for signal attenuation
Number；
Step 6：The positional information Po obtained using step 5Wi-FiWith the position of reference point in RSS Fingerprint databases
Information PoDBIt is compared, filters out and nearer n point Po of the measurement pointi DB, i=1,2 ..., n, then determine respectively with Wi-Fi
The position Po that position obtainsWi-FiMake the difference to obtain the distance between pedestrian and reference pointI=1,2 ..., n, i.e.,：
InvolvedExpression formula is：
<mrow>
<msubsup>
<mi>d</mi>
<mi>i</mi>
<mrow>
<mi>W</mi>
<mi>i</mi>
<mo>-</mo>
<mi>F</mi>
<mi>i</mi>
</mrow>
</msubsup>
<mo>=</mo>
<msqrt>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<msup>
<mi>X</mi>
<mrow>
<mi>W</mi>
<mi>i</mi>
<mo>-</mo>
<mi>F</mi>
<mi>i</mi>
</mrow>
</msup>
<mo>-</mo>
<msubsup>
<mi>X</mi>
<mi>i</mi>
<mrow>
<mi>D</mi>
<mi>B</mi>
</mrow>
</msubsup>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<msup>
<mi>Y</mi>
<mrow>
<mi>W</mi>
<mi>i</mi>
<mo>-</mo>
<mi>F</mi>
<mi>i</mi>
</mrow>
</msup>
<mo>-</mo>
<msubsup>
<mi>Y</mi>
<mi>i</mi>
<mrow>
<mi>D</mi>
<mi>B</mi>
</mrow>
</msubsup>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</mrow>
Wherein, XWi-FiAnd YWi-FiIt is that obtained position coordinates Po is positioned by Wi-Fi signalWi-FiComponent, and have PoWi-Fi=
{XWi-Fi, YWi-Fi}；And Yi DBIt is selected reference point coordinates Poi DBComponent, and have
Step 7：The distance that will be obtained in step 4 and step 6Make the difference, obtain range difference Δ di；
Step 8：The site error △ Po that the velocity error △ Ve and step 5 obtained using step 3 is tried to achieve, as volume card
The quantity of state X=[△ Ve, △ Po] of Kalman Filtering, the range difference Δ d obtained using step 7iAs volume Kalman filtering
Measurement Z=[Δ di], it is filtered resolving using volume Kalman filtering；
Step 9：The speed measured using filtered velocity error △ Ve, the site error △ Po that are obtained in step 8 to IMU
Ve, position Po are corrected, so as to obtain final indoor pedestrian navigation information；
In step 1, when choosing reference point, local every 5 meters more than the barrier take a reference point, the few place of barrier
Every 10 meters take a reference point, and the four direction at each reference point, each 5 groups of data of orientation measurement, measure 40 groups of numbers altogether
According to being handled, the Wi-Fi signal strength of reference point is determined；
In step 5, pass through formula：
<mrow>
<mi>R</mi>
<mi>S</mi>
<mi>S</mi>
<mo>=</mo>
<msub>
<mi>RSS</mi>
<mn>0</mn>
</msub>
<mo>-</mo>
<mn>10</mn>
<mo>&CenterDot;</mo>
<mi>p</mi>
<mo>&CenterDot;</mo>
<msub>
<mi>log</mi>
<mn>10</mn>
</msub>
<mrow>
<mo>(</mo>
<mfrac>
<mi>d</mi>
<msub>
<mi>d</mi>
<mn>0</mn>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>v</mi>
</mrow>
The mathematical modeling established between Wi-Fi signal strength RSS and distance d, in formula, d0For known reference distance, RSS0To join
Examine distance d0The average signal strength at place, p are signal attenuation index, and v is the stochastic variable of Gaussian Profile, and its average is 0, just
Poor σRSSIt is relevant with indoor barrier；Maximum-likelihood estimation is carried out to above formula, obtains Wi-Between Fi signal intensities RSS and distance d
Mathematical modeling is：
<mrow>
<mi>d</mi>
<mo>=</mo>
<msub>
<mi>d</mi>
<mn>0</mn>
</msub>
<mo>&CenterDot;</mo>
<msup>
<mn>10</mn>
<mfrac>
<mrow>
<msub>
<mi>RSS</mi>
<mn>0</mn>
</msub>
<mo>-</mo>
<mi>R</mi>
<mi>S</mi>
<mi>S</mi>
</mrow>
<mrow>
<mn>10</mn>
<mo>&CenterDot;</mo>
<mi>p</mi>
</mrow>
</mfrac>
</msup>
</mrow>
Measurement point and APs distance d are arrived as available from the above equation, so as to resolve the position Po of measurement point using trilaterationWi-FiAnd
Make the difference to obtain site error △ Po with the position that IMU is measured；
In step 8, it is filtered using volume Kalman filtering, the velocity error △ tried to achieve using step 3 and step 5
Ve, site error △ Po the quantity of state X=[△ Ve △ Po] as volume Kalman filtering, the range difference Δ d that step 7 obtains
As the measurement Z=[Δ d] of volume Kalman filtering, CKF algorithm process flows are as follows：
1) time updates
State volume point:
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>S</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<msub>
<mi>&xi;</mi>
<mi>j</mi>
</msub>
<mo>+</mo>
<msub>
<mover>
<mi>X</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
Wherein Sk-1=chol { Pk-1, it is matrix Pk-1Cholesky decompose, i.e. error co-variance matrix Pk-1=Sk-1Sk-1 T, T
Represent transposition；
The state volume point propagated by state equation:
<mrow>
<msubsup>
<mi>X</mi>
<mrow>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
<mo>*</mo>
</msubsup>
<mo>=</mo>
<msub>
<mi>&Phi;X</mi>
<mrow>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
Status predication:
<mrow>
<msub>
<mover>
<mi>X</mi>
<mo>&OverBar;</mo>
</mover>
<mi>k</mi>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mi>m</mi>
</mfrac>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</munderover>
<msubsup>
<mi>X</mi>
<mrow>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
<mo>*</mo>
</msubsup>
</mrow>
Error covariance is predicted:
<mrow>
<msub>
<mover>
<mi>P</mi>
<mo>&OverBar;</mo>
</mover>
<mi>k</mi>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mi>m</mi>
</mfrac>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</munderover>
<msubsup>
<mi>X</mi>
<mrow>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
<mo>*</mo>
</msubsup>
<msubsup>
<mi>X</mi>
<mrow>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
<mrow>
<mo>*</mo>
<mi>T</mi>
</mrow>
</msubsup>
<mo>-</mo>
<msub>
<mover>
<mi>X</mi>
<mo>&OverBar;</mo>
</mover>
<mi>k</mi>
</msub>
<msubsup>
<mover>
<mi>X</mi>
<mo>&OverBar;</mo>
</mover>
<mi>k</mi>
<mi>T</mi>
</msubsup>
<mo>+</mo>
<msub>
<mi>Q</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
2) measurement updaue
State volume point:
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mover>
<mi>S</mi>
<mo>&OverBar;</mo>
</mover>
<mi>k</mi>
</msub>
<msub>
<mi>&xi;</mi>
<mi>j</mi>
</msub>
<mo>+</mo>
<msub>
<mover>
<mi>X</mi>
<mo>&OverBar;</mo>
</mover>
<mi>k</mi>
</msub>
</mrow>
Wherein,
Measure volume point:
Zj,k=h (Xj,k)
Measurement prediction:
<mrow>
<msub>
<mover>
<mi>Z</mi>
<mo>&OverBar;</mo>
</mover>
<mi>k</mi>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mi>m</mi>
</mfrac>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</munderover>
<msub>
<mi>X</mi>
<mrow>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msub>
</mrow>
The new breath variance of estimation:
<mrow>
<msub>
<mi>P</mi>
<mrow>
<mi>z</mi>
<mi>z</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mi>m</mi>
</mfrac>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</munderover>
<msub>
<mi>Z</mi>
<mrow>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msub>
<msubsup>
<mi>Z</mi>
<mrow>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
<mi>T</mi>
</msubsup>
<mo>-</mo>
<msub>
<mover>
<mi>Z</mi>
<mo>&OverBar;</mo>
</mover>
<mi>k</mi>
</msub>
<msubsup>
<mover>
<mi>Z</mi>
<mo>&OverBar;</mo>
</mover>
<mi>k</mi>
<mi>T</mi>
</msubsup>
<mo>+</mo>
<msub>
<mi>R</mi>
<mi>k</mi>
</msub>
</mrow>
Estimate covariance:
<mrow>
<msub>
<mi>P</mi>
<mrow>
<mi>x</mi>
<mi>z</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mi>m</mi>
</mfrac>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</munderover>
<msub>
<mi>X</mi>
<mrow>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msub>
<msubsup>
<mi>Z</mi>
<mrow>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
<mi>T</mi>
</msubsup>
<mo>-</mo>
<msub>
<mover>
<mi>X</mi>
<mo>&OverBar;</mo>
</mover>
<mi>k</mi>
</msub>
<msubsup>
<mover>
<mi>Z</mi>
<mo>&OverBar;</mo>
</mover>
<mi>k</mi>
<mi>T</mi>
</msubsup>
</mrow>
Kalman gains:
<mrow>
<msub>
<mi>K</mi>
<mi>k</mi>
</msub>
<mo>=</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>x</mi>
<mi>z</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msub>
<msubsup>
<mi>P</mi>
<mrow>
<mi>z</mi>
<mi>z</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msubsup>
</mrow>
State updates:
<mrow>
<msub>
<mover>
<mi>X</mi>
<mo>^</mo>
</mover>
<mi>k</mi>
</msub>
<mo>=</mo>
<msub>
<mover>
<mi>X</mi>
<mo>&OverBar;</mo>
</mover>
<mi>k</mi>
</msub>
<mo>+</mo>
<msub>
<mi>K</mi>
<mi>k</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>Z</mi>
<mi>k</mi>
</msub>
<mo>-</mo>
<msub>
<mover>
<mi>Z</mi>
<mo>&OverBar;</mo>
</mover>
<mi>k</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
Evaluated error covariance:
<mrow>
<msub>
<mi>P</mi>
<mi>k</mi>
</msub>
<mo>=</mo>
<msub>
<mover>
<mi>P</mi>
<mo>&OverBar;</mo>
</mover>
<mi>k</mi>
</msub>
<mo>-</mo>
<msub>
<mi>K</mi>
<mi>k</mi>
</msub>
<msub>
<mi>P</mi>
<mrow>
<mi>z</mi>
<mi>z</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msub>
<msubsup>
<mi>K</mi>
<mi>k</mi>
<mi>T</mi>
</msubsup>
<mo>.</mo>
</mrow>
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