Focused on the independence and precision requirements for vehicle navigation, an integrated navigation scheme with geomagnetic matching (GM) and dead reckoning (DR) was proposed. The magnetic reference map was constructed which included magnetic intensities, coordinates of the reference points (RPs) and road sections information. Then, a zero-mean correlation coefficient method was utilized to match the measured magnetic intensities with the magnetic map, and thereby to estimate the vehicle position. The positioning results from GM and DR were fused by a designed EKF to correct the heading and mileage errors of DR. Furthermore, the corrected DR results could effectively reduce the matching search range and solve the discontinuity of GM results at road intersections. Vehicle experiments showed that the proposed scheme could provide accurate and continuous positioning results and meet the demands of vehicle navigation well.
For the vehicle independent navigation applications, the equipped navigation system requires the capability to maintain high performance during the long-term and longdistance travel. Due to the error accumulation of inertial measurement unit (IMU) and odometer, traditional inertial navigation system (INS) and dead reckoning system (DR) could not meet the performance requirements. In addition, the global satellite navigation system (GNSS), which is vulnerable to the unintentional or intentional interference and obstruction, is not usually used as a main method for the vehicle independent navigation system.
In the vehicle navigation field, getting high-performance position information
through novel navigation technologies [
As the odometer assisted magnetic matching algorithm we have proposed in [
Characteristic analysis of geomagnetic anomaly data
As derived from the magnetized crustal permanent magnet, the characteristics of
geomagnetic anomaly are closely related to the location [
GM positioning scheme in road network
Magnetic reference map construction in road network
The magnetic intensity, the traveling distance and the coordinates of the road network
are measured by magnetometer and reference localization system with high-precision,
respectively. After the spatial alignment operation [
X , , T D,T
(M , X , )map M , T d (1) where M ,T is the magnetic intensity sequence, ( X , , T ) is the coordinate and heading sequence, D,T is the mileage data sequence, d is the distance-interval sampling step and M k , X k , k map is the k-th RP in magnetic map.
In the road network condition, the vehicle could travel along any route. Therefore, the magnetic reference map of road network should contain all road sections, jointnodes and the connection relations among them. Fig. 2 shows the construction process of road-network magnetic map.
M1, X1,1 L M2, X2,2 Mk , Xk ,k map
M1, X1,1 Ln M2, X2,2
MnL , X nL ,nL map,n
LN L1 L2 LN ci, j ,ci, j 01,,disccoonnnneeccteteddLLiiaannddLLjj (2) (3) 1, Crs 0, min( posk ) Thp , mnin ( hk ) Thh nL L else where posk is the horizontal distance between two road sections, and Thp is the threshold. hk is the altitude difference and its threshold is Thh . nL is the amount of RPs in current road section and k 0,1, 2 , nL . There will be another division operation on the two road sections at the cross point if they meet the cross detection.
The repeated road sections will result in the non-unique RPs in the magnetic reference map. It is necessary to identify and remove the repeated sections in the whole map. The identification algorithm is, Step 1: Turn detection. The vehicle turning actions at the intersection can be used to divide the road sections directly. The turn detection algorithm is defined as, Trs 1, k knw Th 0, else where Trs is the turn detection result, Th is the threshold of heading variation range and nw is the detection window length. The intermediate point X map,k nw 2 in the turning course is adopted as the division point of the road.
Step 2: Cross detection and repeated section deletion. The cross relation detection is implemented according to the space distance between different road sections. That is, 1, rep 0, nL L ( X mLiap,k X majp,k ) sin(kLi kLj ) nL Thtrj k1 else 3.2
GM positioning online Step 1: Initial road section search. To reduce the computation complexity of GM positioning in road network, a track matching method is utilized to determine the initial road section. The algorithm is expressed as, where Li and Lj mean two different road sections. Thtrj is the average track difference threshold.
Step 3: Connectivity judgment. The basic criterion to judge the connectivity is that the space distance between the end point of current road section and the starting point of another road section is less than the pre-set threshold. Then, the connectivity matrix [ci, j ]N can be expressed as,
0, disconnected Li and Lj [ci, j ]N
1, connected Li and Lj where ci, j
means the connection relation between section Li and section Lj . N is the total number of the sections in road network and i, j 1, 2,, N . (4) (5) (6) (7) wtrj path arg min posk sin k
[map,N ] k1
where map, N means the search range of road sections, and wtrj is the window
length of the DR-derived traveling track. posk sin k is the difference between the
DR traveling track and the road section in magnetic map, and k 1, 2, , wtrj .
Step 2: Optimum position matching. An improved NPROD algorithm [
X opt arg km(wa,nxL ) r k w (M map,ki -M map )(M onl,wi M onl ) i1 w M map,ki -M map 2 M onl,wi M onl i1 2 where M onl and M map are the mean value of online magnetic intensity data and map magnetic intensity data in the sliding matching window, respectively. The mileage distance for the sliding window is w 1 d and the mileage step is d .
One advantage of the sliding window matching is that the magnetic interference from building changes and other vehicles along the travel route can be suppressed. A self-evaluation is proposed to further reduce the mismatching errors. The GM result is valid only if it passes the evaluation. The self-evaluation can be represented as, rn,max ThR pD nwev1 Xˆ opt,n Xˆ opt,n1 Dwev ThD where rn,max is the maximum correlation value and ThR is the threshold. Xˆ opt,n is the nth position matching result, wev is the evaluation sliding-window length, and Dwev is the total mileage increment. pD is the distance difference and ThD is the threshold. Step 3: Road section splice. When the vehicle travels at the joint-node, all the possible connected road sections are introduced in the matching process, according to the connectivity matrix [ci, j ]N . If the GM results are constant in the same road section after the joint-node, this road section will be updated as the new current section. With this method, a continuous GM positioning is then achieved. 4
GM/DR positioning results fusion A designed EKF is used to fuse the GM results with the DR results. The state vector X kf is expressed as,
Xnkf n|n1Xnkf Wn pe 1 0 sin n pn 0 1 cosn Xnkf D 0 0 1 n 0 0 0
Dn cosn pe wpe Dn sin n pn wpn 0 D wD 1 n1 w n (8) (9) (10) (11) X kf [ p e , p n , D , ]T
Z =[peg per , png pnr ] where pe is the east position error, pn is the north position error, D is the traveling distance error and is the heading error of DR.
The difference between GM derived position and DR derived position is adopted as the measurement vector Z , where ( peg , png ) is the GM derived position, and ( per , pnr ) is the DR derived position at the same solution period.
The state equation can then be derived from the dynamic model of DR, where n n1 is the state transition matrix. [wpe , wpn , wD , w ] is the process noise vector. n is the vehicle heading at tn . Dn is the traveling distance between tn and tn1 .
The measurement equation is modeled as,
Zn H n X nkf Vn where Hn is the measurement matrix. [vpe , vpn ] is measurement noise vector. 5
Experiment And Analysis A road test was carried out in a simple urban road network. The test route includes some typical road conditions such as urban canyon, expressway and tunnel. The selfdesigned magnetometer (precision: 50 nT) and odometer (error ratio: 0.8%) are used to measure magnetic and mileage data respectively. The DR heading is provided by a navigation-grade IMU which the bias stability of azimuth gyroscope is 0.02°/h. 5.1
Reference map construction analysis Additionally, the map database of a single road section is a single-dimensional spatial series. The serious position errors will occur if the test route deviates appreciably u l a v n o ilt a e rr o c m u m i x a M ） m （c e n e iffr e d e g a e li M from the RPs trajectory (multi-lane road, big crossroad, etc.). For a superior matching performance, the map construction considering multi lanes should be implemented. 5.2
Positioning performance analysis During online positioning phase, the vehicle route was randomly selected and consisted of some separate road sections in the test road network. Fig.4 shows the position errors of original GM results. The maximum value of GM position errors is greater than 67m which could not be applied directly to correct DR errors. Fig.6 compares the position errors between the DR results and the GM/DR results. With the proposed GM/DR scheme, the errors of heading angle, mileage and DR reIn Fig. 5, after the self-evaluation operation, the GM position error is 3.34m (2σ) and the maximal value is reduced to 12.11m. Therefore utilizing the maximum correlation value and mileage difference to evaluate the original GM results is effective. It should be noted that the self-evaluation operation will degrade the continuity of GM results. The maximal positioning interval after evaluation is 293 meters in this experiment. y ilit b a b o r p e v lit a u m u C sults could be estimated and corrected by the GM results after self-evaluation in real time. This approach prevents the position errors from growing over time and the maximum error in either direction is less than 5 meters. Subsequently high performances of the vehicle independent navigation system are achieved.
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time（s) Acknowledgment This work was supported by National Key Research Program of China “Collaborative Precision Positioning Project” (No.2016YFB0501900) and Entrepreneurship and Innovation Leadership Project of Qingdao (16-8-3-5-zhc).