WO2008138622A1

WO2008138622A1 - Method for determining a speed of an entity

Info

Publication number: WO2008138622A1
Application number: PCT/EP2008/003916
Authority: WO
Inventors: Harald Haas
Original assignee: Jacobs University Bremen Ggmbh
Priority date: 2007-05-15
Filing date: 2008-05-15
Publication date: 2008-11-20
Also published as: EP2162760A1

Abstract

The present invention relates to a method and a corresponding device for determining the speed of a moving entity carrying at least two antennas for receiving a transmission signal, said antennas being displaced at a predetermined distance. In order to provide a more simple and accurate method which can be used with different transmission signals a method is proposed comprising the steps of: receiving a transmission signal by the at least two antennas, determining signal characteristics from the transmission signal as received by the at least two antennas, determining a time offset between the reception of the transmission signal at the at least two antennas by comparing the signal characteristics determined for the at least two antennas, and determining the speed of the moving entity from the determined time offset, the distance of the at least two antennas and the direction of movement of the moving entity relative to the arrangement of the at least two antennas.

Description

Method for determining a speed of an entity

The present invention relates to a method and a corresponding device for determining the speed of a moving entity.

Known mobile speed estimation algorithms can be briefly grouped into two categories: time-domain approaches, e.g. based on the covariance approximations on the envelope level crossing rates (LCR) or average fade duration, and frequency-domain approaches based on the Doppler spectrum or on some parametric spectral analysis. Such methods for speed estimation include estimating the maximum Doppler frequency using spectrum methods, calculating the squared deviations of the logarithmically compressed received envelope, zero- crossing estimators, frequency domain time covariance analysis and wavelet- based approaches. These methods give generally good results at vehicular speeds (larger than 30km/h). However, these algorithms are quite complicated and they do not work satisfactorily at very low speeds (e.g. pedestrians speeds up to 6km/h).

One of the largest obstacles to effective navigation and positioning using pedestrian dead reckoning is the lack of accurate speed estimation algorithms. Existing methods are either complex or provide results that are unsatisfactory at low velocities associated with pedestrians and other slow moving entities.

Pedestrian dead reckoning (PDR) is a popular choice for positioning and naviga- tion in areas (e.g. indoors) where GPS based solutions cannot be used. Two pieces of information are essential before a valid location estimation can be made: a reference point with known coordinates and the velocity (speed and heading) at sufficiently close and successive intervals. Given the needed information, displacement of the user from the reference location can be approximated and hence an estimate of the new location coordinates can be obtained. Accurate heading information is readily available from sensors such as a ring laser gyro as described by J. CoIMn et al., "Indoor Positioning System Using Accelerometry and High Accuracy Heading Sensors", in Proceedings of GPS/GNSS 2003 Conference. Portland, OR: Institute of Navigation, Sep. 912, 2003; it is the speed esti- mate that has been difficult to obtain with a sufficient degree of accuracy. Step length estimation based devices as described by J. Kappi et al., "MEMS-IMU based pedestrian navigator for handheld devices", in Proceedings of GPS/GNSS 2001 Conference. Salt Lake City, UT: Institute of Navigation, Sep. 1114, 2001 , pp. 1369 1373 and by C. Randell et al., "Personal position measurement using dead reckoning", in Proceedings of the Seventh IEEE International Symposium on Wearable Computers 2003, pp. 166173, Oct. 1821 , 2005 can only be used by pedestrians and must be mounted directly on the person. Frequent updates of the absolute position are also required as errors tend to accumulate with every step. While methods based on the level crossing rate (LCR) of the received Ray- leigh fading envelope as described by A. Abdi and M. Kaveh, "Level crossing rate in terms of the characteristic function: a new approach for calculating the fading rate in diversity systems", in IEEE Transactions on Communications, vol. 50, no. 9, pp. 13971400, Sep. 2002 and by L. Zhao and J. W. Mark, "Mobile speed esti- mation based on average fade slope duration", IEEE Transactions on Communications, vol. 52, no. 12, pp. 20662069. Dec. 2004 typically provide good results for high speeds, the accuracy drops considerably at speeds associated with pedestrians and other low velocity entities. Continuous wavelet transform (CWT) can also be used to extract speed information from the aforementioned envelope with a good degree of accuracy as described by R. Narasimhan and D. C. Cox, "Speed estimation in wireless systems using wavelets", IEEE Transactions on Communications, vol. 47, no. 9, pp. 13571364, Sep. 1999. However, such a procedure is computationally complex and expensive.

It is therefore an object of the invention to provide an improved method for de- termining a speed of an entity, wherein the speed of the entity can also be determined even at low velocities.

This object is solved by a method according to claim 1 as well as by a device for determining the speed of a moving entity according to claim 17.

Therefore, a method for determining the speed of a moving entity carrying at least two antennas for receiving a transmission signal is provided. The antennas are displaced at a predetermined distance. A transmission signal is received by the at least two antennas. Signal characteristics of the transmission signal as received by the at least two antennas are determined. A time offset between the reception of the transmission signal at the at least two antennas is determined by comparing the signal characteristics determined for the at least two antennas. A first rough speed of the moving entity is estimated for the determined time offset, the predetermined distance of the at least two antennas and a direction of movement of the moving entity relative to the at least two antennas. A spatial correlation function is determined. The estimated first rough speed of the moving entity is used for mapping at least one cross-correlation coefficient with respect to signal characteristics. A travelled distance is determined based on the cross- correlation coefficient. The speed of the moving entity is determined based on the determined time offset and the determined travelled distance.

The invention also relates to a device for determining the speed of a moving entity. The device comprises at least two antennas for receiving a transmission signal. The antennas can be carried by the moving entity and are displaced at a predetermined distance. The device comprises a signal characteristics determination means for determining signal characteristics of the transmission signal as received by the at least two antennas. The device furthermore comprises a time offset determination means for determining a time offset between the reception of the transmission signal at the at least two antennas by comparing the signal characteristics determined by the at least two antennas. The device furthermore comprises a speed determination means for determining the speed of the moving entity from the determined time offset, the predetermined distance between the at least two antennas and the direction of movement of the moving entity relative to the arrangement of the at least two antennas.

The algorithm according to the invention is simple to implement, performs uniformly for all speed ranges and is able to provide highly accurate results. A two antenna solution is described. The algorithm is applied in two steps. The first step reuses the algorithm as described by Mostafa Afgani and Harald Haas, "Speed Estimation Using Relative Radio Frequency Signature Matching" as a tracking method to acquire knowledge about the behavior of the spatial correlation function as described by G. D. Durgin and T. S. Rappaport, "Theory of multipath shape factors for small-scale fading wireless channels", IEEE Transactions on Antennas and Propagation, Volume 48, Issue 5, 682 - 693 May 2000. It also - A -

serves as a very rough speed estimate. In the second step this knowledge is utilized to simply estimate the speed with high accuracy. It exploits the fact that a certain cross-correlation value can then be directly mapped to a certain distance φd using the spatial correlation model as described by G. D. Durgin and T. S. Rappaport, "Theory of multipath shape factors for small-scale fading wireless channels", IEEE Transactions on Antennas and Propagation, Volume 48, Issue 5, 682 - 693 May 2000. Having φd and the elapsed time, the speed can then be easily be computed. The algorithm generally shows very high accuracy and is most importantly extremely noise resistant.

In other words, the invention relates to the idea to provide a method of speed estimation using relative radio frequency (RF) signature matching. The algorithm consists of two parts. In the first part the RF signatures at two antennae separated by a known distance are correlated to determine the time it takes for the trailing antenna to experience the same channel conditions as that experienced by the leading antenna. As the antenna separation is predefined and known (e.g. in a MIMO (multiple-input-multipleoutput) device), a rough speed estimate is calculated from an estimate of the time delay. Using this rough estimate each cross-correlation coefficient can be mapped, originally calculated to determine the lag, to a certain distance. Then the spatial correlation function associated with this location can be determined. The relevant content of Mostafa Afgani and Harald Haas, "Speed Estimation Using Relative Radio Frequency Signature Matching" is incorporated to this application by reference.

Once the spatial correlation function is determined, the second step of the algorithm can be performed. Here, an antenna scenario is assumed (any of the two antennas in the original scenario can be chosen). By acquiring channel estimates at known discrete times the travelled distance can be easily found by considering cross-correlation coefficients of these estimates. Clearly, knowing the travelled distance and the elapsed time, the speed can be determined. As will be shown later, this speed estimation algorithm according to the invention produces accu- rate estimates at both high and low velocities for all possible channel scenarios. In addition, its performance only degrades marginally at low SNR levels. Furthermore, it is of low computational complexity as the main operation only involves the calculation of correlation values between two channel estimates. 16

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Further aspects of the invention are described in the dependent claims.

Embodiments and advantages of the invention will now be described with reference to the figures.

Fig. 1 shows a graph depicting the relative error with respect to corre- lation coefficient values according to the invention, and

Fig. 2 shows a graph depicting a correlation function p(r).

According to the embodiments of the invention, a method for determining a speed of an entity is described. The underline algorithm is applied in two steps. In the first step RF signatures of at least two antennae separated by a known distance are correlated to determine the time offset between the two antennas. Based on the time offset, a rough speed estimate can be calculated. The rough speed estimate can be used to estimate cross-correlation coefficients, from which a distance can be calculated based on a spatial correlation module.

The multipath effect is a common phenomenon in typical terrestrial environments. In addition to frequency selective fading, signal frequencies can also experience spreading caused by Doppler shifts. The signal received from a multipath channel by an antenna can be represented by:

(=0

where L(t) is the number of multipath components, A₁ is the amplitude, Φ, is the carrier phase shift, r, is the time delay, and θ, is the angle of arrival (AoA) of component /. The amplitude is modeled as a Rayleigh distributed random variable and the AoA and phase shift are uniformly distributed as described by R. B. Ertel et al., Overview of spatial channel models for antenna array communication systems", IEEE Personal Communications, vol. 5, no. 1 , pp. 1022, Feb. 1998. Furthermore, the delay is exponentially distributed as described by P. Hoher, "A statistical discrete-time model for the WSSUS multi-path channel", IEEE Transactions on Vehicular Technology, vol. 41 , no. 4, pp. 461468, Nov. 1992. a(θ_t(t)) is known as the array response vector. When the signal and antenna array (con- taining m antennae) are restricted to a two-dimensional space, the array response vector is given by

exp -jψι,_m] (2)

where ^Λ*) = [*• «*(*«(«)) + y, sⁱn(fl,(t))]0 and ^ = X is the wavenumber as described by R. B. Ertel et al., Overview of spatial channel models for antenna array communication systems", IEEE Personal Communications, vol. 5, no. 1 , pp. 1022, Feb. 1998. Λ is the carrier wavelength. The maximum Doppler shift , fd_max, experienced by a receiver is dependent on the speed and is given by

h_^ = \ O⁾

where v is the speed as described by T. S. Rappaport, Wireless Communications, Prentice Hall, 1996.

As stated above, a channel response that shows rapid variations in space but remains relatively unchanged in time is essential to the success of the speed estimation algorithm. It requires a multi-antenna setup and an accessible RF source such as a local digital television transmitter. For each spatial dimension, at least two antennae are required. For simplicity, movement can be confined to a single spatial dimension only (the idea applies to the general three dimensional case in a straight-forward manner) and the antenna array can be aligned parallel to the direction of motion.

In the second step of the algorithm, an antenna scenario is assumed (any of the two antennas in the original scenario can be chosen). It should be noted that the antenna is moving with a constant speed V₀ for a time t₀ along a direction θ₀ over some area with radius r₀. An accurate approximation of the spatial correlation function is derived in G. D. Durgin and T. S. Rappaport, "Theory of multipath shape factors for small-scale fading wireless channels", IEEE Transactions on Antennas and Propagation, Volume 48, Issue 5, 682 - 693 May 2000 as

p(r) « exp[-23Λ²(l + 7cos[2(0_mαl - *„)]) (τ) 1 W

where r is the distance, Λ is the angular spread defined as

Y is the angular constriction defined as

_ F₀F₂ - F₁ ² 7 Fi - I-F₁I= ' (6)

θ_max is the azimuthal direction of maximum fading defined as

0_mαx = | BTg(F₀F₂ - F₁ ²) (7)

and F_n are the Fourier coefficient of p(θ) the angular multipath power distribution in the azimuth plane (APD) from G. D. Durgin and T. S. Rappaport, "Theory of multipath shape factors for small-scale fading wireless channels", IEEE Transac- tions on Antennas and Propagation, Volume 48, Issue 5, 682 - 693 May 2000.

For simplicity we define a new parameter K defined as

K = Λ²(l + 7 cos[2(0_mαχ - θo))) (8)

such that our spatial correlation function becomes p(τ-) « exp[-23tf(-)²l (9)

As mentioned above, perfect knowledge of the spatial correlation model is assumed, which essentially means that the value of K is known, which according to the definition of the multipath shape factors is a number between 0 and 1.

Using the previously mentioned settings, it is assumed that a channel estimate can be obtained every At, where At < < t₀. Cross-correlating the complex envelope S₀(T) received at t = 0 with all the other received complex envelopes will result to the correlation coefficient [C₁, C₂, C₃ c_m], where

(so(τ)s_n(τ)) c_n = R_n(O) = (10)

V(S₀(T)S₀(T)) ■ (S_n(T)S_n(T))

corresponding to the time vector [U, t₂, t₃ t_m], where t_n = nΔt. Using the inverse spatial correlation function in eqn. (9) the associated distances can be calculated as

r_{n =} P „--!^I(,C„_n) * _ = A i _λ./ ^ Wc_n) ( 1 1)

to obtain the distance vector [T₁, r₂, r₃, ..., r_m].

Knowing the distances and the elapsed time, the speed estimates can be obtained as

Tn T_n ....

"-- - r ⁼ ^Ki ⁽¹²⁾

forming the vector of estimated speeds [V₁, V₂, v₃ v_m]. As a final step, the mean of all these values can be taken to get the final result

Clearly this algorithm would be too optimistic if applied directly assuming one of the classical models for spatial correlation with full angular spread. It is evident from eqn. (4) - (7) that the spatial correlation is highly dependent on the instantaneous multipath shape factors as well as the wavelength. The shape factors in turn are directly derived from the Fourier coefficients of the APD.

Since it is almost impossible to derive an analytic expression for the instantaneous APD, because of its high dependency on the relative geometry of the surroundings, it is unrealistic to assume some fixed spatial correlation function. This assumption was also confirmed by K. Kalliola et al., "Angular power distribution and mean effective gain of mobile antenna in different propagation environments", IEEE Transactions on Vehicular Technology, vol. 51 , pages 823 - 838, 2002.

To overcome this problem, this instantaneous spatial correlation function can be directly approximated rather than the APD. This is done using the same algorithm mentioned in Mostafa Afgani and Harald Haas, "Speed Estimation Using Relative Radio Frequency Signature Matching" and extending it to comply with the present invention which practically forms the first step of the complete algorithm.

As stated before, the main target of the first step of the algorithm is to get a good approximation of the instantaneous spatial correlation function i.e. try to approxi- mate K. Again it is assumed that this spatial correlation function remains constant for some time tO over some area with radius rθ. The algorithm in Mostafa Afgani and Harald Haas, "Speed Estimation Using Relative Radio Frequency Signature Matching"assumes a one-dimensional and two antenna solution, where a rough speed estimate can be obtained from a knowledge of the fixed interantenna distance and the time it takes for the trailing antenna to experience the same channel conditions as the leading antenna. The leading antenna is referred to as antenna A and the trailing antenna as antenna S. In addition to that, it is assumed that the received envelopes at the two antennas are correlated by less than 0.8 i.e. the antenna separation d_a is large enough.

Again similar to step two, the complex envelope received at antenna A at time t' = 0 is cross-correlated with the envelopes received at antenna S at times V_n = nΔf, where Δf < < t₀ and n = 1 , 2, 3, ...m. Similar to step 2 this process produces the cross-correlation coefficients [c\, c'₂, C₃, .... c'_m], where

corresponding to the time vector [t\, V₂, V₃ t'_m]. If it is assumed that V₀ is big enough for antenna B to pass through the same location at which antenna A was at V = 0, the highest correlation coefficient produced by this operation can be searched and it can be assumed that the corresponding time is the time it took antenna S to travel the distance d_a. In other words,

c^ maxtc; , ^, ..., ^) (15)

Using (15), a rough estimate of the speed can be obtained using

Again as in step 2, every c'_n can be mapped to some distance r'_π using

< = d_o - O4_t (iη

Logically, it can be argued that the speed has already been estimated and we do not need to proceed to step two. Unfortunately, this algorithm was shown to have relatively large errors since it is highly dependent on the interantenna distance and can therefore only be used to get a rough estimate of the speed. Using any of the correlation coefficients with its corresponding distance, the model in eqn. (9) can be fitted into the measurement and by that easily approximate K using

K = -*§*<£)^» (.8)

Of course the existence of AWGN in our channel cannot be ignored as well as detection errors, which in turn produce errors in v'_est. Therefore, it is highly important to take into account that the pairs of cross-correlation coefficients and dis- tances calculated in this manner will definitely include an error. As a result of that, a way must be found to choose a c'_n that would minimize the relative error e_κ in estimating K. It is assumed that each c'_π has some error e_n. Since clearly we don't know how big the error at each c'_n is, it is assumed all of them to have approximately the same error. Based on that assumption the range of values of c' that would minimize ' ' need to be found. It is known that

_κ, HO , λ a ϊn(c') (19)

where D is some constant. It is also known that

»n(c) _{= iJ} In(C^ - e)

K = D (20)

Taking these two expressions it is known that

_K'.K „ _DW _{= D}Mc±__DH'_: e) _{= D}H*£ r (21)

From eqn. (11 ) it is known that

r_{2 = z)}lα(c_- e) ₍₂₂₎

Substituting eqn. (22) into eqn. (21 )

Fig. 1 shows a graph depicting the relative error with respect to correlation coefficient values according to the invention. Fig. 2 shows a graph depicting a correlation function p(r). Here, e_κ is plotted vs. c'. It can be clearly seen that the relative error is minimized for values of c' ranging between 0.2 and 0.7. This somewhat intuitive result can be explained by the shape of the correlation function p(r) as can be seen in Fig. 2. Clearly from the graph p(r) is steepest in this region which means that big variations in the correlation values (in our case the error) result in very small variations in the distance (small error in our result), which is exactly what we pursue.

In the light of this discussion, a C_n E [0.2, 0.7] can be chosen to estimate K in eqn. 18. Now, it is also why the antenna separation is restricted to be big enough such that the cross-correlation between the received complex envelopes at the two antennas is less than 0.8.

Once K is calculated, step two of the algorithm can be processed and the speed can be calculated accurately.

To investigate the performance of the algorithm in different scenarios, 4 different APDs are used, each with three different SNR levels. A symbol duration of T₅ = 224μs and a carrier frequency f_c = 467MHz is used. From 2 it is clear that d_a = OAK is a very reasonable antenna separation that would guaranty that the algo- rithm will perform well over a wide range of APD's. Accordingly, this means d_a = 26 cm.

Claims

C l a i m s

1. Method of determining the speed of a moving entity carrying at least two antennas for receiving a transmission signal, said antennas being displaced at a predetermined distance, comprising the steps of: - receiving a transmission signal by the at least two antennas, determining signal characteristics of the transmission signal as received by the at least two antennas, determining a time offset between the reception of the transmission signal at the at least two antennas by comparing the signal characteristics determined for the at least two antennas, and estimating a first rough speed of the moving entity from the determined time offset, the predetermined distance of the at least two antennas and a direction of movement of the moving entity relative to the at least two antennas, and determining a spatial correlation function, - using the estimated first rough speed of the moving entity for mapping at least one cross-correlation coefficient with respect to the signal characteristics, determining a travelled distance based on the cross-correlation coefficient and determining the speed of the moving entity based on the determined time offset and the determined travelled distance.

2. Method as claimed in claim 1 , wherein the moving entity carries two antennas, preferably arranged along a line parallel to the direction of regular movement of said moving entity, wherein for each antenna signal characteristics are determined from the received transmission signal and wherein the determined signal characteristics are compared to determine said time offset.

3. Method as claimed in claim 1 , wherein the moving entity carries a plurality of antennas, preferably arranged in a common plane or a common sphere, wherein for each antenna signal characteristics are determined from the received transmission signal and wherein the signal characteristics are compared to determine the time offsets between the reception of the transmission signal at the plurality of antennas.

4. Method as claimed in claim 3, wherein said antennas are arranged at the corners of a polygon having equally long side lengths, at equal distances along the circumference of a circle or equi- spaced on the surface of a sphere.

5. Method as claimed in claim 3 or 4, wherein the direction of movement of the moving entity relative to the arrangement of the at least two antennas is determined from the differences of time offsets determined for the plurality of antennas.

6. Method as claimed in any one of the preceding claims, wherein the comparison of the signal characteristics is performed continuously.

7. Method as claimed in any one of claims 1 to 5, wherein signal characteristics determined from a portion of the signal as received by the antenna located foremost in movement direction are stored as reference characteristics and wherein the same signal characteristics are determined from the transmission signals received by the other antennas and compared to the to the reference characteristics to determine the time offset(s).

8. Method as claimed in any one of the preceding claims, wherein said signal characteristics are an envelope signal, amplitude peak values, energy values, delay, multipath delay characteristics, maximum delay, root- means-square (RMS) of delay, maximum Doppler frequency, Doppler spectrum or spectral characteristics of the transmission signal.

9. Method as claimed in any one of the preceding claims, wherein an envelope signal is determined as signal characteristic from the transmission signal as received by the at least two antennas and used for determining the time offset between the reception of the transmission signal at the at least two antennas by comparing the envelope signals determined for the at least two antennas.

10. Method as claimed in claim 9, wherein at least a portion of the envelope signal determined from the transmission signal received by the antenna located foremost in movement direction is stored as reference portion and that the other envelope signals are compared to this reference portion to determine the time offset(s).

11. Method as claimed in any one of the preceding claims, wherein the signal characteristics are compared using a pattern or signal matching method.

12. Method as claimed in any one of the preceding claims, wherein the direction of movement of the moving entity relative to the arrangement of the at least two antennas is determined by use of direction measurement means, in particular a navigation system or an acceleration sensor.

13. Method as claimed in any one of the preceding claims, wherein the at least two antennas are aligned with the direction of movement of the moving entity.

14. Method as claimed in any one of the preceding claims, wherein said at least two antennas are identical.

15. Method as claimed in any one of the preceding claims, wherein said at least two antennas are adapted for receiving transmission signals of a wireless communication system, in particular of a GSM, UMTS, WiMax, WiFi system, or of a digital broadcast system, in particular a DVB-T system.

16. Method as claimed in any one of the preceding claims, wherein the moving entity is a mobile phone, a navigation system, a computer, a PDA, a vehicle or a piece of clothing.

17. Device for determining the speed of a moving entity comprising: at least two antennas for receiving a transmission signal, said antennas being carried by said moving entity and displaced at a predetermined distance, signal characteristics determination means for determining signal charac- teristics from the transmission signal as received by the at least two antennas, time offset determination means for determining a time offset between the reception of the transmission signal at the at least two antennas by comparing the signal characteristics determined for the at least two antennas, and speed determination means for determining the speed of the moving entity from the determined time offset, the distance of the at least two antennas and the direction of movement of the moving entity relative to the arrangement of the at least two antennas.

18. Moving entity, in particular mobile phone, navigation system, computer, PDA, vehicle or piece of clothing, comprising a device for determining the speed of the moving entity as defined in claim 17.

19. Computer program for determining the speed of a moving entity carrying at least two antennas for receiving a transmission signal, said antennas being dis- placed at a predetermined distance, said computer program comprising program code means for causing a computer to carry out the following steps when said computer program is run on a computer: determining signal characteristics from the transmission signal as received by the at least two antennas, - determining a time offset between the reception of the transmission signal at the at least two antennas by comparing the signal characteristics determined for the at least two antennas, and determining the speed of the moving entity from the determined time offset, the distance of the at least two antennas and the direction of movement of the moving entity relative to the arrangement of the at least two antennas.