JOINT NON-COHERENT INTEGRAL VECTOR TRACKING METHOD BASED ON SPATIAL DOMAIN

Abstract

The present invention discloses a joint non-coherent integral vector tracking method based on a spatial domain, which is used for further improving the performance of a vector tracking GPS (Global Positioning System) receiver. In a new vector tracking strategy design, a phase discriminator/a frequency discriminator in a traditional vector tracking loop is discarded, and baseband signals of visible satellites in each channel are taken as an observation value after performing non-coherent integration, and EKE (abbreviation of Extended Kalman Filter) is used to estimate directly and to solve the position, the velocity, a clock error, etc. of the GPS receiver. Because of the existence of non-coherent integral calculation, when GPS satellite signals are relatively weak, a carrier to noise ratio of an observation value may be effectively improved, and the tracking sensitivity is improved.

Claims

1. A joint non-coherent integral vector tracking method based on a spatial domain, comprising the following steps: (1) receiving satellite signals through a GPS antenna, superposing baseband signals in each channel, and realizing non-coherent integration of the signals among different channels, so as to improve a tracking sensitivity in a low signal to noise ratio condition; (2) using a result after the non-coherent integration as an observation value, and using an Extended Kalman Filter to perform an optimal estimation on navigation state parameters; and (3) predicting a code phase difference and a carrier frequency difference of each tracking channel according to a result of the estimation, so as to directly form a closed-loop tracking loop.

2. The tracking method according to claim 1, wherein a tracking period of a joint non-coherent integral vector tracking loop based on the spatial domain is one second.

3. The tracking method according to claim 1, wherein the joint non-coherent integration in the step (1) is $\begin{array}{c}{I}_{P,k,k+1}=\underset{l=1}{\overset{L}{.Math.}}.Math.I_{P,l,k,k+1}=L.Math.N.Math.A_{k+1}+{\eta }_{k+1}\\ I_{E,k,k+1}=\underset{l=1}{\overset{L}{.Math.}}.Math.I_{E,l,k,k+1}=0.5.Math.L.Math.N.Math.A_{k+1}+{\eta }_{k+1}\\ I_{L,k,k+1}=\underset{l=1}{\overset{L}{.Math.}}.Math.I_{L,l,k,k+1}=0.5.Math.L.Math.N.Math.A_{k+1}+{\eta }_{k+1}\\ A_{k+1}=\frac{1}{L}.Math.\underset{i=1}{\overset{L}{.Math.}}.Math.{\stackrel{\_}{A}}_{k+1}\end{array}$ where L is the number of visible GPS satellites, N is the number of integral points within a [k k+1] period; η.sub.k+1 is a zero-mean-value Gaussian white noise; I.sub.P, l, k, k+1 is a coherent integration result of an I.sub.th satellite prompt signal in the [k, k+1] period; l.sub.P, k, k+1, I.sub.E, k, k+1 and I.sub.L, k, k+1 are coherent integration results of GPS baseband signals and local reproduction signals, which are selected by using as observation values of the tracking loop; and Ā.sub.k+1=ā.sub.l(k+1){circumflex over (ā)}.sub.l(k+1), a.sub.j(k+1) is a signal amplitude at a k+1 moment, and A.sub.k+1 is an average value of the signal amplitudes a all the channels, which is an unknown quantity, and is taken as a state vector of the tracking loop.

4. The tracking method according to claim 1, wherein a system equation of the Extended Kalman. Filter in a vector tracking loop system in the step (2) is ${\left[\begin{array}{c}{I}_P\\ I_E\\ I_L\end{array}\right]}_{k+1}={\left[\begin{array}{ccccccccc}0& 0& 0& 0& 0& 0& 0& 0& L.Math.N\\ 0& 0& 0& 0& 0& 0& 0& 0& 0.5.Math.L.Math.N\\ 0& 0& 0& 0& 0& 0& 0& 0& 0.5.Math.L.Math.N\end{array}\right]\left[\begin{array}{c}\delta .Math..Math.X\\ \delta .Math..Math.Y\\ \delta .Math..Math.Z\\ \delta .Math..Math.V_x\\ \delta .Math..Math.V_y\\ \delta .Math..Math.V_z\\ \Delta .Math..Math.t_b\\ \Delta .Math..Math.t_d\\ A\end{array}\right]}_{k+1}+R_{k+1}$

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0021] FIG. 1 is a structural diagram of a tracking loop of a GPS receiver of the present invention;

[0022] FIG. 2 is a working flow diagram of a GPS receiver of the present invention;

[0023] FIG. 3 is a structural principle of a GPS receiver of the present invention;

[0024] and FIG. 4 is an algorithm flow diagram of a GPS receiver of the present invention..

DETAILED DESCRIPTION OF THE INVENTION

[0025] In the working process of the GPS receiver, in order to obtain a pseudo range (distance) and a pseudo range rate (the visual direction velocity) of each tracking channel, it is required to use a received GPS intermediate-frequency signal and a local reproduced carrier and a reproduced pseudo random sequence of each tracking channel to perform coherent and integral calculations. We assume that the current moment is k moment, and the next moment is k+1 moment, in a tracking process, we need to utilize data at the k moment to estimate signal parameters of the k+1 moment.

[0026] Taking a tracking channel of the l.sub.th satellite as an example, assuming that a pseudo random code phase at the current moment is τ.sub.l,k (unit: meter), a pseudo random code frequency is ƒ.sub.code, l, k (unit: chip/second), a clock error of the GPS receiver is t.sub.i, k (unit: meter), a clock drift of the GPS receiver is t.sub.d,k (unit: meter/second), the position of the GPS receiver is P.sub.k, the velocity of the GPS receiver is V.sub.k, the position of the satellite is P.sub.satellite, i, k and the velocity of the satellite is V.sub.satellite, l, k,

[0027] wherein

P.sub.k=[X.sub.k Y.sub.k Z.sub.k].sup.T   (1)

V.sub.k=[V.sub.x,k V.sub.y,k V.sub.z,k].sup.T   (2)

P.sub.satellite,l,k=[X.sub.satellite,l,k Y.sub.satellite, l, k Z.sub.satellite,l,k].sup.T   (3)

V.sub.satellite,l,k=[V.sub.x,satellite,l,k V.sub.y,satellite, l, k Z.sub.z,satellite,l,k].sup.T   (4)

[0028] the relation between the position/velocity of the GPS receiver at the k moment and the position/velocity of the GPS receiver at the k+1 moment is

P.sub.k+1=P.sub.k+V.sub.k+V.sub.kt.sub.k,k+1+δP.sub.k+1   (5)

V.sub.k+1=V.sub.k+δV.sub.k+1   (6)

{circumflex over (P)}.sub.k+1=P.sub.k+V.sub.kt.sub.k,k+1   (7)

{circumflex over (V)}.sub.k+1=V.sub.k   (8)

[0029] wherein {circumflex over (P)}.sub.k+1 is a prediction value of the position of the GPS receiver at the k+1 moment; {circumflex over (V)}.sub.k+1 is a prediction value of the velocity of the GPS receiver at the k+1 moment; δP.sub.k+1 is an error of the prediction value of the position of the GPS receiver at the k+1 moment; and δV.sub.k+1 is an error of the prediction value of the velocity of the GPS receiver at the k+1 moment.

[0030] We know that the tracking process of the tracking loop of the GPS receiver is substantively a tracking process on the change in code phase and the carrier Doppler frequency of the received GPS satellite signals. The change in the relative position between the GPS receiver and the GPS satellite causes the change in the code phase, the change in the relative velocity between the GPS receiver and the OPS satellite causes the change in the Doppler frequency, and they satisfy the following relation there between

[00001]$\begin{array}{cc}{\mathrm{\Delta \tau }}_l\left(k,k+1\right)={\left[\left(P_{k+1}-P_k\right)-\left(P_{\mathrm{satellite},l,k+1}-P_{\mathrm{satellite},l,k}\right)\right]}^T.Math.a_{j,k+1}+\Delta .Math..Math.t_{b,k+1}& \left(9\right)\\ \Delta .Math..Math.{\mathrm{df}}_l\left(k,k+1\right)=f_{L.Math..Math.1}.Math.\frac{{\left[\left(V_{k+1}-V_k\right)-\left(V_{\mathrm{satellite},l,k+1}-V_{\mathrm{satellite},l,k}\right)\right]}^T.Math.a_{j,k+1}+\Delta .Math..Math.t_{d,k+1}}{c}& \left(10\right)\end{array}$

[0031] wherein, Δτ.sub.l (k, k+1) is a variation quantity of the code phase with meter being the unit from a k moment to a k+1 moment; P.sub.satellite, l, k is the position of the satellite l within a [k, k+1] period, which may be obtained by means of direct calculation of a navigation message; Δt.sub.b, k+1 is a variation quantity of the clock error of the receiver within the [k, k+1] period, and the unit is meter; Δdf.sub.l(k, k+1) is a variation quantity of the Doppler frequency with Hz being the unit within the [k, k+1] period; f.sub.L1=1575.42 MHz is the carrier frequency of a GPS signal at an L1 waveband; V.sub.satellite, l, k is the velocity of the satellite l within the [k, k+1] period, which may be obtained by means of direct calculation of the navigation message; α.sub.j, k+1 is a unit vector of a visual direction projection from k to k+1 moment; and Δt.sub.d, k+1 is a variation quantity of the clock error drift of the receiver within the [k, k+1] period, and the unit is m/s; c=2.99792458×10.sup.8 meter/second, which is the light velocity in vacuum.

[0032] Assuming that a reproduced code and a carrier of a local tracking loop at the current moment (k moment) have been synchronized, namely, the code phase τ.sub.l(k) and the carrier Doppler frequency df.sub.l(k) at the k moment are known, the code phase and the carrier Doppler frequency at the k+1 moment are:

τ.sub.l(k+1)=τ.sub.l(k)+Δτ.sub.l(k, k+1)+t.sub.k, k+1f.sub.l,code, k   (11)

df.sub.l(k+1)=df.sub.l(k)+Δdf.sub.l(k, k+1)   (12)

f.sub.l(k+1)=f.sub.IF30 df.sub.l(k+1)   (13)

[0033] wherein τ.sub.l(k+1) is a code phase of the satellite l at the k+1 moment; df.sub.l(k+1) is the carrier Doppler frequency of the satellite l at the k+1 moment; f.sub.l(k+1) is the carrier frequency of the satellite l at the k+1 moment f.sub.l,code,k=1.023/1575.42f.sub.l(k) is a code frequency, and the unit is chip/s.

[0034] By substituting formula (5) and formula (6) into formula (9) and formula (10), it can be obtained:

[00002]$\begin{array}{cc}{\mathrm{\Delta \tau }}_l\left(k,k+1\right)={\left[V_k.Math.t_{k,k+1}+\delta .Math..Math.P_{k+1}-\Delta .Math..Math.P_{\mathrm{satellite},l,k}\right]}^T.Math.a_{j,k+1}+\Delta .Math..Math.t_{b,k+1}& \left(14\right)\\ .Math.\Delta .Math..Math.{\mathrm{df}}_l\left(k,k+1\right)=f_{L.Math..Math.1}.Math.\frac{{\left[\delta .Math..Math.V_{k+1}-V_{\mathrm{satellite},l,k}\right]}^T.Math.a_{j,k+1}+\Delta .Math..Math.t_{d,k+1}}{c}.Math..Math..Math.\mathrm{wherein}.Math..Math..Math.\Delta .Math..Math.P_{\mathrm{satellite},l,k}=\left(P_{\mathrm{satellite},l,k+1}-P_{\mathrm{satellite},l,k}\right);.Math..Math..Math.\Delta .Math..Math.V_{\mathrm{satellite},l,k}=\left(V_{\mathrm{satellite},l,k+1}-V_{\mathrm{satellite},l,k}\right).& \left(15\right)\end{array}$

[0035] By substituting formula (12), formula (14), and formula (15) into formula (11) and formula (13), it can be obtained:

[00003]$\begin{array}{cc}{\tau }_l\left(k+1\right)={\tau }_l\left(k\right)+{\left[V_k.Math.t_{k,k+1}+\delta .Math..Math.P_{k+1}-\Delta .Math..Math.P_{\mathrm{satellite},l,k}\right]}^T.Math.a_{j,k+1}+\Delta .Math..Math.t_{b,k+1}+t_{k,k+1}.Math.\underset{l,\mathrm{code},k}{f}& \left(16\right)\\ f_l\left(k+1\right)=f_{\mathrm{IF}}+{\mathrm{df}}_l\left(k\right)+f_{L.Math..Math.1}.Math.\frac{{\left[\delta .Math..Math.V_{k+1}-\Delta .Math..Math.V_{\mathrm{satellite},l,k}\right]}^T.Math.a_{j,k+1}+\Delta .Math..Math.t_{d,k+1}}{c}& \left(17\right)\end{array}$

[0036] wherein a.sub.j, k+1 is a view direction unit vector of the GPS receiver pointing to the l.sub.th satellite within the [k, k+1] period, since the GPS receiver is far away from the satellite, the change in the relative position between the GPS satellite and the G PS receiver can be neglected within the [k, k+1] period, namely, regarding a.sub.j, k+1 as a fixed value, which may be obtained through direct calculation of the position of the receiver and the position of the GPS satellite at the k moment, and is a known quantity; ΔP.sub.satellite, l, k and a ΔV.sub.satellite, i, k are the variation quantities of the position and the velocity of the l.sub.th satellite within the [k, k+1] period, which may he obtained through direct calculation of navigation message data of the GPS satellite, and is a known quantity; f.sub.If is a central frequency of an intermediate-frequency signal of the GPS receiver, and is a known quantity; and df.sub.l(k) is the Doppler frequency of the l.sub.th satellite at the k moment, and because carrier synchronization has been completed at the k moment, the carrier Doppler frequency at the k moment is known. In formula (16) and formula (17), unknown quantities which can affect the code phase and the Doppler frequency of the l.sub.th satellite at the k+1 moment are a position error δP.sub.k+1, a velocity error δV.sub.k+1, a clock error t.sub.b, k+1, and a clock drift error t.sub.d, k+1 of the GPS receiver at the k+1 moment. Therefore, it is very natural to choose δP, δV, Δt.sub.b and Δt.sub.d as state vectors of the tracking loop.

[0037] Assuming a complex model of an L1 waveband baseband signal of the l.sub.th satellite signal received by the GPS receiver at the k+1 moment as

s.sub.l(k+1)=a.sub.l(k+1)C.sub.l(k+1)D.sub.l(k+1)exp[j2πf.sub.code,j(k+1)t.sub.k+1+jδφ.sub.l,k+1]+η.sub.l   (18)

[0038] wherein a.sub.j(k+1) is a signal amplitude at the k+1 moment; C.sub.l(k+1) is a pseudo random code at the k+1 moment; D.sub.l(k+1) is a navigation message data bit at the k+1 moment, with the value thereof being ±1; δφ.sub.l,k+1 is a carrier phase difference at the k+1 moment; and η.sub.l is a zero-mean-value Gaussian white noise.

[0039] In a vector tracking process, we only care the code phase and the carrier frequency, and are not interested in the carrier phase difference and the signal amplitude, and therefore, formula (18) may be rewritten as the following form:

s.sub.l(k+1)=ā.sub.l(k+1)D.sub.l(k+1)C.sub.l(k+1)exp[j2πf.sub.cord,l(k+1)t.sub.k+1]+η.sub.l

wherein ā.sub.l=a.sub.l(k+1)exp(jδφ.sub.l,k+1).   (19)

[0040] Further, from formula (16) and formula (l e), we may obtain a “true value” of a local promptly reproduced intermediate-frequency signal of the l.sub.th satellite:

s.sub.local,l(k+1)={circumflex over (ā)}.sub.l(k+1)D.sub.l(k+1)C.sub.l[τ.sub.l(k+1)]exp[j2πf.sub.l(k+1)t.sub.k+1]  (20) (20)

[0041] wherein D.sub.l(k+1) is a navigation message data bit, and since a navigation message is updated once every two hours, we may regard same as a known quantity herein. The “true value” of the local reproduced intermediate-frequency signal and the received GPS intermediate frequency signal are used to perform coherent integration, and the coherent integration result within the [k, k+1] period is:

[00004]$\begin{array}{cc}\underset{t=t_u}{\overset{t_{k+1}}{.Math.}}.Math.s_l\left(t\right).Math.S_{\mathrm{Local},l}\left(t\right)=\underset{t=t_k}{\overset{t_{k+1}}{.Math.}}.Math.{\stackrel{\_}{a}}_l\left(t\right).Math.{\stackrel{\_}{\hat{a}}}_l\left(t\right).Math.D_l\left(k+1\right).Math.D_l\left(k+1\right).Math.D_l\left(k+1\right).Math.C_l\left(t\right).Math.C_l\left[{\tau }_l\left(t\right)\right].Math.\exp \left[j.Math..Math.2.Math.\pi .Math..Math.f_l\left(t\right).Math.t\right].Math.\exp \left[j.Math..Math.2.Math.\pi .Math..Math.f_{\mathrm{carr},l}\left(t\right).Math.t_{k+1}\right]& \left(21\right)\end{array}$

[0042] Further, since the local promptly reproduced intermediate-frequency signal of the l.sub.th satellite generated by us is a “true value”, namely, a locally reproduced code being “accurately” aligned with the reproduced code in the received GPS signal, the locally reproduced carrier frequency is also “accurate”. In addition, the amplitude change of the GPS signal is very small within the [k, k+1] time period and can be regarded as a constant value, and therefore, the following relation exists in formula (21):

C.sub.l(t)C.sub.l[τ.sub.l(t)]≈1   (22)

exp[j2πf.sub.l(t)t]exp[j2πf.sub.cord,l(t)t.sub.k+1≈1   23)

[0043] Therefore, formula (21) can be simplified as the following form:

[00005]$\begin{array}{cc}{I}_{P,l,k+1}=\underset{t=t_k}{\overset{t_{k+1}}{.Math.}}.Math.s_l\left(t\right).Math.s_{\mathrm{Local},l}\left(t\right)=\underset{t=t_k}{\overset{t_{k+1}}{.Math.}}.Math.{\stackrel{\_}{a}}_l\left(t\right).Math.{\stackrel{\_}{\hat{a}}}_l\left(t\right)+{\eta }_{k,k+1}=N.Math.{\stackrel{\_}{A}}_{k+1}+{\eta }_{l,k,k+1}& \left(24\right)\end{array}$

[0044] wherein I.sub.P, l, k, k+1 is a coherent integration result of the l.sub.th satellite prompt signal in the [k, k+1] period; Ā.sub.k+1=ā.sub.l(k+1); N is the number of integration points within the [k, k+1] period; and η.sub.l, k, k+1 is a zero-mean-value Gaussian white noise.

[0045] By the same reasoning, we can obtain coherent integration results of a early signal and a late signal early/late 0.5 chip):

I.sub.E, l, k, k+1=0.5.Math.N.Math.Ā.sub.k+1+η.sub.l,k,k+1   (25)

I.sub.L, l, k, k+1=0.5.Math.N.Math.Ā.sub.k+1+η.sub.l,k,k+1   (26)

[0046] in an environment where signals fade seriously, the most effective method for improving the signal to noise ratio is to perform coherent integration and non-coherent integration. The traditional non-coherent integration is realized by accumulating coherent integration results of a certain path of satellite signals within a continuous time interval. Although this method is easy in implementation, since the Doppler frequency changes over time, with the increase in non-coherent integration time, the change in the Doppler frequency will have serious impacts on the integration result. As for this problem, the present invention proposes a new non-coherent integration method, namely, performing joint non-coherent integration on coherent integration results of different satellite tracking channels, such that the signal to noise ratio can be significantly improved without increasing an integration time.

[0047] From formula (24), formula (25) and formula (the joint non-coherent integration of the prompt signals of different satellite tracking channels may be obtained, which is:

[00006]$\begin{array}{cc}{I}_{P,k,k+1}=\underset{l=1}{\overset{L}{.Math.}}.Math.I_{P,l,k,k+1}=L.Math.N.Math.A_{k+1}+{\eta }_{k+1}& \left(27\right)\\ I_{E,k,k+1}=\underset{l=1}{\overset{L}{.Math.}}.Math.I_{E,l,k,k+1}=0.5.Math.L.Math.N.Math.A_{k+1}+{\eta }_{k+1}& \left(28\right)\\ I_{L,k,k+1}=\underset{l=1}{\overset{L}{.Math.}}.Math.L_{P,l,k,k+1}=0.5.Math.L.Math.N.Math.A_{k+1}+{\eta }_{k+1}& \left(29\right)\\ A_{k+1}=\frac{1}{L}.Math.\underset{i=1}{\overset{L}{.Math.}}.Math.{\stackrel{\_}{A}}_{k+1}& \left(30\right)\end{array}$

[0048] wherein L is the number of visible GPS satellites.

[0049] In formula (27), formula (28), formula (29) and formula (30), I.sub.P, k, k+1, I.sub.E, k , k+1 and I.sub.L, k, k+1 are coherent integration results of GPS baseband signals and local reproduction signals, which are selected by us as observation quantities of the tracking loop; and A.sub.k+1 is an average value of the signal amplitudes of all channels, which is an unknown quantity, and may be taken as a state vector of the tracking loop.

[0050] In summary, the state vectors of the whole discrete system are δP, δV, t.sub.b, t.sub.d and A, and by combining formula (l), formula (2), formula (5) and formula (6), we establish a system equation of the Kalman Filter in the vector tracking loop system, which is:

[00007]$\begin{array}{cc}{\left[\begin{array}{c}\delta .Math..Math.X\\ \delta .Math..Math.Y\\ \delta .Math..Math.Z\\ \delta .Math..Math.V_x\\ \delta .Math..Math.V_y\\ \delta .Math..Math.V_z\\ \Delta .Math..Math.t_b\\ \Delta .Math..Math.t_d\\ A\end{array}\right]}_{k+1}={\left[\begin{array}{ccccccccc}1& 0& 0& t_{k,k+1}& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& t_{k,k+1}& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& t_{k,k+1}& 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 1& t_{k,k+1}& 0\\ 0& 0& 0& 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}\delta .Math..Math.X\\ \delta .Math..Math.Y\\ \delta .Math..Math.Z\\ \delta .Math..Math.V_x\\ \delta .Math..Math.V_y\\ \delta .Math..Math.V_z\\ \Delta .Math..Math.t_b\\ \Delta .Math..Math.t_d\\ A\end{array}\right]}_k+Q_k& \left(31\right)\end{array}$

[0051] wherein t.sub.t, k+1 is an integration time within a [k, k+1] period, and in specific implementation, we select one second.

[0052] The observation quantities of the systems are I.sub.P, I.sub.E and I.sub.L, which can be obtained by r leans of calculation through formula (20), formula (24), formula (25), and formula 6), and by combining formula (27), formula (28), formula (29), and formula (30), we establish an observation equation of the Kalman Filter in the vector tracking loop system, which is:

[00008]$\begin{array}{cc}{\left[\begin{array}{c}{I}_P\\ I_E\\ I_L\end{array}\right]}_{k+1}={\left[\begin{array}{ccccccccc}0& 0& 0& 0& 0& 0& 0& 0& L.Math.N\\ 0& 0& 0& 0& 0& 0& 0& 0& 0.5.Math.L.Math.N\\ 0& 0& 0& 0& 0& 0& 0& 0& 0.5.Math.L.Math.N\end{array}\right]\left[\begin{array}{c}\delta .Math..Math.X\\ \delta .Math..Math.Y\\ \delta .Math..Math.Z\\ \delta .Math..Math.V_x\\ \delta .Math..Math.V_y\\ \delta .Math..Math.V_z\\ \Delta .Math..Math.t_b\\ \Delta .Math..Math.t_d\\ A\end{array}\right]}_{k+1}+R_{k+1}& \left(32\right)\end{array}$