CN106054226A - Satellite signal blind area positioning method combining mobile cellular network and satellite navigation system - Google Patents

Abstract

The invention belongs to the field of electronic communication and automatic control, and relates to a method for achieving the positioning of a receiver in a satellite signal blind area through combining a mobile cellular network and a satellite navigation system. The method comprises the steps that the receiver employs two different methods for independently calculating the position coordinates firstly through employing a satellite signal transmitted by a base station: one method is that the receiver deduces the position coordinates at a next moment based on a positioning result at a former moment, and the other method is that the receiver measures the pseudo-distance between the base station and the receiver through employing the satellite signal, and then calculates the position through employing a triangulation location principle; afterwards, the receiver combines the positioning results, obtained through the above two methods, as an observation value, and carries out the filtering of the results through employing a Kalman filtering algorithm, so as to determine the final position coordinates of the a user. The method is low in arrangement cost in actual use, is easy to install, and can obtain higher positioning precision.

Description

Mobile cellular network and satellite navigation system combined satellite signal blind area positioning method

Technical Field

The invention belongs to the field of electronics, communication and automatic control, and relates to user positioning based on a navigation satellite, in particular to user positioning in a signal blind area of the navigation satellite.

Background

In a navigation satellite signal blind area, such as inside a building or a tunnel, under a viaduct, and the like, a user receiver generally cannot directly acquire a satellite signal, that is, cannot directly calculate a position by using the navigation satellite signal. In this case, if positioning using satellite signals is still needed, the satellite signals are amplified and forwarded by other devices located in good areas of the satellite signals so that users in the blind areas receive valid satellite signals to realize positioning, such as satellite signal repeater forwarding technology used for indoor positioning. But for environments where the infrastructure is incomplete, satellite repeater deployment will encounter significant challenges. At present, the coverage rate of a mobile cellular network is very high, the coverage radius of a cellular cell base station is gradually reduced, and the blind area of a mobile signal is small, so that a user can still receive a satellite signal in the blind area of the navigation satellite signal by forwarding the navigation satellite signal by using the mobile cellular base station, and further positioning is realized; in the area where the user can directly receive the satellite signal, the receiver can further improve the positioning accuracy by using the forwarded satellite signal.

Disclosure of Invention

The invention provides a method for realizing positioning of a receiver in a satellite signal blind area by combining a mobile cellular network and a satellite navigation system. When a base station receives a navigation satellite signal, the signal is processed to obtain navigation data, then the navigation data is modulated by using a new spread spectrum code (different from the spread spectrum codes used by all navigation satellites), and then the signal is forwarded at a certain power on the frequency band used by the same navigation satellite signal. When the satellite signal is forwarded, the base station maintains the code phase, the carrier phase and the doppler shift of the original satellite signal by using certain signal processing. The transmission power of the base station for transmitting the satellite signals is to ensure that each receiver can simultaneously receive the satellite signals transmitted by three or more base stations. The receiver can realize navigation positioning by using the received and retransmitted satellite signals. The receiver adopts two different methods for positioning, and then the data measured by the two methods are fused through a Kalman filter to realize the final high-precision positioning.

The invention discloses a method for positioning a satellite signal blind area by combining a mobile cellular network and a satellite navigation system, which comprises the following steps:

the method comprises the following steps: positioning by two positioning methods

The invention requires the cellular network base station to be able to transmit the navigation satellite signal, the signal transmitting power meets the relevant regulations and ensures that each user receiver can receive at least 3 or more than 3 satellite signals transmitted by the base station at any time. The coordinates of each base station are accurately measured and may be transmitted to the user receiver via cellular signaling data. Each base station first needs to process the received satellite signals to obtain ephemeris data. Since the amount of mobile network traffic handled by each base station at the same time may be different, the delay time for satellite signal processing may also be different. Different signal processing delays can cause receiver-to-base station ranging errors even if the receiver differentially processes signals from different base stations. The invention adopts two positioning methods, which are specifically as follows:

the first positioning method comprises the following steps:

first, a signal transfer processing time error is eliminated. Is recorded at time t_kSignals measured by the receiver from satellites s_iVia base station b_jThe time elapsed for forwarding to the receiver isThen

${\mathrm{\Δt}}_{s_i,b_j,u}^{\left(t_k\right)}={\mathrm{\δt}}_{s_i,b_j}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_j,u}^{\left(t_k\right)}+{\mathrm{\δt}}_c+{\mathrm{\δt}}_{s_i,b_j,u}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_j}^{\left(t_k\right)}+{\mathrm{\δt}}_{m,b_j}^{\left(t_k\right)},i,j=1,2,3,4---\left(4\right)$

Wherein,is the signal from a satellite s_iTo base station b_jThe time of (d);is a signal from the base station b_jTime to receiver; t is t_cIs the receiver clock error;is the signal from a satellite s_iTo base station b_jPropagation errors experienced by the receiver;the time that the signal is transmitted from the base station antenna after the signal reaches the base station antenna and is processed by the base station;representing other measurement errors.

The differential operation of the propagation times of the signals coming from the same satellite and forwarded to the receiver via the same base station, but measured at different times, results in:

${\mathrm{\Δt}}_{s_i,b_j,u}^{\left(t_0\right)}-{\mathrm{\Δt}}_{s_i,b_j,u}^{\left(t_1\right)}={\mathrm{\δt}}_{s_i,b_j}^{(t_0,t_1)}+{\mathrm{\δt}}_{b_j,u}^{(t_0,t_1)}+{\mathrm{\δt}}_{s_i,b_j,u}^{(t_0,t_1)}+{\mathrm{\δt}}_{b_j}^{(t_0,t_1)}+{\mathrm{\δt}}_{m,b_j}^{(t_0,t_1)},---\left(2\right)$

wherein the receiver clock difference t_cWill be eliminated;

t₀and t₁The interval between the two is less than or equal to 1 second,andconsidered to be zero. The receiver can obtain satellite coordinates after decoding the satellite data. The receiver can obtain the coordinate information of the base station through signaling when accessing the base station,and the coordinate calculation of the satellite and the base station can be used for obtaining.

The receiver respectively transmits signals to different base stations at two successive time instants (t)₀And t₁) The measured propagation times being differentially operated, i.e.

$\left\{\begin{array}{c}{\mathrm{\Δt}}_{s_i,b_1,u}^{\left(t_0\right)}-{\mathrm{\Δt}}_{s_i,b_1,u}^{\left(t_1\right)}={\mathrm{\δt}}_{s_i,b_1}^{(t_0,t_1)}+{\mathrm{\δt}}_{b_1,u}^{(t_0,t_1)}+{\mathrm{\δt}}_{m,b_1}^{(t_0,t_1)}\\ {\mathrm{\Δt}}_{s_i,b_2,u}^{\left(t_0\right)}-{\mathrm{\Δt}}_{s_i,b_2,u}^{\left(t_1\right)}={\mathrm{\δt}}_{s_i,b_2}^{(t_0,t_1)}+{\mathrm{\δt}}_{b_2,u}^{(t_0,t_1)}+{\mathrm{\δt}}_{m,b_2}^{(t_0,t_1)}\\ {\mathrm{\Δt}}_{s_i,b_3,u}^{\left(t_0\right)}-{\mathrm{\Δt}}_{s_i,b_3,u}^{\left(t_1\right)}={\mathrm{\δt}}_{s_i,b_3}^{(t_0,t_1)}+{\mathrm{\δt}}_{b_3,u}^{(t_0,t_1)}+{\mathrm{\δt}}_{m,b_3}^{(t_0,t_1)}\end{array}\right.---\left(3\right)$

Let Can be expressed asWhereini is 0,1, i.e. at time t_iCoordinates of the user;is a base station b_j(j is 1,2,3) andis represented at time t_iSlave base station b_jThe distance to the user receiver. Equation (3) can be further expressed as:

$\left\{\begin{array}{c}{l}_1=\left|\right|{\stackrel{\→}{x}}_{u,0}-{\stackrel{\→}{x}}_{b_1}\left|\right|-\left|\right|{\stackrel{\→}{x}}_{u,1}-{\stackrel{\→}{x}}_{b_1}\left|\right|+{\mathrm{\ρ}}_1+e_1\\ l_2=\left|\right|{\stackrel{\→}{x}}_{u,0}-{\stackrel{\→}{x}}_{b_2}\left|\right|-\left|\right|{\stackrel{\→}{x}}_{u,1}-{\stackrel{\→}{x}}_{b_2}\left|\right|+{\mathrm{\ρ}}_2+e_2\\ l_3=\left|\right|{\stackrel{\→}{x}}_{u,0}-{\stackrel{\→}{x}}_{b_3}\left|\right|-\left|\right|{\stackrel{\→}{x}}_{u,1}-{\stackrel{\→}{x}}_{b_3}\left|\right|+{\mathrm{\ρ}}_3+e_3\end{array}\right.---\left(4\right)$

equation (4) can be further organized as:

$\left\{\begin{array}{c}\left|\right|{\stackrel{\→}{x}}_{u,1}-{\stackrel{\→}{x}}_{b_1}\left|\right|=\left|\right|{\stackrel{\→}{x}}_{u,0}-{\stackrel{\→}{x}}_{b_1}\left|\right|-l_1+{\mathrm{\ρ}}_1+e_1\\ \left|\right|{\stackrel{\→}{x}}_{u,1}-{\stackrel{\→}{x}}_{b_2}\left|\right|=\left|\right|{\stackrel{\→}{x}}_{u,0}-{\stackrel{\→}{x}}_{b_2}\left|\right|-l_2+{\mathrm{\ρ}}_2+e_2\\ \left|\right|{\stackrel{\→}{x}}_{u,1}-{\stackrel{\→}{x}}_{b_3}\left|\right|=\left|\right|{\stackrel{\→}{x}}_{u,0}-{\stackrel{\→}{x}}_{b_3}\left|\right|-l_3+{\mathrm{\ρ}}_3+e_3\end{array}\right.---\left(5\right)$

if the subscriber receiver is at time t₀When the position of the receiver is known, the receiver is calculated according to the formula (5) at the time t₁The position of the time. The calculated user position is

${\stackrel{\→}{x}}_{u,1}=f({\stackrel{\→}{x}}_{u,0},{\stackrel{\→}{x}}_{b_i},{\mathrm{\ρ}}_i,l_i),i=1,2,3---\left(6\right)$

The second positioning method comprises the following steps:

when the subscriber receiver receives the retransmitted signal from the base station, it can use the signal to measure the time taken for the signal to be retransmitted from the satellite to the subscriber via the base stationAt time t_kMeasured timeWill be shown in equation (1). The signals from the same satellite are retransmitted through different base stations and the time required for them to reach the user receiver will be different. Assuming the same satellite(s)₁) Signals are transmitted through four base stations b_j(j-1, 2,3,4) forwarding, then there are

$\left\{\begin{array}{c}{\mathrm{\Δt}}_{s_1,b_1,u}^{\left(t_k\right)}={\mathrm{\δt}}_{s_1,b_1}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_1,u}^{\left(t_k\right)}+{\mathrm{\δt}}_c+{\mathrm{\δt}}_{s_1,b_1,u}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_1}^{\left(t_k\right)}+{\mathrm{\δt}}_{m,b_1}^{\left(t_k\right)}\\ {\mathrm{\Δt}}_{s_1,b_2,u}^{\left(t_k\right)}={\mathrm{\δt}}_{s_1,b_2}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_2,u}^{\left(t_k\right)}+{\mathrm{\δt}}_c+{\mathrm{\δt}}_{s_1,b_2,u}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_2}^{\left(t_k\right)}+{\mathrm{\δt}}_{m,b_2}^{\left(t_k\right)}\\ {\mathrm{\Δt}}_{s_1,b_3,u}^{\left(t_k\right)}={\mathrm{\δt}}_{s_1,b_3}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_3,u}^{\left(t_k\right)}+{\mathrm{\δt}}_c+{\mathrm{\δt}}_{s_1,b_3,u}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_3}^{\left(t_k\right)}+{\mathrm{\δt}}_{m,b_3}^{\left(t_k\right)}\\ {\mathrm{\Δt}}_{s_1,b_4,u}^{\left(t_k\right)}={\mathrm{\δt}}_{s_1,b_4}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_4,u}^{\left(t_k\right)}+{\mathrm{\δt}}_c+{\mathrm{\δt}}_{s_1,b_4,u}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_4}^{\left(t_k\right)}+{\mathrm{\δt}}_{m,b_4}^{\left(t_k\right)}\end{array}\right.---\left(7\right)$

Let To measure, andis the signal from a satellite s₁To base station b_jThe time required for propagation can be determined by satellite s₁And base station b_jThe coordinates of (2) are calculated.Can be expressed as follows:

$\left\{\begin{array}{c}{\mathrm{\ΔT}}_{b_1,u}^{\left(t_k\right)}={\mathrm{\δt}}_{b_1,u}^{\left(t_k\right)}+{\mathrm{\δt}}_c+{\mathrm{\δt}}_{s_1,b_1,u}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_1}^{\left(t_k\right)}+{\mathrm{\δt}}_{m,b_1}^{\left(t_k\right)}\\ {\mathrm{\ΔT}}_{b_2,u}^{\left(t_k\right)}={\mathrm{\δt}}_{b_2,u}^{\left(t_k\right)}+{\mathrm{\δt}}_c+{\mathrm{\δt}}_{s_1,b_2,u}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_2}^{\left(t_k\right)}+{\mathrm{\δt}}_{m,b_2}^{\left(t_k\right)}\\ {\mathrm{\ΔT}}_{b_3,u}^{\left(t_k\right)}={\mathrm{\δt}}_{b_3,u}^{\left(t_k\right)}+{\mathrm{\δt}}_c+{\mathrm{\δt}}_{s_1,b_3,u}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_3}^{\left(t_k\right)}+{\mathrm{\δt}}_{m,b_3}^{\left(t_k\right)}\\ {\mathrm{\ΔT}}_{b_4,u}^{\left(t_k\right)}={\mathrm{\δt}}_{b_4,u}^{\left(t_k\right)}+{\mathrm{\δt}}_c+{\mathrm{\δt}}_{s_1,b_4,u}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_4}^{\left(t_k\right)}+{\mathrm{\δt}}_{m,b_4}^{\left(t_k\right)}\end{array}\right.---\left(8\right)$

base station b_j(j ═ 1,2,3,4) are typically close together, and the receiver can receive the retransmitted signals from these four base stations simultaneously;considered to be equal. Satellite signal retransmission processing time of each base stationEquality is assumed in the present positioning method. According to equation (8), one can further obtain:

$\left\{\begin{array}{c}{\mathrm{\ΔT}}_{b_1,u}^{\left(t_k\right)}-{\mathrm{\ΔT}}_{b_2,u}^{\left(t_k\right)}={\mathrm{\δt}}_{b_1,u}^{\left(t_k\right)}-{\mathrm{\δt}}_{b_2,u}^{\left(t_k\right)}\\ {\mathrm{\ΔT}}_{b_1,u}^{\left(t_k\right)}-{\mathrm{\ΔT}}_{b_3,u}^{\left(t_k\right)}={\mathrm{\δt}}_{b_1,u}^{\left(t_k\right)}-{\mathrm{\δt}}_{b_3,u}^{\left(t_k\right)}\\ {\mathrm{\ΔT}}_{b_1,u}^{\left(t_k\right)}-{\mathrm{\ΔT}}_{b_4,u}^{\left(t_k\right)}={\mathrm{\δt}}_{b_1,u}^{\left(t_k\right)}-{\mathrm{\δt}}_{b_4,u}^{\left(t_k\right)}\end{array}\right.---\left(9\right)$

letWhereinAt a time t_kCoordinates of the user receiver;is a base station b_jThe coordinates of (a). Equation (9) can be written as:

according to the formula (10), the user position coordinates can be obtained by calculationThe calculated user position is recorded as

${\stackrel{\→}{x}}_{u,k}=g({\stackrel{\→}{x}}_{b_i},{\mathrm{\ξ}}_i),i=1,2,3---\left(11\right)$

The second step is that: fusing two positioning results by using Kalman filter

The main errors of the respective positioning results of the first step and the second step are caused by different factors, and if the two positioning results are combined to determine the coordinates of the receiver, the influence of the respective factors on the positioning errors can be weakened, and the positioning accuracy can be improved. Therefore, the positioning results of the two positioning methods in the first step are taken as observed values, and the results are filtered by using a Kalman filter to determine the final positioning result.

The state transition matrix of the Kalman filter is a unit matrix, and the state transition model is as follows:

$\stackrel{\→}{x}\left(k\right)=\stackrel{\→}{x}(k-1)+\stackrel{\→}{w}\left(k\right)---\left(12\right)$

whereinRepresents the coordinates of the user's position at the k-th measurement instant, andis a process noise vector.

The positioning results measured by the first positioning method and the second positioning method are combined to be used as an observed value of the Kalman filter, namely

$\stackrel{\→}{y}\left(k\right)\stackrel{\mathrm{\Δ}}{=}\[{\stackrel{\→}{y}}_1^T\left(k\right),{\stackrel{\→}{y}}_2^T\left(k\right)\]---\left(13\right)$

WhereinWhile

The relationship matrix h (k) between the observed values and the state values is defined as:

$H\left(k\right)\stackrel{\mathrm{\Δ}}{=}\[H_1^T\left(k\right),H_2^T\left(k\right)\]---\left(14\right)$

anddefined as a unit matrix. The corresponding measurement noise matrix is defined as:

$v\left(k\right)\stackrel{\mathrm{\Δ}}{=}\[v_1^T\left(k\right),v_2^T\left(k\right)\]---\left(15\right)$

wherein v is₁(k) And v₂(k) Are respectively corresponding measured valuesAndmeasurement error and noise. The observation model is

$\stackrel{\→}{y}\left(k\right)=H\left(k\right)\stackrel{\→}{x}\left(k\right)+v\left(k\right)---\left(16\right)$

And filtering by using a standard Kalman filtering algorithm to obtain the position coordinates of the final user.

The method for jointly positioning the mobile cellular network and the satellite navigation system can improve the positioning precision of the user, and is low in deployment cost and easy to install in practical application.

Detailed Description

The first positioning method comprises the following steps:

the signal forwarding processing time error is first eliminated. Is recorded at time t_kSignals measured by the receiver from satellites s_iVia base station b_jThe time elapsed for forwarding to the receiver isThen there is

${\mathrm{\Δt}}_{s_i,b_j,u}^{\left(t_k\right)}={\mathrm{\δt}}_{s_i,b_j}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_j,u}^{\left(t_k\right)}+{\mathrm{\δt}}_c+{\mathrm{\δt}}_{s_i,b_j,u}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_j}^{\left(t_k\right)}+{\mathrm{\δt}}_{m,b_j}^{\left(t_k\right)},i,j=1,2,3,4---\left(1\right)$

Wherein,is the signal from a satellite s_iTo base station b_jThe time of (d);is a signal from the base station b_jTime to receiver; t is t_cIs a receiverClock error;is the signal from a satellite s_iTo base station b_jPropagation errors experienced by the receiver;the time that the signal is transmitted from the base station antenna after the signal reaches the base station antenna and is processed by the base station;representing other measurement errors.

By operating differentially the propagation times of signals coming from the same satellite and forwarded to the receiver via the same base station, but measured at different times, it is obtained

${\mathrm{\Δt}}_{s_i,b_j,u}^{\left(t_0\right)}-{\mathrm{\Δt}}_{s_i,b_j,u}^{\left(t_1\right)}={\mathrm{\δt}}_{s_i,b_j}^{(t_0,t_1)}+{\mathrm{\δt}}_{b_j,u}^{(t_0,t_1)}+{\mathrm{\δt}}_{s_i,b_j,u}^{(t_0,t_1)}+{\mathrm{\δt}}_{b_j}^{(t_0,t_1)}+{\mathrm{\δt}}_{m,b_j}^{(t_0,t_1)},---\left(2\right)$

Wherein the receiver clock difference t_cWill be eliminated; in general, t is₀And t₁The interval therebetween is small (1 second or less), and therefore,andmay be considered to be zero. The receiver can obtain satellite coordinates after decoding the satellite data, and can obtain the coordinate information of the base station through signaling when accessing the base station, so that the receiver can obtain the satellite coordinates after decoding the satellite dataAnd the coordinate calculation of the satellite and the base station can be used for obtaining.

The receiver respectively transmits signals to different base stations at two successive time instants (t)₀And t₁) The measured propagation times being differentially operated, i.e.

$\left\{\begin{array}{c}{\mathrm{\Δt}}_{s_i,b_1,u}^{\left(t_0\right)}-{\mathrm{\Δt}}_{s_i,b_1,u}^{\left(t_1\right)}={\mathrm{\δt}}_{s_i,b_1}^{(t_0,t_1)}+{\mathrm{\δt}}_{b_1,u}^{(t_0,t_1)}+{\mathrm{\δt}}_{m,b_1}^{(t_0,t_1)}\\ {\mathrm{\Δt}}_{s_i,b_2,u}^{\left(t_0\right)}-{\mathrm{\Δt}}_{s_i,b_2,u}^{\left(t_1\right)}={\mathrm{\δt}}_{s_i,b_2}^{(t_0,t_1)}+{\mathrm{\δt}}_{b_2,u}^{(t_0,t_1)}+{\mathrm{\δt}}_{m,b_2}^{(t_0,t_1)}\\ {\mathrm{\Δt}}_{s_i,b_3,u}^{\left(t_0\right)}-{\mathrm{\Δt}}_{s_i,b_3,u}^{\left(t_1\right)}={\mathrm{\δt}}_{s_i,b_3}^{(t_0,t_1)}+{\mathrm{\δt}}_{b_3,u}^{(t_0,t_1)}+{\mathrm{\δt}}_{m,b_3}^{(t_0,t_1)}\end{array}\right.---\left(3\right)$

Let Can be expressed asWhereini is 0,1, i.e. at time t_iCoordinates of the user;is a base station b_j(j is 1,2,3) andis represented at time t_iSlave base station b_jThe distance to the user receiver. Thus, equation (3) can be further expressed as:

$\left\{\begin{array}{c}{l}_1=\left|\right|{\stackrel{\→}{x}}_{u,0}-{\stackrel{\→}{x}}_{b_1}\left|\right|-\left|\right|{\stackrel{\→}{x}}_{u,1}-{\stackrel{\→}{x}}_{b_1}\left|\right|+{\mathrm{\ρ}}_1+e_1\\ l_2=\left|\right|{\stackrel{\→}{x}}_{u,0}-{\stackrel{\→}{x}}_{b_2}\left|\right|-\left|\right|{\stackrel{\→}{x}}_{u,1}-{\stackrel{\→}{x}}_{b_2}\left|\right|+{\mathrm{\ρ}}_2+e_2\\ l_3=\left|\right|{\stackrel{\→}{x}}_{u,0}-{\stackrel{\→}{x}}_{b_3}\left|\right|-\left|\right|{\stackrel{\→}{x}}_{u,1}-{\stackrel{\→}{x}}_{b_3}\left|\right|+{\mathrm{\ρ}}_3+e_3\end{array}\right.---\left(4\right)$

equation (4) can be further organized as:

$\left\{\begin{array}{c}\left|\right|{\stackrel{\→}{x}}_{u,1}-{\stackrel{\→}{x}}_{b_1}\left|\right|=\left|\right|{\stackrel{\→}{x}}_{u,0}-{\stackrel{\→}{x}}_{b_1}\left|\right|-l_1+{\mathrm{\ρ}}_1+e_1\\ \left|\right|{\stackrel{\→}{x}}_{u,1}-{\stackrel{\→}{x}}_{b_2}\left|\right|=\left|\right|{\stackrel{\→}{x}}_{u,0}-{\stackrel{\→}{x}}_{b_2}\left|\right|-l_2+{\mathrm{\ρ}}_2+e_2\\ \left|\right|{\stackrel{\→}{x}}_{u,1}-{\stackrel{\→}{x}}_{b_3}\left|\right|=\left|\right|{\stackrel{\→}{x}}_{u,0}-{\stackrel{\→}{x}}_{b_3}\left|\right|-l_3+{\mathrm{\ρ}}_3+e_3\end{array}\right.---\left(5\right)$

thus, if the user receiver is at time t₀When the position of the receiver is known, then according to equation (5), the receiver can be calculated at time t₁The position of the time. The calculated user position is recorded as

${\stackrel{\→}{x}}_{u,1}=f({\stackrel{\→}{x}}_{u,0},{\stackrel{\→}{x}}_{b_i},{\mathrm{\ρ}}_i,l_i),i=1,2,3---\left(6\right)$

With positioning method one, the receiver can calculate its position at the next time from the position at the previous time. When a user enters a satellite signal blind area from a satellite signal effective area, the user's first position in the blind area can be calculated from the precise position obtained at the previous moment. When the user moves in the blind area, the position of the next moment can be continuously calculated according to the position of the previous moment. However, the problem is that if the position calculation at the previous time has an error, the error will be caused to the current position calculation, and then the accumulated error will become larger. Therefore, to reduce the accumulated error, two errors will be corrected by the method.

The second positioning method comprises the following steps:

when the subscriber receiver receives the retransmitted signal from the base station, it can use the signal to measure the time taken for the signal to be retransmitted from the satellite to the subscriber via the base stationAt time t_kMeasured timeWill be shown in equation (1). The signals from the same satellite are retransmitted through different base stations and the time required for them to reach the user receiver will be different. Assuming the same satellite(s)₁) The signal is passed through fourBase station b_j(j-1, 2,3,4) forwarding, then there are

$\left\{\begin{array}{c}{\mathrm{\Δt}}_{s_1,b_1,u}^{\left(t_k\right)}={\mathrm{\δt}}_{s_1,b_1}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_1,u}^{\left(t_k\right)}+{\mathrm{\δt}}_c+{\mathrm{\δt}}_{s_1,b_1,u}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_1}^{\left(t_k\right)}+{\mathrm{\δt}}_{m,b_1}^{\left(t_k\right)}\\ {\mathrm{\Δt}}_{s_1,b_2,u}^{\left(t_k\right)}={\mathrm{\δt}}_{s_1,b_2}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_2,u}^{\left(t_k\right)}+{\mathrm{\δt}}_c+{\mathrm{\δt}}_{s_1,b_2,u}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_2}^{\left(t_k\right)}+{\mathrm{\δt}}_{m,b_2}^{\left(t_k\right)}\\ {\mathrm{\Δt}}_{s_1,b_3,u}^{\left(t_k\right)}={\mathrm{\δt}}_{s_1,b_3}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_3,u}^{\left(t_k\right)}+{\mathrm{\δt}}_c+{\mathrm{\δt}}_{s_1,b_3,u}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_3}^{\left(t_k\right)}+{\mathrm{\δt}}_{m,b_3}^{\left(t_k\right)}\\ {\mathrm{\Δt}}_{s_1,b_4,u}^{\left(t_k\right)}={\mathrm{\δt}}_{s_1,b_4}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_4,u}^{\left(t_k\right)}+{\mathrm{\δt}}_c+{\mathrm{\δt}}_{s_1,b_4,u}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_4}^{\left(t_k\right)}+{\mathrm{\δt}}_{m,b_4}^{\left(t_k\right)}\end{array}\right.---\left(7\right)$

Let To measure, andis the signal from a satellite s₁To base station b_jThe time required for propagation can be determined by satellite s₁And base station b_jThe coordinates of (2) are calculated. In this way it is possible to obtain,can be expressed as follows:

$\left\{\begin{array}{c}{\mathrm{\ΔT}}_{b_1,u}^{\left(t_k\right)}={\mathrm{\δt}}_{b_1,u}^{\left(t_k\right)}+{\mathrm{\δt}}_c+{\mathrm{\δt}}_{s_1,b_1,u}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_1}^{\left(t_k\right)}+{\mathrm{\δt}}_{m,b_1}^{\left(t_k\right)}\\ {\mathrm{\ΔT}}_{b_2,u}^{\left(t_k\right)}={\mathrm{\δt}}_{b_2,u}^{\left(t_k\right)}+{\mathrm{\δt}}_c+{\mathrm{\δt}}_{s_1,b_2,u}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_2}^{\left(t_k\right)}+{\mathrm{\δt}}_{m,b_2}^{\left(t_k\right)}\\ {\mathrm{\ΔT}}_{b_3,u}^{\left(t_k\right)}={\mathrm{\δt}}_{b_3,u}^{\left(t_k\right)}+{\mathrm{\δt}}_c+{\mathrm{\δt}}_{s_1,b_3,u}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_3}^{\left(t_k\right)}+{\mathrm{\δt}}_{m,b_3}^{\left(t_k\right)}\\ {\mathrm{\ΔT}}_{b_4,u}^{\left(t_k\right)}={\mathrm{\δt}}_{b_4,u}^{\left(t_k\right)}+{\mathrm{\δt}}_c+{\mathrm{\δt}}_{s_1,b_4,u}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_4}^{\left(t_k\right)}+{\mathrm{\δt}}_{m,b_4}^{\left(t_k\right)}\end{array}\right.---\left(8\right)$

because of the base station b_j(j ═ 1,2,3,4) are typically close together (the receiver can receive the retransmitted signals from these four base stations simultaneously), so the receiver can receive the retransmitted signals from these four base stations at the same timeMay be considered equal. In addition, the satellite signal retransmission processing time of each base stationEquality is also assumed in the present method. Thus, ignoring the difference in measurement error, according to equation (8), one can further obtain:

$\left\{\begin{array}{c}{\mathrm{\ΔT}}_{b_1,u}^{\left(t_k\right)}-{\mathrm{\ΔT}}_{b_2,u}^{\left(t_k\right)}={\mathrm{\δt}}_{b_1,u}^{\left(t_k\right)}-{\mathrm{\δt}}_{b_2,u}^{\left(t_k\right)}\\ {\mathrm{\ΔT}}_{b_1,u}^{\left(t_k\right)}-{\mathrm{\ΔT}}_{b_3,u}^{\left(t_k\right)}={\mathrm{\δt}}_{b_1,u}^{\left(t_k\right)}-{\mathrm{\δt}}_{b_3,u}^{\left(t_k\right)}\\ {\mathrm{\ΔT}}_{b_1,u}^{\left(t_k\right)}-{\mathrm{\ΔT}}_{b_4,u}^{\left(t_k\right)}={\mathrm{\δt}}_{b_1,u}^{\left(t_k\right)}-{\mathrm{\δt}}_{b_4,u}^{\left(t_k\right)}\end{array}\right.---\left(9\right)$

letWhereinAt a time t_kCoordinates of the user receiver;is a base station b_jThe coordinates of (a). Thus, equation (9) can be written as:

according to the formula (10), the user position coordinates can be obtained by calculationThe calculated user position is recorded as

${\stackrel{\→}{x}}_{u,k}=g({\stackrel{\→}{x}}_{b_i},{\mathrm{\ξ}}_i),i=1,2,3---\left(11\right)$

For the two positioning methods, as for the first method, the main positioning error is that the positioning error at each moment is accumulated in the positioning result at each subsequent moment; for the second method, the main positioning errors come from different signal processing times of each base station. The main errors of the respective positioning results of the two methods are caused by different factors, and if the two positioning results are combined to determine the coordinates of the receiver, the influence of the respective factors on the positioning errors can be weakened, and the positioning accuracy can be improved. Therefore, the positioning results of the two methods can be used as observation values to filter the results by using a Kalman filter to determine the final positioning result.

Claims (1)

1. A method for positioning a satellite signal blind area by combining a mobile cellular network and a satellite navigation system comprises the following steps:

the method comprises the following steps: positioning by two positioning methods

The first positioning method comprises the following steps:

firstly, eliminating the error of signal forwarding processing time; is recorded at time t_kSignals measured by the receiver from satellites s_iVia base station b_jThe time elapsed for forwarding to the receiver isThen

${\mathrm{\Δt}}_{s_i,b_j,u}^{\left(t_k\right)}={\mathrm{\δt}}_{s_i,b_j}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_j,u}^{\left(t_k\right)}+{\mathrm{\δt}}_c+{\mathrm{\δt}}_{s_i,b_j,u}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_j}^{\left(t_k\right)}+{\mathrm{\δt}}_{m,b_j}^{\left(t_k\right)},i,j=1,2,3,4---\left(1\right)$

Wherein,is the signal from a satellite s_iTo base station b_jThe time of (d);is a signal from the base station b_jTime to receiver; t is t_cIs the receiver clock error;is the signal from a satellite s_iTo base station b_jPropagation errors experienced by the receiver;the time that the signal is transmitted from the base station antenna after the signal reaches the base station antenna and is processed by the base station;represents other measurement errors;

the differential operation of the propagation times of the signals coming from the same satellite and forwarded to the receiver via the same base station, but measured at different times, results in:

${\mathrm{\Δt}}_{s_i,b_j,u}^{\left(t_0\right)}-{\mathrm{\Δt}}_{s_i,b_j,u}^{\left(t_1\right)}={\mathrm{\δt}}_{s_i,b_j}^{(t_0,t_1)}+{\mathrm{\δt}}_{b_j,u}^{(t_0,t_1)}+{\mathrm{\δt}}_{s_i,b_j,u}^{(t_0,t_1)}+{\mathrm{\δt}}_{b_j}^{(t_0,t_1)}+{\mathrm{\δt}}_{m,b_j}^{(t_0,t_1)},---\left(2\right)$

wherein the receiver clock difference t_cWill be eliminated;

t₀and t₁The interval between the two is less than or equal to 1 second,andconsidered to be zero; the receiver decodes the satellite data to obtain satellite coordinates; the receiver obtains the coordinate information of the base station through signaling when accessing the base station,calculating and obtaining coordinates of a satellite and a base station;

the receiver respectively transmits signals to different base stations at two successive time instants (t)₀And t₁) The measured propagation times being differentially operated, i.e.

$\left\{\begin{array}{c}{\mathrm{\Δt}}_{s_i,b_1,u}^{\left(t_0\right)}-{\mathrm{\Δt}}_{s_i,b_1,u}^{\left(t_1\right)}={\mathrm{\δt}}_{s_i,b_1}^{(t_0,t_1)}+{\mathrm{\δt}}_{b_1,u}^{(t_0,t_1)}+{\mathrm{\δt}}_{m,b_1}^{(t_0,t_1)}\\ {\mathrm{\Δt}}_{s_i,b_2,u}^{\left(t_0\right)}-{\mathrm{\Δt}}_{s_i,b_2,u}^{\left(t_1\right)}={\mathrm{\δt}}_{s_i,b_2}^{(t_0,t_1)}+{\mathrm{\δt}}_{b_2,u}^{(t_0,t_1)}+{\mathrm{\δt}}_{m,b_2}^{(t_0,t_1)}\\ {\mathrm{\Δt}}_{s_i,b_3,u}^{\left(t_0\right)}-{\mathrm{\Δt}}_{s_i,b_3,u}^{\left(t_1\right)}={\mathrm{\δt}}_{s_i,b_3}^{(t_0,t_1)}+{\mathrm{\δt}}_{b_3,u}^{(t_0,t_1)}+{\mathrm{\δt}}_{m,b_3}^{(t_0,t_1)}\end{array}\right.---\left(3\right)$

Let Is shown asWhereinI.e. at time t_iCoordinates of the user;is a base station b_j(j is 1,2,3) andis represented at time t_iSlave base station b_jDistance to the user receiver; equation (3) is further expressed as:

$\left\{\begin{array}{c}{l}_1=\left|\right|{\stackrel{\→}{x}}_{u,0}-{\stackrel{\→}{x}}_{b_1}\left|\right|-\left|\right|{\stackrel{\→}{x}}_{u,1}-{\stackrel{\→}{x}}_{b_1}\left|\right|+{\mathrm{\ρ}}_1+e_1\\ l_2=\left|\right|{\stackrel{\→}{x}}_{u,0}-{\stackrel{\→}{x}}_{b_2}\left|\right|-\left|\right|{\stackrel{\→}{x}}_{u,1}-{\stackrel{\→}{x}}_{b_2}\left|\right|+{\mathrm{\ρ}}_2+e_2\\ l_3=\left|\right|{\stackrel{\→}{x}}_{u,0}-{\stackrel{\→}{x}}_{b_3}\left|\right|-\left|\right|{\stackrel{\→}{x}}_{u,1}-{\stackrel{\→}{x}}_{b_3}\left|\right|+{\mathrm{\ρ}}_3+e_3\end{array}\right.---\left(4\right)$

equation (4) is further organized as:

$\left\{\begin{array}{c}\left|\right|{\stackrel{\→}{x}}_{u,1}-{\stackrel{\→}{x}}_{b_1}\left|\right|=\left|\right|{\stackrel{\→}{x}}_{u,0}-{\stackrel{\→}{x}}_{b_1}\left|\right|-l_1+{\mathrm{\ρ}}_1+e_1\\ \left|\right|{\stackrel{\→}{x}}_{u,1}-{\stackrel{\→}{x}}_{b_2}\left|\right|=\left|\right|{\stackrel{\→}{x}}_{u,0}-{\stackrel{\→}{x}}_{b_2}\left|\right|-l_2+{\mathrm{\ρ}}_2+e_2\\ \left|\right|{\stackrel{\→}{x}}_{u,1}-{\stackrel{\→}{x}}_{b_3}\left|\right|=\left|\right|{\stackrel{\→}{x}}_{u,0}-{\stackrel{\→}{x}}_{b_3}\left|\right|-l_3+{\mathrm{\ρ}}_3+e_3\end{array}\right.---\left(5\right)$

if the subscriber receiver is at time t₀When the position of the receiver is known, the receiver is calculated according to the formula (5) at the time t₁The position of the time; the calculated user position is

${\stackrel{\→}{x}}_{u,1}=f({\stackrel{\→}{x}}_{u,0},{\stackrel{\→}{x}}_{b_i},{\mathrm{\ρ}}_i,l_i),i=1,2,3---\left(6\right)$

The second positioning method comprises the following steps:

when the subscriber receiver receives the retransmitted signal from the base station, it uses the signal to measure the time it takes for the signal to be retransmitted from the satellite to the subscriber via the base stationAt time t_kMeasured timeWill be as shown in equation (1); the signals from the same satellite are forwarded through different base stations, and the time required for them to reach the user receiver will be different; assuming the same satellite(s)₁) Signals are transmitted through four base stations b_j(j-1, 2,3,4) forwarding, then there are

$\left\{\begin{array}{c}{\mathrm{\Δt}}_{s_1,b_1,u}^{\left(t_k\right)}={\mathrm{\δt}}_{s_1,b_1}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_1,u}^{\left(t_k\right)}+{\mathrm{\δt}}_c+{\mathrm{\δt}}_{s_1,b_1,u}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_1}^{\left(t_k\right)}+{\mathrm{\δt}}_{m,b_1}^{\left(t_k\right)}\\ {\mathrm{\Δt}}_{s_1,b_2,u}^{\left(t_k\right)}={\mathrm{\δt}}_{s_1,b_2}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_2,u}^{\left(t_k\right)}+{\mathrm{\δt}}_c+{\mathrm{\δt}}_{s_1,b_2,u}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_2}^{\left(t_k\right)}+{\mathrm{\δt}}_{m,b_2}^{\left(t_k\right)}\\ {\mathrm{\Δt}}_{s_1,b_3,u}^{\left(t_k\right)}={\mathrm{\δt}}_{s_1,b_3}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_3,u}^{\left(t_k\right)}+{\mathrm{\δt}}_c+{\mathrm{\δt}}_{s_1,b_3,u}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_3}^{\left(t_k\right)}+{\mathrm{\δt}}_{m,b_3}^{\left(t_k\right)}\\ {\mathrm{\Δt}}_{s_1,b_4,u}^{\left(t_k\right)}={\mathrm{\δt}}_{s_1,b_4}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_4,u}^{\left(t_k\right)}+{\mathrm{\δt}}_c+{\mathrm{\δt}}_{s_1,b_4,u}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_4}^{\left(t_k\right)}+{\mathrm{\δt}}_{m,b_4}^{\left(t_k\right)}\end{array}\right.---\left(7\right)$

Let To measure, andis the signal from a satellite s₁To base station b_jTime required for propagation through satellite s₁And base station b_jIn a coordinate systemCalculating out;is represented as follows:

$\left\{\begin{array}{c}{\mathrm{\ΔT}}_{b_1,u}^{\left(t_k\right)}={\mathrm{\δt}}_{b_1,u}^{\left(t_k\right)}+{\mathrm{\δt}}_c+{\mathrm{\δt}}_{s_1,b_1,u}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_1}^{\left(t_k\right)}+{\mathrm{\δt}}_{m,b_1}^{\left(t_k\right)}\\ {\mathrm{\ΔT}}_{b_2,u}^{\left(t_k\right)}={\mathrm{\δt}}_{b_2,u}^{\left(t_k\right)}+{\mathrm{\δt}}_c+{\mathrm{\δt}}_{s_1,b_2,u}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_2}^{\left(t_k\right)}+{\mathrm{\δt}}_{m,b_2}^{\left(t_k\right)}\\ {\mathrm{\ΔT}}_{b_3,u}^{\left(t_k\right)}={\mathrm{\δt}}_{b_3,u}^{\left(t_k\right)}+{\mathrm{\δt}}_c+{\mathrm{\δt}}_{s_1,b_3,u}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_3}^{\left(t_k\right)}+{\mathrm{\δt}}_{m,b_3}^{\left(t_k\right)}\\ {\mathrm{\Δ}}_{b_4,u}^{\left(t_k\right)}={\mathrm{\δt}}_{b_4,u}^{\left(t_k\right)}+{\mathrm{\δt}}_c+{\mathrm{\δt}}_{s_1,b_4,u}^{\left(t_k\right)}+{\mathrm{\δt}}_{b_4}^{\left(t_k\right)}+{\mathrm{\δt}}_{m,b_4}^{\left(t_k\right)}\end{array}\right.---\left(8\right)$

base station b_j(j ═ 1,2,3,4) close to each other, and the receiver receives the retransmitted signals from the four base stations at the same time;considered equal; satellite signal retransmission processing time of each base stationEquality is assumed; according to equation (8), further obtained is:

$\left\{\begin{array}{c}{\mathrm{\ΔT}}_{b_1,u}^{\left(t_k\right)}-{\mathrm{\ΔT}}_{b_2,u}^{\left(t_k\right)}={\mathrm{\δt}}_{b_1,u}^{\left(t_k\right)}-{\mathrm{\δt}}_{b_2,u}^{\left(t_k\right)}\\ {\mathrm{\ΔT}}_{b_1,u}^{\left(t_k\right)}-{\mathrm{\ΔT}}_{b_3,u}^{\left(t_k\right)}={\mathrm{\δt}}_{b_1,u}^{\left(t_k\right)}-{\mathrm{\δt}}_{b_3,u}^{\left(t_k\right)}\\ {\mathrm{\ΔT}}_{b_1,u}^{\left(t_k\right)}-{\mathrm{\ΔT}}_{b_4,u}^{\left(t_k\right)}={\mathrm{\δt}}_{b_1,u}^{\left(t_k\right)}-{\mathrm{\δt}}_{b_4,u}^{\left(t_k\right)}\end{array}\right.---\left(9\right)$

letWhereinAt a time t_kCoordinates of the user receiver;is a base station b_jThe coordinates of (a); equation (9) is written as:

according to the formula (10), calculating and obtaining the position coordinates of the userThe calculated user position is recorded as

${\stackrel{\→}{x}}_{u,k}=g({\stackrel{\→}{x}}_{b_i},{\mathrm{\ξ}}_i),i=1,2,3---\left(11\right)$

The second step is that: fusing two positioning results by using Kalman filter

The state transition matrix of the Kalman filter is a unit matrix, and the state transition model is as follows:

$\stackrel{\→}{x}\left(k\right)=\stackrel{\→}{x}(k-1)+\stackrel{\→}{w}\left(k\right)---\left(12\right)$

whereinRepresents the coordinates of the user's position at the k-th measurement instant, andis a process noise vector;

the positioning results measured by the first positioning method and the second positioning method are combined to be used as an observed value of the Kalman filter, namely

$\stackrel{\→}{y}\left(k\right)\stackrel{\mathrm{\Δ}}{=}\[{\stackrel{\→}{y}}_1^T\left(k\right),{\stackrel{\→}{y}}_2^T\left(k\right)\]---\left(13\right)$

WhereinWhile

The relationship matrix h (k) between the observed values and the state values is defined as:

$H\left(k\right)\stackrel{\mathrm{\Δ}}{=}\[H_1^T\left(k\right),H_2^T\left(k\right)\]---\left(14\right)$

anddefining the array as a unit array; the corresponding measurement noise matrix is defined as:

$v\left(k\right)\stackrel{\mathrm{\Δ}}{=}\[v_1^T\left(k\right),v_2^T\left(k\right)\]---\left(15\right)$

wherein v is₁(k) And v₂(k) Are respectively corresponding measured valuesAndmeasurement error and noise. The observation model is

$\stackrel{\→}{y}\left(k\right)=H\left(k\right)\stackrel{\→}{x}\left(k\right)+v\left(k\right)---\left(16\right)$

And filtering by using a standard Kalman filtering algorithm to obtain the position coordinates of the end user.