CN111220946A - Multi-moving-target positioning error elimination method based on improved extended Kalman filtering - Google Patents

Multi-moving-target positioning error elimination method based on improved extended Kalman filtering Download PDF

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CN111220946A
CN111220946A CN202010064784.XA CN202010064784A CN111220946A CN 111220946 A CN111220946 A CN 111220946A CN 202010064784 A CN202010064784 A CN 202010064784A CN 111220946 A CN111220946 A CN 111220946A
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time
signal
error
anchor node
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汪洋
易黎
郭士串
刘力
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Nanjing Fiberhome Telecommunication Technologies Co ltd
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Nanjing Fiberhome Telecommunication Technologies Co ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
    • G01S5/0294—Trajectory determination or predictive filtering, e.g. target tracking or Kalman filtering
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/02—Services making use of location information
    • H04W4/023—Services making use of location information using mutual or relative location information between multiple location based services [LBS] targets or of distance thresholds
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/02—Services making use of location information
    • H04W4/029—Location-based management or tracking services
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W64/00—Locating users or terminals or network equipment for network management purposes, e.g. mobility management

Abstract

The invention discloses a method for eliminating positioning errors of multiple moving targets based on improved extended Kalman filtering, which realizes the positioning of multiple targets in a mode of combining time division multiplexing and wavelength division multiplexing, and converts received signals into pulses with concentrated energy in a Fourier domain through fractional Fourier transform; screening data by using a threshold value set by RSSI; using two-way ranging to reduce offset generated by a system clock by adopting relative time; judging whether an NLOS error exists in the ranging process by using a Wylie algorithm; reducing system processing time errors by using the time difference TDOA when a signal reaches two anchor nodes; and (3) solving the position of the moving target at a certain moment by using a CHAN algorithm as an observed value, constructing a state equation, and estimating the motion track of the moving target by using an estimated NLOS error improved extended Kalman positioning algorithm. The invention realizes the positioning of more moving targets with lower cost and realizes the balance of positioning precision requirement and power consumption; the error in the distance measurement is comprehensively considered and eliminated.

Description

Multi-moving-target positioning error elimination method based on improved extended Kalman filtering
Technical Field
The invention discloses a method for eliminating positioning errors of multiple moving targets based on improved extended Kalman filtering, and relates to the technical field of wireless ranging and positioning of the moving targets.
Background
The rapid development of the internet of things puts higher requirements on wireless communication technology, and the LPWAN which is specially designed for the application of the internet of things with low bandwidth, low power consumption, long distance and large connection is also rapidly started. LoRa (Long Range) is an ultra-Long distance wireless transmission scheme based on spread spectrum technology adopted and popularized by Semtech corporation in the united states. Because loRa works in the unlicensed frequency band, the network construction can be carried out without application, the network architecture is simple, and the operation cost is low, so that the wireless communication technology widely adopted in the field of Internet of things is formed.
Location-Based Services (LBS) positioning technology is a key basic technology for internet of things application. The location method of the distance measurement is to calculate the position of the node by measuring the angle or distance between the nodes and the like and by trilateration or maximum likelihood estimation. In urban roads or complex indoor environments, due to the influence of various obstacles, interference of factors such as multipath effect and NLOS error received in signal transmission reduces positioning accuracy. Methods of eliminating NLOS errors can be classified into indirect methods and direct methods. The indirect method combines NLOS error elimination and positioning together and simultaneously carries out positioning, needs more base stations to participate in positioning, abandons ranging data containing NLOS errors according to a certain judgment principle, or carries out weighted average on all results according to accuracy. The direct method firstly preprocesses the ranging data, judges and eliminates various error sources possibly existing, and then uses clean data as target positioning.
In the prior art, the positioning difficulty of a plurality of moving targets is high, the cost is high, the balance between the positioning precision requirement and the power consumption is difficult to realize, and the distance measurement error is also large.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: aiming at the defects of the prior art, the method for eliminating the positioning error of the multiple moving targets based on the improved extended Kalman filtering is provided, so that the multiple moving targets can be positioned at low cost, and various error sources in positioning can be eliminated systematically. In the invention, the moving target carries a low-power consumption LoRa signal transmitter similar to a worker plate, the transmission time of the signal is obtained by communicating with a plurality of fixed anchor nodes with known position information nearby, the related information is transmitted to a server in real time through an LPWAN gateway for corresponding processing, and the track information of the moving target is correspondingly set and displayed in real time at a client according to the requirement.
The invention adopts the following technical scheme for solving the technical problems:
the method for eliminating the positioning error of the multiple moving targets based on the improved extended Kalman filtering realizes the positioning of the multiple targets in a mode of combining time division multiplexing and wavelength division multiplexing, and specifically comprises the following steps:
converting a received signal into pulses with concentrated energy in a Fourier domain through fractional Fourier transform, and distinguishing direct signals in multipath effects;
setting a certain threshold value for RSSI, and if the intensity of a signal received by an anchor node is lower than the threshold value, discarding ranging data of the anchor node at the current moment;
using two-way ranging to reduce offset generated by a system clock by adopting relative time;
aiming at repeated ranging data obtained by multiple times of communication in a very short time, judging whether an NLOS error exists in the ranging process by using a Wylie algorithm, if so, estimating the size of the NLOS error by using a least square method, and if not, directly using the data for subsequent calculation;
reducing system processing time errors by using the time difference TDOA when a signal reaches two anchor nodes;
aiming at the information of a plurality of distance measurements, the CHAN algorithm is used for further reducing the positioning error and solving the position of a moving target at a certain moment;
and taking the result of the CHAN algorithm as an observed value, constructing a state equation, and estimating the motion track of the moving target by using the estimated NLOS error improved extended Kalman positioning algorithm.
As a further preferable aspect of the present invention, the fractional fourier transform specifically includes:
1-1) the fractional Fourier transform of the function f (t) is defined as:
Figure BDA0002375632870000021
in formula (1), the integral kernel K (α; u, t) is defined as follows:
Figure BDA0002375632870000022
in the formula (2), u is a fractional Fourier domain, t is signal detection time, i is a parameter from a frequency domain to a time domain,
Figure BDA0002375632870000023
the rotation angle is fractional order p Fourier transform;
1-2) the expression of the Chirp signal is as follows:
Figure BDA0002375632870000024
in the formula (3), the reaction mixture is,
Figure BDA0002375632870000025
is an initial phase, f0As a center frequency, take
Figure BDA0002375632870000026
f00; k is frequency modulation, determines the speed of signal frequency change, and has a bandwidth B ═ kT, where T is the time domain width of Chirp signal, and a relative width ζ ═ B/f0；
1-3) the fractional Fourier transform of the p order of the Chirp signal is represented as:
Figure BDA0002375632870000027
further carrying out simplification and variable substitution to obtain a fractional Fourier transform of the Chrip signal:
Figure BDA0002375632870000031
the formula (5) is that the Chirp signal is converted into
Figure BDA0002375632870000032
Has the best energy gathering property on the fractional order Fourier transform domain;
1-4) for Gaussian noise, the time shift of the signal in the time domain is τ0In the FRFT domain, as a frequency shift τ0cos α, separating the gaussian noise and the echo signal by a fractional fourier transform, when the following relationship exists:
Figure BDA0002375632870000033
as a further preferable aspect of the present invention, the specific method for reducing the offset generated by the system clock by using the relative time using the two-way ranging includes:
the mobile target A as the initiator of the distance measurement initiates a ranging request, the anchor node B as the responder listens and responds to the radio information sent by the A, and the bidirectional ranging is described as follows:
a sends a radio message to B and records its transmission time stamp t1B receives the information and delays it by a specific time treplyBThen sending a reply to A, and finally A receives the reply and records a receiving time stamp t2；
Device a knows its own transmission time stamp t using its own local clock1And receiving a time stamp t2Thus, the calculated round trip time is calculated:
troundA＝t2-t1；
device B knows its own delay treplyBThen the arrival time of the signal can be determined by the following equation:
TOA＝(t2-t1-treplyB)/2。
as a further preferred scheme of the present invention, the Wylie algorithm is used to determine whether an NLOS error exists in the ranging process, and the least square method is used to estimate the size of the NLOS error, and the specific method is as follows:
2-1) in hypothesis testing, smoothing distance measurement values of each anchor node at different moments to obtain a measurement distance standard deviation, and if the measurement distance standard deviation is far larger than the standard deviation in an LOS environment, judging that a non-line-of-sight error exists;
the TOA measurement for the ith anchor node is:
Figure BDA0002375632870000041
wherein the content of the first and second substances,
Figure BDA0002375632870000042
is a TOA measurement in LOS environment, niCompliance for systematic measurement errors
Figure BDA0002375632870000043
biFor the additional delay error caused by NLOS, it is a large positive mean random variable with mean value of μeiVariance is
Figure BDA0002375632870000044
Smoothing with a polynomial of order N:
Figure BDA0002375632870000045
fitting to obtain unknown coefficients
Figure BDA0002375632870000046
And then estimating the measured value:
Figure BDA0002375632870000047
estimate of standard deviation for multiple replicates:
Figure BDA0002375632870000048
if it is
Figure BDA0002375632870000049
K is the number of repeated measurement, the signal received by the anchor node is NLOS signal, sigmaiIs the standard deviation of the ith anchor node,
Figure BDA00023756328700000410
for the unknown coefficients of the fit to be,
Figure BDA00023756328700000411
refers to the ith anchor node signal reception time;
2-2) in a non-line-of-sight environment, rewriting equation (6) into a vector form:
r＝F(X)+n+b(10)
wherein r is the TOA measurement and F (X) is the true TOA as a function of the anchor node coordinates
Figure BDA00023756328700000412
Vector form of (1);
wherein x and y are coordinates of the node to be measured, and xi、yiCoordinates of the ith anchor node, n and b are formula (6)
A corresponding vector form;
assuming b is known, the estimated value of the moving target position in the least square sense is:
Figure BDA00023756328700000413
wherein J (X) ═ r-F (X) -b)TR-1(r-F(X)-b)；
Locating the function F (X) at a reference point X0And (3) performing linearization, and neglecting high-order terms, obtaining:
F(X)≈F(X0)+F0(X-X0) (12)
wherein the initial position X of the mobile station0Can be obtained by the formula (21), F0Is F (X) at X0A jacobian matrix of (d);
let y be r- (F (X)0)-F0X0)＝F0X+b+n
Then J (X) ═ y-F0X-b)TR-1(y-F0X-b)
Taking J (X) as the minimum value, and obtaining the value by using the least square principle
Figure BDA0002375632870000051
Figure BDA0002375632870000052
Wherein the content of the first and second substances,
Figure BDA0002375632870000053
indicates the position estimate without NLOS error, and
Figure BDA0002375632870000054
when b is unknown, to estimate b, let
Figure BDA0002375632870000055
Wherein the content of the first and second substances,
Figure BDA0002375632870000056
its covariance matrix Qv＝E[vvT]In the least squares sense:
Figure BDA0002375632870000057
wherein the content of the first and second substances,
Figure BDA0002375632870000058
and
Figure BDA00023756328700000510
for the lower and upper bounds of the NLOS error in one measurement, 0 and the set { r }i+rj-RijJ ≠ i } minimum;
equation (14) is a weighted least squares problem with constraints and is solved by the lagrange optimization method.
As a further preferable embodiment of the present invention, the method further includes tracking the moving target trajectory using a TDOA-EKF algorithm, specifically including:
Ri，0for the distance difference between the i anchor nodes and the 0 th anchor node to the moving target:
Figure BDA0002375632870000059
in the formula (15), x and y are horizontal and vertical coordinates of the moving object, xi、yiAs anchor node abscissa and ordinate, TOAiThe time when the signal reaches the ith anchor node from the moving target, c is the speed of light, x0.y0Coordinates of the 0 th anchor node;
equation (15) is transformed to yield:
Figure BDA0002375632870000061
in formula (16), Xi，0Is the distance on the abscissa between the ith anchor node and the 0 th anchor node, Yi，0Is the distance on the ordinate between the ith anchor node and the 0 th anchor node,
Figure BDA0002375632870000062
irrespective of x, y, R0The relation between the three is set to be linearly independent, and a linear equation set is established:
Figure BDA0002375632870000063
considering the presence of TDOA observed noise, the error vector is:
Figure BDA0002375632870000064
in the formula (18), the reaction mixture,
Figure BDA0002375632870000065
then a weighted least squares method (WLS) is applied to obtain:
Figure BDA0002375632870000066
wherein Q is a distance measurement error covariance matrix of different anchor systems ;
further using a weighted least squares method (WLS) can be obtained:
z’＝(G’TΨ’-1G’)-1GTΨ’-1h (20)
wherein, z ═ x [ [ (x-x)0)2，(y-y0)2]T；
The final estimation result of the obtained positioning is:
Figure BDA0002375632870000067
assuming that the mobile station moves on a two-dimensional plane, the vector for the motion state at the time k
Figure BDA0002375632870000068
Wherein, [ x ]k，yk]Coordinates of the moving object on the horizontal and vertical axes are shown,
Figure BDA0002375632870000069
the velocity of the moving object on the horizontal and vertical axes is shown. The equation of state taking into account random acceleration can be expressed as:
S(k)＝ΦS(k-1)+FW(k) (22)
wherein the content of the first and second substances,
Figure BDA0002375632870000071
at is the interval between the samples to be taken,
Figure BDA0002375632870000072
for random acceleration, since W (k) can be regarded as white noise, its covariance matrix is defined as
Figure BDA0002375632870000073
The EKF measurement equation is:
z(k)＝H(k)S(k)+n(k)+b(k) (23)
wherein the content of the first and second substances,
Figure BDA0002375632870000074
iterative process of EKF:
S(k|k-1)＝ΦS(k-1|k-1)
P(k|k-1)＝ΦP(k-1|k-1)ΦT+ΓQIT
K(k)＝P(k|k-1)HT(k-1)[H(k-1)P(k|k-1)HT(k-1)+R(k)]-1(24)
P(k|k)＝[I-K(k)H(k-1)]P(k|k-1)
S(k|k)＝S(k|k-1)+K(k)[z(k)-H(k-1)S(k|k-1)]
in the equation (24), the equation is a state prediction equation, an error covariance prediction equation, a kalman gain, a state update equation, and an error covariance update equation.
As a further preferable aspect of the present invention, the method further comprises:
the receiving beacon is loaded with 3 LoRa chips with different frequency bands, the beacon carried by the moving target selects a proper transmitting frequency band to transmit a LoRa signal in a frequency modulation mode according to the load of the nearby receiving beacon, and frequency division multiplexing is realized;
according to the requirement for tracking the real-time performance of the moving target, the signal transmitting frequency is adjusted, and the receiver receives signals of different targets in the signal transmitting interval, so that time division multiplexing is realized and the throughput capacity of the node is improved.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
1. the positioning of more moving targets is realized with lower cost, and the balance between the positioning precision requirement and the power consumption is realized; the error in the distance measurement is comprehensively considered and eliminated.
2. And identifying whether the NLOS error exists in the ranging, and estimating the NLOS error according to different environments.
3. And (3) improving an extended Kalman algorithm based on NLOS errors to realize the track tracking of the moving target.
Drawings
FIG. 1 is a diagram of a fractional Fourier transform rake signal in accordance with the present invention;
FIG. 2 is a schematic diagram of two-way ranging in the present invention;
FIG. 3 is a schematic diagram of TDOA in accordance with the present invention;
FIG. 4 is a flow chart of TDOA-EKF algorithm location in the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
The technical scheme of the invention is further explained in detail by combining the attached drawings:
the invention realizes the multi-target positioning by combining time division multiplexing and wavelength division multiplexing, converts the received signals into pulses with very concentrated energy in a Fourier domain by fractional Fourier transform, and distinguishes direct signals in multipath effect so as to improve the distance resolution precision and the capacity of resisting interference and multipath effect on the target.
If the strength of the signal received by the anchor node is low, the influence of environmental interference can be greatly improved, the introduced ranging error is too large, and the positioning accuracy can be greatly reduced, so that a certain threshold value is set for the RSSI, and if the RSSI is lower than the threshold value, the ranging data of the anchor node at the current moment is abandoned. Due to the influence of factors such as temperature, crystal aging and the like, a system clock can generate offset, and the problem can be effectively solved by utilizing two-way ranging and adopting relative time.
And (3) obtaining repeated ranging data through multiple communications within a very short time, judging whether an NLOS error exists in the ranging process by using a Wylie algorithm, if so, estimating the size of the NLOS error by using a least square method, and if not, directly using the data for subsequent calculation. Because the system processes signals with a certain time delay, absolute time is difficult to measure, the time difference TDOA when the signals reach two anchor nodes is utilized to reduce the error of the system processing time, and theoretically, the intersection point of a plurality of hyperbolas is the position of a moving target. However, due to the existence of various errors, the plurality of hyperbolas do not intersect at one point, and the CHAN algorithm can fully utilize the information of a plurality of distance measurements, further reduce the positioning error, and obtain the moving target position at a certain moment. And finally, taking the result of the CHAN algorithm as an observed value, constructing a state equation, and estimating the motion track of the moving target by utilizing the estimated NLOS error improved extended Kalman positioning algorithm.
Implementation of one-target positioning and ranging precision improvement
1.1 in order to reduce hardware cost, the technology of combining wavelength division multiplexing and time division multiplexing is adopted, the positioning of a plurality of moving targets can be realized, when the real-time requirement is high, the signal transmitting frequency can be improved, and when the real-time requirement is not high, the signal transmitting frequency can be reduced, so that the power consumption of equipment is reduced, and meanwhile, personalized setting can be provided for a heavy target. The signal receiving equipment is provided with 3 LoRa chips with different frequency bands to realize wavelength division multiplexing and improve the throughput capacity of the equipment, and the transmitting device carried by the moving target realizes matching communication with the receiving devices with different frequency bands through frequency hopping. Anchor nodes are widely arranged on two sides of an urban road and used for receiving signals sent by a moving target, the anchor nodes are arranged on telegraph poles with the length of more than 3m, the positions of the anchor nodes are fixed and known, the positions of the target nodes are variable, the anchor nodes transmit signals every 5mm, the signals are continuously transmitted for 20 times, and the anchor nodes are in cyclic communication with surrounding anchor nodes again after 10 seconds until the target nodes leave the effective ranging range of the anchor nodes. The receive sensitivity is the minimum input power required by the receiver to ensure that the required bit error rate is achieved. The smaller the minimum signal-to-noise ratio required for demodulation, the higher the anchor node reception performance. The minimum signal-to-noise ratio requirement is related to the speed of the mobile station, the radio environment in which it is located and the required communication quality. Practical tests show that-120 dBm is selected as the threshold for anchor node selection.
Fig. 1 shows a schematic diagram of a fractional fourier transform rake signal, and the fractional fourier transform specifically includes the following steps:
1-1) the basic definition of a fractional Fourier transform giving the function f (t) from the point of view of the integral kernel is:
Figure BDA0002375632870000091
in formula (1), the integral kernel K (α; u, t) is defined as follows:
Figure BDA0002375632870000092
in the formula (2), the reaction mixture is,
Figure BDA0002375632870000093
is the rotation angle of the fractional fourier transform.
1-2) the expression of the Chirp signal is as follows:
Figure BDA0002375632870000094
in the formula (3), the reaction mixture is,
Figure BDA0002375632870000095
is an initial phase, f0As the center frequency, for the convenience of derivation, take
Figure BDA0002375632870000096
f00. k is the modulation frequency, determines the speed of the signal frequency change,the bandwidth B is kT, wherein T is the time domain width of the Chirp signal, and the relative width zeta is B/f0。
1-3) the fractional Fourier transform of the p order of the Chirp signal can be represented as follows:
Figure BDA0002375632870000097
further carrying out simplification and variable substitution to obtain a fractional Fourier transform of the Chrip signal:
Figure BDA0002375632870000098
the formula (5) is that the Chirp signal is converted into
Figure BDA0002375632870000101
Has the best energy gathering properties in the fractional fourier transform domain.
1-4) for Gaussian noise, the phenomenon of energy convergence does not occur. And because FRFT has time-shift characteristic, when the time shift of the signal in time domain is tau0In the FRFT domain, as a frequency shift τ0cos α. therefore, by means of a fractional fourier transform, gaussian noise and echo signals can be better separated, when the following relationship exists:
Figure BDA0002375632870000102
1.2 reducing the problem of system clock drift by using two-way ranging, which is schematically shown in fig. 2, a mobile target a as the initiator of the distance measurement can initiate a ranging request, and an anchor node B as the responder can listen and respond to the radio information sent by a, then the two-way ranging is described as follows: a sends a radio message to B and records its transmission time stamp t1B receives the information and sends a reply to A after a specific time delay treplyB, and finally A receives the reply and records a receiving time stamp t2. With their own local clocks, device A can know its own transmission timeTimestamp t1And receiving a time stamp t2Thus, the calculated round trip time is calculated:
troundA＝t2-t1
and device B can know its own delay treplyBThen the arrival time of the signal can be determined by the following equation:
TOA＝(t2-t1-treplyB)/2
second, NLOS error discrimination and estimation
Firstly, judging whether an NLOS error exists by utilizing a Wylie algorithm, and estimating the NLOS error by utilizing a least square method.
2-1) in hypothesis testing, smoothing the distance measurement value of each anchor node at different moments to obtain a measurement distance standard deviation, and if the measurement distance standard deviation is far larger than the standard deviation under the LOS environment, judging that a non-line-of-sight error exists. The TOA measurement for the ith anchor node is:
Figure BDA0002375632870000103
wherein the content of the first and second substances,
Figure BDA0002375632870000104
is a TOA measurement in LOS environment, niCompliance for systematic measurement errors
Figure BDA0002375632870000105
biFor the additional delay error caused by NLOS, it is a large positive mean random variable with mean value of μeiVariance is
Figure BDA0002375632870000106
Smoothing with a polynomial of order N:
Figure BDA0002375632870000111
obtaining the unknown coefficient
Figure BDA0002375632870000112
And then estimating the measured value:
Figure BDA0002375632870000113
standard deviation of multiple replicates:
Figure BDA0002375632870000114
if it is
Figure BDA0002375632870000115
The signal received by the anchor node is an NLOS signal.
2-2) in a non-line-of-sight environment, rewriting equation (6) into a vector form:
r＝F(X)+n+b (10)
wherein r is the TOA measurement and F (X) is the true TOA as a function of the anchor node coordinates
Figure BDA0002375632870000116
In vector form.
Assuming b is known, the estimated value of the moving target position in the least square sense is:
Figure BDA0002375632870000117
wherein J (X) ═ r-F (X) -b)TR-1(r-F(X)-b)
Locating the function F (X) at a reference point X0And (3) performing linearization, and neglecting high-order terms, obtaining:
F(X)≈F(X0)+F0(X-X0) (12)
wherein the initial position X of the mobile station0Can be obtained by the formula (21), F0Is F (X) at X0The jacobian matrix of (a).
Let y be r- (F (X)0)-F0X0)＝F0X+b+n
Then J (X) ═ y-F0X-b)TR-1(y-F0X-b)
Taking J (X) as the minimum value, and obtaining the value by using the least square principle
Figure BDA0002375632870000118
Figure BDA0002375632870000119
Wherein the content of the first and second substances,
Figure BDA00023756328700001110
indicates the position estimate without NLOS error, and
Figure BDA00023756328700001111
when b is unknown, to estimate b, let
Figure BDA0002375632870000121
Wherein the content of the first and second substances,
Figure BDA0002375632870000122
its covariance matrix Qv＝E[vvT]。
In the least squares sense:
Figure BDA0002375632870000123
wherein the content of the first and second substances,
Figure BDA0002375632870000124
and
Figure BDA0002375632870000125
for the lower and upper bounds of the NLOS error in one measurement, 0 and the set { r }i+rj-RijJ ≠ i } minimum value. Equation (14) is a weighted least squares problem with constraints, which can beTo be solved by a lagrangian optimization method.
Third, TDOA-EKF moving target track tracking
TDOA diagram As shown in FIG. 3, TDOA algorithm is an improvement of TOA algorithm, which does not directly use the signal arrival time, but uses the time difference of the signals received by two anchor nodes to determine the position of the moving target, and this requires strict synchronization of the base station time, but when the transmission characteristics of the moving channel between two base stations are similar, the error caused by multipath effect can be reduced, and the positioning accuracy is also improved. Ri，0For the distance difference between the i anchor nodes and the 0 th anchor node to the moving target:
Figure BDA0002375632870000126
in the formula (15), x and y are horizontal and vertical coordinates of the moving object, xi、yiAs anchor node abscissa and ordinate, TOAiThe time when the signal reaches the ith anchor node from the moving target, and c is the speed of light.
Equation (15) is transformed to yield:
Figure BDA0002375632870000127
in formula (16), Xi，0Is the distance on the abscissa between the ith anchor node and the 0 th anchor node, Yi，0Is the distance on the ordinate between the ith anchor node and the 0 th anchor node,
Figure BDA0002375632870000128
irrespective of x, y, R0The relationship between the three is assumed to be linearly independent, and a linear equation set is established:
Figure BDA0002375632870000129
considering the presence of TDOA observed noise, the error vector is:
Figure BDA0002375632870000131
in the formula (18), the reaction mixture,
Figure BDA0002375632870000132
then applying a weighted least squares method (WLS) can result in:
Figure BDA0002375632870000133
q is the range error covariance matrix for a different anchor line .
Further using a weighted least squares method (WLS) can be obtained:
z’＝(G’TΨ’-1G’)-1GTΨ’-1h (20)
wherein, z ═ x [ [ (x-x)0)2，(y-y0)2]T
The final estimation result of the obtained positioning is:
Figure BDA0002375632870000134
assuming that the mobile station moves on a two-dimensional plane, the vector for the motion state at the time k
Figure BDA0002375632870000135
Wherein, [ x ]k，yk]Coordinates of the moving object on the horizontal and vertical axes are shown,
Figure BDA0002375632870000136
the velocity of the moving object on the horizontal and vertical axes is shown. The equation of state taking into account random acceleration can be expressed as:
S(k)＝ΦS(k-1)+ΓW(k) (22)
wherein the content of the first and second substances,
Figure BDA0002375632870000137
at is the interval between the samples to be taken,
Figure BDA0002375632870000138
for random acceleration, since W (k) can be regarded as white noise, its covariance matrix is defined as
Figure BDA0002375632870000139
The TDOA-EKF algorithm positioning flow chart is shown in FIG. 4, and the EKF measurement equation is as follows:
z(k)＝H(k)S(k)+n(k)+b(k) (23)
wherein the content of the first and second substances,
Figure BDA00023756328700001310
iterative process of EKF:
S(k|k-1)＝ΦS(k-1|k-1)
P(k|k-1)＝ΦP(k-1|k-1)ΦT+ΓQIT
K(k)＝P(k|k-1)HT(k-1)[H(k-1)P(k|k-1)HT(k-1)+R(k)]-1(24)
P(k|k)＝[I-K(k)H(k-1)]P(k|k-1)
S(k|k)＝S(k|k-1)+K(k)[z(k)-H(k-1)S(k|k-1)]
in the equation (24), the equation is a state prediction equation, an error covariance prediction equation, a kalman gain, a state update equation, and an error covariance update equation.
The receiving beacon is loaded with 3 LoRa chips with different frequency bands, the beacon carried by the moving target selects a proper transmitting frequency band to transmit a LoRa signal in a frequency modulation mode according to the load of the nearby receiving beacon, and the frequency division multiplexing is realized in the low-cost mode. In addition, according to the requirement for tracking the real-time performance of the moving target, the signal transmitting frequency is adjusted, and the receiver receives signals of different targets in the signal transmitting interval, so that the time division multiplexing is realized, and the throughput capacity of the node is improved.
Due to the beacon itself or the environment, there is often a certain error in the ranging, which directly affects the subsequent target positioning accuracy. Common error sources are clock asynchronism and clock offset, which are caused by self-caused machines, and multipath effect and NLOS error are caused by complex environmental factors in signal propagation. In order to reduce the influence of clock asynchronization, the system can perform master-slave exchange regularly to synchronize the time between the machines. Due to the difference of processing technologies, the crystal oscillators are not completely consistent with the standard time, but the signals are transmitted in the air at the speed of light, so that large ranging deviation can be brought by slight errors, and the relative time of the chip can be utilized for timing by adopting bidirectional ranging, so that the influence of the difference of different crystal oscillators on ranging is reduced. In the process of signal propagation, phenomena such as reflection and diffraction can occur, and the phenomena and the direct signals are mutually interfered, so that when the time of the direct signals and the time of the direct signals reaching a receiver are close, the direct signals cannot be distinguished by the receiver, the signals can be transformed to a Fourier domain through fractional Fourier transform, the energy of the signals is highly gathered, and the direct signals can be effectively separated.
After the series of processing, the obtained time multiplied by the light speed is the distance between the moving target and the anchor node, however, if an obstacle exists, the time of signal arrival has time delay, the moving target transmits signals for many times in a short time, the position of the moving target in the short time can be considered to be unchanged, the obtained data judges whether the obstacle exists or not by using a Wylie algorithm, if the obstacle does not exist, the data is directly used for subsequent calculation, and if the obstacle exists, the size of the NLOS error is estimated by using a least square method. The chips need certain time processing when the signals are transmitted and received, the time of the signals arriving at the two receivers is subtracted by supposing that the processing time of different machines is approximately the same, the time of the signals processed by the system can be approximately offset, the data obtained by the processing can be used for primarily obtaining the position data of the moving target by using a CHAN algorithm, the position data is used as an observed value, a motion equation of the moving target is constructed, and the positioning error can be corrected and the target track can be tracked by using an updating algorithm of an NLOS error correction extended Kalman filter.
The embodiments of the present invention have been described in detail with reference to the drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the gist of the present invention. Although the present invention has been described with reference to a preferred embodiment, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (6)

1. The method for eliminating the positioning error of the multiple moving targets based on the improved extended Kalman filtering realizes the positioning of the multiple targets in a mode of combining time division multiplexing and wavelength division multiplexing, and is characterized by specifically comprising the following steps of:
converting a received signal into pulses with concentrated energy in a Fourier domain through fractional Fourier transform, and distinguishing direct signals in multipath effects;
setting a certain threshold value for RSSI, and if the intensity of a signal received by an anchor node is lower than the threshold value, discarding ranging data of the anchor node at the current moment;
using two-way ranging to reduce offset generated by a system clock by adopting relative time;
aiming at repeated ranging data obtained by multiple times of communication in a very short time, judging whether an NLOS error exists in the ranging process by using a Wylie algorithm, if so, estimating the size of the NLOS error by using a least square method, and if not, directly using the data for subsequent calculation;
reducing system processing time errors by using the time difference TDOA when a signal reaches two anchor nodes;
aiming at the information of a plurality of distance measurements, the CHAN algorithm is used for further reducing the positioning error and solving the position of a moving target at a certain moment;
and taking the result of the CHAN algorithm as an observed value, constructing a state equation, and estimating the motion track of the moving target by using the estimated NLOS error improved extended Kalman positioning algorithm.
2. The improved extended kalman filter-based method for eliminating positioning errors of multiple moving targets according to claim 1, wherein the specific step of the fractional fourier transform comprises:
1-1) the fractional Fourier transform of the function f (t) is defined as:
Figure FDA0002375632860000011
in formula (1), the integral kernel K (α; u, t) is defined as follows:
Figure FDA0002375632860000012
in the formula (2), u is a fractional Fourier domain, t is signal detection time, i is a parameter from a frequency domain to a time domain,
Figure FDA0002375632860000013
the rotation angle is fractional order p Fourier transform;
1-2) the expression of the Chirp signal is as follows:
Figure FDA0002375632860000014
in the formula (3), the reaction mixture is,
Figure FDA0002375632860000024
is an initial phase, f0As a center frequency, take
Figure FDA0002375632860000025
f00; k is frequency modulation, determines the speed of signal frequency change, and the bandwidth B is kT, wherein T is the Chirp signal time domainWidth, relative width ζ ═ B/f0；
1-3) the fractional Fourier transform of the p order of the Chirp signal is represented as:
Figure FDA0002375632860000021
further carrying out simplification and variable substitution to obtain a fractional Fourier transform of the Chrip signal:
Figure FDA0002375632860000022
the formula (5) is that the Chirp signal is converted into
Figure FDA0002375632860000023
Has the best energy gathering property on the fractional order Fourier transform domain;
1-4) for Gaussian noise, the time shift of the signal in the time domain is τ0In the FRFT domain, as a frequency shift τ0cos α, separating the gaussian noise and the echo signal by a fractional fourier transform, when the following relationship exists:
Figure FDA0002375632860000026
3. the method for eliminating the positioning error of the multiple moving targets based on the improved extended kalman filter as claimed in claim 1, wherein the specific method for reducing the offset generated by the system clock by using the relative time through the two-way ranging comprises:
the mobile target A as the initiator of the distance measurement initiates a ranging request, the anchor node B as the responder listens and responds to the radio information sent by the A, and the bidirectional ranging is described as follows:
a sends a radio message to B and records its transmission time stamp t1B receives the information and delays it by a specific time treplyBThen sending a reply to A, and finally A receives the reply and records a receiving time stampt2；
Device a knows its own transmission time stamp t using its own local clock1And receiving a time stamp t2Thus, the calculated round trip time is calculated:
troundA＝t2-t1；
device B knows its own delay treplyBThen the arrival time of the signal can be determined by the following equation:
TOA＝(t2-t1-treplyB)/2。
4. the improved extended kalman filter-based multi-moving-target positioning error elimination method according to claim 1, wherein the Wylie algorithm is used to determine whether an NLOS error exists in the ranging process, and the least square method is used to estimate the size of the NLOS error, and the specific method is as follows:
2-1) in hypothesis testing, smoothing distance measurement values of each anchor node at different moments to obtain a measurement distance standard deviation, and if the measurement distance standard deviation is far larger than the standard deviation in an LOS environment, judging that a non-line-of-sight error exists;
the TOA measurement for the ith anchor node is:
Figure FDA0002375632860000036
wherein the content of the first and second substances,
Figure FDA0002375632860000037
is a T0A measurement value n in LOS environmentiCompliance for systematic measurement errors
Figure FDA0002375632860000039
biAdditional delay error introduced for NL0S, which is a large positive mean random variable with mean μeiVariance is
Figure FDA0002375632860000038
Smoothing with a polynomial of order N:
Figure FDA0002375632860000031
fitting to obtain unknown coefficients
Figure FDA00023756328600000310
And then estimating the measured value:
Figure FDA0002375632860000032
estimate of standard deviation for multiple replicates:
Figure FDA0002375632860000033
if it is
Figure FDA00023756328600000311
K is the number of repeated measurement, the signal received by the anchor node is NLOS signal, sigmaiIs the standard deviation of the ith anchor node,
Figure FDA0002375632860000034
for the unknown coefficients of the fit to be,
Figure FDA0002375632860000035
refers to the ith anchor node signal reception time;
2-2) in a non-line-of-sight environment, rewriting equation (6) into a vector form:
r＝F(X)+n+b (10)
wherein r is the TOA measurement and F (X) is the true TOA as a function of the anchor node coordinates
Figure FDA0002375632860000041
Vector form of (1);
whereinX and y are coordinates of the node to be measured, xi、yiIs the coordinates of the ith anchor node, and n and b are equations (6)
A corresponding vector form;
assuming b is known, the estimated value of the moving target position in the least square sense is:
Figure FDA0002375632860000042
wherein J (X) ═ r-F (X) -b)TR-1(r-F(X)-b)；
Locating the function F (X) at a reference point X0And (3) performing linearization, and neglecting high-order terms, obtaining:
F(X)≈F(X0)+F0(X-X0) (12)
wherein the initial position X of the mobile station0Can be obtained by the formula (21), F0Is F (X) at X0A jacobian matrix of (d);
let y be r- (F (X)0)-F0X0)＝F0X+b+n
Then J (X) ═ y-F0X-b)TR-1(y-F0X-b)
Taking J (X) as the minimum value, and obtaining the value by using the least square principle
Figure FDA0002375632860000043
Figure FDA0002375632860000044
Wherein the content of the first and second substances,
Figure FDA0002375632860000045
indicates the position estimate without NLOS error, and
Figure FDA0002375632860000046
when b is unknown, to estimate b, let
Figure FDA0002375632860000047
Wherein the content of the first and second substances,
Figure FDA0002375632860000048
its covariance matrix Qv＝E[vvT]In the least squares sense:
Figure FDA0002375632860000049
wherein the content of the first and second substances,
Figure FDA00023756328600000411
and
Figure FDA00023756328600000410
for the lower and upper bounds of the NLOS error in one measurement, 0 and the set { r }i+rj-RijJ ≠ i } minimum;
equation (14) is a weighted least squares problem with constraints and is solved by the lagrange optimization method.
5. The improved extended kalman filter-based multi-moving-target positioning error elimination method according to claim 1, further comprising performing moving-target trajectory tracking using TDOA-EKF algorithm, specifically comprising:
Ri,0for the distance difference between the i anchor nodes and the 0 th anchor node to the moving target:
Figure FDA0002375632860000051
in the formula (15), x and y are horizontal and vertical coordinates of the moving object, xi、yiAs anchor node abscissa and ordinate, TOAiThe time when the signal reaches the ith anchor node from the moving target, c is the speed of light, x0.y0Coordinates of the 0 th anchor node;
equation (15) is transformed to yield:
Figure FDA0002375632860000052
in formula (16), Xi，0Is the distance on the abscissa between the ith anchor node and the 0 th anchor node, Yi，0Is the distance on the ordinate between the ith anchor node and the 0 th anchor node,
Figure FDA0002375632860000057
irrespective of x, y, R0The relation between the three is set to be linearly independent, and a linear equation set is established:
Figure FDA0002375632860000053
considering the presence of TDOA observed noise, the error vector is:
Figure FDA0002375632860000054
in the formula (18), the reaction mixture,
Figure FDA0002375632860000055
then a weighted least squares method (WLS) is applied to obtain:
Figure FDA0002375632860000056
wherein Q is a distance measurement error covariance matrix of different anchor systems ;
further using a weighted least squares method (WLS) can be obtained:
z’＝(G’TΨ’-1G’)-1GTΨ’-1h (20)
wherein, z ═ x [ [ (x-x)0)2，(y-y0)2]T；
The final estimation result of the obtained positioning is:
Figure FDA0002375632860000061
assuming that the mobile station moves on a two-dimensional plane, the vector for the motion state at the time k
Figure FDA0002375632860000062
Wherein, [ x ]k,yk]Coordinates of the moving object on the horizontal and vertical axes are shown,
Figure FDA0002375632860000063
the velocity of the moving object on the horizontal and vertical axes is shown. The equation of state taking into account random acceleration can be expressed as:
S(k)＝ΦS(k-1)+ΓW(k) (22)
wherein the content of the first and second substances,
Figure FDA0002375632860000064
at is the interval between the samples to be taken,
Figure FDA0002375632860000065
for random acceleration, since W (k) can be regarded as white noise, its covariance matrix is defined as
Figure FDA0002375632860000066
The EKF measurement equation is:
z(k)＝H(k)S(k)+n(k)+b(k) (23)
wherein the content of the first and second substances,
Figure FDA0002375632860000067
iterative process of EKF:
Figure FDA0002375632860000068
in the equation (24), the equation is a state prediction equation, an error covariance prediction equation, a kalman gain, a state update equation, and an error covariance update equation.
6. The improved extended kalman filter-based multi-moving-target positioning error elimination method according to claim 1, further comprising:
the receiving beacon is loaded with 3 LoRa chips with different frequency bands, the beacon carried by the moving target selects a proper transmitting frequency band to transmit a LoRa signal in a frequency modulation mode according to the load of the nearby receiving beacon, and frequency division multiplexing is realized;
according to the requirement for tracking the real-time performance of the moving target, the signal transmitting frequency is adjusted, and the receiver receives signals of different targets in the signal transmitting interval, so that time division multiplexing is realized and the throughput capacity of the node is improved.
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