CN105372630A - Ultra-wideband communication system positioning method based on level quantification detection - Google Patents

Abstract

The invention relates to a positioning method of an ultra-wideband communication system based on level quantization detection. At least four positioning detection nodes are set to locate nodes to be positioned and detected; a binary hypothesis testing model for level quantization detection is established; and the optimal quantization level threshold and False alarm probability; construct the quantization function of three-level detection, and calculate the detection statistics; construct the binary hypothesis testing model and signal detection judgment criterion after the observation sample is quantified; calculate and judge the optimal decision according to the quantization function of three-level detection Threshold and detection statistics, and take the arrival time of the first recorded passing decision signal as the time when each positioning detection node receives the signal of the node to be positioned, and establish a system of equations about the coordinates of the detection node to be positioned to obtain the node to be positioned The first coordinate value, the second coordinate value, the third coordinate value and the fourth coordinate value calculate the actual coordinates of the node to be positioned.

Description

Location method of UWB communication system based on level quantization detection

technical field

The invention relates to the field of positioning, in particular to a positioning method for an ultra-wideband communication system based on level quantization detection.

Background technique

Since UWB technology was allowed to be applied to civilian products by the Federal Communications Commission of the United States, it has been widely concerned by many scientific research institutions. Nowadays, with the integration of mobile Internet and local life services, people's demand for location-based services is becoming stronger and stronger. As a special communication system, ultra-wideband has the advantages of anti-multipath fading, strong penetrating power, and high positioning accuracy in wireless positioning, so it is considered to be a wireless positioning technology with great potential.

With the rapid development of the mobile Internet, people's demand for perceiving location information while experiencing wireless Internet services is also increasing. In daily life, people often need to obtain services based on location information instantly through terminals. For example, before entering the shopping mall, you can find a parking space through the terminal navigation guidance; during the shopping process, if you search for "food", you will be presented with store discount information based on location and orientation, and you can get the best route guidance. However, in practical applications, in shopping malls, airports, museums, mines and other indoor or easily occluded places, location services based on mobile terminals cannot provide a good user experience due to the ineffective coverage of GPS signals. With the promotion of commercial demand, it is urgent to build an indoor positioning system similar to GPS, so as to meet the needs of more accurate positioning and navigation, monitoring management, health care and so on. Therefore, it is of great practical value to carry out the research on UWB-based wireless positioning technology.

Contents of the invention

The technical problem to be solved by the present invention is to provide a positioning method of an ultra-wideband communication system based on level quantization detection with high positioning performance in view of the above-mentioned prior art.

The technical solution adopted by the present invention to solve the above-mentioned technical problems is: a positioning method for an ultra-wideband communication system based on level quantization detection, which is characterized in that it includes the following steps in sequence:

(1) It is assumed that the UWB communication system has a node O(x _o , y _o , z _o ) to be positioned and at least four positioning detection nodes A(x _A , y _A , z _A ), B(x _B ,y _B ,z _B ), C(x _C ,y _C ,z _C ) and D(x _D ,y _D ,z _D ), and assuming that the location detection node A receives the node O to be positioned the time t _A of the signal;

(2) Establish a binary hypothesis testing model for level quantization detection, set the number of observation samples r _k in the observation sample sequence R as N _t , N _t observed samples meet the following criteria for binary hypothesis testing:

$\left\{\begin{array}{c}{h}_{{\mathrm{\θ}}_0}:r_k={\mathrm{\θ}}_0+{\mathrm{no}}_k\\ h_{{\mathrm{\θ}}_1}:r_k={\mathrm{\θ}}_1+{\mathrm{no}}_k\end{array}\right.$ Formula 1);

Among them, k=0,1,...,N _t -1, n _k is zero-mean Gaussian white noise;

(3) According to the probability distribution function f(x) and cumulative distribution function F(x), calculate the optimal quantization level threshold q _m , where, The calculation formula of the optimal quantization level threshold q _m is as follows:

$q_m=\log \left(\frac{{\∫}_{t_{m-1}}^{t_m}{f}_{{\mathrm{\θ}}_1}\left(x\right)dx}{{\∫}_{t_{m-1}}^{t_m}{f}_{{\mathrm{\θ}}_0}\left(x\right)dx}\right)=\log \left(\frac{f(t_m-{\mathrm{\θ}}_1)-f(t_{m-1}-{\mathrm{\θ}}_1)}{f(t_m-{\mathrm{\θ}}_0)-f(t_{m-1}-{\mathrm{\θ}}_0)}\right)$ Formula (2);

$-\frac{f^{\′}\left(t_m\right)}{f\left(t_m\right)}=\frac{q_m+q_{m+1}}{2}$ Formula (3);

Among them, m is the number of quantization levels;

(4) According to the Newman-Pearson criterion, the random test function Q(r) and the threshold t, calculate the false alarm probability a, where,

$\mathrm{\α}=\mathrm{E.}\left(Q\right(r);h_{{\mathrm{\θ}}_0})$ Formula (4);

$Q\left(x\right)={\∫}_x^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}}\exp (-\frac{1}{2}{t}^2)dt$ Formula (5);

$P_{LR}={\∫}_{\{x,L\left(x\right)>\mathrm{\τ}\}}p(x;h_{\mathrm{\θ}1})dx=a$ Formula (6);

$L\left(x\right)=\frac{p(x;h_{{\mathrm{\θ}}_0})}{p(x;h_{\mathrm{\θ}1})}>\mathrm{\τ}$ Formula (7);

(5) Construct the quantization function Q _c (r _k,i ) of three-level detection, and calculate the detection statistic T _c (R _i ), where,

$Q_c\left(r_{k,i}\right)=\left\{\begin{array}{cc}1,& r_{k,i}\&Greater\; Equal;c\\ 0,& -c<r_{k,i}<c\\ -1,& r_{k,i}\&le;-c\end{array}\right.$ Formula (8);

$T_c\left(R_i\right)={\mathrm{\&Sigma;}}_{k=0}^{N_{t-1}}{Q}_c\left(r_{k,i}\right)$ Formula (9);

Among them, c is a preset constant;

(6) According to the observation sample sequence R in step (2), the i-th observation sample r _k,i in the k-th period is quantized as x _k,i , that is, Q(r _k,i )=x _k,i , And construct the quantified binary hypothesis testing model and signal detection judgment criteria respectively; among them,

The quantified binary hypothesis testing model is:

$\left\{\begin{array}{c}{h}_0:R_i=N_i\\ h_1:R_i=w_i+N_i\end{array}\right.$ Formula (10);

Among them, w _i is a constant, N _i is a random noise vector, 0￡i￡N-1;

The judgment criteria for signal detection are:

$\left\{\begin{array}{c}{h}_0:T\left(R_i\right)<{\mathrm{\&lambda;}}_{N_i,\mathrm{\&alpha;}}\\ h_1:T\left(R_i\right)>{\mathrm{\&lambda;}}_{N_i,\mathrm{\&alpha;}}\end{array}\right.$ Formula (11);

in, is the test statistic, is the judgment threshold;

(7) According to the quantization function Q _c (r _k,i ) of three-level detection, the number of observation samples satisfying |r _k,i |≥c obtained in the observation sample sequence R is N ₁ , and the calculation and the number of samples The optimal decision threshold α _opt corresponding to N ₁ :

${\mathrm{\&alpha;}}_{opt}={\&Integral;}_{{\mathrm{\&lambda;}}_{N_t,\mathrm{\&alpha;}}}^{\mathrm{\&infin;}}{f}_{T_c}^{N_1}\left(x\right)dx$ Formula (12);

Among them, the number of observed samples of [c,∞) is N _1p , and the detection statistic T _c (R _i )=2N _1p -N ₁ ;

(8) Compare the obtained optimal decision threshold α _opt with the detection statistic T _c (R _i ), and record the arrival time of the first signal that passes the decision in step (6);

(9) The time t _A of receiving the signal of the node O to be positioned by the location detection node A with the first signal arrival time of the record as the location detection node A; repeat step (2) to step (8) again to obtain the location detection node B, C, D receive the time t _B , t _C and t _D of the node O signal to be positioned;

(10) According to the receiving time corresponding to each positioning detection node, establish a system of equations about the coordinates of the detection node to be positioned, and calculate and obtain the first coordinate value of the node O to be positioned (x' _o , y' _o , z' _o ), the second coordinate value (x” _o ,y” _o ,z” _o ), the third coordinate value (x”' _o ,y”' _o ,z”' _o ) and the fourth coordinate value (x”” _o ,y"" _o ,z"" _o ):

$\left\{\begin{array}{c}{d}_{Ao}^2={({x^{\&prime;}}_o-x_A)}^2+{({{\mathrm{the\; y}}^{\&prime;}}_o-{\mathrm{the\; y}}_A)}^2+{({z^{\&prime;}}_o-z_A)}^2\\ d_{Bo}^2={({x^{\&prime;}}_o-x_B)}^2+{({{\mathrm{the\; y}}^{\&prime;}}_o-{\mathrm{the\; y}}_B)}^2+{({z^{\&prime;}}_o-z_B)}^2\\ d_{Co}^2={({x^{\&prime;}}_o-x_C)}^2+{({{\mathrm{the\; y}}^{\&prime;}}_o-{\mathrm{the\; y}}_C)}^2+{({z^{\&prime;}}_o-z_C)}^2\end{array}\right.$ Formula (13);

$\left\{\begin{array}{c}{d}_{Ao}^2={({x^{\&prime;\&prime;}}_o-x_A)}^2+{({{\mathrm{the\; y}}^{\&prime;\&prime;}}_o-{\mathrm{the\; y}}_A)}^2+{({z^{\&prime;\&prime;}}_o-z_A)}^2\\ d_{Bo}^2={({x^{\&prime;\&prime;}}_o-x_B)}^2+{({{\mathrm{the\; y}}^{\&prime;\&prime;}}_o-{\mathrm{the\; y}}_B)}^2+{({z^{\&prime;\&prime;}}_o-z_B)}^2\\ d_{\mathrm{D.}o}^2={({x^{\&prime;\&prime;}}_o-x_{\mathrm{D.}})}^2+{({{\mathrm{the\; y}}^{\&prime;\&prime;}}_o-{\mathrm{the\; y}}_{\mathrm{D.}})}^2+{({z^{\&prime;\&prime;}}_o-z_{\mathrm{D.}})}^2\end{array}\right.$ Formula (14);

$\left\{\begin{array}{c}{d}_{Ao}^2={({x^{\&prime;\&prime;\&prime;}}_o-x_A)}^2+{({{\mathrm{the\; y}}^{\&prime;\&prime;\&prime;}}_o-{\mathrm{the\; y}}_A)}^2+{({z^{\&prime;\&prime;\&prime;}}_o-z_A)}^2\\ d_{Co}^2={({x^{\&prime;\&prime;\&prime;}}_o-x_C)}^2+{({{\mathrm{the\; y}}^{\&prime;\&prime;\&prime;}}_o-{\mathrm{the\; y}}_C)}^2+{({z^{\&prime;\&prime;\&prime;}}_o-z_C)}^2\\ d_{\mathrm{D.}o}^2={({x^{\&prime;\&prime;\&prime;}}_o-x_{\mathrm{D.}})}^2+{({{\mathrm{the\; y}}^{\&prime;\&prime;\&prime;}}_o-{\mathrm{the\; y}}_{\mathrm{D.}})}^2+{({z^{\&prime;\&prime;\&prime;}}_o-z_{\mathrm{D.}})}^2\end{array}\right.$ Formula (15);

$\left\{\begin{array}{c}{d}_{Bo}^2={({x^{\&prime;\&prime;\&prime;\&prime;}}_o-x_B)}^2+{({{\mathrm{the\; y}}^{\&prime;\&prime;\&prime;\&prime;}}_o-{\mathrm{the\; y}}_B)}^2+{({z^{\&prime;\&prime;\&prime;\&prime;}}_o-z_B)}^2\\ d_{Co}^2={({x^{\&prime;\&prime;\&prime;\&prime;}}_o-x_C)}^2+{({{\mathrm{the\; y}}^{\&prime;\&prime;\&prime;\&prime;}}_o-{\mathrm{the\; y}}_C)}^2+{({z^{\&prime;\&prime;\&prime;\&prime;}}_o-z_C)}^2\\ d_{\mathrm{D.}o}^2={({x^{\&prime;\&prime;\&prime;\&prime;}}_o-x_{\mathrm{D.}})}^2+{({{\mathrm{the\; y}}^{\&prime;\&prime;\&prime;\&prime;}}_o-{\mathrm{the\; y}}_{\mathrm{D.}})}^2+{({z^{\&prime;\&prime;\&prime;\&prime;}}_o-z_{\mathrm{D.}})}^2\end{array}\right.$ Formula (16);

$\left\{\begin{array}{c}{d}_{Ao}=c\&Center\; Dot;t_A\\ d_{Bo}=c\&Center\; Dot;t_B\\ d_{Co}=c\&Center\; Dot;t_C\\ d_{\mathrm{D.}o}=c\&CenterDot;t_{\mathrm{D.}}\end{array}\right.$ Formula (17);

Among them, d _AO , d _BO , d _CO and d _DO are the distances from the positioning detection nodes A, B, C and D to the node O to be positioned respectively, and c represents the light propagation speed;

(11) According to the obtained first coordinate value (x' _o , y' _o , z' _o ), the second coordinate value (x” _o , y” _o , z” _o ), the third coordinate value of the node O to be positioned value (x"' _o , y"' _o , z"' _o ) and the fourth coordinate value (x"" _o , y"" _o , z"" _o ), calculate the actual coordinate of the node O to be positioned (x _o ,y _o ,z _o ):

$\left\{\begin{array}{c}{x}_o=\frac{\frac{{x^{\&prime;}}_o}{d_{Ao}^2+d_{Bo}^2+d_{Co}^2}+\frac{{x^{\&prime;\&prime;}}_o}{d_{Ao}^2+d_{Bo}^2+d_{\mathrm{D.}o}^2}+\frac{{x^{\&prime;\&prime;\&prime;}}_o}{d_{Ao}^2+d_{Co}^2+d_{\mathrm{D.}o}^2}+\frac{{x^{\&prime;\&prime;\&prime;\&prime;}}_o}{d_{Bo}^2+d_{Co}^2+d_{\mathrm{D.}o}^2}}{\frac{1}{d_{Ao}^2+d_{Bo}^2+d_{Co}^2}+\frac{1}{d_{Ao}^2+d_{Bo}^2+d_{\mathrm{D.}o}^2}+\frac{1}{d_{Ao}^2+d_{Co}^2+d_{\mathrm{D.}o}^2}+\frac{1}{d_{Bo}^2+d_{Co}^2+d_{\mathrm{D.}o}^2}}\\ {\mathrm{the\; y}}_o=\frac{\frac{{{\mathrm{the\; y}}^{\&prime;}}_o}{d_{Ao}^2+d_{Bo}^2+d_{Co}^2}+\frac{{{\mathrm{the\; y}}^{\&prime;\&prime;}}_o}{d_{Ao}^2+d_{Bo}^2+d_{\mathrm{D.}o}^2}+\frac{{{\mathrm{the\; y}}^{\&prime;\&prime;\&prime;}}_o}{d_{Ao}^2+d_{Co}^2+d_{\mathrm{D.}o}^2}+\frac{{{\mathrm{the\; y}}^{\&prime;\&prime;\&prime;\&prime;}}_o}{d_{Bo}^2+d_{Co}^2+d_{\mathrm{D.}o}^2}}{\frac{1}{d_{Ao}^2+d_{Bo}^2+d_{Co}^2}+\frac{1}{d_{Ao}^2+d_{Bo}^2+d_{\mathrm{D.}o}^2}+\frac{1}{d_{Ao}^2+d_{Co}^2+d_{\mathrm{D.}o}^2}+\frac{1}{d_{Bo}^2+d_{Co}^2+d_{\mathrm{D.}o}^2}}\\ z_o=\frac{\frac{{z^{\&prime;}}_o}{d_{Ao}^2+d_{Bo}^2+d_{Co}^2}+\frac{{z^{\&prime;\&prime;}}_o}{d_{Ao}^2+d_{Bo}^2+d_{\mathrm{D.}o}^2}+\frac{{z^{\&prime;\&prime;\&prime;}}_o}{d_{Ao}^2+d_{Co}^2+d_{\mathrm{D.}o}^2}+\frac{{z^{\&prime;\&prime;\&prime;\&prime;}}_o}{d_{Bo}^2+d_{Co}^2+d_{\mathrm{D.}o}^2}}{\frac{1}{d_{Ao}^2+d_{Bo}^2+d_{Co}^2}+\frac{1}{d_{Ao}^2+d_{Bo}^2+d_{\mathrm{D.}o}^2}+\frac{1}{d_{Ao}^2+d_{Co}^2+d_{\mathrm{D.}o}^2}+\frac{1}{d_{Bo}^2+d_{Co}^2+d_{\mathrm{D.}o}^2}}\end{array}\right.$ Formula (18).

Compared with the prior art, the present invention has the advantages of: setting at least four positioning detection nodes in the ultra-wideband communication system to locate the detection node to be positioned, and establishing a binary hypothesis testing model for level quantization detection; calculating the optimal Quantify the level threshold and false alarm probability; construct the quantization function of three-level detection, and calculate the detection statistics; construct the binary hypothesis testing model and signal detection judgment criterion after the observation sample is quantified; according to the quantization function of three-level detection, calculate , judging the optimal decision threshold and detection statistics, and taking the first recorded arrival time of the decision signal as the time when each positioning detection node receives the signal of the node to be positioned, and establishing a group of equations about the coordinates of the detection node to be positioned, The first coordinate value, the second coordinate value, the third coordinate value and the fourth coordinate value of the node to be positioned are obtained, and the actual coordinates of the node to be positioned are calculated. Based on the original three-point positioning detection method, the method can have higher positioning performance by establishing a binary hypothesis testing model of level quantization detection.

Description of drawings

FIG. 1 is a schematic flow diagram of a positioning method for an ultra-wideband communication system based on level quantization detection in an embodiment of the present invention;

Fig. 2 is a graph of the positioning performance of the positioning method in the embodiment of the present invention.

detailed description

The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments.

As shown in Figure 1, in this embodiment, the UWB communication system positioning method based on level quantization detection includes the following steps in turn:

Step 1. Set the UWB communication system to have a node to be positioned O(x _o , y _o , z _o ) and at least four positioning detection nodes respectively A(x _A ,y _A ,z _A ), B(x _B , y _B ,z _B ), C(x _C ,y _C ,z _C ) and D(x _D ,y _D ,z _D ), each positioning detection node receives the signal of the node O to be positioned respectively, where it is assumed that the positioning detection node The time when A receives the signal of the node O to be positioned is _tA ;

Step 2, establish a binary hypothesis testing model for level quantization detection, set the number of observation samples r _k in the observation sample sequence R as N _t , N _t observed samples meet the following criteria for binary hypothesis testing:

$\left\{\begin{array}{c}{h}_{{\mathrm{\&theta;}}_0}:r_k={\mathrm{\&theta;}}_0+{\mathrm{no}}_k\\ h_{{\mathrm{\&theta;}}_1}:r_k={\mathrm{\&theta;}}_1+{\mathrm{no}}_k\end{array}\right.$ Formula 1);

Among them, k=0,1,...,N _t -1, n _k is zero-mean Gaussian white noise;

Step 3, according to the probability distribution function f(x) and cumulative distribution function F(x), calculate the optimal quantization level threshold q _m , where, The calculation formula of the optimal quantization level threshold q _m is as follows:

$q_m=\log \left(\frac{{\&Integral;}_{t_{m-1}}^{t_m}{f}_{{\mathrm{\&theta;}}_1}\left(x\right)dx}{{\&Integral;}_{t_{m-1}}^{t_m}{f}_{{\mathrm{\&theta;}}_0}\left(x\right)dx}\right)=\log \left(\frac{f(t_m-{\mathrm{\&theta;}}_1)-f(t_{m-1}-{\mathrm{\&theta;}}_1)}{f(t_m-{\mathrm{\&theta;}}_0)-f(t_{m-1}-{\mathrm{\&theta;}}_0)}\right)$ Formula (2);

$-\frac{f^{\&prime;}\left(t_m\right)}{f\left(t_m\right)}=\frac{q_m+q_{m+1}}{2}$ Formula (3);

Among them, m is the number of quantization levels;

Step 4, according to the Newman-Pearson criterion, the random test function Q(r) and the threshold τ, calculate the false alarm probability α, where,

The formula for calculating the false alarm probability α is:

$\mathrm{\&alpha;}=\mathrm{E.}\left(Q\right(r);h_{{\mathrm{\&theta;}}_0})$ Formula (4);

The random test function Q(r) is:

$Q\left(x\right)={\&Integral;}_x^{\mathrm{\&infin;}}\frac{1}{\sqrt{2\mathrm{\&pi;}}}\exp (-\frac{1}{2}{t}^2)dt$ Formula (5);

$P_{LR}={\&Integral;}_{\{x,L\left(x\right)>\mathrm{\&tau;}\}}p(x;h_{\mathrm{\&theta;}1})dx=a$ Formula (6);

$L\left(x\right)=\frac{p(x;h_{{\mathrm{\&theta;}}_0})}{p(x;h_{\mathrm{\&theta;}1})}>\mathrm{\&tau;}$ Formula (7);

Step 5, construct the quantization function Q _c (r _k,i ) of three-level detection, and calculate the detection statistic T _c (R _i ), where,

$Q_c\left(r_{k,i}\right)=\left\{\begin{array}{cc}1,& r_{k,i}\&Greater\; Equal;c\\ 0,& -c<r_{k,i}<c\\ -1,& r_{k,i}\&le;-c\end{array}\right.$ Formula (8);

$T_c\left(R_i\right)={\mathrm{\&Sigma;}}_{k=0}^{N_{t-1}}{Q}_c\left(r_{k,i}\right)$ Formula (9);

Among them, c is a preset constant, r _k,i is the i-th observation sample in the k-th period;

Step 6, according to the observation sample sequence R in step 2, quantize the i-th observation sample r _k,i in the k-th period into x _k,i , that is, Q(r _k,i )=x _k,i , and respectively Construct a quantified binary hypothesis testing model and signal detection judgment criteria; among them,

The quantified binary hypothesis testing model is:

$\left\{\begin{array}{c}{h}_0:R_i=N_i\\ h_1:R_i=w_i+N_i\end{array}\right.$ Formula (10);

Among them, w _i is a constant, N _i is a random noise vector, 0≤i≤N-1;

The judgment criteria for signal detection are:

$\left\{\begin{array}{c}{h}_0:T\left(R_i\right)<{\mathrm{\&lambda;}}_{N_i,\mathrm{\&alpha;}}\\ h_1:T\left(R_i\right)>{\mathrm{\&lambda;}}_{N_i,\mathrm{\&alpha;}}\end{array}\right.$ Formula (11);

in, is the test statistic, is the judgment threshold;

Step 7, according to the quantization function Q _c (r _k,i ) of the three-level detection, obtain the observation samples satisfying |r _k,i |≥c in the observation sample sequence R as N ₁ , and calculate the number of samples The optimal decision threshold α _opt corresponding to N ₁ :

${\mathrm{\&alpha;}}_{opt}={\&Integral;}_{{\mathrm{\&lambda;}}_{N_t,\mathrm{\&alpha;}}}^{\mathrm{\&infin;}}{f}_{T_c}^{N_1}\left(x\right)dx$ Formula (12);

Among them, the number of observed samples of [c,∞) is N _1p , and the detection statistic T _c (R _i )=2N _1p -N ₁ ;

Step 8, compare the obtained optimal decision threshold α _opt with the detection statistic T _c (R _i ), and record the arrival time of the first signal that passed the decision in step 6;

Step 9, use the recorded arrival time of the first signal that passes the decision as the time t _A when the positioning detection node A receives the signal of the node O to be positioned; repeat steps 2 to 8 again, and obtain the positioning detection nodes B, C, Time t _B , t _C and t _D when D receives the signal of node O to be positioned; so far, the time taken for the signal of node O to be positioned to reach detection nodes A, B, C and D to be positioned is t _A , t _B , t _C and t _D ;

Step 10, according to the receiving time t _A , t _B , t _C and t D corresponding to each positioning detection node A, B, C and _D , establish a system of equations about the coordinates of the detection node O to be located, and obtain the undetermined The first coordinate value (x' _o , y' _o , z' _o ), the second coordinate value (x” _o , y” _o , z” _o ), the third coordinate value (x”' _o , y"' _o ,z"' _o ) and the fourth coordinate value (x"" _o ,y"" _o ,z"" _o ):

$\left\{\begin{array}{c}{d}_{Ao}^2={({x^{\&prime;}}_o-x_A)}^2+{({{\mathrm{the\; y}}^{\&prime;}}_o-{\mathrm{the\; y}}_A)}^2+{({z^{\&prime;}}_o-z_A)}^2\\ d_{Bo}^2={({x^{\&prime;}}_o-x_B)}^2+{({{\mathrm{the\; y}}^{\&prime;}}_o-{\mathrm{the\; y}}_B)}^2+{({z^{\&prime;}}_o-z_B)}^2\\ d_{Co}^2={({x^{\&prime;}}_o-x_C)}^2+{({{\mathrm{the\; y}}^{\&prime;}}_o-{\mathrm{the\; y}}_C)}^2+{({z^{\&prime;}}_o-z_C)}^2\end{array}\right.$ Formula (13);

$\left\{\begin{array}{c}{d}_{Ao}^2={({x^{\&prime;\&prime;}}_o-x_A)}^2+{({{\mathrm{the\; y}}^{\&prime;\&prime;}}_o-{\mathrm{the\; y}}_A)}^2+{({z^{\&prime;\&prime;}}_o-z_A)}^2\\ d_{Bo}^2={({x^{\&prime;\&prime;}}_o-x_B)}^2+{({{\mathrm{the\; y}}^{\&prime;\&prime;}}_o-{\mathrm{the\; y}}_B)}^2+{({z^{\&prime;\&prime;}}_o-z_B)}^2\\ d_{\mathrm{D.}o}^2={({x^{\&prime;\&prime;}}_o-x_{\mathrm{D.}})}^2+{({{\mathrm{the\; y}}^{\&prime;\&prime;}}_o-{\mathrm{the\; y}}_{\mathrm{D.}})}^2+{({z^{\&prime;\&prime;}}_o-z_{\mathrm{D.}})}^2\end{array}\right.$ Formula (14);

$\left\{\begin{array}{c}{d}_{Ao}^2={({x^{\&prime;\&prime;\&prime;}}_o-x_A)}^2+{({{\mathrm{the\; y}}^{\&prime;\&prime;\&prime;}}_o-{\mathrm{the\; y}}_A)}^2+{({z^{\&prime;\&prime;\&prime;}}_o-z_A)}^2\\ d_{Co}^2={({x^{\&prime;\&prime;\&prime;}}_o-x_C)}^2+{({{\mathrm{the\; y}}^{\&prime;\&prime;\&prime;}}_o-{\mathrm{the\; y}}_C)}^2+{({z^{\&prime;\&prime;\&prime;}}_o-z_C)}^2\\ d_{\mathrm{D.}o}^2={({x^{\&prime;\&prime;\&prime;}}_o-x_{\mathrm{D.}})}^2+{({{\mathrm{the\; y}}^{\&prime;\&prime;\&prime;}}_o-{\mathrm{the\; y}}_{\mathrm{D.}})}^2+{({z^{\&prime;\&prime;\&prime;}}_o-z_{\mathrm{D.}})}^2\end{array}\right.$ Formula (15);

$\left\{\begin{array}{c}{d}_{Bo}^2={({x^{\&prime;\&prime;\&prime;\&prime;}}_o-x_B)}^2+{({{\mathrm{the\; y}}^{\&prime;\&prime;\&prime;\&prime;}}_o-{\mathrm{the\; y}}_B)}^2+{({z^{\&prime;\&prime;\&prime;\&prime;}}_o-z_B)}^2\\ d_{Co}^2={({x^{\&prime;\&prime;\&prime;\&prime;}}_o-x_C)}^2+{({{\mathrm{the\; y}}^{\&prime;\&prime;\&prime;\&prime;}}_o-{\mathrm{the\; y}}_C)}^2+{({z^{\&prime;\&prime;\&prime;\&prime;}}_o-z_C)}^2\\ d_{\mathrm{D.}o}^2={({x^{\&prime;\&prime;\&prime;\&prime;}}_o-x_{\mathrm{D.}})}^2+{({{\mathrm{the\; y}}^{\&prime;\&prime;\&prime;\&prime;}}_o-{\mathrm{the\; y}}_{\mathrm{D.}})}^2+{({z^{\&prime;\&prime;\&prime;\&prime;}}_o-z_{\mathrm{D.}})}^2\end{array}\right.$ Formula (16);

$\left\{\begin{array}{c}{d}_{Ao}=c\&CenterDot;t_A\\ d_{Bo}=c\&Center\; Dot;t_B\\ d_{Co}=c\&Center\; Dot;t_C\\ d_{\mathrm{D.}o}=c\&CenterDot;t_{\mathrm{D.}}\end{array}\right.$ Formula (17);

Among them, d _AO , d _BO , d _CO and d _DO are the distances from the positioning detection nodes A, B, C and D to the node O to be positioned respectively, and c represents the light propagation speed;

Step 11, according to the obtained first coordinate value (x' _o , y' _o , z' _o ), the second coordinate value (x” _o , y” _o , z” _o ), the third coordinate value of the node O to be positioned value (x"' _o , y"' _o , z"' _o ) and the fourth coordinate value (x"" _o , y"" _o , z"" _o ), calculate the actual coordinate of the node O to be positioned (x _o ,y _o ,z _o ):

Formula (18).

In this embodiment, a computer simulation is performed on the performance of the positioning method of the ultra-wideband communication system to understand its positioning performance. Among them, the ultra-wideband communication system adopts the IEEE802.15.4a ultra-wideband channel model CM1 environment, and the positioning method in this embodiment is compared with the traditional non-coherent energy detection positioning method; pulse period T _f =100ns, sampling frequency f _s =4GHz, signal-to-noise ratio SNR=E _p /N ₀ , the average estimation error of the positioning method is MAE, where, The transmission signal of the detection node O to be located adopts a Gaussian second-order derivative pulse signal, and the false alarm probability α is set to α=10 ⁻⁴ ; the simulation results are shown in FIG. 2 .

It can be seen from the simulation results that the sampling rate of incoherent energy detection is lower than that of level quantization, resulting in a larger average estimation error MAE; the positioning method based on two-level quantization is smaller after kalman filtering; With the improvement of the level quantization degree, the location estimation error MAE of the location method gradually becomes smaller, that is, the location estimation performance improves gradually. It can be seen that the UWB communication system positioning method based on level quantization detection in the present invention has better positioning performance.

Claims (1)

1. The ultra-wideband communication system positioning method based on level quantization detection is characterized by sequentially comprising the following steps of:

(1) setting an ultra-wideband communication system having a node O (x) to be positioned_o,y_o,z_o) And at least four positioning detection nodes A (x) respectively receiving signals of the nodes O to be positioned_A,y_A,z_A)、B(x_B,y_B,z_B)、C(x_C,y_C,z_C) And D (x)_D,y_D,z_D) And assume that the positioning detection node A receives a waiting signalTime t of positioning node O signal_A；

(2) Establishing a binary hypothesis test model for level quantitative detection, and setting an observation sample R in an observation sample sequence R_kIs N_t，N_tEach observation sample meets the following binary hypothesis testing criteria:

$\left\{\begin{array}{c}{H}_{{\mathrm{\&theta;}}_0}:r_k={\mathrm{\&theta;}}_0+n_k\\ H_{{\mathrm{\&theta;}}_1}:r_k={\mathrm{\&theta;}}_1+n_k\end{array}\right.$ formula (1);

wherein k is 0,1, …, N_t-1，n_kIs zero mean white gaussian noise;

(3) calculating an optimal quantization level threshold q according to the probability distribution function f (x) and the cumulative distribution function F (x)_mWhereinoptimal quantization level threshold q_mThe calculation formula of (a) is as follows:

$q_m=log\left(\frac{{\&Integral;}_{t_{m-1}}^{t_m}{f}_{{\mathrm{\&theta;}}_1}\left(x\right)dx}{{\&Integral;}_{t_{m-1}}^{t_m}{f}_{{\mathrm{\&theta;}}_0}\left(x\right)dx}\right)=log\left(\frac{F(t_m-{\mathrm{\&theta;}}_1)-F(t_{m-1}-{\mathrm{\&theta;}}_1)}{F(t_m-{\mathrm{\&theta;}}_0)-F(t_{m-1}-{\mathrm{\&theta;}}_0)}\right)$ formula (2);

$-\frac{f^{\&prime;}\left(t_m\right)}{f\left(t_m\right)}=\frac{q_m+q_{m+1}}{2}$ formula (3);

wherein m is the number of quantization levels;

(4) calculating the false alarm probability alpha according to the Newman-Pearson criterion, the random check function Q (r) and the threshold tau, wherein,

$\mathrm{\&alpha;}=E\left(Q\right(r);H_{{\mathrm{\&theta;}}_0})$ formula (4);

$Q\left(x\right)={\&Integral;}_x^{\mathrm{\&infin;}}\frac{1}{\sqrt{2\mathrm{\&pi;}}}\exp (-\frac{1}{2}{t}^2)dt$ formula (5);

P_LR＝∫_{x,L(x)>τ}p(x；H_θ1) dx ═ a formula (6);

$L\left(X\right)=\frac{p(X;H_{{\mathrm{\&theta;}}_0})}{p(X;H_{\mathrm{\&theta;}1})}>\mathrm{\&tau;}$ formula (7);

(5) construction of a quantization function Q for three-level detection_c(r_k,i) And calculating a detection statistic T_c(R_i) Wherein

$Q_c\left(r_{k,i}\right)=\left\{\begin{array}{cc}1,& r_{k,i}\&GreaterEqual;c\\ 0,& -c<r_{k,i}<c\\ -1,& r_{k,i}\&le;-c\end{array}\right.$ formula (8);

$T_c\left(R_i\right)={\mathrm{\&Sigma;}}_{k=0}^{N_{t-1}}{Q}_c\left(r_{k,i}\right)$ formula (9);

wherein c is a preset constant;

(6) according to the observation sample sequence R in the step (2), the ith observation sample R in the kth period is used_k,iQuantized to x_k,iI.e. Q (r)_k,i)＝x_k,iRespectively constructing a quantized binary hypothesis test model and a signal detection judgment criterion; wherein, the quantized binary hypothesis test model is as follows:

$\left\{\begin{array}{c}{H}_0:R_i=N_i\\ H_1:R_i=w_i+N_i\end{array}\right.$ formula (10);

wherein, w_iIs a constant number, N_iIs a random noise vector, i is more than or equal to 0 and less than or equal to N-1;

the signal detection judgment criterion is as follows:

$\left\{\begin{array}{c}{H}_0:T\left(R_i\right)<{\mathrm{\&lambda;}}_{N_i,\mathrm{\&alpha;}}\\ H_1:T\left(R_i\right)>{\mathrm{\&lambda;}}_{N_i,\mathrm{\&alpha;}}\end{array}\right.$ formula (11);

wherein,in order to test the statistics of the test,is a decision threshold;

(7) quantization function Q based on three-level detection_c(r_k,i) Obtaining observation samples in the observation sample sequence R satisfies | R_k,iThe number of samples, | is more than or equal to c is N₁And calculating the number of samples N₁Corresponding optimal decision threshold α_opt：

${\mathrm{\&alpha;}}_{opt}={\&Integral;}_{{\mathrm{\&lambda;}}_{N_t,\mathrm{\&alpha;}}}^{\mathrm{\&infin;}}{f}_{T_c}^{N_1}\left(x\right)dx$ Formula (12);

wherein the number of [ c, ∞ ] observation samples is N_1pDetecting the statistic T_c(R_i)＝2N_1p-N₁；

(8) Comparing the resulting optimal decision threshold α_optAnd the detection statistic T_c(R_i) Recording the arrival time of the signal determined in the first passing step (6);

(9) taking the recorded arrival time of the first judged signal as the time t when the positioning detection node A receives the signal of the node O to be positioned_A(ii) a Repeating the steps (2) to (8) again to respectively obtain the time t when the positioning detection node B, C, D receives the signal of the node O to be positioned_B、t_CAnd t_D；

(10) Establishing an equation set related to the coordinates of the node to be positioned according to the receiving time corresponding to each positioning detection node, and calculating and acquiring a first coordinate value (x ') of the node to be positioned O according to the equation set'_o,y'_o,z'_o) Second coordinate value (x) "_o,y”_o,z”_o) And the third coordinate value (x'_o,y”'_o,z”'_o) And a fourth coordinate value (x') "_o,y””_o,z””_o)：

$\left\{\begin{array}{c}{d}_{AO}^2={({x^{\&prime;}}_o-x_A)}^2+{({y^{\&prime;}}_o-y_A)}^2+{({z^{\&prime;}}_o-z_A)}^2\\ d_{BO}^2={({x^{\&prime;}}_o-x_B)}^2+{({y^{\&prime;}}_o-y_B)}^2+{({z^{\&prime;}}_o-z_B)}^2\\ d_{CO}^2={({x^{\&prime;}}_o-x_C)}^2+{({y^{\&prime;}}_o-y_C)}^2+{({z^{\&prime;}}_o-z_C)}^2\end{array}\right.$ Formula (13);

$\left\{\begin{array}{c}{d}_{AO}^2={({x^{\&prime;\&prime;}}_o-x_A)}^2+{({y^{\&prime;\&prime;}}_o-y_A)}^2+{({z^{\&prime;\&prime;}}_o-z_A)}^2\\ d_{BO}^2={({x^{\&prime;\&prime;}}_o-x_B)}^2+{({y^{\&prime;\&prime;}}_o-y_B)}^2+{({z^{\&prime;\&prime;}}_o-z_B)}^2\\ d_{DO}^2={({x^{\&prime;\&prime;}}_o-x_D)}^2+{({y^{\&prime;\&prime;}}_o-y_D)}^2+{({z^{\&prime;\&prime;}}_o-z_D)}^2\end{array}\right.$ formula (14);

$\left\{\begin{array}{c}{d}_{AO}^2={({x^{\&prime;\&prime;\&prime;}}_o-x_A)}^2+{({y^{\&prime;\&prime;\&prime;}}_o-y_A)}^2+{({z^{\&prime;\&prime;\&prime;}}_o-z_A)}^2\\ d_{CO}^2={({x^{\&prime;\&prime;\&prime;}}_o-x_C)}^2+{({y^{\&prime;\&prime;\&prime;}}_o-y_C)}^2+{({z^{\&prime;\&prime;\&prime;}}_o-z_C)}^2\\ d_{DO}^2={({x^{\&prime;\&prime;\&prime;}}_o-x_D)}^2+{({y^{\&prime;\&prime;\&prime;}}_o-y_D)}^2+{({z^{\&prime;\&prime;\&prime;}}_o-z_D)}^2\end{array}\right.$ formula (15);

$\left\{\begin{array}{c}{d}_{BO}^2={({x^{\&prime;\&prime;\&prime;\&prime;}}_o-x_B)}^2+{({y^{\&prime;\&prime;\&prime;\&prime;}}_o-y_B)}^2+{({z^{\&prime;\&prime;\&prime;\&prime;}}_o-z_B)}^2\\ d_{CO}^2={({x^{\&prime;\&prime;\&prime;\&prime;}}_o-x_C)}^2+{({y^{\&prime;\&prime;\&prime;\&prime;}}_o-y_C)}^2+{({z^{\&prime;\&prime;\&prime;\&prime;}}_o-z_C)}^2\\ d_{DO}^2={({x^{\&prime;\&prime;\&prime;\&prime;}}_o-x_D)}^2+{({y^{\&prime;\&prime;\&prime;\&prime;}}_o-y_D)}^2+{({z^{\&prime;\&prime;\&prime;\&prime;}}_o-z_D)}^2\end{array}\right.$ formula (16);

$\left\{\begin{array}{c}{d}_{AO}=c\&CenterDot;t_A\\ d_{BO}=c\&CenterDot;t_B\\ d_{CO}=c\&CenterDot;t_C\\ d_{DO}=c\&CenterDot;t_D\end{array}\right.$ formula (17);

wherein d is_AO、d_BO、d_COAnd d_DOThe distances from the positioning detection nodes A, B, C and D to the node O to be positioned respectively, and c represents the propagation speed of the light;

(11) according to the acquired first coordinate value (x ') of the node O to be positioned'_o,y'_o,z'_o) Second coordinate value (x) "_o,y”_o,z”_o) And the third coordinate value (x'_o,y”'_o,z”'_o) And a fourth coordinate value (x') "_o,y””_o,z””_o) Calculating the actual coordinate (x) of the node O to be positioned_o,y_o,z_o)：

$\left\{\begin{array}{c}{x}_o=\frac{\frac{{x^{\&prime;}}_o}{d_{AO}^2+d_{BO}^2+d_{CO}^2}+\frac{{x^{\&prime;\&prime;}}_o}{d_{AO}^2+d_{BO}^2+d_{DO}^2}+\frac{{x^{\&prime;\&prime;\&prime;}}_o}{d_{AO}^2+d_{CO}^2+d_{DO}^2}+\frac{{x^{\&prime;\&prime;\&prime;\&prime;}}_o}{d_{BO}^2+d_{CO}^2+d_{DO}^2}}{\frac{1}{d_{AO}^2+d_{BO}^2+d_{CO}^2}+\frac{1}{d_{AO}^2+d_{BO}^2+d_{DO}^2}+\frac{1}{d_{AO}^2+d_{CO}^2+d_{DO}^2}+\frac{1}{d_{BO}^2+d_{CO}^2+d_{DO}^2}}\\ y_o=\frac{\frac{{y^{\&prime;}}_o}{d_{AO}^2+d_{BO}^2+d_{CO}^2}+\frac{{y^{\&prime;\&prime;}}_o}{d_{AO}^2+d_{BO}^2+d_{DO}^2}+\frac{{y^{\&prime;\&prime;\&prime;}}_o}{d_{AO}^2+d_{CO}^2+d_{DO}^2}+\frac{{y^{\&prime;\&prime;\&prime;\&prime;}}_o}{d_{BO}^2+d_{CO}^2+d_{DO}^2}}{\frac{1}{d_{AO}^2+d_{BO}^2+d_{CO}^2}+\frac{1}{d_{AO}^2+d_{BO}^2+d_{DO}^2}+\frac{1}{d_{AO}^2+d_{CO}^2+d_{DO}^2}+\frac{1}{d_{BO}^2+d_{CO}^2+d_{DO}^2}}\\ z_o=\frac{\frac{{z^{\&prime;}}_o}{d_{AO}^2+d_{BO}^2+d_{CO}^2}+\frac{{z^{\&prime;\&prime;}}_o}{d_{AO}^2+d_{BO}^2+d_{DO}^2}+\frac{{z^{\&prime;\&prime;\&prime;}}_o}{d_{AO}^2+d_{CO}^2+d_{DO}^2}+\frac{{z^{\&prime;\&prime;\&prime;\&prime;}}_o}{d_{BO}^2+d_{CO}^2+d_{DO}^2}}{\frac{1}{d_{AO}^2+d_{BO}^2+d_{CO}^2}+\frac{1}{d_{AO}^2+d_{BO}^2+d_{DO}^2}+\frac{1}{d_{AO}^2+d_{CO}^2+d_{DO}^2}+\frac{1}{d_{BO}^2+d_{CO}^2+d_{DO}^2}}\end{array}\right.$ Formula (18).