CN105807257B - A kind of direct localization method of the distributed self-adaption with noise constraints - Google Patents

Abstract

The invention belongs to field of signal processing, distributed self-adaption localization method in a kind of passive location system based on the time difference is provided, to solve the contradiction for having between distributed self-adaption convergence speed of the algorithm and steady-state behaviour, the performance of the direct location algorithm of distributed self-adaption is further improved.First, each receiver obtains the discrete reception signal of base band by gathered data, then carries out noise power estimation, carries out first time data exchange between neighbours' receiver afterwards, then sets iteration update core control parameter β_k, then carry out intermediate estimate ψ_k,nAdaptive computing carries out second of data exchange between neighbours' receiver, the estimate p of last iterative estimate transmitter site again afterwards_k,n；Until reaching stable state, transmitter site estimate is exported.Present invention introduces noise informations, are obviously improved positioning performance and tracking performance；The contradiction of positioning convergence rate and steady-state behaviour can be overcome.

Description

A Distributed Adaptive Direct Localization Method with Noise Constraint

technical field

The invention belongs to the field of signal processing, in particular to a distributed self-adaptive positioning method in a time difference-based passive positioning system.

Background technique

At present, the time difference-based passive positioning technology can be divided into two categories according to whether it needs to explicitly calculate the time difference value: the classic two-step positioning method and the emerging direct positioning method. The classic two-step positioning method first estimates the time difference value through the received signal in the first step, and then uses the estimated time difference value to solve the position in the second step; while the emerging direct positioning algorithm does not need to explicitly calculate the time difference Instead, the received signal is directly used to estimate the position of the target. In the case of low signal-to-noise ratio of the received signal, the positioning accuracy of the direct positioning method is higher; the direct positioning method can be divided into two types: batch processing method and adaptive method. The batch processing method requires a two-dimensional or three-dimensional grid search for the positioning area, which has a large amount of calculation, poor real-time performance, and no ability to track the target; although the positioning accuracy of the adaptive method is slightly lower than that of the batch processing method, However, the calculation amount of this method is much less than that of the batch method, and it has the ability of target tracking, which is very suitable for real-time processing and implementation.

The adaptive direct positioning algorithm is divided into centralized and distributed. Based on the algorithm of the centralized architecture, the signals received by each receiver in the network are transmitted to the receiver of the fusion center, and the positioning operation is performed on the specific receiver, that is, the centralized processing method; such as the literature "Adaptive direct position determination of emitters based on time differences of arrival" (ChinaSIP'13, 2013, S.Zhong, W.Xia, and Z.He) is the method adopted. However, the centralized processing method has poor scalability, multi-hop communication problems, high requirements for network communication bandwidth, and poor robustness due to the existence of fusion center receivers and reference signals; at the same time, because all position estimation operations All are performed at the fusion center receiver, so the calculation burden and energy consumption of the fusion center receiver are very large. In order to overcome the above problems, a positioning algorithm based on a distributed architecture is proposed, such as the document "Distributed adaptive direct position determination of emitters in sensornetworks" (Signal Processing, 2016, Wei Xia and Wei Liu), (Xia Wei, Liu Wei, Zhu Lingfeng, A distributed adaptive direct positioning method based on time difference; the patent with the publication number CN104537257A, the publication date is 2015.4.22, and the invention name is "a distributed adaptive direct positioning method under the color receiving signal"; the publication number is CN105137392A, the publication date is shown in the invention patent of 2015.12.9. In the distributed method, the status of each receiver in the network is the same, and it has better scalability, and there is no reference signal and fusion center receiver Problem; each receiver only communicates with its neighboring receivers, so that energy consumption and communication costs are in a controllable range. At each moment, first of all, each receiver uses the original information received by all receivers in its neighborhood to convert the existing The estimated value of the position is updated to a local intermediate estimated value; then, each receiver weights and combines the intermediate estimated values of all receivers in its neighborhood to obtain a new estimated value of position; in the second step, each receiver obtains The new position estimates of all contain the intermediate value information of its neighbor receivers, and its neighbor receivers contain the information of its neighbor receivers, and then complete the diffusion of information in the entire network; thus the obtained position estimate It is globally optimal rather than locally optimal. In order to further improve the performance of the distributed self-adaptive direct positioning algorithm, obtain fast convergence speed while obtaining good steady-state performance, in the present invention we have introduced noise constraints, and finally A distributed adaptive direct positioning method with variable step size is obtained.

Contents of the invention

The purpose of the present invention is to rationally use the noise information in the received signal, solve the contradiction between the convergence speed and the steady-state performance of the existing distributed adaptive algorithm, and provide a distributed adaptive direct positioning method with noise constraints; further Improving the performance of distributed adaptive direct localization algorithms.

The technical solution of the present invention: a distributed adaptive direct positioning method with noise constraints, comprising the following steps:

Step 1: collect data, each receiver receives the signal transmitted by the transmitter at the same time, demodulates and samples the signal, and obtains the discrete received signal of the baseband, specifically:

Assuming there are K space-separated receivers, the signal x _k (t) received by each receiver is expressed as:

x _k (t)=s(t-τ _k )+v _k (t),k=1,2,…,K

Among them, s(t) represents the baseband transmission signal of the transmitter, v _k (t) represents the spatially independent zero-mean additive white Gaussian noise, τ _k represents the transmission delay between the transmission signal from the transmitter to the receiver, and represents for:

τ _k ＝||p ^o -p _k ||/c,k＝1,2,…K

Among them, p ^o represents the position vector of the transmitter, p _k represents the position vector of the receiver k, and the constant c represents the propagation speed of the electromagnetic wave signal;

Each received signal is sampled with a sampling period T _s , so that The discrete received signal can be obtained:

x _k [n]=s(nT _s -τ _k )+v _k (nT _s ),k=1,2,…K

Step 2: Noise power estimation. Each receiver uses the known conditions and the signals received by it to estimate the noise power in the signal received by each receiver, using express;

Step 3: For the first data exchange, each receiver transmits the discrete baseband signal received by itself and the estimated noise power value to the neighbor receiver, that is, the directly connected receiver, and at the same time receives the corresponding information from the neighbor receiver ( The discrete baseband signal and noise power value received by itself);

Step 4: Iteratively update the core control parameters β _k , k=1, 2,..., K; β _k is the core parameter on receiver k, which controls the step size change of the iterative update of the estimated position value on receiver k; Receiver k uses the noise-related information in its neighborhood, which refers to the set of all its neighbor receivers including the receiver itself, to iteratively update the core control parameters β _k according to the following formula

β _k,n =(1-α)β _k,n-1 +α/2(J _k (p _k,n-1 )-J _k,min ),k=1,2,…K

Among them, β _k,n and β _k,n-1 represent the values of β _k at time n and time n-1 respectively, the initial value β _k,0 = β _init , and the preset control factor α controls the iteration of β _k convergence speed;

Among them, J _k (p) represents the local cost function on the kth receiver, which is defined as follows:

in, Indicates the set of all neighbor receivers except receiver k itself, and the non-negative weighting coefficient a _ik satisfies the following conditions,

when , a _ik ＝0

And e _i,k [n] is called the error function, which is the difference between the signal _xi [n] and the output result of the delay filter. The length of the delay filter is 2M+1, expressed as:

Among them, the function sinc(x)=sin(πx)/πx, is the estimated value of the arrival time difference τ _k,i , τ _k,i represents the difference in propagation delay of the transmitted signal from the transmitter to the kth receiver and the ith receiver, defined as

The minimum value of the local cost function J _k,min on receiver k can be calculated by using the estimated noise power values of receiver k and its neighbor receivers:

Step 5: Detect whether there is a sudden change in the position of the transmitter, and decide whether to reset β _k , k=1, 2,...K or not; use its local cost function on the receiver k to construct the decision statistic as follows

Set the empirical judgment threshold λ _k according to the specific working environment. If Y _k (n)>λ _k , it is considered that the receiver k detects a sudden change in the position of the transmitter; all receivers in the network perform similar detection operations; as long as there is any receiving The detection result of the receiver is that the position of the transmitter changes suddenly, we will reset the β on all receivers, that is, β _k,n = β _init , k=1,2,...K, where β _init is the preset initial value of β;

Step 6: Adaptive operation, receiver k runs the following iterative formula at time n:

Among them, p _k,n-1 represents the estimated value of the transmitter position obtained by receiver k at the n-1 iteration, the initial value p _k,0 = p _init , ψ _k,n is the receiver k at the nth iteration The intermediate estimated value obtained in the iteration; μ _k is the basic step size of the position iteration, and the preset adjustment factor γ is used to determine the influence of the change of β _k on the iterative step size of the position estimation; the last item is approximated by the instantaneous gradient value, as follows:

in,

The first term on the right side of the equal sign in the above formula expands to

where the function f( ) is defined as follows

The second item is

Step 7: For the second data exchange, each receiver transmits the intermediate estimated value ψ _k,n calculated in the previous step to its neighbor receivers, and at the same time receives the results from the neighbor receivers;

Step 8: Combine, each receiver according to the formula

Calculate the estimated value p _k,n of the transmitter position after the nth iteration; where, Represents the set of all neighbor receivers including receiver k including itself, b _lk is a preset non-negative weighting coefficient, and satisfies the following conditions:

when , b _lk ＝0

Step 9: When p _{k, n} the difference between the iterative estimated values of Q consecutive times are less than the set threshold δ, that is:

||p _k,n -p _k,n-1 ||≤δ

Then the position estimate of the transmitter is considered to be obtained.

The working principle of the present invention

Taking a two-dimensional plane as an example, both the transmitter position vector and the receiver position vector are two-dimensional vectors. The distance from the transmitter to each receiver is different, so each receiver receives the same signal with different time delays. Here, it is assumed that the noises at different receivers are independent of each other and are all additive white Gaussian noise; The received signal is demodulated and sampled, and finally a discrete baseband signal is obtained, as follows:

x _k [n]=s(nT _s -τ _k )+v _k (nT _s ),k=1,2,…K

where T _s is the sampling period, τ _k is the time delay of the transmitted signal from the transmitter to the kth receiver; at the same time, each receiver estimates the noise power in its received signal, using express;

Design a delay filter based on the sinc function, whose length is selected as 2M+1, and the choice of M should ensure that the truncation error basically does not affect the positioning accuracy; taking receiver k and its neighbor receiver i as an example, define the following error function

where the estimated time difference of arrival can be expressed as follows

where p _k,n represent the transmitter position vector estimated by receiver k in the nth iteration, p _k and p _i represent the position vectors of receiver k and receiver i respectively, and the constant c represents the electromagnetic wave propagation velocity;

When the transmitter position estimate p _k,n gradually converges to the real transmitter position p ^o , the error function e _i,k [n] gradually tends to zero. And because for all neighbor receivers of receiver k The above error function can be constructed, so its weighted summation can define a local cost function of the following form

There are K receivers in total. In order to obtain the global optimal solution, the following global cost function is defined

However, this global cost function is not suitable for distributed processing. Through some approximation and simplification methods, such as second-order Taylor series expansion, the following modified cost function can be obtained

Each receiver has estimated the noise power in the received signal before, in order to improve the performance of the algorithm, make full use of relevant information, introduce noise constraints on the basis of the original cost function, and obtain the noise constraint cost function:

where the local cost function minimum is

The noise-constrained cost function can be solved in a distributed adaptive manner on each receiver, and because it makes full use of noise-related information, the positioning performance is significantly improved. At the same time, in the present invention, we add a detection mechanism for sudden changes in the position of the transmitter, so that the distributed adaptive direct positioning method with noise constraints has better tracking performance. This distributed adaptive direct positioning method with noise constraints is essentially a variable step size method, which solves the contradiction between positioning convergence speed and steady-state performance to a certain extent.

Description of drawings

FIG. 1 is a schematic diagram of the workflow of the Noise Constrained Distributed Adaptive Direct Positioning (NCD-ADPD) method of the present invention.

Fig. 2 is a schematic diagram of the signal model and the basic concept of the present invention.

Fig. 3 is an exemplary diagram of the network topology structure of the transmitter and receiver of the implementation example of the present invention.

Fig. 4 is the signal-to-noise ratio at each receiver in the network of the implementation example of the present invention, the upper figure corresponds to Figs. 5-7, and the lower figure corresponds to Fig. 8.

Fig. 5 is a comparison diagram of the core parameter β at each receiver and the final positioning performance of the distributed adaptive direct positioning method with noise constraints and the distributed adaptive direct positioning method (D-ADPD) without noise constraints of the present invention.

Fig. 6 is a comparison diagram of the convergence speed of the method with noise constraints and the method without noise constraints under different parameter settings of the present invention.

Fig. 7 is a comparison chart of the learning curves of the core parameter β _k under different parameter settings of the method with noise constraints in the present invention.

Fig. 8 is a comparison chart of tracking performance between the method with noise constraint and the method without noise constraint in the present invention when the location of the transmitter changes suddenly.

Detailed ways

The present invention will be described in further detail below in conjunction with the accompanying drawings and implementation examples. A distributed adaptive direct positioning method with noise constraints, including the following steps:

1. Initialization: each receiver prepares for initialization, and sets the initial value of position iteration p _k,0 = p _init ,k=1,2,...K, where p _init =[6066,4955], and the core control parameter β The initial value of _k β _k,0 = β _init ,k=1,2,...K, where β _init =18 or 6, set the location iteration step size of each receiver μ _k =2×10 ^-4 or 1.5×10 ^{- 4} and the control factor α=0.001 or 0.002 or 0.0006, the real value of the transmitter position p ^o =[6000,5000], the adjustment factor γ=0.2 or 0.3 or 0.9;

2. Collect data: each receiver starts to receive the signal transmitted by the transmitter at the same time, demodulates and samples the signal, and obtains the discrete received signal of the baseband;

3. Estimation of noise power: each receiver estimates the power of noise in the received signal;

4. The first data exchange: each receiver transmits the discrete baseband signal received by itself and the estimated noise power value to the neighbor receiver, and at the same time receives the corresponding information from the neighbor receiver;

5. Iteratively update the core parameter β _k : each receiver uses the received signal in its neighborhood and the estimated noise power information to iteratively update β _k ;

6. Transmitter position mutation detection: Each transmitter constructs a decision statistic based on the information in its neighborhood to detect whether there is a sudden change in the transmitter’s position. If there is a sudden change, the core parameter β _k is reset, otherwise, no processing is done;

7. Adaptive operation: Each receiver uses the received signal in the neighborhood and the new β _k obtained in the previous steps to update the position estimate obtained from the previous iteration to a new intermediate estimate

8. The second data exchange: each receiver transmits the intermediate estimated value calculated in the previous step to its neighbor receiver, and receives the result from the neighbor receiver at the same time;

9. Combination: Each receiver weights and combines all intermediate estimated values in its neighborhood to obtain a new estimated value of the transmitter position vector for this iteration;

10. Output result: According to the preset threshold, it is judged whether the positioning iterative operation enters a steady state. If it does not reach a steady state, repeat steps 2-9 until it reaches a steady state, and output the estimated value of the transmitter position.

Figure 4 shows the two network SNR conditions used in this simulation experiment, the low SNR condition shown in the upper figure corresponds to Figure 5-7; the high SNR condition shown in the lower figure corresponds to the 8. In order to obtain better transmitter position mutation detection results.

As shown in Figure 5, even if the noise power in the received signal of each receiver is set differently, no matter the method with noise constraint or the method without noise constraint, the positioning performance of different nodes with the same method is basically the same, and the convergence process of the core parameter β _k is also basically the same . The parameter selection makes the method with noise constraint and the method without noise constraint have similar initial convergence speed. It can be seen that the steady-state performance of the method with noise constraint is obviously better than that of the method without noise constraint.

Figures 6 and 7 show that when the method with noise constraints has the same steady-state performance as the method without noise constraints, the convergence speed of the method with noise constraints is much faster than the method without noise constraints; and lists, different parameter settings In this case, the learning curve of the core parameter β _k and its influence on the positioning convergence curve; at the beginning of the iteration, the estimated value is far away from the real value, and a large β corresponds to a large iteration step size, which in turn corresponds to a fast convergence speed; and when When the convergence process tends to a steady state, a small β corresponds to a small step size, and then an ideal steady-state performance is obtained.

It can be seen from Figure 8 that the tracking performance of the noise-constrained distributed adaptive direct positioning method with a transmitter position mutation detection mechanism is better than that of the method without noise constraints.

The above is only a specific embodiment of the present invention. Any feature disclosed in this specification, unless specifically stated, can be replaced by other equivalent or alternative features with similar purposes; all the disclosed features, or All method or process steps may be combined in any way, except for mutually exclusive features and/or steps.

Claims (3)

1. A distributed adaptive direct positioning method with noise constraints, comprising the following steps: Step 1: collect data, each receiver receives the signal transmitted by the transmitter at the same time, and demodulates and samples the received signal to obtain a discrete baseband received signal; Step 2: Noise power estimation, each receiver estimates the noise power in its received signal k=1,2,...K, K represents the number of receivers; Step 3: For the first data exchange, neighbor receivers exchange their own discrete baseband received signals and noise power; Step 4: Set the core control parameters β _k of receiver k, k=1,2,...,K; and iteratively update according to the following formula: β _k,n =(1-α)β _k,n-1 +α/2(J _k (p _k,n-1 )-J _k,min ),k=1,2,…K Among them, β _k,n and β _k,n-1 represent the value of β _k at time n and time n-1 respectively, the initial value β _k,0 = β _init , α is the preset control factor; J _k ( p) represents the local cost function on receiver k, and J _k,min is the minimum value of the local cost function on receiver k; Step 5: Adaptive operation, receiver k runs the following iterative formula at time n: <mrow><msub><mi>&amp;psi;</mi><mrow><mi>k</mi><mo>,</mo><mi>n</mi></mrow></mrow></msub><mo>=</mo><msub><mi>p</mi><mrow><mi>k</mi><mo>,</mo><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msub><mo>-</mo><msub><mi>&amp;mu;</mi><mi>k</mi></msub><mrow><mo>(</mo><mn>1</mn><mo>+</mo><msub><mi>&amp;gamma;&amp;beta;</mi><mrow><mi>k</mi><mo>,</mo><mi>n</mi></mrow></msub><mo>)</mo></mrow><msup><mi>c</mi><mn>2</mn></msup><msubsup><mi>T</mi><mi>s</mi><mn>2</mn></msubsup><mfrac><mrow><mo>&amp;part;</mo><msub><mi>J</mi><mi>k</mi></msub><mrow><mo>(</mo><mi>p</mi><mo>)</mo></mrow></mrow><mrow><mo>&amp;part;</mo><mi>p</mi></mrow></mfrac><msub><mo>|</mo><mrow><mi>p</mi><mo>=</mo><msub><mi>p</mi><mrow><mi>k</mi><mo>,</mo><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msub></mrow></msub><mo>,</mo><mi>k</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>...</mo><mo>,</mo><mi>K</mi></mrow> Among them, p _k,n-1 represents the estimated value of the transmitter position obtained by receiver k at the n-1 iteration, the initial value p _k,0 = p _init , ψ _k , _n is the receiver k at the nth iteration The intermediate estimated value obtained in the iteration; μ _k is the basic step size of the iteration at the preset position, γ is the preset adjustment factor, the constant c represents the propagation speed of the electromagnetic wave signal, and T _s is the sampling period of the received signal; Step 6: The second data exchange, neighbor receivers exchange their intermediate estimated value ψ _k,n ; Step 7: Combining, calculate the estimate p _k,n of the transmitter position after the nth iteration: in, Represents the set of all neighbor receivers including receiver k including itself, b _lk is a preset non-negative weighting coefficient, and satisfies the following conditions: Step 8: When the difference between the iterative estimated values of p _{k, n} consecutive Q times is less than the set threshold δ, that is: ||p _k,n -p _k,n-1 ||≤δ A decision is made to obtain an estimate of the position of the transmitter. 2. by the distributed self-adaptive direct positioning method of band noise constraint described in claim 1, it is characterized in that, the specific processing procedure of the received signal of described step 1 is: Assuming there are K space-separated receivers, the signal x _k (t) received by each receiver is expressed as: x _k (t)=s(t-τ _k )+v _k (t),k=1,2,…,K Among them, s(t) represents the baseband transmission signal of the transmitter, v _k (t) represents the spatially independent zero-mean additive white Gaussian noise, τ _k represents the transmission delay between the transmission signal from the transmitter to the receiver, and represents for: τ _k ＝||p ^o -p _k ||/c,k＝1,2,…K Among them, p ^o represents the position vector of the transmitter, p _k represents the position vector of the receiver k, and the constant c represents the propagation speed of the electromagnetic wave signal; Each received signal is sampled with a sampling period T _s , so that The discrete received signal can be obtained: x _k [n]=s(nT _s −τ _k )+v _k (nT _s ), k=1, 2, . . . K. 3. according to the distributed self-adaptive direct positioning method of the arbitrary described band noise constraint of claim 1～2, it is characterized in that, the local cost function minimum value J _{k on the receiver k in the described step 4,min} is according to the receiver The noise power values of k and its neighbor receivers are calculated as: in, Indicates the set of all neighbor receivers except receiver k itself, a _ik is a preset non-negative weighting coefficient, and satisfies the following conditions: when , a _ik =0.