A non-line-of-sight EKF target localization method based on residual discrimination

Abstract

The application discloses a non-line-of-sight EKF target positioning method based on residual discrimination, solves the problems of current high-power-consumption high-complexity positioning algorithms and low positioning accuracy, and the non-line-of-sight EKF target positioning method based on residual discrimination only needs time of arrival (TOA) and angle of arrival (AOA) information to complete the identification of line-of-sight (LOS) and non-line-of-sight (NLOS) and positioning in the non-line-of-sight (NLOS) environment, greatly reduces the complexity of the algorithm, and realizes low power consumption and low complexity; since the Kalman filtering algorithm is used for predicting, correcting and updating the position information of a mobile target, the extended Kalman filtering is applied to more correctly describe the system model, and therefore the accuracy of the mobile target positioning can be further improved.

Description

Technical Field

[0001] This invention belongs to the field of communication technology, and specifically relates to a non-line-of-sight EKF target localization method based on residual discrimination. Background Technology

[0002] Research on wireless positioning technology aims to improve positioning accuracy in complex wireless environments by utilizing the available resources of different communication standards. Non-line-of-sight (NLOS) error is a significant factor affecting positioning accuracy. When operating in an NLOS environment, electromagnetic signals reach the tag node through scattering or diffraction from the positioning anchor node, resulting in NLOS error.

[0003] Methods for NLOS signal processing in positioning problems can be mainly divided into two categories: one is based on the characteristics of the received signal. Since distance measurement in a LOS (Line-Of-Sight) environment follows a Gaussian distribution, it is possible to determine whether NLOS propagation is occurring by checking whether multiple measurements follow a Gaussian distribution, thus enabling analysis and processing. The other is based on residual information. This method estimates the target node's location using the combined LOS and NLOS measurements, and then uses this estimated location for NLOS identification. The paper "An Improved Kalman Filter Indoor Positioning Algorithm Based on CHAN" proposes an improved Kalman filter positioning algorithm based on CHAN using the second method. It constructs a positioning solution equation system using the ranging results from five or more base stations and selects the CHAN algorithm, which is sensitive to positioning errors in non-line-of-sight situations, for solving the equations. The solution results are then compared with the locations of each base station using residual processing, and different confidence regions are defined. Since distance measurement is significantly affected by NLOS, while angle measurement is generally less affected, further measures are taken to reduce the influence of NLOS and improve indoor positioning accuracy. Summary of the Invention

[0004] This invention provides a non-line-of-sight (NLOS) target localization method based on residual discrimination. It is an improved extended Kalman filter (EKF) tracking algorithm based on the TOA-AOA method. By introducing residuals to determine the severity of the non-line-of-sight (NLOS) impact on the current positioning point, the method of dividing confidence intervals is used to process the Kalman gain of different regions affected by NLOS differently. Finally, the time of arrival (TOA) and angle of arrival (AOA) are used as two-dimensional observations of the improved extended Kalman filter (EKF) for localization. This method achieves NLOS elimination and tracking of moving targets, while also achieving low complexity and high accuracy.

[0005] This invention provides a non-line-of-sight EKF target localization method based on residual discrimination, the method comprising the following steps:

[0006] Step 1: Construct a 2D EKF positioning model based on TOA and AOA for preliminary positioning; according to the target positioning model of wireless sensor networks in non-line-of-sight environments, the base station records the reception time and angle of the source signal, and calculates the distance r. k By using angle α, the position information of the moving target can be obtained;

[0007] Step 2: Identify line-of-sight (LOS) and non-line-of-sight (NLOS) base stations for each base station; calculate the target node position based on the time of arrival (TOA) and angle of arrival (AOA) measurements of each node, and compare the positioning error with the set threshold value to identify LOS and NLOS base stations.

[0008] Step 3: Construct residuals and divide confidence intervals; determine Kalman gain and update Kalman gain according to the line-of-sight occlusion of the positioning environment;

[0009] Step 4: Correct the EKF model and update the state and prediction; After adjusting the EKF gain, substitute the original Time of Arrival (TOA) and Angle of Arrival (AOA) algorithm positioning results at the current measurement time into different regions for extended Kalman filtering. Use extended Kalman filtering to predict, correct and update the state variables of the moving target (x,y) and output the final moving target position estimation result (x,y).

[0010] Preferably, the location information of the moving target in step 1 is the coordinates of the base station at time k as the moving target moves on a two-dimensional plane (x, k). k ,y k The velocities in the x and y directions are v0 and v0, x and v y The state of the target is (x, v) x ,y,v y Then, the arrival time TOA and arrival angle AOA at time k are:

[0011]

[0012] Where (x, y) represents the position coordinates of the signal source in the two-dimensional coordinate system, denoted as [x, y]. T k is the number of base station nodes, and its value is a positive integer ≥ 3; r k Let be the distance from the k-th base station to the moving target;

[0013] If the target moves within the monitoring range of the base station, then the observations of the time of arrival (TOA) and angle of arrival (AOA) under the NLOS environment at time k using a two-dimensional Kalman filter are expressed as follows:

[0014]

[0015] Among them, Vk It represents the observation noise of the system; NLOS k This represents non-line-of-sight error, and is generally expressed using a uniform distribution or an exponential distribution.

[0016] The probability density distribution function of the non-line-of-sight (NLOS) error model is:

[0017]

[0018] The non-line-of-sight (NLOS) error follows the mean μ and variance σ. NLOS Gaussian distribution, μ and σ NLOS It is a non-line-of-sight localization algorithm based on Gaussian mixture model that adjusts parameter values.

[0019] Preferably, step 2, which involves identifying line-of-sight (LOS) and non-line-of-sight (NLOS) base stations, includes the following steps:

[0020] Step 2.1 Take two UWB nodes, located at points A and B respectively, and move the target point C to the location to be determined;

[0021] Let r1, r2, and r3 be the distances to AC, BC, and AB, respectively. Let θ1 and θ2 be the angles to ∠CAB and ∠CBA, respectively. Record the distances AC1 and AC2 using the arrival time TOA as r1′ and r2′, respectively. Record the angles obtained using the arrival angle AOA as θ1′ and θ2′, respectively. Then, the coordinates of C1 and C2 can be obtained based on the angle and distance information:

[0022]

[0023]

[0024] Where r1′=r1+Δr1, r2′=r2+Δr2 are the errors in the TOA distance measurement.

[0025] θ1′=θ1+Δθ1,θ2′=θ2+Δθ2,Δr1,Δr2,Δθ1,Δθ2 are the errors in the measurement of the angle of arrival (AOA);

[0026] Step 2.2 Let δ1 = |x1 - x2|, δ2 = |y1 - y2|. Substituting the estimated coordinates C1 and C2 from Step 2.1 into the above equation, we can obtain...

[0027] δ1=|r3-r2′cosθ2′-r1′cosθ1′|

[0028] =|r3-(r2+Δr2)cos(θ2+Δθ2)-(r1+Δr1)cos(θ1+Δθ1)|

[0029] =|r3-r2 cosθ2 cosΔθ2+Δr2 cosθ2 cosΔθ2-r2 sinθ2 sinΔθ2-Δr2 sinθ2 sinΔθ2-r1 cosθ1 cosΔθ1+Δr1 cosθ1 cosΔθ1-r1 sinθ1 sinΔθ1-Δr1 sinθ1 sinΔθ1|

[0030] The error of the positioning system in the line-of-sight (LOS) case is caused only by Gaussian noise. Δr1, Δr2, Δθ1, Δθ2 are very small, so we have cosΔθ1≈1, cosΔθ2≈1, sinΔθ1≈Δθ1, sinΔθ2≈Δθ2.

[0031] Ignoring the quadratic term of the Gaussian error, we get:

[0032] δ1≈|r3-r2 cosθ2-r1 cosθ1+Δr2 cosθ2+Δr1 cosθ1-r1Δθ1 sinθ1-r2Δθ2 sinθ2|

[0033] =|Δr1 cosθ1+Δr2 cosθ2-r1Δθ1 sinθ1-r2Δθ2 sinθ2|

[0034] =δ1′

[0035] Similarly, we can conclude that:

[0036] δ2≈|Δr1 sinθ1+Δr2 sinθ2-r1Δθ1 cosθ1-r2Δθ2 cosθ2|

[0037] =δ1′

[0038] The derivation yields δ1≈δ1′, δ2≈δ2′;

[0039] Step 2.3 Let TH1 = λδ1′, TH2 = λδ2′, where λ is an undetermined parameter. Since Δr1, Δr2, Δθ1, and Δθ2 are unknown, they need to be selected based on the actual situation; r1, r2, θ1, and θ2 can be approximated by measured values.

[0040] TH1=λδ1′=λ|σ r cosθ1′+σ r cosθ2′-r1σ θ sinθ1′-r2σ θ sinθ2′|

[0041] TH2=λδ2′=λ|σ r sinθ1′+σ r sinθ2′-r1σ θcosθ1′-r2σ θ cosθ2′|

[0042] Where, σ r ,σ θ These are the standard distance measurement error and the angle measurement error, respectively, depending on the current positioning scenario;

[0043] Step 2.4 Divide the base stations according to the NLOS determination strategy:

[0044]

[0045] Here, TH1 represents the threshold for determining LOS base stations, and TH2 represents the threshold for NLOS base stations.

[0046] Preferably, the structural residual in step 3 includes the following steps:

[0047] Step 3.1 defines the residual as:

[0048]

[0049] Among them, D i Represents the i-th base station BS i Using the localization results from line-of-sight (LOS) and non-line-of-sight (NLOS) algorithms, D k This represents the positioning results of all base stations identified as line-of-sight (LOS) base stations at time k;

[0050] The smallest residual value is selected as the criterion for determining the confidence interval of positioning performance;

[0051] Let the minimum residual value of r at this moment be:

[0052] β=min Res(X r )

[0053] Step 3.2 The confidence factor γ is a regional discrimination index used to classify the degree to which the current positioning result is affected by non-line-of-sight (NLOS). The confidence factor for the current measurement time k is:

[0054]

[0055] Preferably, in step 3, determining the Kalman gain involves dividing the localization area into n regions, where n ≥ 3; and processing the Kalman gain of each of the n regions as follows:

[0056]

[0057] In the formula, μ1 and μ2 can be selected according to different positioning environments, and different Kalman filter gains K1 are selected according to different regions. When 0 < γ < μ1, it is a reliable region, and the positioning result is less affected by non-line-of-sight (NLOS), so the current extended Kalman filter gain is not changed. When μ1 < γ < μ2, it is a fuzzy region, and the impact of NLOS occlusion on the algorithm cannot be ignored, but it is within an acceptable range. At this time, it is necessary to adjust the relationship between the measured value and the predicted value. In the formula, 0 < α < 1 is used to reduce the impact of NLOS on the positioning result. When γ > μ2, the positioning result is severely affected by NLOS interference and is an unreliable region. In this case, the current result is discarded.

[0058] Preferably, the unreliable region is reclassified and its extended Kalman gain is corrected to utilize more data in cases where NLOS is very severe. The measurement standard deviation is compared with a threshold to determine whether the deviation of the current measurement value is within the tolerable error range. The data classified into the unreliable region is processed again. If the measurement standard deviation is greater than the threshold, it indicates that the current measurement value is severely affected by NLOS and is discarded. Otherwise, the positioning result at the current moment is classified into the fuzzy region.

[0059]

[0060] Where K2 is the updated extended Kalman gain, and σ is the measurement standard deviation.

[0061] Preferably, the prediction, correction, and update of the state variables of the moving target (x, y) using extended Kalman filtering in step 4 refers to extended Kalman filtering being an estimation method, where the target's state equation and observation equation are:

[0062] X k+1 =f[k,X k ]+W k

[0063] Z k =h[k,X k ]+V k

[0064] Where, f[k,X k ] and h[k,X k [W] represents the nonlinear state function and observation function containing information at time k, respectively. k and V k Let W(k) be the process noise and observation noise of the system; the mean of the process noise W(k) is 0, and the variance is Q = diag[w, w], where w is 1e-3.

[0065] The recurrence relation for the extended Kalman filter is as follows:

[0066]

[0067]

[0068]

[0069]

[0070]

[0071] In the above formula, the initial values ​​of the filter and the filter covariance matrix are respectively:

[0072] X(0)=E[X(0)],P(0)=var[X(0)]

[0073] Compared to the linear Kalman filter equation, the state transition Φ(k+1|k) and the observation matrix H(k+1) are replaced by Jacobian matrices of f[*] and h[*].

[0074] Based on the observation equation, the expression for the observation matrix H can be derived as follows:

[0075]

[0076] Step 4, which modifies the EKF model and updates the state and prediction, further includes setting the EKF parameters to the following if the moving target is moving at a constant velocity in a two-dimensional plane:

[0077]

[0078] X k =[xv x yv y ] T

[0079] If the moving target undergoes uniformly accelerated motion in a two-dimensional plane, then:

[0080]

[0081] X k =[xv x a x yv y a y ] T .

[0082] Preferably, step 4 involves using an extended Kalman filter to predict, correct, and update the state variables of the moving target (x, y).

[0083] At this point, the state and covariance formulas in the original Kalman filter (EKF) process are updated as follows:

[0084]

[0085]

[0086] in, This represents the estimation result of the state variables at time K. This is the estimate at time K+1, and this is the updated estimate. Let K be the prediction error covariance matrix. This is the updated estimate.

[0087] Preferably, the state vector in the update phase This is the final state vector, which includes the predicted moving target's position information (x, y) and velocity information (v). x ,v y ) and acceleration information (a x ,a y ).

[0088] This invention provides a non-line-of-sight (LOS) EKF target localization method based on residual discrimination, which solves the problems of high power consumption, high complexity, and low positioning accuracy of current localization algorithms. The LOS and NLOS identification and localization algorithms used in this invention often involve multiple technologies, requiring a large amount of prior information and complex statistical knowledge. The proposed residual discrimination-based NLS EKF target localization method only needs the Time of Arrival (TOA) and Angle of Arrival (AOA) information to complete the identification of LOS and NLOS and localization in NLOS environments, greatly reducing the algorithm's complexity and achieving low power consumption and low complexity. Since the Kalman filter algorithm is used to predict, correct, and update the position information of moving targets, applying the extended Kalman filter more accurately describes the system model, thus further improving the accuracy of moving target localization. Attached Figure Description

[0089] Figure 1 A flowchart illustrating a non-line-of-sight EKF target localization method based on residual discrimination.

[0090] Figure 2 A flowchart of a non-line-of-sight EKF target localization method based on residual discrimination.

[0091] Figure 3 This is a non-line-of-sight EKF target localization method based on residual discrimination, as shown in the localization diagram.

[0092] Figure 4 A non-line-of-sight EKF target localization method based on residual discrimination, using uniformly accelerated motion trajectory tracking.

[0093] Figure 5A comparison chart of errors in uniformly accelerated motion prediction for a non-line-of-sight EKF target localization method based on residual discrimination.

[0094] Figure 6 A cumulative distribution map of a non-line-of-sight EKF target localization method based on residual discrimination.

[0095] Figure 7 A graph showing the relationship between the number of non-line-of-sight base stations and the root mean square error of prediction in a non-line-of-sight target localization method based on residual discrimination for uniformly accelerated motion. Detailed Implementation

[0096] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention.

[0097] The complete system flow of this invention provides a non-line-of-sight EKF target localization method based on residual discrimination, such as... Figure 1 As shown, the method includes the following steps:

[0098] Step 1: Construct a 2D EKF positioning model based on TOA and AOA for preliminary positioning; according to the target positioning model of wireless sensor networks in non-line-of-sight environments, the base station records the reception time and angle of the source signal, and calculates the distance r. k By using angle α, the position information of the moving target can be obtained;

[0099] Step 2: Identify line-of-sight (LOS) and non-line-of-sight (NLOS) base stations for each base station; calculate the target node position based on the time of arrival (TOA) and angle of arrival (AOA) measurements of each node, and compare the positioning error with the set threshold value to identify LOS and NLOS base stations.

[0100] Step 3: Construct residuals and divide confidence intervals; determine Kalman gain and update Kalman gain according to the line-of-sight occlusion of the positioning environment;

[0101] Step 4: Correct the EKF model and update the state and prediction; After adjusting the EKF gain, substitute the original Time of Arrival (TOA) and Angle of Arrival (AOA) algorithm positioning results at the current measurement time into different regions for extended Kalman filtering. Use extended Kalman filtering to predict, correct and update the state variables of the moving target (x,y) and output the final moving target position estimation result (x,y).

[0102] In one embodiment, the location information of the moving target in step 1 is the coordinates of the base station at time k as the moving target moves on a two-dimensional plane (x, k).k ,y k The velocities in the x and y directions are v0 and v0, x and v y The state of the target is (x, v) x ,y,v y Then, the arrival time TOA and arrival angle AOA at time k are:

[0103]

[0104] Where (x, y) represents the position coordinates of the signal source in the two-dimensional coordinate system, denoted as [x, y]. T k is the number of base station nodes, and its value is a positive integer ≥ 3; r k Let be the distance from the k-th base station to the moving target;

[0105] If the target moves within the monitoring range of the base station, then the observations of the time of arrival (TOA) and angle of arrival (AOA) under the NLOS environment at time k using a two-dimensional Kalman filter are expressed as follows:

[0106]

[0107] Among them, V k It represents the observation noise of the system; NLOS k This represents non-line-of-sight error, and is generally expressed using a uniform distribution or an exponential distribution.

[0108] The probability density distribution function of the non-line-of-sight (NLOS) error model is:

[0109]

[0110] The non-line-of-sight (NLOS) error follows the mean μ and variance σ. NLOS Gaussian distribution, μ and σ NLOS It is a non-line-of-sight localization algorithm based on Gaussian mixture model that adjusts parameter values.

[0111] In one embodiment, step 2, identifying line-of-sight (LOS) and non-line-of-sight (NLOS) base stations, includes the following steps:

[0112] Step 2.1 Take two UWB nodes, located at points A and B respectively, and move the target point C to the location to be determined;

[0113] Let r1, r2, and r3 be the distances to AC, BC, and AB, respectively. Let θ1 and θ2 be the angles to ∠CAB and ∠CBA, respectively. Record the distances AC1 and AC2 using the arrival time TOA as r1′ and r2′, respectively. Record the angles obtained using the arrival angle AOA as θ1′ and θ2′, respectively. Then, the coordinates of C1 and C2 can be obtained based on the angle and distance information:

[0114]

[0115]

[0116] Where r1′=r1+Δr1, r2′=r2+Δr2 are the errors in the TOA distance measurement.

[0117] θ1′=θ1+Δθ1,θ2′=θ2+Δθ2,Δr1,Δr2,Δθ1,Δθ2 are the errors in the measurement of the angle of arrival (AOA);

[0118] Step 2.2 Let δ1 = |x1 - x2|, δ2 = |y1 - y2|. Substituting the estimated coordinates C1 and C2 from Step 2.1 into the above equation, we can obtain...

[0119] δ1=|r3-r2′cosθ2′-r1′cosθ1′|

[0120] =|r3-(r2+Δr2)cos(θ2+Δθ2)-(r1+Δr1)cos(θ1+Δθ1)|

[0121] =|r3-r2 cosθ2 cosΔθ2+Δr2 cosθ2 cosΔθ2-r2 sinθ2 sinΔθ2-Δr2 sinθ2 sinΔθ2-r1 cosθ1 cosΔθ1+Δr1 cosθ1 cosΔθ1-r1 sinθ1 sinΔθ1-Δr1 sinθ1 sinΔθ1|

[0122] The error of the positioning system in the line-of-sight (LOS) case is caused only by Gaussian noise. Δr1, Δr2, Δθ1, Δθ2 are very small, so we have cosΔθ1≈1, cosΔθ2≈1, sinΔθ1≈Δθ1, sinΔθ2≈Δθ2.

[0123] Ignoring the quadratic term of the Gaussian error, we get:

[0124] δ1≈|r3-r2 cosθ2-r1 cosθ1+Δr2 cosθ2+Δr1 cosθ1-r1Δθ1 sinθ1-r2Δθ2 sinθ2|

[0125] =|Δr1 cosθ1+Δr2 cosθ2-r1Δθ1 sinθ1-r2Δθ2 sinθ2|

[0126] =δ1′

[0127] Similarly, we can conclude that:

[0128] δ2≈|Δr1 sinθ1+Δr2 sinθ2-r1Δθ1 cosθ1-r2Δθ2 cosθ2|

[0129] =δ1′

[0130] The derivation yields δ1≈δ1′, δ2≈δ2′;

[0131] Step 2.3 Let TH1 = λδ1′, TH2 = λδ2′, where λ is an undetermined parameter. Since Δr1, Δr2, Δθ1, and Δθ2 are unknown, they need to be selected based on the actual situation; r1, r2, θ1, and θ2 can be approximated by measured values.

[0132] TH1=λδ1′=λ|σ r cosθ1′+σ r cosθ2′-r1σ θ sinθ1′-r2σ θ sinθ2′|

[0133] TH2=λδ2′=λ|σ r sinθ1′+σ r sinθ2′-r1σ θ cosθ1′-r2σ θ cosθ2′|

[0134] Where, σ r ,σ θ These are the standard distance measurement error and the angle measurement error, respectively, depending on the current positioning scenario;

[0135] Step 2.4 Divide the base stations according to the NLOS determination strategy:

[0136]

[0137] Here, TH1 represents the threshold for determining LOS base stations, and TH2 represents the threshold for NLOS base stations.

[0138] In one embodiment, the structural residual in step 3 includes the following steps:

[0139] Step 3.1 defines the residual as:

[0140]

[0141] Among them, D i Represents the i-th base station BS i Using the localization results from line-of-sight (LOS) and non-line-of-sight (NLOS) algorithms, D k This represents the positioning results of all base stations identified as line-of-sight (LOS) base stations at time k;

[0142] The smallest residual value is selected as the criterion for determining the confidence interval of positioning performance;

[0143] Let the minimum residual value of r at this moment be:

[0144] β=min Res(X r )

[0145] Step 3.2 The confidence factor γ is a regional discrimination index used to classify the degree to which the current positioning result is affected by non-line-of-sight (NLOS). The confidence factor for the current measurement time k is:

[0146]

[0147] In one embodiment, determining the Kalman gain in step 3 involves dividing the localization area into n regions, where n ≥ 3; and processing the Kalman gain of each of the n regions as follows:

[0148]

[0149] In the formula, μ1 and μ2 can be selected according to different positioning environments, and different Kalman filter gains K1 are selected according to different regions. When 0 < γ < μ1, it is a reliable region, and the positioning result is less affected by non-line-of-sight (NLOS), so the current extended Kalman filter gain is not changed. When μ1 < γ < μ2, it is a fuzzy region, and the impact of NLOS occlusion on the algorithm cannot be ignored, but it is within an acceptable range. At this time, it is necessary to adjust the relationship between the measured value and the predicted value. In the formula, 0 < α < 1 is used to reduce the impact of NLOS on the positioning result. When γ > μ2, the positioning result is severely affected by NLOS interference and is an unreliable region. In this case, the current result is discarded.

[0150] In one embodiment, the untrusted region is reclassified and its extended Kalman gain is corrected to utilize more data in cases where NLOS is very severe. The measurement standard deviation is compared with a threshold to determine whether the deviation of the current measurement value is within the tolerable error range. The data classified into the untrusted region is processed again. If the measurement standard deviation is greater than the threshold, it indicates that the current measurement value is severely affected by NLOS and is discarded. Otherwise, the positioning result at the current moment is classified into the fuzzy region.

[0151]

[0152] Where K2 is the updated extended Kalman gain, and σ is the measurement standard deviation.

[0153] Preferably, the prediction, correction, and update of the state variables of the moving target (x, y) using extended Kalman filtering in step 4 refers to extended Kalman filtering being an estimation method, where the target's state equation and observation equation are:

[0154] X k+1 =f[k,X k ]+W k

[0155] Z k =h[k,X k ]+V k

[0156] Where, f[k,X k ] and h[k,X k [W] represents the nonlinear state function and observation function containing information at time k, respectively. k and V k Let W(k) be the process noise and observation noise of the system; the mean of the process noise W(k) is 0, and the variance is Q = diag[w, w], where w is 1e-3.

[0157] The recurrence relation for the extended Kalman filter is as follows:

[0158]

[0159]

[0160]

[0161]

[0162]

[0163] In the above formula, the initial values ​​of the filter and the filter covariance matrix are respectively:

[0164] X(0)=E[X(0)],P(0)=var[X(0)]

[0165] Compared to the linear Kalman filter equation, the state transition Φ(k+1|k) and the observation matrix H(k+1) are replaced by Jacobian matrices of f[*] and h[*].

[0166] Based on the observation equation, the expression for the observation matrix H can be derived as follows:

[0167]

[0168] Step 4, which modifies the EKF model and updates the state and prediction, further includes setting the EKF parameters to the following if the moving target is moving at a constant velocity in a two-dimensional plane:

[0169]

[0170] X k =[xv x yvy ] T

[0171] If the moving target undergoes uniformly accelerated motion in a two-dimensional plane, then:

[0172]

[0173] X k =[xv x a x yv y a y ] T .

[0174] In one embodiment, step 4 involves using an extended Kalman filter to predict, correct, and update the state variables of the moving target (x, y).

[0175] At this point, the state and covariance formulas in the original Kalman filter (EKF) process are updated as follows:

[0176]

[0177]

[0178] in, This represents the estimation result of the state variables at time K. This is the estimate at time K+1, and this is the updated estimate. Let K be the prediction error covariance matrix. This is the updated estimate.

[0179] In one embodiment, the state vector during the update phase This is the final state vector, which includes the predicted moving target's position information (x, y) and velocity information (v). x ,v y ) and acceleration information (a x ,a y ).

[0180] This invention provides a non-line-of-sight (LOS) EKF target localization method based on residual discrimination, which solves the problems of high power consumption, high complexity, and low positioning accuracy of current localization algorithms. The LOS and NLOS identification and localization algorithms used in this invention often involve multiple technologies, requiring a large amount of prior information and complex statistical knowledge. The proposed residual discrimination-based NLS EKF target localization method only needs the Time of Arrival (TOA) and Angle of Arrival (AOA) information to complete the identification of LOS and NLOS and localization in NLOS environments, greatly reducing the algorithm's complexity and achieving low power consumption and low complexity. Since the Kalman filter algorithm is used to predict, correct, and update the position information of moving targets, applying the extended Kalman filter more accurately describes the system model, thus further improving the accuracy of moving target localization.

[0181] Example 1

[0182] This invention proposes a non-line-of-sight EKF target localization method based on residual discrimination, such as... Figure 2 As shown, the steps are as follows:

[0183] Step 1: Construct a 2D EKF localization model based on TOA and AOA for preliminary localization:

[0184] Based on the target localization model of wireless sensor networks in non-line-of-sight environments, the base station records the reception time and angle of the source signal, and calculates the distance r. k By using angle α, the position information of the moving target can be obtained.

[0185] The moving target moves on a two-dimensional plane, and the coordinates of the base station at time k are (x, k). k ,y k The target's state is (x, v). x ,y,v y Then the TOA and AOA values ​​at time k are:

[0186]

[0187] Where (x, y) represents the position coordinates of the signal source in the two-dimensional coordinate system, denoted as [x, y]. T k is the number of base station nodes, and its value is a positive integer ≥ 3; r k Let k be the distance from the k-th base station to the mobile target. In this embodiment, k is set to 5.

[0188] If the target moves within the monitoring range of the base station, the observations of the TOA and AOA two-dimensional Kalman filters in the NLOS environment at time k can be expressed as:

[0189]

[0190] Among them, V k The system's observation noise follows a Gaussian distribution with variance of 5 and mean of 0; NLOS k Non-line-of-sight error is generally distributed using uniform or exponential distribution.

[0191] The probability density distribution function of the NLOS error model is:

[0192]

[0193] In this example, the NLOS error follows a mean μ of 0 and a variance σ. NLOS It follows a Gaussian distribution with a value of 30.

[0194] Step 2: Identify LOS / NLOS base stations for each base station.

[0195] This example calculates the target node's location based on the TOA and AOA measurements of each node, and compares the positioning error with a set threshold to identify LOS and NLOS base stations. Details are as follows:

[0196] (2.1) There are two UWB nodes, located at points A and B respectively, and the target point C is the location to be located. Let r1, r2, and r3 be the distances to AC, BC, and AB respectively, and let θ1 and θ2 be the angles of ∠CAB and ∠CBA respectively. The distances AC1 and AC2 measured via TOA are recorded as r1′ and r2′, and the resulting angles measured via AOA are recorded as θ1′ and θ2′ respectively. Then, the coordinates of C1 and C2 can be obtained based on the angle and distance information:

[0197]

[0198]

[0199] Where r1′=r1+Δr1, r2′=r2+Δr2 are the errors in the TOA distance measurement.

[0200] θ1′=θ1+Δθ1, θ2′=θ2+Δθ2, Δr1, Δr2, Δθ1, Δθ2 are the errors in AOA angle measurement.

[0201] (2.2) Let δ1=|x1-x2|, δ2=|y1-y2|. Substitute the estimated coordinates of C1 and C2 in step (2.1) into the above formula, and after a series of derivations, we can obtain δ1≈δ1′, δ2≈δ2′.

[0202] (2.3) Let TH1 = λδ1′, TH2 = λδ2′, where λ is an undetermined parameter. Since Δr1, Δr2, Δθ1, and Δθ2 are unknown, they need to be selected based on the actual situation. r1, r2, θ1, and θ2 can be approximated by measured values.

[0203] TH1=λδ1′=λ|σ r cosθ1′+σ r cosθ2′-r1σ θ sinθ1′-r2σ θ sinθ2′|

[0204] TH2=λδ2′=λ|σ r sinθ1′+σ r sinθ2′-r1σ θ cosθ1′-r2σ θ cosθ2′|

[0205] Where, σ r ,σ θ These are the standard distance measurement error and the angle measurement error, respectively, depending on the current positioning scenario.

[0206] (2.4) Divide the base stations according to the NLOS determination strategy:

[0207]

[0208] Step 3: Define the residuals and divide the confidence intervals.

[0209] The residuals between all base station positioning results and non-line-of-sight base station positioning results are processed as follows:

[0210] (3.1) Define the residual as

[0211]

[0212] Among them, D i Represents the i-th base station BS i Using the localization results from the TOA and AOA algorithms, D k This represents the location results of all base stations identified as LOS at time k. As can be seen from the above formula, as the LOS situation improves, D... k The value keeps increasing, Res(X) k The value of ) decreases accordingly. Therefore, the magnitude of the residual value represents the quality of the positioning result; the larger the residual value, the worse the positioning result; the smaller the residual value, the better the positioning result. Therefore, this paper selects the minimum residual value as the criterion for determining the confidence interval of positioning performance. Let the minimum residual value of r at this moment be denoted as .

[0213] β=min Res(Xr )

[0214] (3.2) The confidence factor γ is a regional discrimination index used to classify the degree to which the current positioning result is affected by NLOS. The confidence factor for the current measurement time k is:

[0215]

[0216] Step 4: Determine the Kalman gain

[0217] The positioning area is divided into three regions, and the Kalman gain in the three regions is processed as follows:

[0218]

[0219] In the above formula, μ1 and μ2 can be selected according to different positioning environments, and different Kalman filter gains K1 can be selected according to different regions. In this example, μ1 and μ2 are 0.66 and 0.68 respectively. In simulations of other environments, μ1 and μ2 can be set to 0.5 and 1.5 times the confidence factor γ. If you want to improve the positioning accuracy, adjust the values ​​of μ1 and μ2 to make the confidence region narrower.

[0220] This experiment is to select a suitable offset coefficient for this simulation in subsequent experiments. The offset coefficient α needs to be selected according to the actual situation. Assuming that the target is undergoing uniform acceleration, based on the residual results, the values ​​of μ1 and μ2 are selected as 0.66 and 0.68 respectively using the normal distribution. Table I shows the relationship between the offset coefficient and the root mean square error obtained by MATLAB simulation in the environment of this paper.

[0221] Table 1 Relationship between coefficients and RMS

[0222]

[0223]

[0224] Step 5: Update the Kalman gain again (re-divide the untrusted region).

[0225] This step is for situations where the positioning environment is severely obstructed by line of sight, resulting in too much data being discarded using the above method, making accurate positioning impossible. If the line-of-sight obstruction is not severe, this step can be skipped.

[0226] The data classified as unreliable regions are processed again. If the standard deviation of the measurement is greater than the threshold, it indicates that the current measurement value is severely affected by NLOS and should be discarded. Otherwise, it is classified into the fuzzy region.

[0227]

[0228] Where K2 is the updated extended Kalman gain, and σ is the measurement standard deviation.

[0229] Step 6: Update the EKF model and correct the predicted state and covariance.

[0230] After adjusting the EKF gain, the original TOA and AOA algorithm positioning results at the current measurement time are substituted into different regions for extended Kalman filtering.

[0231] If the moving target is moving at a constant velocity in a two-dimensional plane, then the parameters of EKF are set as follows:

[0232]

[0233] X k =[xv x yv y ] T

[0234] If the moving target undergoes uniformly accelerated motion in a two-dimensional plane, then:

[0235]

[0236] X k =[xv x a x yv y a y ] T

[0237] Compared to the linear Kalman filter equation, the state transition Φ(k+1|k) and the observation matrix H(k+1) are replaced by Jacobian matrices of f[*] and h[*].

[0238] Based on the observation equation, the expression for the observation matrix in the text can be derived as follows:

[0239]

[0240] State in the original EKF process Covariance The formula is updated as follows:

[0241]

[0242]

[0243] Step 7: Output location information

[0244] Based on the state vector of the update phase Output the final position. This final state vector includes the predicted position information (x, y) and velocity information (v) of the moving target. x ,v y ) and acceleration information (a x ,a y ).

[0245] The relationship between the number of LOS / NLOS base stations and RMS is as follows: Figure 7 As shown, it can be seen that compared with several basic algorithms, the method of this invention has the best effect on reducing NLOS.

[0246] Simulation results show that, under the influence of NLOS, the proposed method improves the localization accuracy by approximately 19.72% compared to the two-dimensional Kalman filter method based on TOA and AOA. Furthermore, compared to the unscented Kalman filter and the traditional Kalman filter method, the localization accuracy of the proposed algorithm is improved by approximately 35.96% and 68.72%, respectively.

[0247] The effects of the present invention will be further illustrated below with simulation experiments:

[0248] A. Simulation conditions

[0249] The location coordinates of the observation base station are (200, 300). The observation interval T of the extended Kalman filter is set to 0.5s, the number of samplings N is 50, and the observation noise follows a Gaussian distribution with a mean of 0 and a variance of 5. The mean of the process noise is 0, the variance is Q = diag[w, w], and ω is 1e-3. The NLOS error follows an exponential distribution and the multipath effect is not considered.

[0250] B. Simulation Content

[0251] (1) Simulation Experiment 1

[0252] This experiment uses the methods described in the implementation for simulation. MATLAB is used for the simulation. The location coordinates of the observed base station are (200, 300). The observation interval T of the extended Kalman filter is set to 0.5s, the number of samples N is 50, and the observation noise follows a Gaussian distribution with a mean of 0 and a variance of 5. The process noise has a mean of 0, a variance of Q = diag[w, w], and ω is 1e-3. The NLOS error follows an exponential distribution, and the multipath effect is not considered. This simulation compares the proposed algorithm with TOA and AOA two-dimensional extended Kalman filtering, unscented Kalman filtering, and traditional Kalman filtering algorithms.

[0253] Assuming the moving target undergoes uniformly accelerated motion on a two-dimensional plane, with initial coordinates (-100, 200), a moving speed of (2, 50), and acceleration of (1, -10), the simulation results are as follows. Figure 3 , 4As shown in Figures 5 and 6, Figure 3 A comparison of the tracking results of four algorithms with the actual trajectory is shown, such as... Figure 4 The results of the root mean square error comparison are shown below. Figure 5 The image shown is a graph of the cumulative distribution results.

[0254] (2) Simulation Experiment 2

[0255] This experiment investigates the relationship between the number of LOS / NLOS base stations and RMS under different environments. A moving target undergoes uniformly accelerated motion in a two-dimensional plane. By adjusting other parameters, such as the positions of the base stations, the number of LOS / NLOS base stations is changed, and the positioning error under the current conditions is calculated. The simulation results are as follows: Figure 7 As shown.

[0256] C. Simulation Results

[0257] Depend on Figure 4 It is evident that when the target is moving at a constant speed, the traditional Kalman filter algorithm has a very serious error and can no longer accurately predict the target's trajectory. The unscented Kalman filter method has a slightly better positioning accuracy than the traditional Kalman filter method. The extended Kalman filter method based on TOA and AOA reduces the NLOS error to some extent due to the introduction of two-dimensional observations. The TOA-AOA improved extended Kalman algorithm based on residual discrimination proposed in this paper has the trajectory closest to the real trajectory and the highest positioning accuracy.

[0258] Depend on Figure 5 As can be seen, the positioning errors of all four algorithms gradually increase over time. This is due to the memory property of the Kalman filter; a deviation in the estimation result at the previous moment may affect the result at the next moment, and the traditional Kalman method is most affected by the filter's memory property. Under these circumstances, the algorithm presented in this paper still achieves the highest accuracy among the four algorithms.

[0259] Figure 6 The cumulative distribution curves of the four algorithms are compared. It can be seen that under severe NLOS interference, there is still an 80% probability that the error of the algorithm in this paper is within 13 meters. In contrast, the probability of the error within 13 meters for the two-dimensional EKF observation method based on TOA and AOA is only 50.8%, and that for the unscented Kalman method and the traditional Kalman method is only 27.8% and 31.3%, respectively. The algorithm in this paper has the best positioning performance among the four algorithms, which greatly improves the positioning accuracy in the NLOS environment and successfully reduces non-line-of-sight errors.

[0260] Figure 7The relationship between the number of LOS / NLOS base stations and RMS under different environments is described. As can be seen from the figure, the positioning accuracy of each algorithm increases with the increase of NLOS base stations. Among them, the RMS of the algorithm in this paper changes the least, indicating that it reduces NLOS error more thoroughly. The other three algorithms are severely affected by the NLOS environment, and the mean square error increases significantly. Among them, the traditional Kalman filter method is most severely affected by the NLOS environment and can no longer accurately describe the target's trajectory.

[0261] Based on the simulation results and analysis above, the effectiveness, reliability, and robustness of the method proposed in this invention are verified. This invention introduces residuals to determine the severity of non-line-of-sight (NLOS) influence on the current positioning point, and divides confidence intervals to apply different processing to the Kalman gain in different regions affected by NLOS. Then, TOA and AOA are used as improved EKF two-dimensional observations for positioning, achieving the goal of NLOS elimination and positioning of the target. Simulation results demonstrate the effectiveness of the algorithm, which can eliminate NLOS errors to a certain extent and has high positioning accuracy.

[0262] This invention provides a non-line-of-sight (LOS) EKF target localization method based on residual discrimination, which solves the problems of high power consumption, high complexity, and low positioning accuracy of current localization algorithms. The LOS and NLOS identification and localization algorithms used in this invention often involve multiple technologies, requiring a large amount of prior information and complex statistical knowledge. The proposed residual discrimination-based NLS EKF target localization method only needs the Time of Arrival (TOA) and Angle of Arrival (AOA) information to complete the identification of LOS and NLOS and localization in NLOS environments, greatly reducing the algorithm's complexity and achieving low power consumption and low complexity. Since the Kalman filter algorithm is used to predict, correct, and update the position information of moving targets, applying the extended Kalman filter more accurately describes the system model, thus further improving the accuracy of moving target localization.

Claims

1. A non-line-of-sight EKF target localization method based on residual discrimination, characterized in that, The method includes the following steps: Step 1: Construct a 2D EKF positioning model based on TOA and AOA for preliminary positioning; according to the target positioning model of wireless sensor networks in non-line-of-sight environments, the base station records the reception time and angle of the source signal, and calculates the distance. and angle To obtain the location information of the moving target; Step 2: Identify line-of-sight (LOS) and non-line-of-sight (NLOS) base stations for each base station; calculate the target node position based on the time of arrival (TOA) and angle of arrival (AOA) measurements of each node, and compare the positioning error with the set threshold value to identify LOS and NLOS base stations. Step 3: Construct residuals and divide confidence intervals; determine Kalman gain and update Kalman gain according to the line-of-sight occlusion of the positioning environment; Step 4: Correct the EKF model and update the state and prediction; After adjusting the EKF gain, substitute the original Time of Arrival (TOA) and Angle of Arrival (AOA) algorithm positioning results at the current measurement time into different regions for extended Kalman filtering. Use extended Kalman filtering to predict, correct and update the state variables of the moving target (x,y) and output the final moving target position estimation result (x,y). The prediction, correction, and update of the state variables of the moving target (x, y) using extended Kalman filtering is an estimation method employing extended Kalman filtering. The target's state equation and observation equation are: in, and Each contains Nonlinear state function and observation function for time information, and The system's process noise and observation noise; process noise The mean is 0 and the variance is , It is 1e-3; The recurrence relation for the extended Kalman filter is as follows: In the above formula, For the new interest value, Given the observation matrix, the initial values ​​for the filter and the filter covariance matrix are as follows: Compared to the linear Kalman filter equation, the state transition and observation matrix Depend on and Replace it with the Jacobian matrix; The observation matrix can be derived from the observation equation. H The expression is: The step 4 of modifying the EKF model and updating the state and prediction further includes setting the EKF parameters as follows: If the moving target is moving at a constant velocity in a two-dimensional plane, the parameters of the EKF model are: If the moving target undergoes uniformly accelerated motion in a two-dimensional plane, then: 。 2. The non-line-of-sight EKF target localization method based on residual discrimination according to claim 1, characterized in that, The position information of the moving target mentioned in step 1 refers to the movement of the moving target on a two-dimensional plane. The coordinates of the time base station are , and The velocities in the directions are respectively and The target's status is ,but The arrival time (TOA) and angle of arrival (AOA) values ​​at each moment are: in, The position coordinates of the signal source in the two-dimensional coordinate system are denoted as . ; The number of base station nodes, its value is... Positive integers; For the first The distance from each base station to the moving target; If the target moves within the monitoring range of the base station, then the time of arrival (TOA) and angle of arrival (AOA) in an NLOS environment are determined by a two-dimensional Kalman filter. The observed value at time t is represented as: in, This represents the system's observation noise; This represents non-line-of-sight error, and is generally expressed using a uniform distribution or an exponential distribution. The probability density distribution function of the non-line-of-sight (NLOS) error model is: Among them, the non-line-of-sight NLOS error follows the average value. and variance Gaussian distribution and It is a non-line-of-sight localization algorithm based on Gaussian mixture model that adjusts parameter values.

3. The non-line-of-sight EKF target localization method based on residual discrimination according to claim 1, characterized in that, Step 2, which involves identifying line-of-sight (LOS) and non-line-of-sight (NLOS) base stations, includes the following steps: Step 2.1 Take two UWB nodes, located at points A and B respectively, and move the target point C to the location to be determined; remember , and Let the distances to AC, BC, and AB be respectively, and let them be... and Let be the angle values ​​of ∠CAB and ∠CBA, respectively. The distances AC1 and AC2 measured over the arrival time TOA are denoted as . , The obtained angles are measured using the angle of arrival (AOA) and recorded as follows: and Then, the coordinates of C1 and C2 can be obtained based on the angle and distance information: Arrival time in, , Errors in Time of Arrival (TOA) distance measurement , , Errors in the measurement of the angle of arrival (AOA); Step 2.2 Note Substituting the estimated coordinates of C1 and C2 from step 2.1 into the above formula, we can obtain... The positioning system's error in line-of-sight (LOS) conditions is caused solely by Gaussian noise. Very small, therefore ; Ignoring the quadratic term of the Gaussian error, we get: Similarly, we can conclude that: The derivation yields ; Step 2.3 ,in These are parameters to be determined, because The answer is unknown and needs to be selected based on the actual situation. If a measured value can be used as an approximation, then... in, These are the standard distance measurement error and the angle measurement error, respectively, depending on the current positioning scenario; Step 2.4 Divide the base stations according to the NLOS determination strategy: in, TH1 This indicates that the threshold for determining the LOS base station is being used. TH2 This indicates the threshold for NLOS base stations.

4. The non-line-of-sight EKF target localization method based on residual discrimination according to claim 3, characterized in that, Step 3, which involves constructing the residual, includes the following steps: Step 3.1 defines the residual as: in, Indicates the first base stations The localization results using line-of-sight (LOS) and non-line-of-sight (NLOS) algorithms, express Location results for all locations identified as line-of-sight (LOS) base stations at any given time; The smallest residual value is selected as the criterion for determining the confidence interval of positioning performance; Record this moment The minimum residual value is: Step 3.2 Confidence Factor It is a regional discrimination index that classifies the degree to which the current positioning results are affected by non-line-of-sight (NLOS). Current measurement time The confidence factor is: 。 5. The non-line-of-sight EKF target localization method based on residual discrimination according to claim 1, characterized in that, Step 3, determining the Kalman gain, involves dividing the localization area into n regions, where n ≥ 3; and processing the Kalman gain in each of the n regions as follows: In the formula It can be selected according to different positioning environments, and different Kalman filter gains can be selected according to different regions. ,when When the region is considered reliable, the localization result is less affected by non-line-of-sight (NLOS) and does not change the current extended Kalman filter gain; when In the ambiguous region, non-line-of-sight NLOS occlusion has a significant impact on the algorithm, but it remains within acceptable limits. Therefore, it is necessary to adjust the relationship between the measured and predicted values, as shown in the equation. This is used to reduce the impact of non-line-of-sight (NLOS) on positioning results; when If the localization result is severely affected by non-line-of-sight (NLOS) interference and is considered an unreliable area, then the current result should be discarded.

6. The non-line-of-sight EKF target localization method based on residual discrimination according to claim 5, characterized in that, For unreliable regions, the extended Kalman gain is adjusted to utilize more data even when NLOS is severe. The standard deviation of the measurement is compared with a threshold to determine whether the deviation of the current measurement value is within the tolerable error range. Data classified into unreliable regions are processed again. If the standard deviation of the measurement is greater than the threshold, it means that the current measurement value is severely affected by NLOS and is discarded. Otherwise, the positioning result at the current time is classified into the fuzzy region. in, For the updated extended Kalman gain, To measure the standard deviation.

7. A non-line-of-sight EKF target localization method based on residual discrimination according to claim 1, characterized in that, Step 4 describes using an extended Kalman filter to predict, correct, and update the state variables of the moving target (x, y). At this point, the state and covariance formulas in the original Kalman filter (EKF) process are updated as follows: in, This represents the estimation result of the state variables at time K. This is the estimate at time K+1, and this is the updated estimate. Let K be the prediction error covariance matrix. This is the updated estimate.

8. The non-line-of-sight EKF target localization method based on residual discrimination according to claim 1, characterized in that, State vector during the update phase This is the final state vector, which includes the predicted location information of the moving target. Speed ​​information And acceleration information.

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