Track aliasing discrimination method based on Gaussian probability model

Abstract

The invention discloses a track aliasing discrimination method based on a Gaussian probability model, and belongs to the field of radar data processing. The method specifically comprises the following steps: firstly, for a scene in which N targets are measured by a single sensor, obtaining a measured value Z (k) of the N targets at a k moment, and further calculating a to-be-estimated position X (k) of each target; aiming at the adjacent targets i and j, taking the difference delta X (k) of the to-be-estimated positions at the moment k as a Gaussian probability model; converting into expressions of three measurement dimensions of distance, orientation and pitching; then, judging whether the difference delta X (k) of the to-be-estimated positions is smaller than the resolution of a sensor, and if so, indicating that the tracks of the targets i and j have probability aliasing; otherwise, aliasing is avoided; and finally, on the premise of satisfying Gaussian distribution, solving the difference delta X (k) of the positions to be estimated, respectively calculating to obtain aliasing probabilities of three measurement dimensions of distance, azimuth and pitching, and carrying out product fusion to finally obtain the track aliasing probabilities of the targets i and j. According to the method, the robustness of a judgment algorithm is improved, and the accuracy of track aliasing judgment is improved.

Description

Technical Field

[0001] The invention belongs to the field of radar data processing, and in particular is a track aliasing discrimination method based on a Gaussian probability model. Background Art

[0002] The track is the target state estimation trajectory formed by the sensor target tracking of the measurement set of the same target. When processing multi-target data, each tracking track must first be assigned a track number, and all parameters corresponding to a given track are referenced by its track number.

[0003] In a single-sensor multi-target observation scenario, when the motion trajectories of two targets are close, as the target tracking distance gradually increases, the sensor cannot distinguish them, and track interruption and intersection are likely to occur, resulting in track number aliasing.

[0004] In the process of multi-sensor data fusion, it is necessary to classify multiple tracks from different sensors by using track-to-track association, so as to eliminate duplicate tracks, and use fusion algorithms to achieve continuous, reliable and high-precision tracking of multiple targets. The disordered track numbering will affect the performance of track association.

[0005] In the field of air traffic control, the frequent intersection of flight paths increases the risk of aircraft collision. Therefore, accurate prediction of the risk of intersection collision is also a guarantee for the safe navigation of aircraft.

[0006] Currently, the simplest and most direct method to determine track aliasing is to calculate the Euclidean distance or Mahalanobis distance between two tracks, and compare the Euclidean distance or Mahalanobis distance with the set threshold to determine whether the tracks are aliased.

[0007] Among them, the Euclidean distance method does not consider the impact of measurement errors, is sensitive to measurement noise, and is difficult to accurately judge in scenarios with large measurement noise; while the Mahalanobis distance method ignores the sensor's own resolution.

[0008] Both discrimination methods are hard discrimination. The threshold has a great influence on the discrimination result and is difficult to set accurately. Therefore, it is impossible to accurately estimate the aliasing probability between tracks, which brings great challenges to the association between measurement and existing tracks. Summary of the invention

[0009] Aiming at the problem of track number aliasing caused by the close distance between multiple targets, the present invention proposes a track aliasing discrimination method based on Gaussian probability model, which can obtain the multi-target track aliasing interval and provide auxiliary information for multi-target tracking by analyzing the changing trend of aliasing probability.

[0010] The track aliasing discrimination method based on the Gaussian probability model has the following specific steps:

[0011] Step 1: For a scenario where a single sensor measures N targets, obtain the measurement value Z(k) of the sensor detecting the N targets at time k;

[0012]

[0013] Z r (k) represents the actual distance r of the target acquired by the sensor; Z θ (k) represents the actual azimuth angle θ of the target acquired by the sensor; Indicates the actual pitch angle of the target acquired by the sensor k is an integer greater than or equal to 1.

[0014] Step 2: Using the measured values ​​Z(k) of N targets, calculate the estimated position X(k) of each target at time k;

[0015] The relationship is as follows:

[0016]

[0017] Where W(k) represents the Gaussian measurement noise with zero mean, that is, W(k)~N(0,σ 2 ). At this moment, the estimated values ​​of each target meet the mean Z(k) and the variance σ 2 and are independently normally distributed.

[0018] Step 3: Calculate the difference between the estimated positions of neighboring targets i and j at time k as the Gaussian probability model;

[0019] The model expression is:

[0020] ΔX(k)=(X i (k)-X j (k))

[0021] =(Z i (k)-Z j (k))+(W j (k)-W i (k))

[0022] =ΔZ(k)+ΔW(k)

[0023] The model satisfies the condition that ΔZ(k) is the mean and Δσ 2 is the Gaussian distribution of the variance. Where ΔZ(k) is the difference between the measurements of the two targets,

[0024] Step 4: Convert the Gaussian probability model ΔX(k) into the expression of three measurement dimensions: distance, azimuth and elevation, namely:

[0025]

[0026] Step 5: Determine whether the Gaussian probability model ΔX(k) is less than the sensor resolution d m If yes, it means that the tracks of targets i and j will overlap with each other; otherwise, it is considered that the tracks of targets i and j will not overlap with each other;

[0027] The condition that the difference ΔX(k) of the estimated position satisfies is -d m ≤ΔX≤d m ;in,

[0028] Step 6: Under the premise that ΔX(k) satisfies Gaussian distribution, solve the difference ΔX(k) between the estimated positions and calculate the aliasing probabilities of the three measurement dimensions of distance, azimuth and elevation respectively;

[0029] The calculation formula is:

[0030]

[0031] Step 7: Multiply and fuse the aliasing probabilities of the three measurement dimensions of distance, azimuth and pitch to finally obtain the track aliasing probability of targets i and j:

[0032]

[0033] The advantages of the present invention are:

[0034] 1) A track aliasing discrimination method based on a Gaussian probability model solves the problem that the traditional Euclidean distance discrimination method does not consider measurement errors and is sensitive to measurement noise. Incorporating measurement errors into the track aliasing discrimination method expands the tracking scenarios applicable to the algorithm and improves the robustness of the judgment algorithm.

[0035] 2) A track aliasing discrimination method based on the Gaussian probability model. Compared with the Mahalanobis distance discrimination method, it can consider the probability distribution characteristics of the measurement and also incorporate the sensor's own resolution into the judgment, thereby establishing a more complete judgment model and improving the accuracy of track aliasing discrimination.

[0036] 3) A track aliasing discrimination method based on a Gaussian probability model. Compared with other traditional aliasing discrimination methods, it does not need to introduce a discrimination threshold for a one-size-fits-all hard discrimination. Instead, a Gaussian probability model is established to calculate the dynamic aliasing probability between different tracks and obtain the multi-target track aliasing interval, providing auxiliary information for subsequent multi-target tracking. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a track aliasing scene diagram in the present invention;

[0038] Figure 2 This is a flow chart of a track aliasing discrimination method based on a Gaussian probability model of the present invention;

[0039] Figure 3 Schematic diagram of Gaussian probability model in the present invention;

[0040] Figure 4 Schematic diagram of the sensor array coordinate system in the present invention. DETAILED DESCRIPTION

[0041] The present invention will be further described in detail below with reference to the accompanying drawings.

[0042] Common track aliasing scenarios include: Figure 1 As shown in the figure, when two targets are crossing each other, due to factors such as the target distance is too close, the sensor's viewing angle is limited, the sensor's measurement noise is too large, the sensor's own resolution is too low, or the selected tracking model does not match, the track numbering may be mixed, the track is interrupted and a new track number is started, and other errors may occur. In response to this situation, it is necessary to dynamically predict and evaluate the risk of track aliasing in a timely manner, and manage and correct the track numbering at the same time. Provide the correct track number for subsequent multi-sensor data fusion and improve the quality of the comprehensive track.

[0043] Based on this, the present invention proposes a track aliasing discrimination method based on a Gaussian probability model, which is used to dynamically estimate the track aliasing probability, provide prior information for subsequent multi-target tracking, and assist in improving tracking accuracy.

[0044] like Figure 2 As shown, the specific steps are as follows:

[0045] Step 1: For a scenario where a single sensor measures N targets, obtain the measurement value Z(k) of the sensor detecting the N targets at time k;

[0046]

[0047] Z r (k) represents the actual distance r of the target acquired by the sensor; Z θ (k) represents the actual azimuth angle θ of the target acquired by the sensor; Indicates the actual pitch angle of the target acquired by the sensor k is an integer greater than or equal to 1.

[0048] Step 2: Using the measured values ​​Z(k) of N targets, calculate the estimated position X(k) of each target at time k;

[0049] The relationship between the measured value at the kth moment and the position to be estimated is as follows

[0050]

[0051] The measurement value corresponding to the filtering value of a single sensor for a single target at the k-th moment is unique. Here, the target measurement value of the single sensor is set as a definite value. That is, the value to be estimated for the target at this moment satisfies:

[0052]

[0053] where W(k) represents Gaussian measurement noise with a mean of zero, i.e., W(k) ~ Ν(0, σ 2 ). The values to be estimated for each target at this moment conform to a normal distribution with a mean of Z(k) and a variance of σ 2 and are independent of each other.

[0054] Step 3: Calculate the difference between the estimated positions of neighboring targets i and j at the k-th moment as the Gaussian probability model;

[0055] The estimated positions of each target at each moment follow independent normal distributions. Therefore, the difference between the estimated positions of any two targets at any moment also conforms to a normal distribution. Let the estimated positions of targets i and j be expressed as

[0056]

[0057] Then the difference between their estimated positions, that is, the model expression is:

[0058] ΔX(k) = (X i (k) - X j (k))

[0059] = (Z i (k) - Z j (k)) + (W j (k) - W i (k))

[0060] = ΔZ(k) + ΔW(k)

[0061] The difference between the estimated positions of the two targets in this model satisfies a Gaussian distribution with ΔZ(k) as the mean and Δσ 2 as the variance. Among them, ΔZ(k) is the difference between the measurements corresponding to the two targets,

[0062] Step 4: Convert the Gaussian probability model ΔX(k) into expressions in the three measurement dimensions of distance, azimuth, and elevation, that is:

[0063]

[0064] Step 5: Determine whether the Gaussian probability model ΔX(k) is less than the sensor resolution d m, if so, it indicates that there is a probability of track aliasing between targets i and j; otherwise, it is considered that there is no track aliasing between targets i and j;

[0065] The condition satisfied by the difference in the position to be estimated ΔX(k) is -d m ≤ΔX≤d m ; where

[0066] Step 6: On the premise that ΔX(k) follows a Gaussian distribution, solve the difference in the position to be estimated ΔX(k), and calculate the aliasing probabilities for the three measurement dimensions of distance, azimuth, and elevation respectively;

[0067] As shown in the appendix Figure 3 shown, the calculation formula is:

[0068]

[0069] Step 7: Multiply and fuse the aliasing probabilities for the three measurement dimensions of distance, azimuth, and elevation to finally obtain the track aliasing probability between targets i and j:

[0070]

[0071] Then the non-aliasing probability of the target is:

[0072]

[0073] Example:

[0074] First, in the scenario where a single sensor detects N targets, model the measurement and the position to be estimated of the targets. Step 101: Let the measurement values of the N targets detected by the single sensor at the k-th moment be

[0075] Z(k) = [Z 1 (k), Z 2 (k),..., Z N (k)]

[0076] The position to be estimated of the target at this moment is

[0077] X(k) = [X 1 (k), X 2 (k),..., X N (k)]

[0078] The measurement value corresponding to the filtered value of a single target by the single sensor at the k-th moment is unique. Here, the target measurement value of the single sensor is set as a definite value, that is, the value to be estimated of the target at this moment satisfies:

[0079]

[0080] where, W(k) = [W1 (k),W 2 (k),...,W N (k)] is a Gaussian measurement noise with a mean of zero, that is, W(k)~N(0,σ 2 ). Then the estimated value of the target at this moment meets the mean value Z(k)=[Z 1 (k),Z 2 (k),...,Z N (k)];

[0081] The variance is And they are normally distributed independently. For the Nth target, its probability density function is:

[0082]

[0083] Step 102: Modeling the difference between the target positions to be estimated. The positions to be estimated of each target at each moment follow a mutually independent normal distribution, so the difference between the positions to be estimated of any two targets at any moment also conforms to a normal distribution.

[0084] Assume that the estimated positions of targets i and j can be expressed as

[0085]

[0086] The difference between the estimated positions of the two is

[0087] ΔX(k)=(X i (k)-X j (k))

[0088] =(Z i (k)-Z j (k))+(W j (k)-W i (k))

[0089] =ΔZ(k)+ΔW(k)

[0090] And meet

[0091]

[0092] That is, the difference between the two target positions to be estimated satisfies ΔZ(k) as the mean, Δσ 2 is the Gaussian distribution of the variance. ΔZ(k) is the difference between the corresponding measurements of the two targets,

[0093] Step 2: Determine the track aliasing probability based on Gaussian probability.

[0094] Step 201: Establish the aliasing probability of the difference of the target position to be estimated in different measurement dimensions. The difference of the target position to be estimated at time k ΔX(k) can be expressed as

[0095]

[0096] Among them, each measurement dimension is defined as follows: the origin is located at the center of the sensor array, r is the distance from the coordinate origin to the spatial measurement point; θ is the angle between the radial direction of the measurement point and the normal plane determined by the intersection of the array surface and the horizontal plane and the normal line of the array surface (positive when pointing upward), which is called the pitch angle; The angle between the radial projection of the measuring point on the normal plane and the normal line of the array surface is positive when it points to the front of the array surface, which is called the direction angle. The coordinate system of the sensor array surface is shown in the attached figure. Figure 4 shown.

[0097] Assume the difference between the measured values ​​is

[0098]

[0099] The sensor resolution is

[0100]

[0101] Then when the difference of the target position to be estimated satisfies -d m ≤ΔX≤d m When , the sensor will not be able to distinguish the corresponding measurements of multiple targets, and the tracks will be aliased. The aliasing probability in the distance dimension is

[0102]

[0103] The probability of aliasing of the direction angle is

[0104]

[0105] The pitch angle aliasing probability is

[0106]

[0107] Step 202: When the distance, azimuth, and pitch are all aliased, the track is aliased; at this time, the track aliasing probability is the product of the probability distribution of each dimension.

Claims

1. A track aliasing discrimination method based on Gaussian probability model, characterized in that: The following steps are involved: Step 1: For a scenario where a single sensor measures N targets, obtain the measurement value Z(k) of the sensor detecting the N targets at time k; Z r (k) represents the actual distance r of the target acquired by the sensor; Z θ (k) represents the actual azimuth angle θ of the target acquired by the sensor; Indicates the actual pitch angle of the target acquired by the sensor k is an integer greater than or equal to 1; Step 2: Using the measured values ​​Z(k) of N targets, calculate the estimated position X(k) of each target at time k; Step 3: Calculate the difference between the estimated positions of neighboring targets i and j at time k as the Gaussian probability model ΔX(k); The model expression is: ΔX(k)=(X i (k)-X j (k)) =(Z i (k)-Z j (k))+(W j (k)-W i (k)) =ΔZ(k)+ΔW(k) The model satisfies the condition that ΔZ(k) is the mean and Δσ 2 is the Gaussian distribution of variance; W(k) represents the Gaussian measurement noise with zero mean, ΔZ(k) is the difference between the measurements corresponding to the two targets, Step 4: Convert the Gaussian probability model ΔX(k) into the expression of three measurement dimensions: distance, azimuth and elevation, namely: Step 5: Determine whether the Gaussian probability model ΔX(k) is less than the sensor resolution d m If yes, it means that the tracks of targets i and j will overlap with each other; otherwise, it is considered that the tracks of targets i and j will not overlap with each other; Step 6: Under the premise that ΔX(k) satisfies Gaussian distribution, solve the difference ΔX(k) between the estimated positions and calculate the aliasing probabilities of the three measurement dimensions of distance, azimuth and elevation respectively; The calculation formula is: Step 7: Multiply and fuse the aliasing probabilities of the three measurement dimensions of distance, azimuth and pitch to finally obtain the track aliasing probability of targets i and j.

2. A track aliasing discrimination method based on a Gaussian probability model as claimed in claim 1, characterized in that: In step 2, the relationship between the measured value of each target and the position to be estimated is as follows: Among them, W(k)~N(0,σ 2 ), the estimated value of each target at this moment has a mean of Z(k) and a variance of σ 2 and are independently normally distributed.

3. A track aliasing discrimination method based on a Gaussian probability model as claimed in claim 1, characterized in that: In the step five, The condition that the difference ΔX(k) of the estimated position satisfies is -d m ≤ΔX≤d m ;in, 4. A track aliasing discrimination method based on a Gaussian probability model as claimed in claim 1, characterized in that: In step 7, the calculation formula for the track aliasing probability of targets i and j is: in,

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