A high-precision interferometer direction-finding method applied to passive detection systems

Abstract

This invention belongs to the field of passive direction finding technology, and specifically relates to a high-precision interferometer direction finding method applied to passive detection systems. This invention remodels the phase data of the interferometer antenna array channels and proposes a full-baseline least squares direction finding method based on the longest baseline ambiguity number search, which can improve the success rate and accuracy of interferometer direction finding deambiguity. This invention uses a search method starting from the longest baseline for deambiguity, replacing the step-by-step calculation starting from the shortest baseline. This eliminates the problem of low deambiguity probability caused by the cumulative amplification of errors in traditional step-by-step deambiguity, and further improves angle accuracy by utilizing the least squares angle estimation method of all data.

Description

Technical Field

[0001] This invention belongs to the field of passive direction finding technology, and in particular relates to a high-precision interferometer direction finding method for passive detection systems. Background Technology

[0002] The angle of arrival (Angle of Arrival) is a crucial input parameter for passive detection systems to sort signals, a fundamental observation in rendezvous and positioning algorithms, and a vital indicator of situational awareness. Therefore, advanced passive detection systems should possess excellent direction-finding performance. Common direction-finding methods include amplitude comparison, phase comparison, and Doppler direction finding. Airborne systems typically employ phase interferometers for direction finding, which offer advantages such as high accuracy and speed. However, there is a trade-off between the accuracy of interferometer direction finding and the maximum unambiguous viewing angle range. On one hand, the principle of phase interferometers dictates that a longer baseline length results in higher direction-finding accuracy. On the other hand, phase difference measurements between channels suffer from 2π ambiguity; therefore, to avoid ambiguity, the baseline length must be set to ensure the phase difference is within [-π, π]. With a fixed ambiguity viewing angle, this limits the baseline length. The long-short baseline method was proposed to resolve the aforementioned contradictions. Its basic principle is to combine long and short baselines. The short baseline setting ensures the corresponding phase difference is unambiguous, allowing for a rough angle estimate. This angle estimate is then used to deambiguate the phase difference corresponding to the long baseline, and the deambigued long baseline phase difference is used for precise angle estimation. In practice, multiple levels of baselines are set between the longest and shortest baselines. Using the above method to deambiguate step-by-step can obtain the unambiguous phase difference corresponding to all baselines. However, this step-by-step deambiguation method starting from the shortest baseline is prone to failure if any two adjacent baselines fail to deambiguate, leading to the failure of the entire system. Furthermore, the direction-finding accuracy of short baselines is relatively poor. This makes deambiguation failure easy to occur in the initial stage of multi-level baseline step-by-step deambiguation, inevitably resulting in a completely erroneous direction-finding system output. Additionally, the typical long-short baseline method mainly employs two methods for final direction-finding estimation: one is to estimate the angle only based on the longest baseline, and the other is to directly sum all baselines and all unambiguous phase differences to construct a longer baseline, and then estimate the angle. The former method doesn't fully utilize the difference data, while the latter ignores the correlation of errors in the difference data, making them neither optimal estimation methods. Therefore, it is essential to design a high-probability defuzzification method for multi-level baseline interferometer systems. Summary of the Invention

[0003] The purpose of this invention is to address the problem of low defuzzification probability caused by the cumulative amplification of errors in traditional step-by-step defuzzification, and to provide a high-probability, high-precision interferometer direction-finding algorithm that can eliminate the problem of low defuzzification probability caused by the cumulative amplification of errors in traditional step-by-step defuzzification while improving the accuracy of angle estimation.

[0004] To address the aforementioned technical problems, this invention provides a high-probability, high-precision interferometer direction-finding algorithm for multi-baseline phase interferometer antenna arrays, featuring the following technical characteristics: Calculating the maximum possible ambiguity number of the longest baseline of the interferometer, determining the ambiguity number range of the longest baseline, and sequentially assigning values ​​to the ambiguity number of the longest baseline within this range; estimating the unambiguous phase difference of all channels based on the ambiguity number of the longest baseline, combining this with the measured ambiguous phase to obtain the ambiguity number of each channel, and then obtaining the updated unambiguous phase. The estimated residual is then obtained by updating the angle sine and initial phase estimates using the least squares method; the algorithm with the smallest estimated residual among all the above estimates is searched as the optimal estimate, and the optimal angle estimate is calculated using the angle sine value estimation.

[0005] The specific steps are as follows:

[0006] A high-precision interferometer direction finding method for passive detection systems, characterized by comprising the following steps:

[0007] S1. Calculate the maximum possible ambiguity number of the longest baseline based on the array layout parameters of the multi-baseline phase interferometer antenna array. Where round(·) represents rounding to the nearest integer, d M Let λ represent the position of the Mth array element, and λ be the wavelength of the signal. Let the longest baseline ambiguity number k be in the range [-n]. max n max Values ​​are taken sequentially within the range;

[0008] S2. Estimate the longest baseline unambiguous phase. The corresponding estimated sine value of the angle All channels have no blurring phase difference The superscript (k) indicates that the longest baseline ambiguity is k, and the symbol (·) T Represents the matrix transpose; based on the estimated unambiguous phase difference φ (k) There is a fuzzy phase difference between the measured values ​​and the actual values. Obtain the fuzzy number of each channel in

[0009] S3, based on the fuzzy number n (k) There is ambiguous phase data in each channel. Estimation of unambiguous phase data for update channels The phase measurements from each array element's receiving channel satisfy the matrix expression Ay. (k) +e=φ (k) The angle sine and initial phase estimates are updated using the least squares method. in Denotes the pseudo-inverse of a matrix, with the direction matrix A = [a, I]. M×1 ], where I is the identity matrix, Measurement data x is the sine of the angle, i.e., x = sinθ. Let e ​​be the initial phase of the signal at the first array element, and e be the phase error vector, thus obtaining the estimated residual as... The corresponding residual 2-norm is

[0010] S4. Using the estimated residual as the cost function of the fuzzy number fit, the problem of solving for the fuzzy number is transformed into the problem of finding the value of the independent variable when the cost function is minimized. Since the fuzzy number k is an integer and has a finite range, the optimal value of the fuzzy number k is obtained through search. opt To obtain intermediate variables The estimate is then used to obtain the estimate of the angle sine. At this point, the estimated value of the angle is obtained by calculating the arcsine function arcsin(·).

[0011] The present invention has the following beneficial effects.

[0012] This invention remodels the phase data of the interferometer antenna array channel and proposes a full-baseline least squares direction finding method based on the longest baseline ambiguity number search, which can improve the success rate of interferometer direction finding deambiguity resolution and direction finding accuracy.

[0013] This invention employs a search method to deblur from the longest baseline, replacing the stepwise calculation from the shortest baseline. This eliminates the problem of low deblurring probability caused by the cumulative amplification of errors in traditional stepwise deblurring, and improves the accuracy of angles by using the least squares angle estimation method of all data. Attached Figure Description

[0014] Figure 1 This is a flowchart of the high-probability, high-precision interferometer direction-finding algorithm of the present invention.

[0015] Figure 2 This is a schematic diagram of a multi-baseline interferometer antenna array.

[0016] Figure 3 The success rate of deblurring with the signal-to-noise ratio is the change between the stepwise deblurring when the signal is incident from 0° and the deblurring success rate of the method of this invention.

[0017] Figure 4 The change in angle estimation accuracy of the method of this invention with the signal-to-noise ratio is the stepwise deblurring when the signal is incident from 0° and the angle estimation accuracy with the signal-to-noise ratio.

[0018] Figure 5 The success rate of deblurring with the signal-to-noise ratio is the change between the stepwise deblurring when the signal is incident at 45° and the deblurring success rate of the method of this invention.

[0019] Figure 6The change in angle estimation accuracy of the method of this invention with the signal-to-noise ratio is the stepwise deblurring when the signal is incident from 45°. Detailed Implementation

[0020] The present invention will now be described in detail with reference to the accompanying drawings.

[0021] See Figure 1 This invention provides a high-probability, high-precision interferometer direction-finding algorithm for multi-baseline phase interferometer antenna arrays, featuring the following technical characteristics: Calculating the maximum possible ambiguity number of the longest baseline of the interferometer, determining the ambiguity number range of the longest baseline, and sequentially assigning values ​​to the ambiguity number of the longest baseline within this range; estimating the unambiguous phase difference of all channels based on the ambiguity number of the longest baseline, combining this with the measured ambiguous phase to obtain the ambiguity number of each channel, and then obtaining the updated unambiguous phase. The estimated residual is then obtained by updating the angle sine and initial phase estimates using the least squares method; the algorithm with the smallest estimated residual among all the above estimates is searched as the optimal estimate, and the optimal angle estimate is calculated using the angle sine value estimation.

[0022] First, calculate the maximum possible ambiguity number n of the longest baseline based on the array layout parameters. max Let the longest baseline ambiguity number k be in [-n max ,n max Values ​​are taken sequentially within the range; then, the unambiguous phase of the longest baseline is estimated successively. (superscript) (k) The longest baseline ambiguity number is k (the same below), and the corresponding sine value x of the estimated angle. (k) All channels have no ambiguity phase difference symbol(·) T Represents the matrix transpose, based on the estimated unambiguous phase difference φ (k) There is a fuzzy phase difference between the measured values ​​and the actual values. The fuzzy number of each channel can be obtained. Next, based on the fuzzy number n (k) There is ambiguous phase data in each channel. The updated phases of all channels are unambiguous, and the phase measurements from each array element's receiving channel satisfy the matrix expression Ay. (k) +e=φ (k) By updating the angle sine and initial phase estimates using the least squares method, we can obtain... in Denotes the pseudo-inverse of a matrix, A = [a, I] M×1 ], where I is the identity matrix, d i Let λ represent the position of the i-th array element, and λ be the wavelength of the signal. x is the sine of the angle, i.e., x = sinθ. Let e ​​be the initial phase of the signal at the first array element, and e be the phase error vector, thus obtaining the estimated residual. The corresponding residual 2-norm is Finally, the estimate with the smallest residual among all the above estimates is selected as the optimal estimate, and the optimal angle estimate is obtained by calculating the corresponding angle sine value.

[0023] In the following optional embodiments, a high-probability, high-precision interferometer direction-finding algorithm is used to estimate the angle of a phase interferometer antenna array, verifying the performance of the algorithm in terms of deambiguity probability and direction-finding accuracy.

[0024] In one alternative embodiment: the antenna array of a phase interferometer system is as follows Figure 2 As shown, the four array elements are located at [0, 0.15, 0.6, 1.95] m respectively, and a 1 GHz signal is incident from 0° and 45° azimuths respectively.

[0025] The calculation process of the direction finding algorithm of this invention is as follows:

[0026] (1) Calculate the maximum possible ambiguity number of the longest baseline based on the array layout parameters. In the formula, round(·) represents rounding to the nearest integer, and the longest baseline ambiguity number k is in the range [-n]. max ,n max Values ​​are taken sequentially within the range. In this embodiment, d M =1.95, n max =41;

[0027] (2) When the longest baseline ambiguity number is k, the unambiguous phase of the longest baseline is estimated successively. The corresponding estimated sine value of the angle All channels have no blurring phase difference Based on the estimated unambiguous phase difference φ (k) There is a fuzzy phase difference between the measured values ​​and the actual values. The fuzzy number of each channel can be obtained. in

[0028] (3) Based on the fuzzy number n (k) There is ambiguous phase data in each channel. Estimation of unambiguous phase data for update channels The phase measurements from each array element's receiving channel satisfy the matrix expression Ay. (k) +e=φ (k) By updating the angle sine and initial phase estimates using the least squares method, we can obtain... The estimated residual is obtained as The corresponding residual 2-norm is

[0029] (4) By using the estimated residual as the cost function of the fuzzy number fit, the problem of solving for the fuzzy number is transformed into finding the value of the independent variable when the cost function is minimized. Since the fuzzy number k is an integer with a finite range, the optimization problem can be solved by searching. The optimal value k of the fuzzy number can be obtained through searching. opt To obtain intermediate variables From this estimation, we can obtain an estimate of the sine value of the angle. At this point, the estimated value of the angle can be calculated using the arcsine function arcsin(·).

[0030] To compare the deblurring probability and angle estimation accuracy of the method proposed in this invention with the traditional stepwise deblurring method, comparison graphs were plotted under signal incidence conditions of 0° and 45°, showing the deblurring probability and angle estimation accuracy of the two methods as the signal-to-noise ratio increases. Figure 3-6 As shown.

[0031] from Figures 3 to 6 It can be seen that as the signal-to-noise ratio increases, both the traditional stepwise deblurring method and the method proposed in this invention improve the deblurring probability and angle estimation accuracy. Under the same signal-to-noise ratio conditions, the method proposed in this invention performs better in terms of deblurring probability and angle estimation accuracy, and improves the deblurring probability by about 5%-10% in low signal-to-noise ratio regions.

Claims

1. A high-precision interferometer direction-finding method applied to a passive detection system, characterized in that, comprising the steps of: S1. Calculate the maximum possible ambiguity number of the longest baseline based on the array layout parameters of the multi-baseline phase interferometer antenna array. ,in This indicates rounding to the nearest integer. Indicates the first The position of each array element It is the wavelength of the signal, which makes the longest baseline ambiguity number... exist Take values ​​sequentially within the range; S2. Estimate the longest baseline unambiguous phase difference. The corresponding estimated sine value of the angle All channels have no ambiguity phase difference superscript The longest baseline ambiguity is k, and the symbol is... Represents matrix transpose; based on the estimated unambiguous phase difference across all channels There is a fuzzy phase difference between the measured values ​​and the actual values. Obtain the fuzzy number of each channel ,in ; S3, based on fuzzy numbers There is ambiguous phase data in each channel. Update # Estimation of unambiguous phase difference for each channel The phase measurements from the receiving channels of each array element satisfy the matrix expression. The angle sine and initial phase estimates are updated using the least squares method. ,in Represents the pseudo-inverse of a matrix, and the direction matrix. , It is the identity matrix. Measurement data x is the sine of the angle. , Let e ​​be the initial phase of the signal at the first array element, and e be the phase error vector, thus obtaining the estimated residual as... The corresponding residual 2-norm is ; S4. Using the estimated residual as the cost function of the fuzzy number fit, the problem of solving for the fuzzy number is transformed into the problem of finding the value of the independent variable when the cost function is minimized. Since the fuzzy number k is an integer and has a finite range, the optimal value of the fuzzy number is obtained through search. To obtain intermediate variables The estimate is then used to obtain the estimate of the angle sine. At this point, through the arcsine function The estimated value of the angle is calculated. .

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