A pedestrian state detection method based on variable parameter synchronous compression S transform

Abstract

This invention discloses a pedestrian state detection method based on variable-parameter synchronous compressed S-transform. The specific implementation includes the following steps: First, acquire the pedestrian target echo signal; then, select a window function control factor and perform an improved window function S-transform on the target echo signal; next, rearrange the signal energy along the frequency direction in the time-frequency plane, concentrating the energy at the center frequency, thereby obtaining a variable-parameter synchronous compressed S-transform time-frequency map; finally, use the obtained time-frequency map to identify the pedestrian target gait state. This invention utilizes an error function to modify the window function of the traditional S-transform, enabling the window function to adapt to signal changes, and adds a synchronous compressed transform post-processing process, thereby making the Doppler characteristics of the pedestrian echo clearer and achieving accurate identification of the pedestrian target gait state.

Description

Technical Field

[0001] This invention belongs to the field of vital signal detection, and in particular relates to a pedestrian state detection method based on variable parameter synchronous compressed S-transform. Background Technology

[0002] Non-stationary signals are the most common signals in radar signal processing, and micro-Doppler signals are a special type of non-stationary signal. Time-frequency analysis is an important tool for analyzing the characteristics of micro-Doppler signals. When using traditional time-frequency analysis methods to analyze pedestrian micro-Doppler signals, the time-frequency convergence is low, and the spectral line tailing is severe, making it impossible to accurately distinguish the target's state. Currently, commonly used time-frequency analysis methods mainly include Short-Time Fourier Transform (STFT), Continuous Wavelet Transform (CWT), and S-Transform.

[0003] The basic idea of ​​STFT is to achieve piecewise Fourier transform of a signal through windowing, thereby obtaining the signal's time-varying characteristics. However, its window function is fixed, making it difficult to achieve sufficiently high resolution in both the time and frequency domains in practical applications. CWT analyzes the signal through time-scale analysis and can adaptively adjust the time-frequency window according to the characteristics of high and low frequency signals. However, wavelet basis design is difficult, and it suffers from insufficient time-frequency resolution and complex scale-frequency conversion, thus limiting the fine-grained analysis of signals.

[0004] To overcome the limitations of STFT (Simulated Time Transform) in adjusting the time window length and the phase localization problem of CWT (Concurrent Time Transform), a variable Gaussian window function is introduced in the S-transform. This method yields a time-frequency spectrum with high resolution in the low-frequency range and low resolution in the high-frequency range, meaning the resolution is variable. However, this inverse relationship leads to problems such as excessively wide or narrow window lengths in certain regions, resulting in time positioning failures at low frequencies and frequency positioning failures at high frequencies. This limits the application of the S-transform to some extent. Furthermore, the aforementioned time-frequency analysis method is affected by the Heisenberg-Gabor indeterminacy problem, and its time-frequency spectrum resolution cannot reach optimal levels.

[0005] As can be seen from the above, the existing time-frequency analysis methods still have shortcomings and need to be further improved to enhance time-frequency clustering and thus improve the recognition accuracy of pedestrian target gait state. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the present invention aims to provide a pedestrian state detection method based on variable parameter synchronous compressed S-transform.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A pedestrian state detection method based on variable parameter synchronous compressed S-transform includes the following steps:

[0009] Step 1: Acquire pedestrian radar echo signals, discretize them in the time domain, and obtain discrete sequences;

[0010] Step 2: Perform a Fast Fourier Transform on the discrete sequence to obtain the signal spectrum;

[0011] Step 3: Introduce the error function erf(x) into the window function. Determine the values ​​of control factors α, β, and γ based on the signal spectrum and resolution requirements. After obtaining the window length control function, determine the window function.

[0012] Step 4: Perform a Fast Fourier Transform on the window function to obtain its spectrum;

[0013] Step 5: Periodically extend the signal spectrum and multiply it with the window function spectrum;

[0014] Step 6: Perform an inverse Fourier transform on the result of multiplication in step 5 to obtain the time distribution result of that frequency point;

[0015] Step 7: Repeat steps 4-6 to calculate all frequency points, and finally obtain the spectrum when the parameter S-transform is changed;

[0016] Step 8: Perform synchronous compression transformation on the variable parameter S-transform result obtained in Step 7. The specific method is as follows: take the frequency center after the variable parameter S-transform as the center frequency set, compress the value of each time frequency point corresponding to the interval near the center frequency to the center frequency, and obtain the time spectrum of the variable parameter synchronous compressed S-transform.

[0017] Step 9: Based on the variable parameter synchronous compression S-transform spectrum information, set a threshold to determine the pedestrian status: fast walking, normal walking, slow walking.

[0018] Compared with the prior art, the significant advantages of this invention are:

[0019] 1) By introducing an error function erf(x) into the window function and setting control factors α, β, and γ, the present invention can adaptively adjust the window function according to the signal frequency to achieve higher frequency resolution at low frequencies and higher time resolution at high frequencies.

[0020] 2) This invention combines the variable parameter S-transform with the synchronous compression transform to rearrange the energy of the time-frequency signal, thereby improving the energy concentration and time-frequency resolution. It also addresses the problem that traditional time-frequency analysis methods are affected by the Heisenberg-Gabor indeterminacy problem, which prevents them from achieving optimal time-frequency resolution, thus making the Doppler characteristics of human body echoes clearer. Attached Figure Description

[0021] The present invention will now be described in further detail with reference to the accompanying drawings.

[0022] Figure 1 This is a flowchart of the pedestrian state detection method based on variable parameter synchronous compressed S-transform of the present invention.

[0023] Figure 2 This is an algorithm flowchart of the variable parameter synchronous compression S-transform time-frequency analysis method of the present invention.

[0024] Figure 3 This is a time-frequency analysis result diagram of the signal S-transformation in Embodiment 1 of the present invention.

[0025] Figure 4 This is a time-frequency analysis result diagram of the signal parameter S-transformation in Embodiment 1 of the present invention.

[0026] Figure 5 This is a time-frequency analysis result diagram of the synchronous compression S-transform of signal with variable parameters in Embodiment 1 of the present invention.

[0027] Figure 6 This is a time-frequency analysis result diagram of the signal S-transformation in Embodiment 2 of the present invention.

[0028] Figure 7 This is a time-frequency analysis result diagram of the signal variable parameter S-transformation in Embodiment 2 of the present invention.

[0029] Figure 8 This is a time-frequency analysis result diagram of the synchronous compression S-transform of signal with variable parameters in Embodiment 2 of the present invention.

[0030] Figure 9 This is a time-frequency analysis result diagram of a pedestrian walking quickly in Embodiment 3 of the present invention.

[0031] Figure 10 This is a time-frequency analysis result diagram of a pedestrian walking normally in Embodiment 3 of the present invention.

[0032] Figure 11 This is a time-frequency analysis result diagram of a pedestrian walking slowly in Embodiment 3 of the present invention. Detailed Implementation

[0033] like Figure 1 and Figure 2 As shown, a pedestrian state detection method based on variable parameter synchronous compressed S-transform of the present invention includes the following steps:

[0034] Step 1: Perform time-domain sampling on the pedestrian echo signal s(t), with a sampling frequency of fs and a sampling time interval of . The number of sampling points is Where t is the signal duration, the discrete sequence s[kT] is obtained, k = 0, 1, 2, ..., N-1, where k is the index of the time sampling point and N is the total number of signal sampling points;

[0035] Step 2: Perform a Fast Fourier Transform on the discrete sequence s[kT] to obtain the signal spectrum. Where n is the frequency sampling point index and N is the total number of signal sampling points; and it is then subjected to periodic extension processing to obtain Where m is the index of the extended sampling point, and N is the total number of signal extended sampling points;

[0036] Step 3: Introduce an error function into the window function. Where η is the integration factor. Based on the signal spectrum and resolution requirements, control factors α, β, and γ are determined. After obtaining the window length control function, the window function is determined. The specific steps are as follows:

[0037] Step 3-1: Let the signal sampling rate be f. s ,because in Then take f represents the frequency variable;

[0038] Step 3-2: Determine the range of values ​​for the frequency window length [Δf] min , Δf max ], where Δf min It is the minimum frequency window length, Δf max The maximum frequency window length is given by α, β, and γ, which represent window function control factors, and Δf represents the frequency window range. The ranges of parameters α and γ are then determined using inequalities.

[0039]

[0040] Step 3-3: Select the values ​​of control factors α, β, and γ from steps 3-1 and 3-2, and then substitute these parameters into the window length control function:

[0041]

[0042] Steps 3-4: Substitute the window length control function into the Gaussian window function to obtain the improved window function expression:

[0043] Where t is the time variable, f is the frequency variable, and σ represents the window length control function.

[0044] Step 4: Perform a Fast Fourier Transform on the window function to obtain its spectrum, where... The starting frequency point is given by the following formula:

[0045] Where m is the index of the time sampling point, N is the total number of signal sampling points, and n = 0, 1, 2, ..., N-1, where n is the index of the frequency sampling point and N is the total number of signal sampling points;

[0046] Step 5: Extend the periodic spectrum of the signal. Multiply by the spectrum of the window function G(m, n);

[0047] Step 6: Perform an inverse Fourier transform on the multiplication result from Step 5 to obtain the signal time-domain information at that frequency point.

[0048] Step 7: Calculate the time-domain information of all frequency points. Specifically, determine whether n≥N-1 holds true. If not, add 1 to n and repeat steps 4, 5, and 6 until all frequency points are completed, and obtain the time spectrum of the variable parameter S-transform.

[0049] Step 8: Based on the time spectrum of the variable parameter S obtained in Step 7, to further improve the time-frequency convergence, synchronous compression processing is performed on it. The specific steps are as follows:

[0050] Step 8-1: To obtain the center frequency of the variable-parameter S-transform, its expression needs to be adjusted. The specific steps are as follows:

[0051] Here is the first form of the S-transform expression with varying parameters:

[0052]

[0053] Where t is the time variable, f is the frequency variable, τ is the integral variable, and σ represents the window length control function.

[0054] Because the window function is The simplified form of the variable-parameter S-transform expression is obtained as follows:

[0055]

[0056] Adjust the second form of the variable parameter S-transform, and let g ω (τ)=g(τ-t)exp(j2πfτ), thus obtaining the third form of the variable parameter S-transform expression:

[0057]

[0058] in,() * S(ξ), G represents the complex conjugate. ω (ξ) represent s(τ) and g, respectively. ω The Fourier transform of (τ) is such that, since the window function is a real even window, g * =g. G ω (ξ) can be represented as:

[0059]

[0060] Let τ - t = t′, then the above equation can be rewritten as:

[0061]

[0062] Where G(ω-ξ) is the Fourier transform of the window function. Substituting the above equation into the third form of the variable parameter S-transform expression, we get:

[0063]

[0064] By shifting the above equation, the frequency domain expression of the shifted variable-parameter S-transform can be defined as:

[0065] Where t is the time variable, ω is the frequency variable, and ξ is the integral variable.

[0066] Step 8-2: Obtain the center frequency of the variable parameter S-transform. The specific steps are as follows:

[0067] Consider signal For a harmonic signal with frequency ω0 and amplitude A, the Fourier transform of s(t) is S(ξ) = 2πA·δ(ξ-ω0), where δ represents the Dirac function. Substituting these values ​​into the frequency domain expression of the S-transform, we can obtain the parametric S-transform expression for s(t):

[0068]

[0069] The partial derivative of the above equation with respect to time is:

[0070]

[0071] When the ST corresponding to any point (t, ω) of the signal e When (t, ω) ≠ 0, we obtain the first form of the expression for the center frequency:

[0072]

[0073] The partial derivative of the frequency domain expression of the variable-parameter S-transform with respect to time can be obtained by taking the time partial derivative with respect to the window function. The derivation is as follows:

[0074]

[0075] Where g′ represents the partial derivative of the window function with respect to time.

[0076] Substituting the above equation into the first form of the center frequency expression, we obtain the second form of the center frequency expression:

[0077]

[0078] Step 8-3: After obtaining the signal center frequency in step 8-2, the energy of the variable-parameter S-transform is redistributed along the frequency direction to obtain the variable-parameter synchronous compression S-transform expression for the time-frequency plane:

[0079]

[0080] Where v l The frequency after synchronous compression, Δv l =v l -v l-1 The frequency interval between adjacent points after compression is represented by l∈[1,N], where l is the sampling point index, N is the total number of sampling points in the signal, and the rearrangement interval is [v l -Δv l v l +Δv l ];f k For the discretized frequency points on the variable parameter S-transform spectrum, Δf k =f k -f k-1 The frequency interval on the variable parameter S-transform spectrum is represented by k∈[1,N], where k represents the sampling point index and N represents the total number of sampling points of the signal.

[0081] Step 8-4: Repeat step 8-3 until all center frequency points have been calculated to obtain the time-frequency result.

[0082] Step 9: Use the obtained variable parameters to synchronously compress the S-transform time spectrum, and calculate the Doppler frequency according to the formula. Determine pedestrian walking status: fast walking, normal walking, slow walking; where c is the speed of light, f is the radar operating frequency, v is the speed of the relevant part of the pedestrian, and f d This represents the Doppler frequency. The specific determination method is: set a toe velocity threshold range v. f ∈[5.25, 6.06] m / s (corresponding to trunk velocity v) t If the value is above the threshold range (∈[1.3, 1.5] m / s), it is considered a fast walking state; if it is below the threshold range, it is considered a slow walking state; if it is within the range, it is considered a normal walking state.

[0083] Compared with existing methods and technologies, this invention includes a variable parameter S-transform, which can achieve high-resolution time-frequency analysis by adjusting the value of the control factor, and has a high degree of flexibility. On the other hand, it incorporates a synchronous compression transform, which achieves high-resolution time-frequency representation by rearranging the energy of the signal in the frequency direction, providing powerful assistance for the accurate identification of pedestrian target states.

[0084] The present invention will be further described in detail below with reference to embodiments.

[0085] Example 1

[0086] The simulation signal is a linear frequency modulated signal with a frequency modulation slope k = 400, and its analytical expression is:

[0087]

[0088] Signal sampling frequency f s =1024Hz, therefore β=50. For this linear frequency modulated signal, f max ≈400Hz, f min Since the frequency range is large (≈0Hz), adjustment factors α = 60 and γ = 120 are chosen respectively. Figure 5 The figure shows the time-frequency analysis results of the method of this invention, which uses the erf(x) error function as the window function control function. As can be seen from the figure, this method solves the problems of signal divergence and poor energy concentration at high frequencies in the S-transform, demonstrating the effectiveness of this method in processing linear frequency modulated signals.

[0089] Example 2

[0090] The simulated signal is a nonlinear frequency-modulated signal with a sinusoidal frequency variation, and its analytical expression is:

[0091] s(t)=e j2π[6cos(10πt)+260t] t∈[0,1]

[0092] Signal sampling frequency f s =1024Hz, therefore β=50. For this nonlinear frequency modulated signal, f max ≈450Hz, f min ≈70Hz, the frequency changes sinusoidally with time, so the adjustment factors are α=60 and γ=150 respectively. Figure 8 The time-frequency analysis results of the method of this invention, which uses the ERF error function as the window function control function, show high resolution in all parts of the frequency variation for nonlinear frequency-modulated signals. The problem of severe signal energy divergence at the location of drastic frequency changes has also been well solved, indicating that this method is a time-frequency analysis tool with high time-frequency convergence.

[0093] Example 3

[0094] The simulated signal was a radar echo signal obtained using a human body simulation model provided by Boulic and Thalmann et al. (Reference: The micro-Doppler Effect in Radar. Victor C. Chen. Library of Congress Cataloging-in-Publication Data. 2011). Based on... Figure 9 , Figure 10 , Figure 11 It can be observed that the maximum Doppler frequencies obtained from different time-state velocities differ significantly. Therefore, according to the Doppler frequency calculation formula... Where c is the speed of light, f = 20 GHz is the radar operating frequency, v is the velocity of the relevant part of the pedestrian, and f dIndicates the Doppler frequency. Sets the toe velocity threshold range v. f ∈[5.25, 6.06] m / s (corresponding to trunk velocity v) t If the value is above the threshold range (∈[1.3, 1.5] m / s), it is considered a fast walking state; if it is below the threshold range, it is considered a slow walking state; if it is within the range, it is considered a normal walking state.

[0095] The above embodiment is a pedestrian state detection method based on variable-parameter synchronous compressed S-transform. The specific implementation includes the following steps: First, acquire the pedestrian target echo signal; then, select a window function control factor and perform an improved window function S-transform on the target echo signal; next, rearrange the signal energy along the frequency direction in the time-frequency plane, concentrating the energy at the center frequency, thereby obtaining a variable-parameter synchronous compressed S-transform time-frequency map; finally, use the obtained time-frequency map to identify the pedestrian target gait state. The above embodiment of the present invention uses an error function to modify the window function of the traditional S-transform, enabling the window function to adapt to signal changes and adding a synchronous compressed transform post-processing process, thereby making the Doppler characteristics of the pedestrian echo clearer and achieving accurate identification of the pedestrian target gait state.

[0096] The embodiments of the present invention have been described above in conjunction with the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made according to the purpose of the invention. Any changes, modifications, substitutions, combinations or simplifications made based on the spirit and principle of the technical solution of the present invention shall be equivalent substitutions. As long as they meet the purpose of the invention and do not deviate from the technical principle and inventive concept of the present invention, they shall fall within the protection scope of the present invention.

Claims

1. A pedestrian state detection method based on variable parameter synchronous compressed S-transform, characterized in that, Includes the following steps: Step 1: Acquire pedestrian radar echo signals, discretize them in the time domain, and obtain discrete sequences; Step 2: Perform a Fast Fourier Transform on the discrete sequence to obtain the signal spectrum; Step 3: Introduce an error function into the window function. erf ( x Based on the signal spectrum and resolution requirements, determine the control factors. α , β , γ After obtaining the window length control function, the window function is determined based on the value of ; Step 4: Perform a Fast Fourier Transform on the window function to obtain its spectrum; Step 5: Periodically extend the signal spectrum and multiply it with the window function spectrum; Step 6: Perform an inverse Fourier transform on the result of multiplication in step 5 to obtain the time distribution of frequency points; Step 7: Repeat steps 4-6 to calculate all frequency points, and finally obtain the spectrum when the parameter S-transform is changed; Step 8: Perform synchronous compression transformation on the variable parameter S-transform result obtained in Step 7. The specific method is as follows: take the frequency center after the variable parameter S-transform as the center frequency set, compress the value of each time frequency point corresponding to the interval near the center frequency to the center frequency, and obtain the time spectrum of the variable parameter synchronous compressed S-transform. Step 9: Based on the variable parameter synchronous compression S-transform spectrum information, set a threshold to determine the pedestrian status: fast walking, normal walking, slow walking; In step 8, the formula for calculating the center frequency is: ； in The variable-parameter S-transform after the shift operation. For the parametric S-transform that differentiates and shifts the window function, t For time variables, For frequency variables, sign j Represents an imaginary number.

2. The pedestrian state detection method based on variable parameter synchronous compressed S-transform according to claim 1, characterized in that, In step 3, the specific method for determining the window length control function and the window function is as follows: Step 3-1: Set the signal sampling rate to be... ,because ,in Then take ; f Represents frequency variables; Step 3-2: Determine the range of values ​​for the frequency window length. ,in It is the minimum frequency window length. The maximum frequency window length, α , β , γ This represents the window function control factor. The frequency window range is then represented, and the parameters are determined using inequalities. α and γ The range of values ​​for: ； Step 3-3: Select control factors based on steps 3-1 and 3-2. α , β , γ Then, substitute the parameters into the window length control function: ； Steps 3-4: Substitute the window length control function into the Gaussian window function to obtain the improved window function expression: ,in t For time variables, f For frequency variables, This represents the window length control function.

3. The pedestrian state detection method based on variable parameter synchronous compressed S-transform according to claim 1, characterized in that, In step 8, the formula for calculating the spectrum during the variable-parameter synchronous compressed S-transform is obtained as follows: ； in To synchronize the compressed frequency, This indicates the frequency interval between adjacent points after compression. , l For sampling point index, N The total number of signal sampling points is , and the rearrangement interval is . ; For the discretized frequency points on the variable parameter S-transform spectrum, This represents the frequency interval on the variable-parameter S-transform spectrum. , k Indicates the sampling point index. N This indicates the total number of signal sampling points.

4. The pedestrian state detection method based on variable parameter synchronous compressed S-transform according to claim 1, characterized in that, In step 9, the specific method for determining the pedestrian's state is as follows: using the obtained variable parameter synchronous compression S-transform time spectrum, and calculating the Doppler frequency according to the formula... Determine the pedestrian's walking status: fast walking, normal walking, slow walking; among which... c At the speed of light, f For radar operating frequency, For the speed of the relevant parts of the pedestrian, This represents the Doppler frequency; the specific determination method is: setting a threshold range for toe speed. The corresponding trunk speed is If the value is higher than the threshold range, it is judged as a fast walking state; if it is lower than the threshold range, it is a slow walking state; if it is within the range, it is a normal walking state.

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