A two-step correlation based chirp ultrasonic signal time of flight estimation method

Abstract

The application relates to a two-step correlation-based chirp ultrasonic signal time-of-flight estimation method, and belongs to the method for measuring the time-of-flight of ultrasonic waves. The coarse correlation is used to obtain the non-accurate TOF of the chirp ultrasonic signal, and the fine correlation is used to obtain the accurate TOF of the chirp ultrasonic signal. The application has the advantages that the accurate time-of-flight TOF is obtained through two-step correlation calculation, the amount of calculation is effectively reduced due to the small amount of data participating in the correlation calculation, and a detection method with low calculation amount is provided for the application fields of distance measurement, multi-target tracking and positioning and other ultrasonic time-of-flight detection-based application fields.

Description

Technical Field

[0001] This invention relates to a method for measuring ultrasonic transit time, specifically a chirp ultrasonic signal transit time estimation method based on two-step correlation. Background Technology

[0002] Distance measurement based on ultrasonic Time-of-Flight (TOF) has been widely applied in many engineering applications, such as indoor positioning, mobile robots, and three-dimensional (3D) tracking and positioning systems. Ultrasonic TOF measurement techniques mainly include simple thresholding and cross-correlation techniques. Thresholding techniques detect the arrival time of the ultrasonic wave when the received ultrasonic signal voltage exceeds a predetermined threshold. The advantage of this technique is that it does not require complex calculations and can therefore be implemented with a simple circuit, thus reducing system costs. However, this method relies solely on the amplitude of the received signal, making it susceptible to noise and amplitude variations, resulting in lower measurement accuracy. On the other hand, cross-correlation is a standard TOF estimation technique. This method determines the received signal delay time, or TOF, by finding the maximum value of the cross-correlation operation between the transmitted and received signals. Cross-correlation can reduce noise levels because the cross-correlation of random additive noise is theoretically zero, thus using cross-correlation to reduce additive noise. However, it performs poorly with single-frequency signals because several cycles in a single-frequency signal can produce cross-correlation values ​​similar to the maximum value, easily causing TOF measurement errors and reducing the accuracy of TOF measurements. This technique can improve measurement accuracy when the signal has a certain bandwidth, such as a chirp frequency-modulated signal, and the improvement in accuracy depends on the signal bandwidth. For chirp frequency-modulated signals, cross-correlation is used for Time-of-Flight (TOF) estimation, which is considered the best TOF estimation technique because it utilizes all the information contained in the signal. Cross-correlation is called matched filtering, and when cross-correlation is combined with frequency-modulated signals, pulse compression is achieved.

[0003] Cross-correlation can be performed in both the time and frequency domains. In the time domain, this method simply takes the transmitted signal s. t (t) and received signal s r Cross-correlation is performed on (t-τ0). Since the maximum value of the cross-correlation c(t) occurs at the delay time τ0, τ0 is the desired Time of Flight (TOF). In the frequency domain, to reduce computational complexity, a Fast Fourier Transform (FFT) is used. First, the transmitted signal s... t (t) and received signal s rPerform an FFT on (t-τ0), then calculate the inverse fast Fourier transform (IFFT) of the product of the two FFTs to obtain c(t). Similarly, determine the delay time τ0 based on the maximum value of c(t). In the frequency domain, although Fourier transforms and inverse Fourier transforms are performed on the transmitted and received signals, the computational complexity is less than that of cross-correlation in the time domain due to the use of FFT. Since Fourier transform requires complex calculations and the result needs to be stored for inverse Fourier transform, more memory resources are required. To save memory, even if the FFT is performed at the original data storage location, this means the FFT output is placed in the same memory space containing the input data. Even so, since FFT requires complex number operations, the result needs to be at least twice the length of the input data. This increases the system cost because it requires external memory, limiting the application of this method on a single processor, especially when the receiver and transmitter are far apart. Time-domain cross-correlation calculation is simpler; it does not require storing the result, and the delay time τ0 can be calculated simply by taking the position of the maximum value. While the time-domain cross-correlation method is simple and requires little memory, it is computationally intensive. For example, the duration of the transmitted signal is 5ms, and the sampling time of the received signal is 15ms. When the sampling frequency is 2MHz, the sample data lengths of the transmitted and received signals are 10000 and 30000, respectively. The cross-computation requires approximately 30000 × 10000 = 3 × 10⁻⁶. 8 The calculation involves multiple multiplications and additions. For a processor with a processing speed of 100 MIPS, disregarding loop and jump instructions, and only considering the multiply and accumulate (MAC) instructions assumed to be in a single cycle, the calculation would take 3 seconds to complete, making it difficult to implement in real time.

[0004] To reduce the computational cost of Time-of-Flight (TOF) estimation based on correlation-based chirp ultrasound signals, a two-step cross-correlation method based on coarse and fine cross-correlation is proposed. Compared with traditional correlation-based TOF estimation methods, this method reduces the computational cost, improves real-time performance, and has high practical application value. Summary of the Invention

[0005] This invention provides a chirp ultrasound signal transit time estimation method based on two-step correlation to solve the problem of large computational cost when directly estimating chirp ultrasound signal TOF using correlation.

[0006] The technical solution adopted in this invention is to obtain the inaccurate TOF of the chirp ultrasound signal by coarse correlation and to obtain the accurate TOF of the chirp ultrasound signal by fine correlation.

[0007] This invention uses coarse correlation to obtain an inaccurate Time-of-Flight (TOF) of the chirp ultrasound signal. The specific steps are as follows:

[0008] (1) The received chirp ultrasound signal s r (t) and the emitted chirp ultrasound signal s t (t) is sampled at a frequency of F. s The sampling interval is T s =1 / F s Assuming the number of sampling points for the received signal is N, the number of sampling points for the transmitted signal is M, and the sampled chirp ultrasound received data is s r (n)(1≤n≤N), the sampled chirp ultrasound received data is s t (m)(1≤m≤M);

[0009] (2) For s r (n) Perform equal-interval sampling according to the highest frequency f of the chirp ultrasonic emission signal. e The extraction interval Δ is set to twice the value of Δ, which is expressed as:

[0010]

[0011] in, This indicates rounding down. Divide s by Δ. r (n) Perform equal-interval sampling to obtain the received data s after sampling. re (l), Similarly, the chirp ultrasonic emission data s are analyzed at intervals of Δ. t (m) Equal intervals are used to obtain the extracted transmission data s te (k),

[0012] (3) Calculate s te (k) and s re The cross-correlation of (l) is calculated, and the delay τ corresponding to the maximum cross-correlation value is obtained. c Thus, the inaccurate TOF is obtained as follows:

[0013] TOF c =△τ c T s

[0014] This invention employs fine correlation to obtain accurate Time-of-Flight (TOF) of chirp ultrasound signals. The specific steps are as follows:

[0015] (1) The delay τ obtained from the coarse correlation c And the extraction interval Δ, we can obtain τ c In the original chirp ultrasound received datar The position in (n) is Δτ c ;

[0016] (2) Due to the coarse correlation, the TOF is determined. c With the precise TOF error within one frequency modulation cycle, in terms of Δτ c For reference in s r Data is selected from (n), based on the lowest modulation frequency f of the chirp ultrasonic transmission signal. s Define the selection range and the selection interval as follows:

[0017]

[0018] in To round up, "f s "This is the lowest frequency of the chirp ultrasound signal, in s..." r In (n), Δτ c Using the reference position, select δ data points forward and δ+M data points backward, then the selected data is s. r (Δτ c –δ:Δτ c +δ+M);

[0019] (3) Use the selected received data s r (Δτ c –δ:Δτ c +δ+M) and chirp ultrasonic emission data s t (m) performs cross-correlation calculation, and the delay corresponding to the maximum cross-correlation value is t. f Thus, the accurate TOF is obtained as follows:

[0020] TOF=(△τ c -δ+τ f )T s .

[0021] The chirp ultrasound signal of this invention includes linear frequency modulated chirp signal and nonlinear frequency modulated chirp signal.

[0022] This invention first extracts the raw sampled data and transmitted data of the received signal, performs coarse correlation, and obtains an inaccurate Time-of-Flight (TOF). Then, based on the inaccurate TOF, it selects raw data, and correlates the selected data with the transmitted data to obtain an accurate TOF. Compared with traditional correlation-based TOF estimation methods, this method uses relatively less data, has a lower computational load, and is real-time. It provides a computationally efficient and highly accurate TOF estimation method for ultrasonic applications based on distance measurement, such as ranging, target tracking, and positioning.

[0023] The purpose of this invention is to provide a two-step correlation-based chirp ultrasonic signal transit time estimation method, which improves the computational efficiency, real-time performance and accuracy of a TOF estimation method in engineering applications based on ultrasonic ranging, tracking and positioning, liquid level measurement and other TOF-based applications.

[0024] The TOF estimation method for chirp ultrasound signals disclosed in this invention, based on coarse and fine two-step correlation, has a multiply-accumulate computational complexity of approximately 2M (N / Δ). 2 +2δ+1), while the multiplication and addition operations of the traditional TOF estimation method are about 2MN. According to the specific method of this invention, N is much larger than N / Δ. 2 +2δ+1, it can be seen that the TOF estimation method disclosed in this invention can effectively reduce the amount of computation.

[0025] The advantages of this invention are: it adopts a coarse and fine two-step correlation operation, and by extracting and selecting data, the amount of data participating in the overall cross-correlation operation is small, so the computational load is low, the real-time performance is good, and the required storage space is small. It provides a low-computation TOF estimation method for ultrasonic detection fields based on TOF ranging, such as ranging and target tracking and positioning. Attached Figure Description

[0026] Figure 1 This is a schematic diagram of the TOF estimation principle based on two-step correlation.

[0027] Figure 2 This is a diagram of chirp ultrasound transmission and reception signals;

[0028] Figure 3 This is a graph showing the results of traditional cross-correlation calculations;

[0029] Figure 4 This is a graph showing the results of coarse correlation calculations;

[0030] Figure 5 This is a graph showing the results of fine correlation calculations. Detailed Implementation

[0031] Includes the following steps:

[0032] (I) Coarse correlation estimation of inaccurate TOF

[0033] (1) The received chirp ultrasound signal s r (t) and the emitted chirp ultrasound signal s t (t) is sampled at a frequency of F. s The sampling interval is T s =1 / F s Assuming the number of sampling points for the received signal is N, the number of sampling points for the transmitted signal is M, and the sampled chirp ultrasound received data is s r(n)(1≤n≤N), the sampled chirp ultrasound received data is s t (m)(1≤m≤M);

[0034] (2) For s r (n) Perform equal-interval sampling according to the highest frequency f of the chirp ultrasonic emission signal. e The extraction interval Δ is set to twice the value of Δ, which is expressed as:

[0035]

[0036] in, This indicates rounding down, with Δ intervals for s. r (n) Perform equal-interval sampling to obtain the received data s after sampling. re (l), Similarly, the chirp ultrasonic emission data s are analyzed at intervals of Δ. t (m) Equal intervals are used to obtain the extracted transmission data s te (k),

[0037] (3) Calculate s te (k) and s re The cross-correlation of (l) is calculated, and the delay τ corresponding to the maximum cross-correlation value is obtained. c Thus, the inaccurate TOF is obtained as follows:

[0038] TOF c =△τ c T s (2)

[0039] Since the above process uses extracted data to calculate cross-correlation, and since the amount of data participating in the cross-correlation operation is small, the amount of computation is effectively reduced, but the obtained TOF accuracy is low. Therefore, this process is called coarse correlation.

[0040] (II) Fine correlation estimation of precise TOF

[0041] (1) The delay τ obtained from the coarse correlation c And the extraction interval Δ, we can obtain τ c In the original chirp ultrasound received data r The position in (n) is Δτ c ;

[0042] (2) Due to the coarse correlation, the TOF is determined. c With the precise TOF error within one frequency modulation cycle, in terms of Δτ c For reference in s r Data is selected from (n), based on the lowest modulation frequency f of the chirp ultrasonic transmission signal. sDefine the selection range and the selection interval as follows:

[0043]

[0044] in To round up, "f s "This is the lowest frequency of the chirp ultrasound signal, in s..." r In (n), Δτ c Using the reference position, select δ data points forward and δ+M data points backward, then the selected data is s. r (Δτ c –δ:Δτ c +δ+M);

[0045] (3) Use the selected received data s r (Δτ c –δ:Δτ c +δ+M) and chirp ultrasonic emission data s t (m) Perform cross-correlation calculations.

[0046]

[0047] The delay corresponding to the maximum cross-correlation value is t. f Thus, the accurate TOF is obtained as follows:

[0048] TOF=(△τ c -δ+τ f )T s (5)

[0049] The above correlation uses the selected original sampling data, with the interval consistent with the sampling interval. The coarse correlation uses the extracted data, hence the term coarse correlation. This process is called fine correlation.

[0050] The chirp ultrasound signal includes linear frequency modulated chirp signal and nonlinear frequency modulated chirp signal.

[0051] The invention will now be further described with reference to the accompanying drawings.

[0052] See Figure 1 s r S is a chirp ultrasound received signal acquisition data sequence of length N, s r S is a chirp ultrasound received signal acquisition data sequence of length N, s t This is a chirp ultrasound transmission signal data sequence of length M, with a sampling interval of T. s Δ is the extraction interval, calculated according to formula (1). Using Δ as the interval, s are extracted respectively. r and s t Extracted data sre and s te , for s re and s te Perform cross-correlation operation cross(s) re ,s te ), based on the maximum value, we obtain the value in s r The delay τ in c ;

[0053] The delay τ obtained from coarse correlation c And the extraction interval Δ, to obtain the delay in the received signal data sequence s r The position Δτ in c According to formula (3), the selected interval δ is calculated, with Δτ c For reference in s r If we select data from the middle, then select δ data points forward and δ+M data points backward, then the selected data is s. r (Δτ c –δ:Δτ c +δ+M), according to formula (4), use the selected received data s r (Δτ c –δ:Δτ c +δ+M) and chirp ultrasonic emission data s t (m) Perform cross-correlation calculation, and determine the delay t corresponding to the maximum cross-correlation value. f The accurate TOF is calculated according to formula (5).

[0054] The specific implementation process of the present invention will be described below through specific examples.

[0055] In this example, a linear chirp signal [35-45] kHz / 5 ms is designed (i.e., the duration of the linear chirp is 5 ms, and its lowest frequency f is 0). s and the highest frequency f e The signals are 35kHz and 45kHz respectively. This signal is used for transmission, with a sampling rate of 2MHz. The transmitted signal s... t The length M = 10000 of (n) is used for transmission. Assuming the chirp signal travels for 9ms to reach the receiver, this means the Time-of-Flight (TOF) is 9ms. Considering the width of the transmitted chirp signal, and sampling the received signal for 15ms at a sampling rate of 2MHz, the received signal sequence s... r The length of (n) is 30000 (i.e., N = 30000).

[0056] Ignoring noise and propagation attenuation, the timing relationship between the received and transmitted signals is as follows: Figure 2 As shown. For s t (m) and s r Perform cross-correlation operation on (n), the result is as follows Figure 3 As shown in (a). From its local... Figure 3 (b) It can be seen that the maximum value of the cross-correlation is at 18001, indicating that the propagation time of the transmitted signal to the receiver is (18001-1)*T. s =18000 / F s =9ms, meaning TOF = 9ms, which is consistent with the assumed TOF. This process is based on the traditional correlation-based TOF estimation method, and the cross-correlation calculation requires approximately 3 × 10 8 Perform multiplication operations and operations on 3 × 10 8 Performing addition operations involves a significant amount of computation.

[0057] For the TOF estimation of the chirp signal mentioned above, in order to reduce the computational load, it is preferred to calculate according to formula (2), Δ=22, and with Δ as the interval, respectively for s r (n) and s t (m) is extracted to obtain s te (k) and s re (l), whose lengths are 454 and 1363 respectively. For s te (k) and s re (l) Perform cross-correlation calculation, which is the coarse correlation method disclosed in this invention. The result of the coarse correlation calculation is as follows: Figure 4 As shown in (a). Based on its local... Figure 4 (b) The maximum value determines the delay τ c It is 818, and its value in s r The corresponding position in the (n) sequence is Δτ c =818 × 22 = 17996. To further improve the estimation accuracy of TOF, in s r In the (n) sequence, with Δτ c For reference data selection, the selection interval δ is calculated according to formula (3), resulting in δ = 58, with Δτ c Using the reference position, 58 data points are selected forward and 10058 data points are selected backward. The selected data is s. r (17938:28054), according to formula (4), for s r (17938:28054) and s t Perform cross-correlation calculations at a ratio of 1:10000, which is the fine correlation method disclosed in this invention. The results of the fine correlation calculations are as follows: Figure 5 As shown. The accurate TOF was calculated using formula (5), yielding a precise value of 9000 μs, consistent with the assumption. This demonstrates that the method disclosed in this invention can accurately estimate the TOF of the chirp ultrasound signal. In this example, the coarse correlation calculation requires 1.79 × 10⁻⁶ μs. 6 The sum of the multiplication operations is 1.79 × 10⁻⁶. 6The addition operation reduces the computational cost by approximately 167 times compared to traditional correlation-based TOF estimation methods. This example demonstrates that the TOF estimation method based on coarse and fine two-step correlation chirp ultrasound signals disclosed in this invention has a lower computational cost.

[0058] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for estimating the transit time of chirp ultrasound signals based on two-step correlation, characterized in that, Includes the following steps: (I) Obtaining inaccurate TOF of chirp ultrasound signals by applying coarse correlation to the chirp ultrasound signals: (1) The received chirp ultrasound signal s r (t) and the emitted chirp ultrasound signal s t (t) is sampled at a frequency of F. s The sampling interval is T s =1 / F s Assuming the number of sampling points for the received signal is N, the number of sampling points for the transmitted signal is M, and the sampled chirp ultrasound received data is s r (n) (1 ≤ n ≤ N), the sampled chirp ultrasound received data is s t (m) (1 ≤ m ≤ M); (2) For s r (n) Perform equal-interval sampling, according to the highest frequency f of the chirp ultrasonic emission signal. e The extraction interval Δ is set to twice the value of Δ, which is expressed as: ； in," " indicates rounding down, with Δ intervals for s r (n) Perform equal-interval sampling to obtain the received data s after sampling. re (l), Similarly, the chirp ultrasound emission data s were analyzed at intervals of Δ. t (m) Equal intervals are used to obtain the extracted transmission data s te (k), ; (3) Calculate s te (k) and s re The cross-correlation of (l) is calculated, and the delay τ corresponding to the maximum cross-correlation value is obtained. c Thus, the inaccurate TOF is obtained as follows: ； (II) Using fine correlation to obtain precise TOF of chirp ultrasound signals: (1) The delay τ obtained from the coarse correlation c And the extraction interval Δ, we can obtain τ c In the original chirp ultrasound received data r The position in (n) is Δτ c ; (2) Due to the coarse correlation determined by the TOF c With the precise TOF error within one frequency modulation cycle, in terms of Δτ c For reference in s r Data is selected from (n), based on the lowest modulation frequency f of the chirp ultrasonic transmission signal. s Define the selection range and the selection interval as follows: ； in" "To round up, "f s "This is the lowest frequency of the chirp ultrasound signal, in s..." r In (n), Δτ c Using the reference position, select δ data points forward and δ+M data points backward, then the selected data is s. r (Δτ c – δ : Δτ c +δ+M); (3) Using the selected received data s r (Δτ c – δ : Δτ c +δ+M) and chirp ultrasonic emission data s t (m) performs cross-correlation calculation, and the delay corresponding to the maximum cross-correlation value is t. f Thus, the accurate TOF is obtained as follows: 。 2. The chirp ultrasound signal transit time estimation method based on two-step correlation as described in claim 1, characterized in that: Chirp ultrasound signals include linear frequency modulated chirp signals and nonlinear frequency modulated chirp signals.

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