Multi-path chirp signal arrival time estimation method based on instantaneous frequency fitting

Abstract

The invention discloses a multipath chirp signal arrival time estimation method based on instantaneous frequency fitting. The method comprises the following steps: S1, transmitting a reference signal to the surrounding environment by a loudspeaker of the smart phone, and receiving the reference signal reflected by the surrounding environment in a multi-path manner through a microphone of the smart phone as an echo signal; s2, performing Hilbert transform, derivation and discretization on the echo signal in sequence to obtain a discrete instantaneous frequency, and processing by using a difference method to obtain an instantaneous frequency increment of the discrete instantaneous frequency; and S3, according to the discrete instantaneous frequency, the instantaneous frequency increment and the reference signal, performing variance function construction, linear fitting and calculation processing to obtain the arrival time estimation of the echo signal. The method has the advantages of low calculated amount consumption, robust anti-multipath capability and high-precision estimation result, and can more accurately estimate the arrival time of the signal in a complex indoor acoustic multipath space.

Description

Technical Field

[0001] The invention belongs to the technical field of indoor positioning and acoustic signal processing, and in particular relates to a multipath chirp signal arrival time estimation method based on instantaneous frequency fitting. Background Art

[0002] Chirp signals, as a typical non-stationary broadband signal, are widely used in acoustic indoor positioning. Accurate time difference estimation of linear frequency modulation signals is the basis of these technologies. However, as the application scenarios become more complex, noise and reverberation become more serious, which significantly affects the accuracy of time difference estimation.

[0003] Commonly used time difference estimation methods are cross-correlation and generalized cross-correlation methods based on different weighting coefficients. However, in actual complex scenarios, the following problems usually occur. First, the multipath effect will cause the cross-correlation function to produce multiple peaks, and due to the unknown room impulse response, some multipath peaks may be higher than the direct path peak. Second, multipath effects and noise may destroy part of the phase information of the original signal, which will cause the direct path peak to deviate from the correct sampling point.

[0004] In order to solve these problems and achieve accurate time difference estimation, many new methods have been intensively studied and discussed, including cross-correlation based methods and time-frequency analysis methods.

[0005] The cross-correlation-based method focuses on accurately detecting the direct path peak of the cross-correlation function. The work includes introducing the Hilbert transform interpolation algorithm to extract the signal envelope and accurately detect the peak; sorting the peak candidate set by measuring the reliability of sound source localization; the frequency sliding generalized cross-correlation uses a sliding window method to explore the cross-power spectrum phase and obtain the contribution of different frequency bands to the direct path delay estimation. There are also related studies dedicated to mitigating the impact of multipath effects caused by linear frequency modulation signals. In these studies, the power spectral density of the linear frequency modulation signal was used for rough search, and acoustic reverberation elimination technology was used. However, they still need to select an appropriate threshold to perform a fine search and use the first extreme value matched filter to achieve better performance. When the threshold is not selected properly, its accuracy will be seriously reduced.

[0006] The time-frequency method exploits the linear relationship between signal time and frequency when processing linear frequency modulated signals. The frequency modulated continuous wave method is often used for time difference estimation in radar systems. The researchers introduced the frequency modulated continuous wave method into acoustic ranging by converting the calculation of delay time into the calculation of frequency. However, the window length of the acoustic signal limits the frequency resolution, and the influence of multipath effects still exists in the spectrum. Fractional Fourier transform has also been used to eliminate the strongest multipath component in the cleaning process of each iteration. Although it is effective, its computational cost is high.

[0007] In summary, a new method that can efficiently and accurately estimate the arrival time of chirp signals under indoor acoustic multipath conditions needs to be proposed and studied urgently. Summary of the invention

[0008] In view of the above problems existing in the prior art, the present invention provides a multipath chirp signal arrival time estimation method based on instantaneous frequency fitting, which can achieve high-precision arrival time estimation of received chirp signals under indoor acoustic multipath conditions.

[0009] The present invention adopts the following technical solutions:

[0010] The multipath chirp signal arrival time estimation method based on instantaneous frequency fitting of the present invention comprises:

[0011] S1, the speaker of the smartphone transmits a reference signal to the surrounding environment, and the smartphone microphone receives the reference signal reflected by the surrounding environment through multipath as an echo signal;

[0012] S2, the echo signal is sequentially processed through Hilbert transform, derivation, and discretization to obtain discrete instantaneous frequency, and then the instantaneous frequency increment of the discrete instantaneous frequency is obtained by using the difference method;

[0013] S3. According to the discrete instantaneous frequency, the instantaneous frequency increment and the reference signal, the arrival time estimation of the echo signal is obtained by constructing a variance function, linear fitting and calculation processing.

[0014] In S1, the reference signal is set according to the following formula:

[0015]

[0016] Wherein, s(t) represents the reference signal, f0 represents the starting frequency of the reference signal, B represents the bandwidth of the reference signal, T is the duration of the reference signal, t represents time, t∈[0,T].

[0017] The specific steps of S2 are:

[0018] S2.1, perform Hilbert transform on the echo signal to construct a complex analytical signal of the echo signal, process it to obtain the instantaneous phase, and then derive the instantaneous phase to obtain the instantaneous frequency;

[0019] S2.2, discretizing the instantaneous frequency to obtain a discrete instantaneous frequency, and then using a differential method to obtain an instantaneous frequency increment of the discrete instantaneous frequency;

[0020] In S2.1, the instantaneous phase φ(t) is obtained specifically according to the following complex analysis signal:

[0021] z(t)=y(t)+jH{y(t)}=a(t)e jφ(t)

[0022] Where z(t) represents the complex analysis signal, y(t) represents the echo signal, j is the imaginary unit, a(t) is the complex analysis signal gain, φ(t) is the signal phase, and H{} represents the Hilbert transform.

[0023] In S2, the instantaneous frequency increment is specifically obtained by the following formula:

[0024] μ r (n) = g(n+1) - g(n)

[0025] Among them, μ r (n) represents the instantaneous frequency increment, g(n+1) and g(n) represent the instantaneous frequencies of the n+1th sample point and the nth sample point of the echo signal respectively.

[0026] The specific steps of S3 are:

[0027] S3.1. Set an interval length, and construct a variance function of the instantaneous frequency increment of the reference signal in combination with the instantaneous frequency increment. The interval where the variance function takes the minimum value is used as the fitting interval.

[0028] S3.2. Perform linear fitting on the discrete instantaneous frequencies within the fitting interval according to the reference signal to obtain a straight line equation, and then obtain an arrival time estimate of the echo signal in combination with the reference signal processing.

[0029] The specific steps of S3.1 are:

[0030] S3.1.1, set the number of sampling points M in the fitting interval;

[0031] S3.1.2. Set the variance function of the instantaneous frequency increment of the reference signal according to the following formula:

[0032]

[0033] Among them, D p represents the variance function, p represents the starting position of the fitting interval, M represents the number of sampling points in the fitting interval, μ r (n) represents the instantaneous frequency increment at the nth sampling point, μ represents the frequency change rate of the reference signal, f s represents the sampling frequency of the smartphone;

[0034] S3.1.3. The starting position of the interval where the variance function takes the minimum value is taken as the starting position of the fitting interval.

[0035] In S3.1.3, the minimum value of the variance function is determined by a traversal method.

[0036] The specific steps of S3.2 are:

[0037] S3.2.1. Perform linear fitting on the discrete instantaneous frequencies within the fitting interval according to the reference signal, and perform linear fitting according to the following formula to obtain the linear equation:

[0038]

[0039] In the formula, γ represents the intercept of the fitted straight line, μ represents the frequency change rate of the reference signal, g(n) represents the instantaneous frequency of the nth sample point of the echo signal, M represents the number of sampling points in the fitting interval, b is the unknown quantity to be fitted, and m is the starting sample point of the fitting interval;

[0040] S3.2.2. The equation of the straight line is obtained by fitting. The equation of the straight line is as follows:

[0041]

[0042] In the formula, l represents the frequency value corresponding to the nth sample point. Substitute the starting frequency f0 of the reference signal into the linear equation obtained by fitting instead of l, and convert it into the following formula to obtain the arrival time estimation of the echo signal:

[0043]

[0044] Among them, τ1 represents the arrival time estimate of the wave signal, and f0 represents the starting frequency of the reference signal.

[0045] The beneficial effects of the present invention are:

[0046] A chirped linear frequency modulation signal of 19 to 22 kHz is used as the transmission and reference signal. The instantaneous frequency is solved by a method based on Hilbert transform, and the fitting interval is selected by minimizing the variance of the instantaneous frequency increment within the interval relative to the instantaneous frequency increment of the reference signal. The signal arrival time is inversely calculated by linear fitting based on a known slope, which effectively suppresses the influence of multipath effects and achieves efficient and high-precision signal arrival time estimation in complex indoor acoustic multipath spaces.

[0047] The proposed multipath chirp signal arrival time estimation method based on instantaneous frequency fitting has low computational consumption, robust anti-multipath capability and high-precision estimation results, and can be used for signal arrival time estimation in complex indoor acoustic multipath spaces. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0049] Figure 1 It is a flow chart of the method for estimating the arrival time of multipath chirp signals based on instantaneous frequency fitting according to the present invention;

[0050] Figure 2 is a schematic diagram of a custom signal;

[0051] Figure 3 It is a schematic diagram of the instantaneous frequency of the discretized echo signal. DETAILED DESCRIPTION

[0052] The following describes the embodiments of the present invention through specific embodiments, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict.

[0053] like Figure 1 As shown, a specific embodiment of the multipath chirp signal arrival time estimation method of the present invention comprises the following steps:

[0054] S1. The speaker of the smartphone is arranged indoors to transmit a reference signal to the surrounding environment, and the reference signal reflected by the surrounding environment multipath is received by the smartphone microphone as an echo signal;

[0055] like Figure 2 As shown, the reference signal is set according to the following formula:

[0056]

[0057] Wherein, s(t) represents the reference signal, the reference signal s(t) is a linear frequency modulation signal, f0 represents the starting frequency of the reference signal, B represents the bandwidth of the reference signal, T represents the duration of the reference signal, t represents time, t∈[0,T]. In this embodiment, the customized signal frequency is 19-22kHz, the sampling rate is 48kHz, and the duration is 30ms.

[0058] The received echo signal y(t) is defined as:

[0059]

[0060] Where l represents the number of the arriving multipath signal, L is the total number of multipath signals, and α l is the gain of the lth signal, t is the time, T R is the total duration of the received signal, τ l is the arrival time of the lth signal, e(t) is Gaussian white noise. s(t) is the transmitted reference signal, and the expression is:

[0061]

[0062] Where f0 is the starting frequency of the reference signal, in this case f0 is 19kHz, B is the signal bandwidth 3kHz, and T is the signal duration 30ms. Since the reference signal is only transmitted for one cycle, the reference signal period is the duration of the reference signal. The signal is a linear frequency modulation signal, and its frequency slope is μ.

[0063] S2, the echo signal is sequentially processed through Hilbert transform, derivation, and discretization to obtain discrete instantaneous frequency, and then the instantaneous frequency increment of the discrete instantaneous frequency is obtained by using the difference method;

[0064] The specific steps of S2 are:

[0065] S2.1. Perform Hilbert Transform (HT) on the echo signal to construct a complex analytical signal of the echo signal, and process it to obtain the instantaneous phase, and then derive the instantaneous phase to obtain the instantaneous frequency;

[0066] The instantaneous phase φ(t) is obtained specifically according to the following complex analytical signal:

[0067] z(t)=y(t)+jH{y(t)}=a(t)e jφ(t)

[0068] Where z(t) represents the complex analysis signal, y(t) represents the echo signal, j is the imaginary unit, a(t) is the complex analysis signal gain, φ(t) is the signal phase, and H{} represents the Hilbert transform.

[0069] The Hilbert transform is implemented by the following formula:

[0070]

[0071] After the phase φ(t) is obtained, the instantaneous frequency g(t) is obtained by taking the derivative of the phase:

[0072]

[0073] S2.2, discretizing the instantaneous frequency by using the finite impulse response filter convolution method to obtain the discrete instantaneous frequency, and then using the difference method to obtain the instantaneous frequency increment of the discrete instantaneous frequency;

[0074] The instantaneous frequency increment is obtained by the following formula:

[0075] μ r (n) = g(n+1) - g(n)

[0076] Among them, μ r (n) represents the instantaneous frequency increment, g(n+1) and g(n) represent the instantaneous frequencies of the n+1th sample point and the nth sample point of the echo signal respectively.

[0077] like Figure 3 As shown, based on the sampling rate fs of the smartphone, the instantaneous frequency is discretized, and the discretized instantaneous frequency is g(n), where n is the received signal sampling point, n=1, 2, ..., N, N is the total number of received signal sampling points, N=T R f s , f s is the sampling rate, in this case 48kHz.

[0078] S3. According to the discrete instantaneous frequency, the instantaneous frequency increment and the reference signal, the arrival time estimation of the echo signal is obtained by constructing a variance function, linear fitting and calculation processing.

[0079] The specific steps of S3 are:

[0080] S3.1. Set an interval length as the fitting interval length, that is, the number of sampling points included in the interval, and construct the variance function of the instantaneous frequency increment of the reference signal in combination with the instantaneous frequency increment. The interval where the variance function takes the minimum value is taken as the fitting interval. The fitting interval should satisfy the minimum variance of the instantaneous frequency increment relative to the instantaneous frequency increment of the reference signal in the interval. The length of the fitting interval should be selected between 50 and 300.

[0081] S3.1 The specific steps are:

[0082] S3.1.1, set the number of sampling points M in the fitting interval;

[0083] S3.1.2. Set the variance function of the instantaneous frequency increment of the reference signal according to the following formula:

[0084]

[0085] Among them, D p represents the variance function, p represents the starting position of the fitting interval, that is, p represents the index of the first sampling point in the fitting interval, M represents the number of sampling points in the fitting interval, μr (n) represents the instantaneous frequency increment at the nth sampling point, μ represents the frequency change rate of the reference signal, f s represents the sampling frequency of the smartphone; n is the independent variable, which represents the index of the first sampling point in the fitting interval; D p is the dependent variable.

[0086] S3.1.3. The starting position of the interval where the variance function takes the minimum value is used as the starting position of the fitting interval. The minimum value of the variance function is determined by traversal, and the traversal stops when the end position of the fitting interval is equal to the end position of the echo signal. In other words, let the length of the echo signal be N, and when p+M-1=N, the traversal stops. The selection of the fitting interval is through traversing the variance of the instantaneous frequency increment in the interval relative to the instantaneous frequency increment of the reference signal, and the interval with the smallest variance is used as the fitting interval. Starting from p=1, gradually increase p so that D p Minimum. Then the starting point m of the target interval can be determined as:

[0087]

[0088] S3.2. According to the reference signal, a linear fit with a known slope μ is performed on the discrete instantaneous frequency in the fitting interval to obtain a straight line equation, and the linear fit with a known slope is solved by the least squares method, and then the arrival time estimation of the echo signal is obtained by combining with the reference signal processing.

[0089] S3.2 The specific steps are:

[0090] S3.2.1. Perform a linear fit with a known slope μ on the discrete instantaneous frequencies within the fitting interval according to the reference signal. Use the known slope μ to fit all instantaneous frequency points within the interval. Perform a linear fit according to the following formula to obtain the equation of the straight line:

[0091]

[0092] In the formula, γ is the fitting result, which represents the intercept of the straight line after fitting, and μ represents the frequency change rate of the reference signal. g(n) represents the instantaneous frequency of the nth sample point of the echo signal, M represents the number of sampling points in the fitting interval, b is the unknown quantity to be fitted, and m is the starting sample point of the fitting interval. In the formula, only b and γ are unknown variables;

[0093] S3.2.2. The equation of the straight line is obtained by fitting. The equation of the straight line is as follows:

[0094]

[0095] In the formula, l represents the frequency value corresponding to the nth sample point. Substitute the starting frequency f0 of the reference signal into the linear equation obtained by fitting instead of l, and convert it into the following formula to obtain the arrival time estimation of the echo signal:

[0096]

[0097] Among them, τ1 represents the arrival time estimate of the wave signal, and f0 represents the starting frequency of the reference signal.

[0098] This example uses a chirped linear frequency modulation signal of 19 to 22 kHz as the transmission and reference signal; the instantaneous frequency is solved by a method based on Hilbert transform, and the fitting interval is selected by minimizing the variance of the instantaneous frequency increment within the interval relative to the instantaneous frequency increment of the reference signal; the signal arrival time is inversely calculated by linear fitting based on a known slope, which effectively suppresses the influence of multipath effects and achieves efficient and high-precision signal arrival time estimation in complex indoor acoustic multipath spaces.

[0099] The proposed multipath chirp signal arrival time estimation method based on instantaneous frequency fitting has low computational consumption, robust anti-multipath capability and high-precision estimation results, and can be used for signal arrival time estimation in complex indoor acoustic multipath spaces.

[0100] The embodiments described above are merely descriptions of preferred implementations of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope of the present invention.

Claims

1. A method for estimating the arrival time of a multipath chirp signal based on instantaneous frequency fitting, characterized in that: Includes steps: S1, the speaker of the smartphone transmits a reference signal to the surrounding environment, and the smartphone microphone receives the reference signal reflected by the surrounding environment through multipath as an echo signal; S2, the echo signal is sequentially processed through Hilbert transform, derivation, and discretization to obtain discrete instantaneous frequency, and then the instantaneous frequency increment of the discrete instantaneous frequency is obtained by using the difference method; S3. According to the discrete instantaneous frequency, the instantaneous frequency increment and the reference signal, the arrival time estimation of the echo signal is obtained by constructing a variance function, linear fitting and calculation processing.

2. The method for estimating the arrival time of a multipath chirp signal based on instantaneous frequency fitting according to claim 1, characterized in that: In S1, the reference signal is set according to the following formula: Wherein, s(t) represents the reference signal, f0 represents the starting frequency of the reference signal, B represents the bandwidth of the reference signal, T is the duration of the reference signal, and t represents time, t∈[0,T].

3. The method for estimating the arrival time of a multipath chirp signal based on instantaneous frequency fitting according to claim 1, characterized in that: The specific steps of S2 are: S2.1, perform Hilbert transform on the echo signal to construct a complex analytical signal of the echo signal, process it to obtain the instantaneous phase, and then derive the instantaneous phase to obtain the instantaneous frequency; S2.

2. Discretize the instantaneous frequency to obtain a discrete instantaneous frequency, and then use a differential method to obtain an instantaneous frequency increment of the discrete instantaneous frequency.

4. The method for estimating the arrival time of a multipath chirp signal based on instantaneous frequency fitting according to claim 3, characterized in that: In S2.1, the instantaneous phase φ(t) is obtained specifically according to the following complex analysis signal: z(t)=y(t)+jH{y(t)}=a(t)e jφ(t) Where z(t) represents the complex analysis signal, y(t) represents the echo signal, j is the imaginary unit, a(t) is the complex analysis signal gain, φ(t) is the signal phase, and H{} represents the Hilbert transform.

5. The method for estimating the arrival time of a multipath chirp signal based on instantaneous frequency fitting according to claim 1, characterized in that: In S2, the instantaneous frequency increment is specifically obtained by the following formula: μ r (n)=g(n+1)-g(n) Among them, μ r (n) represents the instantaneous frequency increment, g(n+1) and g(n) represent the instantaneous frequencies of the n+1th sample point and the nth sample point of the echo signal respectively.

6. The method for estimating the arrival time of a multipath chirp signal based on instantaneous frequency fitting according to claim 1, characterized in that: The specific steps of S3 are: S3.

1. Set an interval length, and construct a variance function of the instantaneous frequency increment of the reference signal in combination with the instantaneous frequency increment. The interval where the variance function takes the minimum value is used as the fitting interval. S3.

2. Perform linear fitting on the discrete instantaneous frequencies within the fitting interval according to the reference signal to obtain a straight line equation, and then obtain an arrival time estimate of the echo signal in combination with the reference signal processing.

7. The method for estimating the arrival time of a multipath chirp signal based on instantaneous frequency fitting according to claim 1, characterized in that: The specific steps of S3.1 are: S3.1.1, set the number of sampling points M in the fitting interval; S3.1.

2. Set the variance function of the instantaneous frequency increment of the reference signal according to the following formula: Among them, D p represents the variance function, p represents the starting position of the fitting interval, M represents the number of sampling points in the fitting interval, μ r (n) represents the instantaneous frequency increment at the nth sampling point, μ represents the frequency change rate of the reference signal, f s represents the sampling frequency of the smartphone; S3.1.

3. The starting position of the interval where the variance function takes the minimum value is taken as the starting position of the fitting interval.

8. The method for estimating the arrival time of a multipath chirp signal based on instantaneous frequency fitting according to claim 7, characterized in that: In S3.1.3, the minimum value of the variance function is determined by a traversal method.

9. The method for estimating arrival time of multipath chirp signals based on instantaneous frequency fitting according to claim 1, characterized in that: The specific steps of S3.2 are: S3.2.

1. Perform linear fitting on the discrete instantaneous frequencies within the fitting interval according to the reference signal, and perform linear fitting according to the following formula to obtain the linear equation: In the formula, γ represents the intercept of the fitted straight line, μ represents the frequency change rate of the reference signal, g(n) represents the instantaneous frequency of the nth sample point of the echo signal, M represents the number of sampling points in the fitting interval, b is the unknown quantity to be fitted, and m is the starting sample point of the fitting interval; S3.2.

2. The equation of the straight line is obtained by fitting. The equation of the straight line is as follows: In the formula, l represents the frequency value corresponding to the nth sample point. Substitute the starting frequency f0 of the reference signal into the linear equation obtained by fitting instead of l, and convert it into the following formula to obtain the arrival time estimation of the echo signal: Among them, τ1 represents the arrival time estimate of the wave signal, and f0 represents the starting frequency of the reference signal.

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