TOA and DOA combined estimation dimension reduction method in Beidou and ultra-wideband system
1. A TOA and DOA combined estimation dimension reduction method in a Beidou and ultra-wideband system is characterized by comprising the following steps:
s1, using two array antennas to receive signals and respectively obtaining channel impulse response estimation of two antennasAnd
s2, obtaining TOA estimation of the first antenna by using the sample point number and the expanding and dimension-reducing algorithm of the multi-path cluster
S3, obtaining TOA estimation of the second antenna by using the sampling point number and the multi-path cluster expansion and dimensionality reduction algorithm
And S4, calculating the DOA estimated value by using the geometrical information and the TOA estimated results of the two antennas.
2. The TOA and DOA joint estimation dimension reduction method in the Beidou and ultra-wideband systems according to claim 1, wherein in the step S2, the expansion and dimension reduction algorithm of the sampling point number and the multipath cluster specifically comprises:
s21, calculating the cross covariance matrix of the channel impulse responseE1(τ) andrespectively, the delay matrices for the two antennas, wherein,is a diagonal matrix, B is a coefficient set of channel complex fading,is complex, L × L represents the matrix size, (.)HRepresenting a conjugate transpose operation of a matrix;
s22, mixingMatrix X divided into two dimensions of N × (N-1)1And X2Wherein the matrix X1Is RHFirst N-1 column, matrix X2Is RHThe last N-1 column;
s23 constructing an extended observation matrix
Wherein the content of the first and second substances,is a unit inverse diagonal matrix, (.)*Representing a conjugate operation of the matrix;
s24, carrying out eigenvalue decomposition on the extended observation matrix to obtain a noise subspace U of the extended observation matrixv；
S25, constructing a dimensionality reduction spectrum peak search function
Wherein u ═ 1,0]T，Is a unit diagonal matrix, e1(τ)＝[1,e-jΔωτ,…,e-j(N-1)Δωτ]TN is the number of frequency domain sampling points, the sampling interval is Δ ω ═ 2 pi/N, τ is the true TOA value of the first antenna, j is an imaginary number, so j Δ ω τ represents the l-th path phase information of the first antenna; using the reduced dimension spectral peak search function to search spectral peaks, wherein the time delay corresponding to the peak value is the TOA estimated value of the first antenna
3. The TOA and DOA joint estimation dimension reduction method in the Beidou and ultra-wideband system according to claim 2, wherein in the step S3, the expansion and dimension reduction algorithm of the sampling point number and the multipath cluster specifically comprises:
s31, calculating the cross covariance matrix of the channel impulse response
S32, executing steps S22-S24;
s33, constructing a dimensionality reduction spectrum peak search function
Wherein u ═ 1,0]T，Is a matrix of the unit diagonal,n is the number of sampling points in the frequency domain,representing phase information corresponding to the second antenna; performing spectral peak using the dimensionality reduction spectral peak search functionSearching, the time delay corresponding to the peak value is the TOA estimated value of the second antenna
4. The method for dimension reduction of TOA and DOA combined estimation in Beidou and ultra-wideband systems according to claim 3, wherein in step S4, the DOA estimation value calculation formula is
Where c is the speed of light and d is the spacing between the two antennas.
5. A computer readable storage medium having stored thereon computer program instructions executable by a processor, the computer program instructions when executed by the processor being capable of performing the method steps as described in 1-4 above.
Background
The satellite navigation technology provides position-based service guarantee for modern life and production, but in dense buildings or indoors, the requirement of indoor and outdoor continuous positioning cannot be met only by a single satellite navigation technology due to the fact that satellite signals are shielded. The ultra-wideband is a wireless communication technology for transmitting information by nanosecond or even subnanosecond pulses, and has extremely high time resolution capability, so that the ultra-wideband positioning estimated based on the signal TOA can reach the positioning accuracy of centimeter or even millimeter. Furthermore, if the direction of arrival DOA of the signal can be obtained, this will help in accurate positioning of the ultra wideband signal. The problems of high algorithm complexity, low estimation precision and the like mainly exist in the TOA and DOA parameter estimation in the existing UWB system.
Disclosure of Invention
The invention aims to provide a TOA and DOA combined estimation dimension reduction method in a Beidou and ultra-wideband system, which can obtain doubled frequency domain sampling point number and expanded multipath cluster number, and has lower calculation complexity and higher estimation precision.
In order to achieve the purpose, the technical scheme of the invention is as follows: a TOA and DOA combined estimation dimension reduction method in a Beidou and ultra-wideband system comprises the following steps:
s1, using two array antennas to receive signals and respectively obtaining channel impulse response estimation of two antennasAnd
s2, obtaining TOA estimation of the first antenna by using the sample point number and the expanding and dimension-reducing algorithm of the multi-path cluster
S3, obtaining TOA estimation of the second antenna by using the sampling point number and the multi-path cluster expansion and dimensionality reduction algorithm
And S4, calculating the DOA estimated value by using the geometrical information and the TOA estimated results of the two antennas.
In an embodiment of the present invention, in step S2, the expansion and dimension reduction algorithm for the sampling point number and the multipath cluster specifically includes:
s21, calculating the cross covariance matrix of the channel impulse responseE1(τ) andrespectively, the delay matrices for the two antennas, wherein,is a diagonal matrix, B is a coefficient set of channel complex fading,is complex, L × L represents the matrix size, (.)HRepresenting a conjugate transpose operation of a matrix;
s22, mixingMatrix X divided into two dimensions of N × (N-1)1And X2Wherein the matrix X1Is RHFirst N-1 column, matrix X2Is RHThe last N-1 column;
s23 constructing an extended observation matrix
Wherein the content of the first and second substances,is a unit inverse diagonal matrix, (-) represents the conjugate operation of the matrix;
s24, carrying out eigenvalue decomposition on the extended observation matrix to obtain a noise subspace U of the extended observation matrixv；
S25, constructing a dimensionality reduction spectrum peak search function
Wherein u ═ 1,0]T，Is a unit diagonal matrix, e1(τ)＝[1,e-jΔωτ,…,e-j(N-1)Δωτ]TN is the number of frequency domain samples, the sampling interval is Δ ω ═ 2 pi/N, τ is the true TOA value of the first antenna, j is an imaginary number, sojΔωτIndicating the l path phase information of the first antenna; using the reduced dimension spectral peak search function to search spectral peaks, wherein the time delay corresponding to the peak value is the TOA estimated value of the first antenna
In an embodiment of the present invention, in step S3, the expansion and dimension reduction algorithm for the sampling point number and the multipath cluster specifically includes:
s31, calculating the cross covariance matrix of the channel impulse response
S32, executing steps S22-S24;
s33, constructing a dimensionality reduction spectrum peak search function
Wherein u ═ 1,0]T，Is a matrix of the unit diagonal,n is the number of sampling points in the frequency domain,representing phase information corresponding to the second antenna; using the reduced dimension spectral peak search function to search spectral peaks, wherein the time delay corresponding to the peak value is the TOA estimated value of the second antenna
In one embodiment of the present invention, in step S4, the DOA estimation value is calculated as
Where c is the speed of light and d is the spacing between the two antennas.
The invention also provides a computer readable storage medium having stored thereon computer program instructions executable by a processor, the computer program instructions when executed by the processor being capable of performing the method steps as described above.
Compared with the prior art, the invention has the following beneficial effects:
1. the number of extended equivalent frequency domain sampling points can be obtained, and the value of the extended equivalent frequency domain sampling points is twice of the number of actual frequency domain sampling points;
2. the number of the extended equivalent multipath clusters can be obtained;
3. the calculation complexity of the algorithm can be reduced;
4. and high TOA and DOA joint estimation precision can be obtained.
Drawings
Fig. 1 is a schematic diagram of an antenna array structure used in the present invention;
FIG. 2 is a scatter plot of the estimation results when using the present invention for TOA estimation;
FIG. 3 is a comparison of variation trend of TOA estimation accuracy with signal-to-noise ratio under different multipath cluster numbers;
FIG. 4 is a comparison of DOA estimation accuracy with signal-to-noise ratio variation trend under different multipath cluster numbers;
FIG. 5 is a comparison of TOA estimation accuracy with signal-to-noise ratio variation trend of different algorithms;
fig. 6 is a comparison of the trend of DOA estimation accuracy with signal-to-noise ratio for different algorithms.
Detailed Description
The technical scheme of the invention is specifically explained below with reference to the accompanying drawings.
The invention discloses a TOA and DOA combined estimation dimension reduction method in a Beidou and ultra-wideband system, which comprises the following steps:
s1, using two array antennas to receive signals and respectively obtaining channel impulse response estimation of two antennasAnd
s2, obtaining TOA estimation of the first antenna by using the sample point number and the expanding and dimension-reducing algorithm of the multi-path cluster
S3, obtaining TOA estimation of the second antenna by using the sampling point number and the multi-path cluster expansion and dimensionality reduction algorithm
And S4, calculating the DOA estimated value by using the geometrical information and the TOA estimated results of the two antennas.
The following is a specific implementation of the present invention.
Data model
The system receives the ultra-wideband signal, and the transmitting signal of the ultra-wideband system can be expressed as that adopting the second derivative of the Gaussian pulse as the ultra-wideband transmitting signal and adopting direct sequence binary phase shift keying modulation in the transmitting signal
In the formula bjE { -1, +1} is a sequence of modulated binary data symbols, cnE { -1, +1} is a pseudo-random sequence, T, used to implement multiple access communicationscIndicating the pulse repetition period, TsRepresenting the period of binary data symbols, NcRepresenting the number of pulse repetitions of a single binary data symbol, p (t) being the second derivative of the Gaussian pulse and being expressed as
Where Γ is the pulse forming factor related to the pulse width.
According to the SV (Saleh-Valenzuela) model, a pulse of a transmitted signal generates a plurality of multipath components after passing through a channel, and the multipath components arrive at a receiving end in the form of clusters. Assuming that a signal passes through an ultra-wideband channel to generate K clusters, each cluster has L multipaths, a channel impulse response model of the kth cluster of the ultra-wideband channel can be represented as
Wherein alpha isl (k)Is the channel attenuation coefficient of the ith path in the kth cluster and obeys Rayleigh distribution and phase thetal (k)Is at [0,2 π]Uniformly distributed random variables, delta (-) is a Dirac function,is the channel delay of the l path in the k cluster. Typically, the rate of change of the channel is slow compared to the pulse rate of the transmitted signal, and therefore τl (k)＝τl. Order toRepresenting random complex fading amplitudes, the above equation can be rewritten as:
according to the signal processing basic theory, the time domain form of the kth cluster signal received by the system can be expressed as
Wherein ". sup" denotes a convolution, w(k)(t) is additive white gaussian noise of the kth cluster of received signals. The received signal is converted into a frequency domain form
In the formula Y(k)(ω),S(ω),H(k)(ω),W(k)(ω) represents y(k)(t),s(t),h(k)(t),w(k)(t) Fourier transform.
The received signal is sampled at equal intervals of N (N is more than L) points in a frequency domain, the sampling interval is delta omega-2 pi/N, and the sampled signal can be expressed as
yk＝SEτβk+wk
Wherein the content of the first and second substances,is a received signal y(k)(t) N-point frequency domain equally spaced sampling, ωn＝nΔω(n＝0,1,…,N-1)。S＝diag([S(ω0),…,S(ωN-1)]) Is an N × N diagonal matrix, the diagonal elements are N-point frequency domain equal interval sampling values of the transmitting signal s (t), and E (tau) ═ E (tau)1),e(τ2)，…,e(τL)]Is a delay matrix containing signal multipath delay information, whereinIn addition to this, the present invention is,including the coefficients of the complex fading of the channel in the kth cluster,is a vector of frequency domain samples of noise.
Fig. 1 shows an antenna array structure used in the present invention. As shown in FIG. 1, L far-field signals are incident in the form of parallel waves at an incident angle of { theta }1,θ2,…,θLI.e. DOA. Let τ be [ τ ]1,τ2,…,τL]，Respectively, the times at which the signals arrive at antenna 1 and antenna 2, i.e., TOAs. In the figure d and c represent the antenna spacing and the speed of light, respectively. The frequency domain received signals of the two antennas can be respectively expressed as
Y1＝SE1(τ)B+W1
Wherein, B ═ beta1,β2,…,βK]，E1(τ) andthe delay matrices for the two antennas, respectively, can be expressed as
The channel impulse responses corresponding to the two antennas can be estimated by the following formula
Wherein V1＝W1/S，V2＝W2/S。
Second, TOA and DOA joint estimation method
1. Spreading of frequency domain sampling point number and multipath cluster number
The cross-correlation matrix of the channel impulse response can be calculated by the following formula
Wherein the content of the first and second substances,is a diagonal matrix.Can be divided into two N x (N-1) -dimensional matrices, i.e.
Wherein, X1And X2Respectively comprise a matrix RHThe first N-1 column and the last N-1 column,andrespectively comprise a matrixThe first N-1 line and the last N-1 line. The delay matrix satisfies the following equation
Wherein the content of the first and second substances,can be expressed as
Further, since the delay matrix is a vandermonde matrix and satisfies a conjugate symmetry property, there are
Wherein the content of the first and second substances,as a unit inverse diagonal matrix, a rotation matrixAndcan be respectively represented as
By using the above properties of the delay matrix, an extended observation matrix can be constructed as follows
Wherein the content of the first and second substances,
therefore, the extended observation matrix X can be regarded as an equivalent channel impulse response with doubled frequency sampling points and extended multipath clusters, so that more information sources can be detected and higher spatial freedom can be obtained.
2. Dimension-reducing TOA estimation method
The autocovariance matrix of the extended observation matrix X is RX＝XXH. To RXPerforming eigenvalue decomposition, i.e.
Wherein, UsAnd UvRepresenting signal and noise subspaces, respectivelys＝diag{λ1,λ2,…,λLA and Λv＝diag{λL+1,λL+2,…,λ2NAre diagonal matrices containing L large eigenvalues and 2N-L small eigenvalues, respectively.
Similar to the classical MUSIC algorithm, the two-dimensional TOA spectral peak function can be constructed as
Wherein the content of the first and second substances,
obviously, a two-dimensional spectral peak search would introduce a very large computational complexity. To reduce the computational complexity, one may first reduceIs decomposed into
WhereinThe two-dimensional spectral peak function can be rewritten as
Wherein the content of the first and second substances,and vectorSatisfy the requirement ofu＝[1,0]T. Thus, the above equation can be regarded as an optimization problem as follows
Thus, the following cost function can be constructed
Where ρ is a constant. To obtain extreme values, one can askAboutPartial derivatives of, i.e.
Thus, there areAnd μ ═ 0.5 ρ. In view ofThe constant μ can be further expressed as
Substituting the preceding formula into the vectorCan be changed into
Will be provided withSubstituting the above optimization problem expression, the TOA estimation result of the first antenna can be expressed as
That is, the estimate of the first antenna TOA is obtained by a one-dimensional spectral peak search function given by
Similarly, to obtain the TOA estimate for the second antenna, H may be swapped in constructing the cross-correlation matrix1And H2In the order of (1), i.e.
By derivation similar to the first antenna, the spectral peak search function of the second antenna is obtained, i.e.
Therefore, the TOA estimated values corresponding to the two antennas can be obtained through two times of one-dimensional spectral peak search.
3. DOA estimation method
Finally, the DOA estimate can be obtained by combining the TOA estimate with the array binding information, i.e.
Fig. 2 is a scatter plot of the estimates of TOA at a signal-to-noise ratio of 10dB, where K is 100 and N is 64. As can be clearly seen from the figure, the algorithm of the present invention can obtain a more accurate TOA estimation result.
Fig. 3 and fig. 4 are graphs showing the variation of TOA and DOA estimation performance with signal-to-noise ratio under different multipath cluster numbers, respectively, where N is 64. As can be seen from the figure, the algorithm of the present invention can obtain accurate TOA and DOA joint estimation result, and the estimation accuracy is improved along with the increase of the signal-to-noise ratio and the multipath cluster number.
Fig. 5 and fig. 6 are schematic diagrams of the variation of TOA and DOA estimation performance with the signal-to-noise ratio in different algorithms, respectively, where K is 100 and N is 64. As is clear from the figure, the algorithm of the present invention can obtain more accurate time delay and angle estimation results compared with other algorithms.
The invention also provides a computer readable storage medium having stored thereon computer program instructions executable by a processor, the computer program instructions when executed by the processor being capable of performing the method steps as described above.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The foregoing is directed to preferred embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow. However, any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention are within the protection scope of the technical solution of the present invention.
