CN101915931A - Multilevel interpolation design method of high-precision delay filter - Google Patents

Abstract

The invention relates to the precision delay signal generating technology of the satellite navigation signal simulator. Aiming at the problem that the high-rate digital delay filter is difficult to realize, the design method which uses multiple filters to perform mutual interpolation is provided so as to obtain the precision delay filter. The method comprises the following steps: firstly determining the interpolating factor according to the requirement of the filter, distributing filter parameters, designing the filter, and secondly performing the mutual interpolation of the filters to obtain the required and designed filter.

Description

The multilevel interpolation design method of high-precision delay filter

Technical field

The present invention relates to the precise delay signal generating technique of satellite navigation signal simulator, the multilevel interpolation design method of the high-precision delay filter of proposition can effectively solve at the precise delay signal and produce ubiquitous overlength rank, field filter designing.

Background technology

(Global Navigation Satellite System GNSS) can provide round-the-clock precision positions and temporal information for the anywhere of the earth and terrestrial space to GPS (Global Position System).The GNSS receiver receives the signal of GNSS satellites transmits, measures carrier to the distance of satellite, range rate etc., the position and the speed of mensuration carrier.The GNSS satellite signal simulator has important effect in the development of satellite navigation receiver, test, production run.The GNSS satellite signal simulator is according to the influence of various factorss such as carrier dynamic perfromance, simulation produces each GNSS satellite-signal that receiver is received, satellite navigation signal simulator is a kind of high-precision testing tool, its several typical use comprise: produce the high-dynamic GNSS signal, the catching and tracking performance of Verification Receiver; As the precision standard of comparison, the dynamic measurement precision of check GNSS receiver; Produce specific GNSS signal, the feasibility of confirmatory measurement scheme.

The chronometer time that satellite signal simulator needs the different satellite-signals of real time modelling to arrive receiver postpones and variable in distance, and these time delays and variable in distance are subjected to the factor affecting such as relative motion, ionosphere and troposphere fluctuation between satellite and the receiver.High precision satellite navigation receiver bearing accuracy is a meter level, and then according to the navigator fix theory, the range measurement accuracy of receiver is that bearing accuracy is removed geometric factor, and the geometric factor of general GPS constellation observation is 3, so range measurement accuracy is 0.3 meter.According to measure theory, identify that a kind of measuring accuracy of equipment should be selected the high another kind of equipment more than 10 times of precision standard as a comparison in theory for use, though engineering requires when using that reduction is arranged, the precision of standard of comparison is at least also than high 5 times by the evaluation apparatus precision.Therefore the time delay control accuracy of satellite navigation signal simulator generation signal will reach 0.03-0.05 rice.As seen, the control of the precision of time delay is the key of satellite navigation signal simulator, if the pseudo-range time delay control accuracy will reach 0.05m, i.e. 167ps.For the base-band spread-spectrum signal of 1.023Mcps bit rate, be equivalent to 1/5866 of a symbol width.

The time delay control of satellite signal simulator adopts following two kinds of methods to realize traditionally: the one, and the control of simulation time delay, the signal that this method allows signal generator produce is realized time delay control by several analog filters, but the analog filter time delay is subjected to comprising that external influences such as temperature are very big in this method, and precision is not high yet.The 2nd, digital time delay control.Along with the development of microelectric technique, realize high-precision delay resolution, can be based on the delay control method of digital delay filtering device (Digital Delay Filter).

But but there is very big difficulty when being designed for the digital delay wave filter of satellite navigation signal simulator according to traditional F IR filter design method, the high-precision delay requirement of reason has proposed very high requirement to the exponent number of wave filter, causes in fact can't realizing.As suppose that the accuracy requirement of pseudorange phase control is better than 0.05m, i.e. 0.1667ns.Then for the base-band spread-spectrum signal of 2M bandwidth, if with 4096 times of chip segmentations, i.e. 4096 times of interpolation, the time-delay minimum value that reaches is 0.122ns, pseudorange phase control minimum value is 0.036m, satisfies the accuracy requirement of pseudorange phase control and is better than the 0.05m requirement.Carry out the synthetic calculating of signal with the sampling rate of 40MHz, the technical indicator of 2M bandwidth pseudorange phase control digital delay Design of Filter can be described as passband 2M, stopband 4M, and the stopband rejection ratio is-80dB that sample frequency is 40*256MHz=10.24GHz.Reach the hundreds thousand of rank of digital delay wave filter of above-mentioned requirements in theory, it is exceedingly difficult directly designing high magnification digital delay wave filter like this.Utilize existing Design of Filter instrument, generally adopt the Remez exchange algorithm of polynomial expression in approaching, can be subjected to calculator memory and operating system and restrict, cause program run failure or design result not to reach requirement.

Handling this type of problem in traditional multirate signal processing generally takes sampling rate converter (Sampling Rate Converter is called for short SRC) is realized by multiple conversions.Multiple conversions method consumes resources is many, and the design complexity height.

Summary of the invention

As mentioned above, the key issue that accurate time delay wave filter is realized is actual to be will carry out overlength rank FIR filter designing owing to will obtain the high magnification interpolation filter, this method has adopted a kind of method for designing of the mutual interpolation of a plurality of wave filters of utilizing to obtain accurate time delay wave filter, to adapt to interpolation multiple M ₀Very big situation solves overlength rank filter designing.

This method comprises following step:

(1) determines the two-stage interpolation factor

For interpolation multiple M ₀Very big situation can be chosen the two-stage interpolation factor M ₁, M ₂, satisfy M ₀=M ₁M ₂M ₁, M ₂Choosing method preferably satisfy relatively prime relation, size is more or less the same.

(2) distribute filter parameter

Determine design M according to two-stage interpolation factor distribution condition and the final overlength rank filter characteristic that requires ₁Times interpolation filter

And M ₂Times interpolation filter

Parameter.The sample frequency of supposing the digital baseband signal correspondence is f _s, signal bandwidth is B.The two-stage interpolation factor is respectively M ₁, M ₂M then ₁The design of times interpolation filter design parameter is as follows:

Band connection frequency and stop-band frequency are:

$f_{\mathrm{PASS}1}=\frac{B}{M_1{f}_S},$ $f_{\mathrm{STOP}1}=\frac{f_s-B}{M_1{f}_s}$

Transition band width BW ₁For:

BW ₁＝f _STOP1-f _PASS1

M ₂The design of times interpolation filter design parameter is as follows:

Band connection frequency and stop-band frequency are:

$f_{\mathrm{PASS}2}=\frac{B}{M_2{M}_1{f}_s}$

$f_{\mathrm{STOP}2}=\frac{M_1{f}_S-B}{M_1{M}_2{f}_s}$

Transition band width BW ₂For:

BW ₂＝f _SROP2-f _PASS2

(3) design low range interpolation filter

Utilize MATLAB Design of Filter instrument, passband, stop-band frequency and transition band width according to second step obtained obtain M ₁Times interpolation filter

And M ₂Times interpolation filter

(4) multilevel interpolation design

Will

Regard signal as, it is carried out M ₂Times interpolation, the mode of interpolation be

Insert M between adjacent two numbers ₂Individual zero, interpolation postfilter 1 becomes h ' _M1(n).

H ' _M1(n)=h _M1(1), 0 ... 0, h _M1(2), 0 ..., 0, h _M1(3) ..., h _M1(M ₁) use h _M2(n) to h ' _M1(n) carry out filtering, obtain final higher order filter h _M0(n)

h _M0(n)=h ' _M1(n) * h _M2(n), * represents convolution algorithm.

Because

With

Be the limit sequence,

Also must be that the limit sequence is arranged, its length be:

${\mathrm{<figure-callout\; id="0"\; label="N\; M"\; filenames="HSA00000179036200013.png"\; state="\{\{state\}\}">N</figure-callout>}}_{M_{}}=M_2(N_{M_1}-1)+N_{M_2}$

Wherein

Be respectively the length of two wave filters.Above-mentioned design result is exactly desired M ₀Times interpolation filter.

Because this method for designing simply acts on formation with two wave filters, exponent number M ₀Can only be number of combinations, so be called the constructivity method for designing.

The present invention can be very simple and efficient the long rank of design wave filter, in practicality, do not have the multiple conversions problem, can effectively reduce FPGA consumes resources amount.

Description of drawings

Fig. 1 is the time domain waveform and the frequency domain characteristic of wave filter 1.

Fig. 2 is the time domain waveform and the frequency domain characteristic of wave filter 2.

Fig. 3 is the time domain waveform and the frequency domain characteristic of wave filter 3.

Embodiment

Exposed installation meter effect below by a design example.Suppose the sample frequency f of digital baseband signal correspondence _s=40MHz, signal bandwidth is 10MHz, the time-delay resolution requirement is τ _Δ≤ 25ps.Construct filtering wave by prolonging time device group, require M ₀〉=1000.Get M ₀=1024, M ₁=32, M ₂=32.Suppose that the designing requirement of signal attenuation outside a channel is greater than 110dB.M then ₁Times interpolation filter design parameter is:

$f_{\mathrm{PASS}1}=\frac{10\mathrm{MHz}}{M_1{f}_s}=\frac{1}{128}$

$f_{\mathrm{STOP}1}=\frac{f_s-10\mathrm{MHz}}{M_1{f}_s}=\frac{3}{128}$

Transition band width BW ₁For:

$B{W}_1=f_{\mathrm{STOP}1}-f_{\mathrm{PASS}1}=\frac{1}{64}$

M ₂Times interpolation filter design parameter is:

$f_{\mathrm{PASS}2}=\frac{10\mathrm{MHz}}{M_2{M}_1{f}_s}=\frac{1}{4096}$

$f_{\mathrm{STOP}2}=\frac{{M_{1}f}_s-10\mathrm{MHz}}{M_1{M}_2{f}_s}=\frac{127}{4096}$

Transition band width BW ₂For:

$B{W}_2=f_{\mathrm{STOP}2}-f_{\mathrm{PASS}2}=\frac{63}{2048}$

Design result is:

$N_{M_1}=479$

$N_{M_2}=447$

${\mathrm{<figure-callout\; id="0"\; label="N\; M"\; filenames="HSA00000179036200013.png"\; state="\{\{state\}\}">N</figure-callout>}}_{M_{}}=M_2(N_{M_1}-1)+N_{M_2}=15743$

The time domain waveform of three wave filters and frequency domain characteristic are respectively as accompanying drawing 1,2, shown in 3.

Claims (1)

1. the multilevel interpolation design method of high-precision delay filter, it is characterized in that: adopt the method for designing of the mutual interpolation of a plurality of wave filters to obtain accurate time delay wave filter, this method comprises following step:

(1) determines the two-stage interpolation factor

For interpolation multiple M ₀Very big situation can be chosen the two-stage interpolation factor M ₁, M ₂, satisfy M ₀=M ₁M ₂M ₁, M ₂Choosing method satisfy relatively prime relation, size is more or less the same;

(2) distribute filter parameter

Determine design M according to two-stage interpolation factor distribution condition and the final overlength rank filter characteristic that requires ₁Times interpolation filter

And M ₂Times interpolation filter

Parameter, the sample frequency of establishing the digital baseband signal correspondence is f _s, signal bandwidth is B, the two-stage interpolation factor is respectively M ₁, M ₂, M then ₁The design of times interpolation filter design parameter is as follows:

Band connection frequency and stop-band frequency are:

$f_{\mathrm{PASS}1}=\frac{B}{M_1{f}_s},$ $f_{\mathrm{STOP}1}=\frac{f_s-B}{M_1{f}_s}$

Transition band width BW ₁For:

BW ₁＝f _STOP1-f _PASS1

M ₂The design of times interpolation filter design parameter is as follows:

Band connection frequency and stop-band frequency are:

$f_{\mathrm{PASS}2}=\frac{B}{M_2{M}_1{f}_s}$

$f_{\mathrm{STOP}2}=\frac{M_1{f}_S-B}{M_1{M}_2{f}_s}$

Transition band width BW ₂For:

BW ₂＝f _STOP2-f _PASS2

(3) design low range interpolation filter

Utilize MATLAB Design of Filter instrument, passband, stop-band frequency and transition band width according to second step obtained obtain M ₁Times interpolation filter

And M ₂Times interpolation filter

(4) the multilevel interpolation design will Regard signal as, it is carried out M ₂Times interpolation, the mode of interpolation be

Insert M between adjacent two numbers ₂Individual zero, interpolation postfilter 1 becomes h ' _M1(n),

h′ _M1(n)＝h _M1(1)，0，...0，h _M1(2)，0，...，0，h _M1(3)，......，h _M1(M ₁)

Use h _M2(n) to h ' _M1(n) carry out filtering, obtain final higher order filter h _M0(n)

h _M0(n)=h ' _M1(n) * h _M2(n), * represents convolution algorithm

Because

With Be the limit sequence,

Also must be that the limit sequence is arranged, its length be:

$N_{M_0}=M_2(N_{M_1}-1)+N_{M_2}$

Wherein Be respectively the length of two wave filters, above-mentioned design result is exactly desired M ₀Times interpolation filter.

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