# Patent

## Title
Digital system for estimating signal non-energy parameters using a digital phase locked loop

## Abstract

A digital system of measuring parameters of the signal (phase, frequency and frequency derivative) received in additive mixture with Gaussian noise. The system is based on the use of variables of a PLL for calculating preliminary estimates of parameters and calculating the corrections for these estimates when there is a spurt frequency caused by a receiver motion with a jerk. A jerk is determined if the low pass filtered signal of the discriminator exceeds a certain threshold. The jerk-correction decreases the dynamic errors. Another embodiment includes a tracking filter for obtaining preliminary estimates of parameters to reduce the fluctuation errors. Estimates are taken from the tracking filter when there is no jerk and from the block of jerk-corrections when there is a jerk.

## Background
BACKGROUND OF THE INVENTION
Phase, frequency and frequency derivative are parameters independent of energy of the input signal (i.e., non-energy parameters). There are known methods of estimating signal non-energy parameters based on processing of variables received from a phase-lock loop (PLL).
U.S. Pat. No. 7,869,554, entitled “Phase/frequency estimator-based phase locked loop”, discloses an apparatus and methods described in use a PLL and provided a phase estimation of the input signal from which signal frequency is estimated by a derivative function and low pass filtering.
U.S. Pat. No. 3,895,294, entitled “Phase change measuring circuit”, discloses a device for measuring the phase change of an input signal over a specified period comprising a phase-locked tracking filter including a high frequency voltage-controlled oscillator (VCO), a frequency divider to give local oscillator signal at the same frequency as the input signal and a counter counting cycles of the VCO whose phase change in any period is N times the input phase change to allow 1/N period resolution, N being an arbitrary integer. The phase change measuring circuit thus allows phase measurement with a resolution within a small fraction of one cycle.
U.S. Pat. No. 7,222,035, entitled “Method and apparatus for determining changing signal frequency”, discloses a method and apparatus which include a PLL having a numerically controlled oscillator (NCO) and a filter of frequency estimates (FFE). The PLL tracks the changing signal frequency and outputs non-smoothed frequency estimates into the FFE. The FFE then smoothes noise in the signal to produce a more accurate smoothed frequency estimate of the input signal.
US Patent Publication No. 20140072084, entitled “Digital system and method of estimating quasi-harmonic signal non-energy parameters using a digital Phase Locked Loop”, discloses a digital system and method of measuring (estimating) non-energy parameters of the signal (phase, frequency and frequency rate) received in additive mixture with Gaussian noise. The first embodiment of the measuring system consists of a PLL system tracking variable signal frequency, a block of NCO full phase computation (OFPC), a block of signal phase preliminary estimation (SPPE) and a first type adaptive filter filtering the signal from the output of SPPE. The second embodiment of the invention has no block SPPE, and NCO full phase is fed to the input of a second type adaptive filter.
A DPLL described in U.S. Pat. No. 4,771,250 generates signal phase which is an approximation of the phase of the received signal with a linear estimator. The effect of a complication associated with non-zero transport delays related to the DPLL is then compensated by a predictor. The estimator provides recursive estimates of phase, frequency, and higher order derivatives, while the predictor compensates for transport lag inherent in the loop.
However, the above references, as well as other conventional methods of measuring non-energy signal parameters using PLL are not adaptive to the jerking motion (when, for example, the acceleration varies linearly in time) of the receiver, or adapt to it by expanding the bandwidths of PLL or using smoothing filters. It is not possible to completely eliminate the dynamic measurement errors using conventional methods.
Unlike the methods above, the present invention enables to obtain accurate phase estimates of the input signal and its derivatives by correcting the preliminary estimates at sites with jerking motion and by an additional filtering of phase estimates at sites without such jerking motion.
The present invention can be used in receivers of various navigation systems, such as GPS, GLONASS and GALILEO, which provide precise measurements of signal phase at different rates of frequency change, as well as systems using digital PLLs for speed measurements.
SUMMARY OF THE INVENTION
Accordingly, the present invention is related to a system of estimating quasi-harmonic signal non-energy parameters using a digital Phase Locked Loop that substantially obviates one or more of the disadvantages of the related art.
In one embodiment, a system for estimating parameters of an input signal includes (a) a digital phase locked loop (PLL) that tracks the input signal and includes:

    
    
        i) a phase discriminator (PD) that determines a phase difference between the input signal and reference signals;
        ii) a loop filter (LF) with a control period Tc operating based on:
    
    






  
    
      
        
          
            
              
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            where αLF, βLF, γLF are constants,
            zid is a PD output;
            φir is a phase code for a Numerically Controlled Oscillator (NCO),
            fir is a frequency code for the NCO,
            ΔφNCO is a phase step size in the NCO,
            ΔωNCO is a frequency step size in the NCO, and
            round(.) is an operation of numerical rounding;
        
        
        iii) the NCO having frequency and phase control using φir and fir,
        wherein an output of the NCO is connected to a reference input of the PD;
    
    
    (b) a calculation of full phase (CFP) block that inputs φir and fir and that operates based on φiNCO=φi-1NCO+φir·ΔφNCO+fi-1r·ΔωNCO·Tc; (c) a low-pass filter (LPF) inputting zid;
    
        a preliminary estimation of signal parameters (PESP) block that inputs φiNCO, fir and siγ, outputs a preliminary estimate for a signal phase {circumflex over (φ)}ic,E and a preliminary estimate for a signal frequency {circumflex over (ω)}ic,E based on:

{circumflex over (φ)}ic,E=φiNCO+siγ/12,

{circumflex over (ω)}ic,E=2π·fir−siγ/(2·Tc);

    
    
    (d) a jerk-corrections of preliminary estimates (JCPE) block inputting ziA, wherein the JCPE block outputs an estimate for a signal phase {circumflex over (φ)}ic and an estimate for a signal frequency {circumflex over (ω)}ic based on:






  
    
      
        
          
            
              
                
                  
                    
                      
                        
                          
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Cφ=1−αLF/2+βLF/12+γLF/24,

Cω=(αLF−βLF/2−γLF/6)/Tc, and

    
    
        TA is a threshold.
    
    


Additional features and advantages of the invention will be set forth in the description that follows, and in part will be apparent from the description, or may be learned by practice of the invention. The advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are intended to provide further explanation of the invention as claimed.



BRIEF DESCRIPTION OF THE ATTACHED FIGURES
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention.
In the drawings:
FIG. 1 is a block diagram for a first embodiment of the invention.
FIG. 2 is an example of an arc tangent-type phase discriminator (PD).
FIG. 3 is a block diagram for a second embodiment of the invention.
FIG. 4 illustrates a jerk as a function of time.



DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
Reference will now be made in detail to the preferred embodiments of the present invention, examples of which are illustrated in the accompanying drawings.
In embodiments of the present invention, adaptation to the nature of the movement of the receiver is made not by changing the parameters of FAP, but by changing the algorithm for estimating the signal parameters. For this purpose, corrections that compensate for the dynamic measurement errors during jerking motion are produced.
FIG. 1 shows a block-diagram of the first embodiment of the invention. The measuring system shown in this figure is based on the use of variables of a PLL for calculating preliminary estimates of non-energy signal parameters (i.e., phase, frequency and frequency derivative (frequency drift)) and calculating the corrections when there is a spurt frequency caused by a receiver's jerking motion. The measuring system comprises a digital PLL (101) that has the following main components: a phase discriminator (PD) (102), loop filter (LF) (103), and numerically-controlled oscillator (NCO) (103) with frequency and phase control. Samples Unmix of an analog process Umix(t) at a sampling frequency fs are fed to the discriminator input. An analog process Umix(t)=Uc(t)+Un(t) representing an additive mixture of quasi-harmonic signal Uc(t) and Gaussian noise Un(t). Desired signal Uc(t) is equal to Uc(t)=Ac·cos [φc(t)],
where Ac is the amplitude of the signal,

    
    
        φc(t)=∫ωc(t)·dt+φ0 is the signal phase [in radians],
        ωc(t) is the signal frequency [in radian/s],
        φ0 is the initial signal phase [in radian].
    
    


Signal phase φc(t), signal frequency ωc(t) and frequency derivative {dot over (ω)}c(t) should be estimated (measured).
A loop filter (LF) operates with a control period Tc on the basis of recurrence equations:




  
    
      
        
          
            
              
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where αLF, βLF, γLF are constant transfer coefficients,
zid is the PD output;
φir is the phase code for NCO,
fir is the frequency code for NCO,
ΔφNCO is the phase step size (radian) in the NCO,
ΔωNCO is the frequency step size (radian/s) in the NCO,
round( ) is the operation of a numerical rounding.
A numerically controlled oscillator (NCO) (104) has frequency and phase control. The phase input of the NCO is connected to the phase output φir of the loop filter (LF) and the frequency input of the NCO is connected to the frequency output fir of the LF (103); wherein a complex output of a NCO connected to a reference input of a PD (102).
FIG. 2 shows an example of PD. Input samples Unmix are multiplied by quadrature samples (Inref, Qnref) from the NCO,




  
    
      
        
          
            
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    }
  
  ,




where ANCO is the sample amplitude, and φnw,NCO is the wrapped phase (i.e., 0≦φnw,NCO<+2π) of NCO in radians. Multiplication results




   
  
    
      
        
          
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are fed to the input of low-pass filters, which are typically the reset accumulators Σ↓ with frequency Fc<<fs. The reset frequency of the accumulators Fc is the control frequency in the PLL, for example, Fc=50 Hz . . . 1000 Hz; fs=10 MHz . . . 100 MHz. The outputs of the reset accumulators are




  
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The output of a phase discriminator is

zid=arctan(Qi/Ii) [in radians].

Further, the signal zid from the PD output is inputted to the loop filter (LF) (FIG. 2), which operates with a control period Tc=Ns/fs on the basis of recurrence equation:




  
    
      
        
          
            
              
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  ,




where αLF, βLF, γLF are constant transfer coefficients,
zid is the PD output;
φir is the phase code for the NCO,
fir is the frequency code for the NCO,
ΔφNCO is the phase step size (radian) in the NCO,
ΔωNCO is the frequency step size (radian/s) in the NCO, and
round(.) is the operation of a numerical rounding.
Digital phase samples φir are fed to the NCO phase control input and abruptly change its phase by the corresponding value ΔφiNCO=φir·ΔφNCO, where ΔφNCO is the phase step size. Samples fir (frequency codes) are delivered to the NCO frequency input and determine its frequency ωiref=fir·ΔωNCO, where ΔωNCO is the frequency step size [radian/s] in the NCO.
The measuring system (see FIG. 1) comprises also:
block (105) for calculation of full phase (CFP) of NCO, coupled with the LF outputs, operates on the basis of equation

φiNCO=φi-1NCO+φir·ΔφNCO+fi-1r·ΔωNCO·Tc;

block (106)—a low-pass filter (LPF) coupled with an output zid of a PD;
block (107)—a block for preliminary estimation of signal parameters (PESP) coupled by its inputs with:
the phase output φiNCO of a block for CFP of a NCO,
the frequency output fir of the loop filter,
the output siγ of the loop filter;
where a block for PESP operates on the basis of equations:

{circumflex over (φ)}ic,E=φiNCO+siγ/12,

{circumflex over (ω)}ic,E=2π·fir−siγ/(2·Tc),

{dot over ({circumflex over (ω)})}ic,E=siγ/Tc2;

where

    
    
        {circumflex over (φ)}ic,E is the preliminary estimate for a signal phase [in radians],
        {circumflex over (ω)}ic,E is the preliminary estimate for a signal frequency [radian/s],
        {dot over ({circumflex over (ω)})}ic,E is the preliminary estimate for a signal frequency derivative [radian/s2];
    
    


block (108) is a threshold unit coupled with an output ziA of a LPF; where an output Ji of a threshold unit is given by the formula:

Ji=true, if ziA>TA,

Ji=false, if ziA≦TA,

here TA is a threshold; the threshold value is set equal to (3 . . . 5)·RMS(ziA).
block (109)—a block for jerk-corrections of preliminary estimates (JCPE) coupled with an output ziA of a LPF and with an output Ji of a threshold unit; where the block JCPE operates on the basis of equations:



  
    
      
        
          
            
              
                
                  
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        where
        
            {circumflex over (φ)}ic is the estimate for a signal phase [in radians],
            {circumflex over (ω)}ic is the estimate for a signal frequency [in radian/s],
            {dot over ({circumflex over (ω)})}ic is the estimate for a signal frequency derivative [in radian/s2],

Cφ=1−αLF/2+βLF/12+γLF/24,

Cω=(αLF−βLF/2−γLF/6)Tc,

C{dot over (ω)}=βLF/Tc2.

        
        
    
    


FIG. 3 shows a block-diagram of the second embodiment of the invention. The measuring system is based on the use of variables of a PLL for calculating preliminary estimates of signal parameters (phase, frequency and frequency derivative) and calculating the corrections when there is a spurt frequency caused by a receiver jerking motion. When a frequency spurt is absent, the parameter estimates are obtained by 3rd order tracking filter, whose input is fed by a preliminary assessment of phase. The measuring system FIG. 3 comprises blocks (301), (302), (303), (304), (305), (306), (307), (308), (309). All of these blocks and their connection are the same as in the first embodiment respectively (101), (102), (103), (104), (105), (106), (107), (108), (109), except that the output of unit (308) does not feed unit (309).
Block (309) for jerk-corrections of preliminary estimates (JCPE) coupled with an output ziA of a LPF and operates on the basis of equations:




  
    
      
        
          
            
              
                
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    }
  
  ,




where {circumflex over (φ)}ic,J, {circumflex over (ω)}ic,J, {dot over ({circumflex over (ω)})}ic,J are, respectively, estimates with jerk-corrections for a phase [in radians], frequency [in radian/s] and frequency derivative [radian/s2] of a signal.
Block (309) for jerk-corrections of preliminary estimates (JCPE) reduces dynamic error of estimates due to frequency spurts, but it increases fluctuation errors of estimates. The measuring system, see FIG. 3, comprises a 3rd order tracking filter of phase (TFP) (310) to reduce the fluctuation errors in the absence of frequency spurt; wherein a TFP bandwidth is less than a PLL bandwidth. Block TFP (310) coupled with the outputs {circumflex over (φ)}ic,E of the PESP, operates on the basis of recurrence equations:




  
    
      
        
          
            
              
                φ
                _
              
              i
              
                c
                ,
                T
              
            
            =
            
              
                
                  φ
                  ^
                
                
                  i
                  -
                  1
                
                
                  c
                  ,
                  T
                
              
              +
              
                
                  
                    ω
                    ^
                  
                  
                    i
                    -
                    1
                  
                  
                    c
                    ,
                    T
                  
                
                ·
                
                  T
                  c
                
              
              +
              
                
                  
                    
                      ω
                      .
                    
                    ^
                  
                  
                    i
                    -
                    1
                  
                  
                    c
                    ,
                    T
                  
                
                ·
                
                  
                    T
                    c
                    2
                  
                  /
                  2
                
              
            
          
        
      
      
        
          
            
              
                ω
                _
              
              i
              
                c
                ,
                T
              
            
            =
            
              
                
                  ω
                  ^
                
                
                  i
                  -
                  1
                
                
                  c
                  ,
                  T
                
              
              +
              
                
                  
                    
                      ω
                      .
                    
                    ^
                  
                  
                    i
                    -
                    1
                  
                  
                    c
                    ,
                    T
                  
                
                ·
                
                  T
                  c
                
              
            
          
        
      
      
        
          
            
              
                
                  ω
                  .
                
                _
              
              i
              c
            
            =
            
              
                
                  ω
                  .
                
                ^
              
              
                i
                -
                1
              
              
                c
                ,
                T
              
            
          
        
      
    
    }
  
   




ziT=φiNCO−φic,T,





  
    
      
        
          
            
              
                φ
                ^
              
              i
              
                c
                ,
                T
              
            
            =
            
              
                
                  φ
                  _
                
                i
                
                  c
                  ,
                  T
                
              
              +
              
                
                  α
                  T
                
                ·
                
                  z
                  i
                  T
                
              
            
          
        
      
      
        
          
            
              
                ω
                ^
              
              i
              
                c
                ,
                T
              
            
            =
            
              
                
                  ω
                  _
                
                i
                
                  c
                  ,
                  T
                
              
              +
              
                
                  β
                  T
                
                ·
                
                  
                    z
                    i
                    T
                  
                  /
                  
                    T
                    c
                  
                
              
            
          
        
      
      
        
          
            
              
                
                  ω
                  .
                
                ^
              
              i
              
                c
                ,
                T
              
            
            =
            
              
                
                  
                    ω
                    .
                  
                  _
                
                i
                
                  c
                  ,
                  T
                
              
              +
              
                
                  γ
                  T
                
                ·
                
                  
                    z
                    i
                    T
                  
                  /
                  
                    T
                    c
                    2
                  
                
              
            
          
        
      
    
    }
  
  ,




where αT, βT, γT are constant transfer coefficients of the TFP.
Block (311) decides on which group of estimates for signal parameters should be taken; this block takes the estimates from the TFP block when there is no jerk, otherwise, it takes the estimates from the JCPE (when there is jerk), i.e.



  
    
      
        
          
            
              
                
                  
                    φ
                    ^
                  
                  i
                  c
                
                =
                
                  
                    φ
                    ^
                  
                  i
                  
                    c
                    ,
                    T
                  
                
              
            
          
          
            
              
                
                  
                    ω
                    ^
                  
                  i
                  c
                
                =
                
                  
                    ω
                    ^
                  
                  i
                  
                    c
                    ,
                    T
                  
                
              
            
          
          
            
              
                
                  
                    
                      ω
                      .
                    
                    ^
                  
                  i
                  c
                
                =
                
                  
                    
                      ω
                      .
                    
                    ^
                  
                  i
                  
                    c
                    ,
                    T
                  
                
              
            
          
        
        }
      
      ⁢
      
        

      
      ⁢
      
        
          
            if
            ⁢
            
              
            
            ⁢
            
              J
              i
            
          
          =
          false
        
        ,
        
          

        
        ⁢
        
          
            
              
                
                  
                    φ
                    ^
                  
                  i
                  c
                
                =
                
                  
                    φ
                    ^
                  
                  i
                  
                    c
                    ,
                    J
                  
                
              
            
          
          
            
              
                
                  
                    ω
                    ^
                  
                  i
                  c
                
                =
                
                  
                    ω
                    ^
                  
                  i
                  
                    c
                    ,
                    J
                  
                
              
            
          
          
            
              
                
                  
                    
                      ω
                      .
                    
                    ^
                  
                  i
                  c
                
                =
                
                  
                    
                      ω
                      .
                    
                    ^
                  
                  i
                  
                    c
                    ,
                    J
                  
                
              
            
          
        
      
    
    }
  




  
    
      
        if
        ⁢
        
          
        
        ⁢
        
          J
          i
        
      
      =
      true
    
    ;
  



where
{circumflex over (φ)}ic is the estimate for a signal phase [in radians],
{circumflex over (ω)}ic is the estimate for a signal frequency [in radian/s],
{dot over ({circumflex over (ω)})}ic is the estimate for a signal frequency derivative [in radian/s2].
FIG. 4 shows an example of motion with jerks. This jerking motion consists of: 0<t≦t1 and t>t4 are states without movement, t1<t≦t2 and t3<t≦t4 are states with jerks, when the acceleration varies linearly, t2<t≦t3 is the state with a constant acceleration.
Having thus described a preferred embodiment, it should be apparent to those skilled in the art that certain advantages of the described apparatus have been achieved.
It should also be appreciated that various modifications, adaptations, and alternative embodiments thereof may be made within the scope and spirit of the present invention. The invention is further defined by the following claims.

## Claims

1. A system for estimating non-energy parameters of an input signal, the system comprising:
a) a third order digital phase locked loop (PLL) that tracks the input signal and includes:
i) a phase discriminator (PD) that determines a phase difference between the input signal and reference signals;
ii) a loop filter (LF) with a control period Tc operating based on equations:






  
    
      
        
          
            
              
                φ
                i
                LF
              
              =
              
                
                  α
                  LF
                
                ·
                
                  z
                  i
                  d
                
              
            
            ,
          
        
      
      
        
          
            
              
                s
                i
                γ
              
              =
              
                
                  s
                  
                    i
                    -
                    1
                  
                  γ
                
                +
                
                  
                    γ
                    LF
                  
                  ·
                  
                    z
                    i
                    d
                  
                
              
            
            ,
          
        
      
      
        
          
            
              
                s
                i
                β
              
              =
              
                
                  s
                  
                    i
                    -
                    1
                  
                  β
                
                +
                
                  s
                  i
                  γ
                
                +
                
                  
                    β
                    LF
                  
                  ·
                  
                    z
                    i
                    d
                  
                
              
            
            ,
          
        
      
      
        
          
            
              
                φ
                i
                r
              
              =
              
                round
                ⁡
                
                  (
                  
                    
                      φ
                      i
                      LF
                    
                    /
                    
                      Δ
                      φ
                      NCO
                    
                  
                  )
                
              
            
            ,
          
        
      
      
        
          
            
              
                f
                i
                r
              
              =
              
                round
                ⁡
                
                  (
                  
                    
                      
                        s
                        i
                        β
                      
                      /
                      
                        Δ
                        ω
                        NCO
                      
                    
                    /
                    
                      T
                      c
                    
                  
                  )
                
              
            
            ,
          
        
      
    
    }
  
  ,




where αLF, βLF, γLF are constant transfer coefficients,
zid is a PD output;
φir is a phase code for a Numerically Controlled Oscillator (NCO),
fir is a frequency code for the NCO,
ΔφNCO is a phase step size in the NCO,
ΔωNCO is a frequency step size in the NCO,
siβ is an output of the LF representing a signal that is proportional to a frequency of the input signal;
siγ is an output of the LF representing a signal that is proportional to a rate of change of the frequency of the input signal;
φiLF is an output of the LF representing a signal used to control a phase of the NCO; and
round(.) is an operation of numerical rounding;
iii) the NCO having frequency and phase control, and whose phase input is connected to the phase output φir and whose frequency input is connected to the frequency code fir, wherein a complex output of the NCO is connected to a reference input of the PD;

b) wherein the system is implemented in a receiver, and wherein the receiver is configured to calculate a full phase of the NCO, using the LF outputs φir and fir and operating based on equation


φiNCO=φi-1NCO+φir·ΔφNCO+fi-1·ΔωNCO·Tc;


c) a low-pass filter (LPF) inputting the output zid of the PD and outputting ziA;
d) wherein the receiver is further configured to generate a preliminary estimation of signal parameters using:
the full phase φiNCO,
the frequency code fir, and
the output siγ t of the LF,
wherein the preliminary estimation of signal parameters are based on:


{circumflex over (φ)}ic,E=φiNCO+siγ/12,



{circumflex over (ω)}ic,E=fir·ΔωNCO−siγ/(2·Tc),



{dot over ({circumflex over (ω)})}ic,E=siγ/Tc2;



 where
 {circumflex over (φ)}ic,E is a preliminary estimate for a signal phase,
 {circumflex over (ω)}ic,E is a preliminary estimate for a signal frequency,
 {dot over ({circumflex over (ω)})}ic,E is a preliminary estimate for a signal frequency derivative;
e) wherein the receiver is further configured to generate an output Ji based on the output ziA of the LPF as follows


Ji=true, if ziA>TA,



Ji=false, if ziA≦TA,


 where TA is a threshold;
f) wherein the receiver is further configured to jerk-correct the preliminary estimates by using the output ziA of the LPF and the output Ji according to:




  
    
      
        
          
            
              
                
                  
                    φ
                    ^
                  
                  i
                  c
                
                =
                
                  
                    
                      φ
                      ^
                    
                    i
                    
                      c
                      ,
                      E
                    
                  
                  +
                  
                    
                      z
                      i
                      A
                    
                    ·
                    
                      C
                      φ
                    
                  
                
              
            
          
          
            
              
                
                  
                    ω
                    ^
                  
                  i
                  c
                
                =
                
                  
                    
                      ω
                      ^
                    
                    i
                    
                      c
                      ,
                      E
                    
                  
                  +
                  
                    
                      z
                      i
                      A
                    
                    ·
                    
                      C
                      ω
                    
                  
                
              
            
          
          
            
              
                
                  
                    
                      ω
                      .
                    
                    ^
                  
                  i
                  c
                
                =
                
                  
                    
                      
                        ω
                        .
                      
                      ^
                    
                    i
                    
                      c
                      ,
                      E
                    
                  
                  +
                  
                    
                      z
                      i
                      A
                    
                    ·
                    
                      C
                      
                        ω
                        .
                      
                    
                  
                
              
            
          
        
        }
      
      ⁢
      
        

      
      ⁢
      
        
          
            if
            ⁢
            
              
            
            ⁢
            
              J
              i
            
          
          =
          true
        
        ,
        
          

        
        ⁢
        
          
            
              
                
                  
                    
                      φ
                      ^
                    
                    i
                    c
                  
                  =
                  
                    
                      φ
                      ^
                    
                    i
                    
                      c
                      ,
                      E
                    
                  
                
                ,
              
            
          
          
            
              
                
                  
                    ω
                    ^
                  
                  i
                  c
                
                =
                
                  
                    ω
                    ^
                  
                  i
                  
                    c
                    ,
                    E
                  
                
              
            
          
          
            
              
                
                  
                    
                      ω
                      .
                    
                    ^
                  
                  i
                  c
                
                =
                
                  
                    
                      ω
                      .
                    
                    ^
                  
                  i
                  
                    c
                    ,
                    E
                  
                
              
            
          
        
      
    
    }
  




  
    
      
        if
        ⁢
        
          
        
        ⁢
        
          J
          i
        
      
      =
      false
    
    ,
  



where
{circumflex over (φ)}ic is an estimate for a signal phase,
{circumflex over (ω)}ic is an estimate for a signal frequency,
{dot over ({circumflex over (ω)})}ic is an estimate for a signal frequency derivative,


Cφ=1−αLF/2+βLF/12+γLF/24,



Cω=(αLF−βLF/2−γLF/6)/Tc,



C{dot over (ω)}=βLF/T2.

2. The system of claim 1, wherein the LPF operates based on


ziA=zi-1A+αLPF·(zid−zi-1A),

where αLPF is a constant transfer coefficient, 0<αLPF<1.

3. The system of claim 1, wherein the LPF operates based on


ziA=zi-1A+αLPF·(zid−zi-1A), where 0<αLPF<1.

4. A system for estimating non-energy parameters of an input signal, the system comprising:
a) a third order digital phase locked loop (PLL) that tracks the input signal and includes:
(i) a phase discriminator (PD) that determines a phase difference between the input signal and reference signals;
(ii) a loop filter (LF) with a control period Tc based on equations:






  
    
      
        
          
            
              
                φ
                i
                LF
              
              =
              
                
                  α
                  LF
                
                ·
                
                  z
                  i
                  d
                
              
            
            ,
          
        
      
      
        
          
            
              
                s
                i
                γ
              
              =
              
                
                  s
                  
                    i
                    -
                    1
                  
                  γ
                
                +
                
                  
                    γ
                    LF
                  
                  ·
                  
                    z
                    i
                    d
                  
                
              
            
            ,
          
        
      
      
        
          
            
              
                s
                i
                β
              
              =
              
                
                  s
                  
                    i
                    -
                    1
                  
                  β
                
                +
                
                  s
                  i
                  γ
                
                +
                
                  
                    β
                    LF
                  
                  ·
                  
                    z
                    i
                    d
                  
                
              
            
            ,
          
        
      
      
        
          
            
              
                φ
                i
                r
              
              =
              
                round
                ⁡
                
                  (
                  
                    
                      φ
                      i
                      LF
                    
                    /
                    
                      Δ
                      φ
                      NCO
                    
                  
                  )
                
              
            
            ,
          
        
      
      
        
          
            
              
                f
                i
                r
              
              =
              
                round
                ⁡
                
                  (
                  
                    
                      
                        s
                        i
                        β
                      
                      /
                      
                        Δ
                        ω
                        NCO
                      
                    
                    /
                    
                      T
                      c
                    
                  
                  )
                
              
            
            ,
          
        
      
    
    }
  
  ,




where
αLF, βLF, γLF are constant transfer coefficients,
zid is a PD output;
φir is a phase code for a numerically controlled oscillator (NCO),
fir is a frequency code for the NCO,
ΔφNCO is a phase step size in the NCO,
ΔωNCO is a frequency step size in the NCO,
siβ is an output of the LF representing a signal that is proportional to a frequency of the input signal;
siγ is an output of the LF representing a signal that is proportional to a rate of change of the frequency of the input signal;
φiLF is an output of the LF representing a signal used to control a phase of the NCO;
round(.) is an operation of a numerical rounding; and

(iii) the NCO having frequency and phase control, whose phase input is connected to the phase output φir and a frequency input is connected to the frequency code fir, wherein a complex output of the NCO is connected to a reference input of the PD;

b) wherein the system is implemented in a receiver, and wherein the receiver is configured to calculate a full phase of the NCO, based on the LF outputs φir and fir, and operating based on equation


φiNCO=φi-1NCO+φir·ΔφNCO+fi-1r·ΔωNCO·Tc;


c) a low-pass filter (LPF) inputting the output zid from the PD and outputting ziA;
d) wherein the receiver is configured to generate preliminary estimates of signal parameters based on the full phase output φiNCO, the frequency code fir, and the output siγ according to equations:





  
    
      
        
          
            
              
                φ
                ^
              
              i
              
                c
                ,
                E
              
            
            =
            
              
                φ
                i
                NCO
              
              +
              
                
                  s
                  i
                  γ
                
                /
                12
              
            
          
        
      
      
        
          
            
              
                ω
                ^
              
              i
              
                c
                ,
                E
              
            
            =
            
              
                
                  f
                  i
                  r
                
                ·
                
                  Δ
                  ω
                  NCO
                
              
              -
              
                
                  s
                  i
                  γ
                
                /
                
                  (
                  
                    2
                    ·
                    
                      T
                      c
                    
                  
                  )
                
              
            
          
        
      
      
        
          
            
              
                
                  ω
                  .
                
                ^
              
              i
              
                c
                ,
                E
              
            
            =
            
              
                s
                i
                γ
              
              /
              
                T
                c
                2
              
            
          
        
      
    
    }
  
   




where
{circumflex over (φ)}ic,E is a preliminary estimate for a signal phase,
{circumflex over (ω)}ic,E is a preliminary estimate for a signal frequency,
{dot over ({circumflex over (ω)})}ic,E is a preliminary estimate for a signal frequency derivative;

e) wherein the receiver is further configured to generate an output Ji based on the output ziA of the LPF as follows:


Ji=true, if ziA>TA,



Ji=false, if ziA≦TA,


 where TA is a threshold;
f) wherein the receiver is further configured to perform jerk-corrections of the preliminary estimates based on equations:





  
    
      
        
          
            
              
                φ
                ^
              
              i
              
                c
                ,
                J
              
            
            =
            
              
                
                  φ
                  ^
                
                i
                
                  c
                  ,
                  E
                
              
              +
              
                
                  z
                  i
                  A
                
                ·
                
                  C
                  φ
                
              
            
          
          ,
        
      
    
    
      
        
          
            
              ω
              ^
            
            i
            
              c
              ,
              J
            
          
          =
          
            
              
                ω
                ^
              
              i
              
                c
                ,
                E
              
            
            +
            
              
                z
                i
                A
              
              ·
              
                C
                ω
              
            
          
        
      
    
    
      
        
          
            
              
                ω
                .
              
              ^
            
            i
            
              c
              ,
              J
            
          
          =
          
            
              
                
                  ω
                  .
                
                ^
              
              i
              
                c
                ,
                E
              
            
            +
            
              
                z
                i
                A
              
              ·
              
                C
                
                  ω
                  .
                
              
            
          
        
      
    
  
  }




where
{circumflex over (φ)}ic,J, {circumflex over (ω)}ic,J, {dot over ({circumflex over (ω)})}ic,J are, respectively, estimates with jerk-corrections for a phase, frequency and frequency derivative of the input signal,


Cφ=1−αLF/2+βLF/12±γLF/24,



Cω=(αLF−βLF/2−γLF/6)/Tc,



C{dot over (ω)}=βLF/Tc2;



g) a third order tracking filter of phase (TFP) which operates based on equations:




  
    
      
        
          
            
              
                φ
                _
              
              i
              
                c
                ,
                T
              
            
            =
            
              
                
                  φ
                  ^
                
                
                  i
                  -
                  1
                
                
                  c
                  ,
                  T
                
              
              +
              
                
                  
                    ω
                    ^
                  
                  
                    i
                    -
                    1
                  
                  
                    c
                    ,
                    T
                  
                
                ·
                
                  T
                  c
                
              
              +
              
                
                  
                    
                      ω
                      .
                    
                    ^
                  
                  
                    i
                    -
                    1
                  
                  
                    c
                    ,
                    T
                  
                
                ·
                
                  
                    T
                    c
                    2
                  
                  /
                  2
                
              
            
          
        
      
      
        
          
            
              
                ω
                _
              
              i
              
                c
                ,
                T
              
            
            =
            
              
                
                  ω
                  ^
                
                
                  i
                  -
                  1
                
                
                  c
                  ,
                  T
                
              
              +
              
                
                  
                    
                      ω
                      .
                    
                    ^
                  
                  
                    i
                    -
                    1
                  
                  
                    c
                    ,
                    T
                  
                
                ·
                
                  T
                  c
                
              
            
          
        
      
      
        
          
            
              
                
                  ω
                  .
                
                _
              
              i
              c
            
            =
            
              
                
                  ω
                  .
                
                ^
              
              
                i
                -
                1
              
              
                c
                ,
                T
              
            
          
        
      
    
    }
  
   




ziT=φiNCO−φic,T,







  
    
      
        
          
            
              
                φ
                ^
              
              i
              
                c
                ,
                T
              
            
            =
            
              
                
                  φ
                  _
                
                i
                
                  c
                  ,
                  T
                
              
              +
              
                
                  α
                  T
                
                ·
                
                  z
                  i
                  T
                
              
            
          
        
      
      
        
          
            
              
                ω
                ^
              
              i
              
                c
                ,
                T
              
            
            =
            
              
                
                  ω
                  _
                
                i
                
                  c
                  ,
                  T
                
              
              +
              
                
                  β
                  T
                
                ·
                
                  
                    z
                    i
                    T
                  
                  /
                  
                    T
                    c
                  
                
              
            
          
        
      
      
        
          
            
              
                
                  ω
                  .
                
                ^
              
              i
              
                c
                ,
                T
              
            
            =
            
              
                
                  
                    ω
                    .
                  
                  _
                
                i
                
                  c
                  ,
                  T
                
              
              +
              
                
                  γ
                  T
                
                ·
                
                  
                    z
                    i
                    T
                  
                  /
                  
                    T
                    c
                    2
                  
                
              
            
          
        
      
    
    }
  
  ,



 where αT, βT, γT are constant transfer coefficients of the TFP;
h) wherein the receiver is further configured to output the estimates from the TFP as the estimates of signal parameters when there is no jerk and takes the preliminary estimates otherwise, such that




  
    
      
        
          
            
              
                
                  
                    φ
                    ^
                  
                  i
                  c
                
                =
                
                  
                    φ
                    ^
                  
                  i
                  
                    c
                    ,
                    T
                  
                
              
            
          
          
            
              
                
                  
                    ω
                    ^
                  
                  i
                  c
                
                =
                
                  
                    ω
                    ^
                  
                  i
                  
                    c
                    ,
                    T
                  
                
              
            
          
          
            
              
                
                  
                    
                      ω
                      .
                    
                    ^
                  
                  i
                  c
                
                =
                
                  
                    
                      ω
                      .
                    
                    ^
                  
                  i
                  
                    c
                    ,
                    T
                  
                
              
            
          
        
        }
      
      ⁢
      
        

      
      ⁢
      
        
          
            if
            ⁢
            
              
            
            ⁢
            
              J
              i
            
          
          =
          false
        
        ,
        
          

        
        ⁢
        
          
            
              
                
                  
                    φ
                    ^
                  
                  i
                  c
                
                =
                
                  
                    φ
                    ^
                  
                  i
                  
                    c
                    ,
                    J
                  
                
              
            
          
          
            
              
                
                  
                    ω
                    ^
                  
                  i
                  c
                
                =
                
                  
                    ω
                    ^
                  
                  i
                  
                    c
                    ,
                    J
                  
                
              
            
          
          
            
              
                
                  
                    
                      ω
                      .
                    
                    ^
                  
                  i
                  c
                
                =
                
                  
                    
                      ω
                      .
                    
                    ^
                  
                  i
                  
                    c
                    ,
                    J
                  
                
              
            
          
        
      
    
    }
  




  
    
      
        if
        ⁢
        
          
        
        ⁢
        
          J
          i
        
      
      =
      true
    
    ;
  



where
{circumflex over (φ)}ic is an estimate for a signal phase,
{circumflex over (ω)}ic is an estimate for a signal frequency, and
{dot over ({circumflex over (ω)})}ic is an estimate for a signal frequency derivative.

5. The system of claim 4, wherein the low-pass filter (LPF) is based on equation


z=iA=zi-1A+αLPF·(zid−zi-1A),


where αLPF is a constant transfer coefficient, 0<αLPF<1.

6. A system for estimating parameters of an input signal, the system comprising:
(a) a digital phase locked loop (PLL) that tracks the input signal and includes:
(i) a phase discriminator (PD) that determines a phase difference between the input signal and reference signals;
(ii) a loop filter (LF) with a control period Tc operating based on:






  
    
      
        
          
            
              
                φ
                i
                LF
              
              =
              
                
                  α
                  LF
                
                ·
                
                  z
                  i
                  d
                
              
            
            ,
          
        
      
      
        
          
            
              
                s
                i
                γ
              
              =
              
                
                  s
                  
                    i
                    -
                    1
                  
                  γ
                
                +
                
                  
                    γ
                    LF
                  
                  ·
                  
                    z
                    i
                    d
                  
                
              
            
            ,
          
        
      
      
        
          
            
              
                s
                i
                β
              
              =
              
                
                  s
                  
                    i
                    -
                    1
                  
                  β
                
                +
                
                  s
                  i
                  γ
                
                +
                
                  
                    β
                    LF
                  
                  ·
                  
                    z
                    i
                    d
                  
                
              
            
            ,
          
        
      
      
        
          
            
              
                φ
                i
                r
              
              =
              
                round
                ⁡
                
                  (
                  
                    
                      φ
                      i
                      LF
                    
                    /
                    
                      Δ
                      φ
                      NCO
                    
                  
                  )
                
              
            
            ,
          
        
      
      
        
          
            
              
                f
                i
                r
              
              =
              
                round
                ⁡
                
                  (
                  
                    
                      
                        s
                        i
                        β
                      
                      /
                      
                        Δ
                        ω
                        NCO
                      
                    
                    /
                    
                      T
                      c
                    
                  
                  )
                
              
            
            ,
          
        
      
    
    }
  
  ,





where αLF, βLF, γLF are constants,
zid is a PD output;
 ir is a phase code for a Numerically Controlled Oscillator (NCO),
fir is a frequency code for the NCO,
ΔφNCO is a phase step size in the NCO,
ΔωNCO is a frequency step size in the NCO,
siβ is an output of the LF representing a signal that is proportional to a frequency of the input signal;
siγ is an output of the LF representing a signal that is proportional to a rate of change of the frequency of the input signal;
φiLF is an output of the LF representing a signal used to control a phase of the NCO; and
round(.) is an operation of numerical rounding;

(iii) the NCO having frequency and phase control using φir and fir, wherein an output of the NCO is connected to a reference input of the PD;

(b) wherein the system is implemented in a receiver, and wherein the receiver is configured to calculate a full phase based on φir and fir from the LF and based on


φiNCO=φi-1NCO+φir·ΔφNCO+fi-1r·ΔωNCO·Tc;


(c) a low-pass filter (LPF) inputting zid and outputting ziA;
(d) wherein the receiver is further configured to generate a preliminary estimate for a signal phase {circumflex over (φ)}ic,E and a preliminary estimate for a signal frequency {circumflex over (ω)}ic,E based on:


{circumflex over (φ)}ic,E=φiNCO+siγ/12,



{circumflex over (ω)}ic,E=fir·ΔωNCO−siγ/(2·Tc);


(e) wherein the receiver is further configured to perform jerk-corrections of the preliminary estimates and to output an estimate for a signal phase {circumflex over (φ)}ic and an estimate for a signal frequency {circumflex over (ω)}ic based on:




  
    
      
        
          
            
              
                
                  
                    φ
                    ^
                  
                  i
                  c
                
                =
                
                  
                    
                      φ
                      ^
                    
                    i
                    
                      c
                      ,
                      E
                    
                  
                  +
                  
                    
                      z
                      i
                      A
                    
                    ·
                    
                      C
                      φ
                    
                  
                
              
            
          
          
            
              
                
                  
                    ω
                    ^
                  
                  i
                  c
                
                =
                
                  
                    
                      ω
                      ^
                    
                    i
                    
                      c
                      ,
                      E
                    
                  
                  +
                  
                    
                      z
                      i
                      A
                    
                    ·
                    
                      C
                      ω
                    
                  
                
              
            
          
        
        }
      
      ⁢
      
        

      
      ⁢
      if
      ⁢
      
        
      
      ⁢
      
        

      
      ⁢
      
        
          
            z
            i
            A
          
          >
          
            T
            A
          
        
        ,
        
          

        
        ⁢
        
          
            
              
                
                  
                    
                      φ
                      ^
                    
                    i
                    c
                  
                  =
                  
                    
                      φ
                      ^
                    
                    i
                    
                      c
                      ,
                      E
                    
                  
                
                ,
              
            
          
          
            
              
                
                  
                    ω
                    ^
                  
                  i
                  c
                
                =
                
                  
                    ω
                    ^
                  
                  i
                  
                    c
                    ,
                    E
                  
                
              
            
          
        
      
    
    }
  




  if




  
    
      
        z
        i
        A
      
      ≤
      
        T
        A
      
    
    ,
  



where


Cφ=1−αLF/2+βLF/12+γLF/24,



Cω=(αLF−βLF/2−γLF/6)Tc, and



 TA is a threshold.

7. The system of claim 6, wherein the PD is an arctangent-type PD.

8. The system of claim 6, wherein the PLL is a third order PLL.

9. The system of claim 6, wherein the system also estimates a signal frequency derivative {dot over ({circumflex over (ω)})}ic as follows:
the receiver is configured to generate a preliminary estimate for a signal frequency derivative {dot over ({circumflex over (ω)})}ic,E=siγ/Tc2; and
the receiver is configured to output


{dot over ({circumflex over (ω)})}ic={dot over ({circumflex over (ω)})}ic,E+ziA·C{dot over (ω)}, if ziA>TA,



{dot over ({circumflex over (ω)})}ic={dot over ({circumflex over (ω)})}iC,E, if ziA≦TA,



where C{dot over (ω)}=βLF/Tc2.

10. The system of claim 6, where αLF, βLF, γLF are constant transfer coefficients.

11. A system for estimating non-energy parameters of an input signal, the system comprising:
a) a digital phase locked loop (PLL) that includes:
i) a phase discriminator (PD) that determines a phase difference zid between the input signal and reference signals from a Numerically Controlled Oscillator (NCO);
ii) a loop filter (LF) with a control period Tc based on equations:






  
    
      
        
          
            
              
                s
                i
                γ
              
              =
              
                
                  s
                  
                    i
                    -
                    1
                  
                  γ
                
                +
                
                  γ
                  ·
                  
                    z
                    i
                    d
                  
                
              
            
            ,
          
        
      
      
        
          
            
              
                s
                i
                β
              
              =
              
                
                  s
                  
                    i
                    -
                    1
                  
                  β
                
                +
                
                  s
                  i
                  γ
                
                +
                
                  β
                  ·
                  
                    z
                    i
                    d
                  
                
              
            
            ,
          
        
      
      
        
          
            
              
                φ
                i
                r
              
              =
              
                round
                ⁢
                
                  
                
                ⁢
                
                  (
                  
                    α
                    ·
                    
                      
                        z
                        i
                        d
                      
                      /
                      
                        Δ
                        φ
                        NCO
                      
                    
                  
                  )
                
              
            
            ,
          
        
      
      
        
          
            
              
                f
                i
                r
              
              =
              
                round
                ⁢
                
                  
                
                ⁢
                
                  (
                  
                    
                      
                        s
                        i
                        β
                      
                      /
                      
                        Δ
                        ω
                        NCO
                      
                    
                    /
                    
                      T
                      c
                    
                  
                  )
                
              
            
            ,
          
        
      
    
    }
  
  ,





where α, β, γ are constants,
φir is a phase control signal for the NCO,
fir is a frequency control signal for the NCO,
ΔφNCO is a phase step size in the NCO,
ΔωNCO is a frequency step size in the NCO,
siβ corresponds to a frequency of the input signal;
siγ corresponds to a rate of change of the frequency of the input signal; and
round(.) is numerical rounding; and

iii) the NCO inputting the φir and fir phase and frequency control signals;

b) wherein the system is implemented in a receiver, and wherein the receiver is configured to calculate a full phase φiNCO based on


φiNCO=φi-1NCO+φir·ΔφNCO+fi-1r·ΔωNCO·Tc;


c) a low-pass filter (LPF) inputting the phase difference zid and outputting ziA;
d) wherein the receiver generates a preliminary estimation of signal parameters based on:


{circumflex over (φ)}ic,E=φiNCO+siγ/Kφ,



{circumflex over (ω)}1c,E=ΔωNCO·fir−siγ/(Kω·Tc),



{dot over ({circumflex over (ω)})}ic,E=siγ/Tc2;


 where
 {circumflex over (φ)}ic,E is a preliminary estimate for the phase of the input signal,
 {circumflex over (ω)}ic,E is a preliminary estimate for the frequency of the input signal,
 {dot over ({circumflex over (ω)})}ic,E is a preliminary estimate for a derivative of the frequency of the input signal, and
 Kφ and Kω are constants;
e) wherein the receiver is further configured to generate an output Ji based on


Ji=true, if ziA>TA,



Ji=false, if ziA≦TA,


 where TA is a threshold; and
f) wherein the receiver is further configured to perform jerk-corrections of the preliminary estimates based on:





  
    
      
        
          
            
              
                
                  
                    
                      
                        
                          
                            φ
                            ^
                          
                          i
                          c
                        
                        =
                        
                          
                            
                              φ
                              ^
                            
                            i
                            
                              c
                              ,
                              E
                            
                          
                          +
                          
                            
                              z
                              i
                              A
                            
                            ·
                            
                              (
                              
                                
                                  K
                                  0
                                
                                -
                                
                                  α
                                  /
                                  
                                    K
                                    1
                                  
                                
                                +
                                
                                  β
                                  /
                                  
                                    K
                                    2
                                  
                                
                                +
                                
                                  γ
                                  /
                                  
                                    K
                                    3
                                  
                                
                              
                              )
                            
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            ω
                            ^
                          
                          i
                          c
                        
                        =
                        
                          
                            
                              ω
                              ^
                            
                            i
                            
                              c
                              ,
                              E
                            
                          
                          +
                          
                            
                              z
                              i
                              A
                            
                            ·
                            
                              
                                (
                                
                                  α
                                  -
                                  
                                    β
                                    /
                                    
                                      K
                                      4
                                    
                                  
                                  -
                                  
                                    γ
                                    /
                                    
                                      K
                                      5
                                    
                                  
                                
                                )
                              
                              /
                              
                                T
                                c
                              
                            
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            
                              ω
                              .
                            
                            ^
                          
                          i
                          c
                        
                        =
                        
                          
                            
                              
                                ω
                                .
                              
                              ^
                            
                            i
                            
                              c
                              ,
                              E
                            
                          
                          +
                          
                            
                              z
                              i
                              A
                            
                            ·
                            
                              β
                              /
                              
                                T
                                c
                                2
                              
                            
                          
                        
                      
                    
                  
                
                }
              
              ⁢
              
                
              
              ⁢
              if
              ⁢
              
                
              
              ⁢
              
                J
                i
              
            
            =
            true
          
          ,
          
            

          
          ⁢
          
            
              
                
                  
                    
                      
                        φ
                        ^
                      
                      i
                      c
                    
                    =
                    
                      
                        φ
                        ^
                      
                      i
                      
                        c
                        ,
                        E
                      
                    
                  
                  ,
                
              
            
            
              
                
                  
                    
                      ω
                      ^
                    
                    i
                    c
                  
                  =
                  
                    
                      ω
                      ^
                    
                    i
                    
                      c
                      ,
                      E
                    
                  
                
              
            
            
              
                
                  
                    
                      
                        ω
                        .
                      
                      ^
                    
                    i
                    c
                  
                  =
                  
                    
                      
                        ω
                        .
                      
                      ^
                    
                    i
                    
                      c
                      ,
                      E
                    
                  
                
              
            
          
        
        }
      
      ⁢
      
        
      
      ⁢
      if
      ⁢
      
        
      
      ⁢
      
        J
        i
      
    
    =
    false
  
  ,




where
{circumflex over (φ)}ic is an estimate for the phase of the input signal,
{circumflex over (ω)}ic is an estimate for the frequency of the input signal,
{dot over ({circumflex over (ω)})}ic is an estimate for the derivative of the frequency of the input signal, and
K0, K1, K2, K3, K4, and K5 are constants.

12. The system of claim 11, where
K0=1, K1=2, K2=12, K3=24, K4=2 and K5=6.

13. The system of claim 11, where Kφ=12 and Kω=2.

14. A system for estimating parameters of an input signal, the system comprising:
a) a digital phase locked loop that includes:
i) a phase discriminator that determines a phase difference between the input signal and reference signals from a Numerically Controlled Oscillator (NCO);
ii) a loop filter (LF) with a control period Tc that generates a phase control signal φir for the NCO and a frequency control signal fir for the NCO, and based on:






  
    
      
        
          
            
              
                s
                i
                γ
              
              =
              
                
                  s
                  
                    i
                    -
                    1
                  
                  γ
                
                +
                
                  γ
                  ·
                  
                    z
                    i
                    d
                  
                
              
            
            ,
          
        
      
      
        
          
            
              
                s
                i
                β
              
              =
              
                
                  s
                  
                    i
                    -
                    1
                  
                  β
                
                +
                
                  s
                  i
                  γ
                
                +
                
                  β
                  ·
                  
                    z
                    i
                    d
                  
                
              
            
            ,
          
        
      
      
        
          
            
              
                φ
                i
                r
              
              =
              
                round
                ⁢
                
                  
                
                ⁢
                
                  (
                  
                    α
                    ·
                    
                      
                        z
                        i
                        d
                      
                      /
                      
                        Δ
                        φ
                        NCO
                      
                    
                  
                  )
                
              
            
            ,
          
        
      
      
        
          
            
              
                f
                i
                r
              
              =
              
                round
                ⁢
                
                  
                
                ⁢
                
                  (
                  
                    
                      
                        s
                        i
                        β
                      
                      /
                      
                        Δ
                        ω
                        NCO
                      
                    
                    /
                    
                      T
                      c
                    
                  
                  )
                
              
            
            ,
          
        
      
    
    }
  
  ,





where α, β, γ are constants,
ΔφNCO is a phase step size in the NCO,
ΔωNCO is a frequency step size in the NCO,
siβ corresponds to a frequency of the input signal,
siγ corresponds to a rate of change of the frequency of the input signal, and
round(.) is numerical rounding; and


b) wherein the system is implemented in a receiver, and wherein the receiver is configured to calculate a full phase φiNCO according to


φiNCO=φi-1NCO+φir·ΔφNCO+fi-1r·ΔωNCO·Tc;


c) a low-pass filter (LPF) inputting the phase difference zid and outputting ziA;
d) wherein the receiver uses φiNCO and siγ for generation of:
a preliminary estimate {circumflex over (φ)}ic,E for a phase of the input signal, and
a preliminary estimate {circumflex over (ω)}ic,E for a frequency of the input signal;

e) wherein the receiver is configured to output a true/false value Ji based on ziA; and
f) wherein the receiver is configured to perform jerk-corrections of the preliminary estimates and to generate an estimate {circumflex over (φ)}ic for a phase of the input signal, and an estimate {circumflex over (ω)}ic for the frequency of the input signal, based on Ji, ziA, {circumflex over (φ)}ic,E and {circumflex over (ω)}ic,E.

15. The system of claim 14, wherein the receiver is also configured to generate a preliminary estimate {circumflex over (ω)}ic,E of a derivative of the frequency of the input signal.

16. The system of claim 15, wherein the receiver is also configured to generate an estimate {dot over ({circumflex over (ω)})}ic for the derivative of the frequency of the input signal based on Ji, ziA, {circumflex over (φ)}ic,E, {circumflex over (ω)}ic,E and {dot over ({circumflex over (ω)})}ic,E.

17. The system of claim 16, wherein the preliminary estimates {circumflex over (φ)}ic,E, {circumflex over (ω)}ic,E, and {dot over ({circumflex over (ω)})}ic,E are generated according to


{circumflex over (φ)}ic,E=φiNCO+siγ/Kφ,



{circumflex over (ω)}ic,E=ΔωNCO·fir−siγ/(Kω·Tc),



{dot over ({circumflex over (ω)})}ic,E=siγ/Tc2;

where Kφ and Kω are constants.

18. The system of claim 17, wherein the receiver is also configured to generate the estimates {circumflex over (φ)}ic, {circumflex over (ω)}ic and {dot over ({circumflex over (ω)})}ic according to:




  
    
      
        
          
            
              
                
                  
                    
                      
                        
                          
                            φ
                            ^
                          
                          i
                          c
                        
                        =
                        
                          
                            
                              φ
                              ^
                            
                            i
                            
                              c
                              ,
                              E
                            
                          
                          +
                          
                            
                              z
                              i
                              A
                            
                            ·
                            
                              (
                              
                                
                                  K
                                  0
                                
                                -
                                
                                  α
                                  /
                                  
                                    K
                                    1
                                  
                                
                                +
                                
                                  β
                                  /
                                  
                                    K
                                    2
                                  
                                
                                +
                                
                                  γ
                                  /
                                  
                                    K
                                    3
                                  
                                
                              
                              )
                            
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            ω
                            ^
                          
                          i
                          c
                        
                        =
                        
                          
                            
                              ω
                              ^
                            
                            i
                            
                              c
                              ,
                              E
                            
                          
                          +
                          
                            
                              z
                              i
                              A
                            
                            ·
                            
                              
                                (
                                
                                  α
                                  -
                                  
                                    β
                                    /
                                    
                                      K
                                      4
                                    
                                  
                                  -
                                  
                                    γ
                                    /
                                    
                                      K
                                      5
                                    
                                  
                                
                                )
                              
                              /
                              
                                T
                                c
                              
                            
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            
                              ω
                              .
                            
                            ^
                          
                          i
                          c
                        
                        =
                        
                          
                            
                              
                                ω
                                .
                              
                              ^
                            
                            i
                            
                              c
                              ,
                              E
                            
                          
                          +
                          
                            
                              z
                              i
                              A
                            
                            ·
                            
                              β
                              /
                              
                                T
                                c
                                2
                              
                            
                          
                        
                      
                    
                  
                
                }
              
              ⁢
              
                
              
              ⁢
              if
              ⁢
              
                
              
              ⁢
              
                J
                i
              
            
            =
            true
          
          ,
          
            

          
          ⁢
          
            
              
                
                  
                    
                      
                        φ
                        ^
                      
                      i
                      c
                    
                    =
                    
                      
                        φ
                        ^
                      
                      i
                      
                        c
                        ,
                        E
                      
                    
                  
                  ,
                
              
            
            
              
                
                  
                    
                      ω
                      ^
                    
                    i
                    c
                  
                  =
                  
                    
                      ω
                      ^
                    
                    i
                    
                      c
                      ,
                      E
                    
                  
                
              
            
            
              
                
                  
                    
                      
                        ω
                        .
                      
                      ^
                    
                    i
                    c
                  
                  =
                  
                    
                      
                        ω
                        .
                      
                      ^
                    
                    i
                    
                      c
                      ,
                      E
                    
                  
                
              
            
          
        
        }
      
      ⁢
      
        
      
      ⁢
      if
      ⁢
      
        
      
      ⁢
      
        J
        i
      
    
    =
    false
  
  ,



where K0, K1, K2, K3, K4, and K5 are constants.

19. The system of claim 18, further comprising
g) a third order tracking filter (TFP) that operates based on equations:





  
    
      
        
          
            
              
                
                  
                    
                      
                        φ
                        i
                      
                      _
                    
                    
                      c
                      ,
                      T
                    
                  
                  =
                  
                    
                      
                        φ
                        ^
                      
                      
                        i
                        -
                        1
                      
                      
                        c
                        ,
                        T
                      
                    
                    +
                    
                      
                        ω
                        ^
                      
                      
                        i
                        -
                        1
                      
                      
                        c
                        ,
                        T
                      
                    
                  
                
                ⁣
                
                  
                    ·
                    
                      T
                      c
                    
                  
                  +
                  
                    
                      
                        
                          ω
                          .
                        
                        ^
                      
                      
                        i
                        -
                        1
                      
                      
                        c
                        ,
                        T
                      
                    
                    ·
                    
                      
                        T
                        c
                        2
                      
                      /
                      2
                    
                  
                
              
            
          
          
            
              
                
                  
                    
                      ω
                      i
                    
                    _
                  
                  
                    c
                    ,
                    T
                  
                
                =
                
                  
                    
                      ω
                      ^
                    
                    
                      i
                      -
                      1
                    
                    
                      c
                      ,
                      T
                    
                  
                  +
                  
                    
                      
                        
                          ω
                          .
                        
                        ^
                      
                      
                        i
                        -
                        1
                      
                      
                        c
                        ,
                        T
                      
                    
                    ·
                    
                      T
                      c
                    
                  
                
              
            
          
          
            
              
                
                  
                    
                      
                        ω
                        .
                      
                      i
                    
                    _
                  
                  c
                
                =
                
                  
                    
                      ω
                      .
                    
                    ^
                  
                  
                    i
                    -
                    1
                  
                  
                    c
                    ,
                    T
                  
                
              
            
          
        
        }
      
      ⁢
      
        

      
      ⁢
      
        
          
            z
            i
            T
          
          =
          
            
              φ
              i
              NCO
            
            -
            
              
                φ
                _
              
              i
              
                c
                ,
                T
              
            
          
        
        ,
        
          

        
        ⁢
        
          
            
              
                
                  
                    φ
                    ^
                  
                  i
                  
                    c
                    ,
                    T
                  
                
                =
                
                  
                    
                      
                        φ
                        i
                      
                      _
                    
                    
                      c
                      ,
                      T
                    
                  
                  +
                  
                    
                      α
                      T
                    
                    ·
                    
                      z
                      i
                      T
                    
                  
                
              
            
          
          
            
              
                
                  
                    ω
                    ^
                  
                  i
                  
                    c
                    ,
                    T
                  
                
                =
                
                  
                    
                      
                        ω
                        i
                      
                      _
                    
                    
                      c
                      ,
                      T
                    
                  
                  +
                  
                    
                      β
                      T
                    
                    ·
                    
                      
                        z
                        i
                        T
                      
                      /
                      
                        T
                        c
                      
                    
                  
                
              
            
          
        
      
    
    }
  
  ,




where αT, βT are constants;

wherein the receiver is also configured to output the estimates {circumflex over (φ)}ic,T and {circumflex over (ω)}ic,T from the TFP when there is no jerk and to output the estimates {circumflex over (φ)}ic and {circumflex over (ω)}ic otherwise.