Abstract:
The present invention proposes 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 primary 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. 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.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is a US National Phase of PCT/RU2012/000750, filed on 12 Sep. 2012, incorporated herein by reference in its entirety. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    Phase, frequency and frequency rate 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). 
         [0003]    A method and apparatus are used for estimating changing frequency of a signal received by a satellite receiver, see U.S. Pat. No. 7,222,035. The system includes 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. 
         [0004]    A system according to K. Sithamparanathan,  Digital - PLL Assisted Frequency Estimation with Improved Error Variance , Create-Net Int. Res. Centre, Trento, IEEE Globecom, Nov. 30, 2008-Dec. 4, 2008, includes a PLL having NCO and a moving average filter (MAF) having N-samples length. The frequency estimates are produced by MAF using the frequency information contained in the phase error process of the digital PLL. The precision of frequency estimation by this method is proportional to 1/N. 
         [0005]    The apparatus and methods described in U.S. Pat. No. 7,869,554 use a PLL and provide a phase estimation of the input signal from which signal frequency is estimated by a derivative function and low pass filtering. 
         [0006]    A DPLL described in U.S. Pat. No. 4,771,250 generates signal phase which is an approximation of the phase of a 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. 
         [0007]    K. De Brabandere et al.,  Design and Operation of a Phase - Locked Loop with Kalman Estimator - Based Filter for Single - Phase Applications , IEEE 2006, http:**www.esat.kuleuven.be/electa/publications/fulltexts/pub — 1620.pdf describes the design procedure of a Phase-Locked Loop (PLL) preceded by a Kalman estimator-based filter. It provides a highly accurate and fast estimate of the 50 Hz electrical grid frequency and phase angle in grid-connected power electronic applications. A Kalman filter is placed before the PLL in order to ensure that the PLL input matches an ideal sinusoidal waveform as closely as possible at all times, even when the voltage is highly distorted by the presence of harmonics. This ensures fast and low-distortion operation of the PLL for single-phase applications. 
         [0008]    A method of measuring frequency for sinusoidal signals according to US Patent Publication No. 2011/0050998, published Aug. 31, 2009, entitled  Digital Phase Lock Loop Configurable As A Frequency Estimator , provides for obtaining a current signal phase as an argument of a complex number, the in-phase samples being a real part of the number, while the quadrature samples of quadrature signal decomposition components, converted into digital form and filtered, being an imaginary part of the number; receiving and storing a data block from sequential current differences in signal phases; generating a weight function in accordance with the given mathematical equations, which are used to estimate signal frequency. 
         [0009]    However, the above methods do not provide optimal frequency measurements when frequency is unstable. 
         [0010]    Unlike the methods above, the present invention enables obtaining optimal phase estimates of the input signal and its derivatives at the outputs of a first-type filter or a second-type filter with the help of DPLL variables which are further used to compute NCO full phase and primary phase estimates of the input signal. 
       SUMMARY OF THE INVENTION 
       [0011]    Accordingly, the present invention is related to a method and system for a system and method 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. 
         [0012]    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. 
         [0013]    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 
         [0014]    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. 
           [0015]    In the drawings: 
           [0016]      FIG. 1  is a block diagram for a first embodiment of the invention. 
           [0017]      FIG. 2  is a functional schematic for loop filter of a third order DPLL. 
           [0018]      FIG. 3  is a functional schematic for a block of NCO full phase estimation (OFPC) if NCO has only a frequency control; and if NCO has both frequency and phase control. 
           [0019]      FIG. 4  is a functional schematic for the block of signal phase primary estimation (SPPE). 
           [0020]      FIG. 5  is a functional schematic for the adaptive filter (AF) of a first embodiment of the invention. 
           [0021]      FIG. 6  is a block-diagram for a second embodiment of the invention. 
           [0022]      FIG. 7  is a functional schematic for the adaptive filter (AF) of the second embodiment of the invention. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0023]    Reference will now be made in detail to the preferred embodiments of the present invention, examples of which are illustrated in the accompanying drawings. 
         [0024]      FIG. 1  shows a block-diagram of the first embodiment of the invention. 
         [0025]    The measuring system is based on filtering primary estimates of signal phase which are obtained with a digital PLL system. The measuring system includes a computational block (OFPC) to calculate full phases of NCO, a block of signal phase primary estimation (SPPE), and an adaptive filter (AF) of the first embodiment of the invention filtering signal from the output of SPPE.  FIG. 1  presents a conventional digital PLL system consisting of the following main units: digital phase discriminator (PD), digital loop filter (LF), and digital numerically-controlled oscillator (NCO). 
         [0026]    An input analog process U a (t)=U c (t)+U n  (t) representing an additive mixture of quasi-harmonic signal U c (t) and Gaussian noise U n (t) is converted into a digital form at sampling frequency/rate f s  with the help of analog-to-digital convertor (ADC). Desired signal U c (t) is equal to 
         [0000]        U   c ( t )= A   c  cos [2πφ c ( t )].  (1)
 
         [0027]    where
       A, is the amplitude of the signal,   φ c (t)=∫f c (t)dt+φ 0  is the signal phase [cycles],   f c (t) is the signal frequency [Hz],   φ 0  is the initial phase [in cycles].       
 
         [0032]    Signal phase φ c (t), signal frequency f c (t) and frequency rate {dot over (f)} c (t) should be estimated (measured). Samples of the input process from the ADC output U d (n/f s ) are multiplied by quadrature digital samples from NCO 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               I 
                               n 
                               NCO 
                             
                             = 
                             
                               
                                 A 
                                 NCO 
                               
                                
                               
                                 cos 
                                  
                                 
                                   ( 
                                   
                                     2 
                                      
                                     
                                       πϕ 
                                       n 
                                       NCO 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               Q 
                               n 
                               NCO 
                             
                             = 
                             
                               
                                 A 
                                 NCO 
                               
                                
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     2 
                                      
                                     
                                       πϕ 
                                       n 
                                       NCO 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     } 
                   
                   , 
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0033]    where A NCO  is the sample amplitude, and φ n   NCO  is NCO phase in cycles. Multiplication results 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             I 
                             n 
                           
                           = 
                           
                             
                               
                                 
                                   U 
                                   d 
                                 
                                  
                                 
                                   ( 
                                   
                                     n 
                                     / 
                                     
                                       f 
                                       s 
                                     
                                   
                                   ) 
                                 
                               
                               · 
                               
                                 A 
                                 NCO 
                               
                             
                              
                             
                               cos 
                                
                               
                                 ( 
                                 
                                   2 
                                    
                                   
                                     πϕ 
                                     n 
                                     NCO 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             Q 
                             n 
                           
                           = 
                           
                             
                               
                                 
                                   U 
                                   d 
                                 
                                  
                                 
                                   ( 
                                   
                                     n 
                                     / 
                                     
                                       f 
                                       s 
                                     
                                   
                                   ) 
                                 
                               
                               · 
                               
                                 A 
                                 NCO 
                               
                             
                              
                             
                               cos 
                                
                               
                                 ( 
                                 
                                   2 
                                    
                                   
                                     πϕ 
                                     n 
                                     NCO 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   } 
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0034]    are fed to the input of lower frequency digital filters, which are typically reset accumulators Σ↓ with frequency F c &lt;&lt;f s  ( FIG. 1 ). The reset frequency of accumulators F c  is the control frequency in the PLL, for example, F c =50 Hz . . . 1000 Hz; f s =10 MHz . . . 100 MHz. At the output of the accumulators with frequency F c , the generated samples are 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       I 
                       i 
                       ∑ 
                     
                     = 
                     
                       
                         ∑ 
                         
                           m 
                           = 
                           1 
                         
                         
                           m 
                           = 
                           
                             N 
                             s 
                           
                         
                       
                        
                       
                           
                       
                        
                       
                         I 
                         
                           m 
                           + 
                           
                             
                               ( 
                               
                                 i 
                                 - 
                                 1 
                               
                               ) 
                             
                             · 
                             
                               N 
                               s 
                             
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   and 
                    
                   
                     
 
                   
                    
                   
                     
                       
                         Q 
                         i 
                         ∑ 
                       
                       = 
                       
                         
                           ∑ 
                           
                             m 
                             = 
                             1 
                           
                           
                             m 
                             = 
                             
                               N 
                               s 
                             
                           
                         
                          
                         
                             
                         
                          
                         
                           Q 
                           
                             m 
                             + 
                             
                               
                                 ( 
                                 
                                   i 
                                   - 
                                   1 
                                 
                                 ) 
                               
                               · 
                               
                                 N 
                                 s 
                               
                             
                           
                         
                       
                     
                     , 
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
         [0035]    which are fed to the inputs of the arctangent phase discriminator producing signal z i   d : 
         [0000]    
       
         
           
             
               
                 
                   
                      
                     i 
                     d 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                          
                         π 
                       
                     
                     · 
                     
                       
                         arctg 
                          
                         
                           ( 
                           
                             
                               Q 
                               i 
                               ∑ 
                             
                             / 
                             
                               I 
                               i 
                               ∑ 
                             
                           
                           ) 
                         
                       
                       
                         [ 
                         cycles 
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
         [0036]    Further, signal z i   d  from the PD output comes to the input of the proportionally-integrating loop filter (LF) which in the third order PLL includes three inertia-free members with constant transfer gains α LF , β LF , γ LF , two accumulators Σ β , Σ γ  and two adders ( FIG. 2 ). 
         [0037]    Recurrent equations of the loop filter are: 
         [0038]    a) with a frequency controlled NCO (switch S in position 1 in  FIG. 2 ) 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               ϕ 
                               i 
                               LF 
                             
                             = 
                             0 
                           
                         
                       
                       
                         
                           
                             
                               f 
                               i 
                               γ 
                             
                             = 
                             
                               
                                 f 
                                 
                                   i 
                                   - 
                                   1 
                                 
                                 γ 
                               
                               + 
                               
                                 
                                   γ 
                                   LF 
                                 
                                 · 
                                 
                                    
                                   i 
                                   d 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               f 
                               i 
                               β 
                             
                             = 
                             
                               
                                 f 
                                 
                                   i 
                                   - 
                                   1 
                                 
                                 β 
                               
                               + 
                               
                                 f 
                                 i 
                                 γ 
                               
                               + 
                               
                                 
                                   β 
                                   LF 
                                 
                                 · 
                                 
                                    
                                   i 
                                   d 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               f 
                               i 
                               LF 
                             
                             = 
                             
                               
                                 f 
                                 i 
                                 β 
                               
                               + 
                               
                                 
                                   α 
                                   LF 
                                 
                                 · 
                                 
                                    
                                   i 
                                   d 
                                 
                               
                             
                           
                         
                       
                     
                     } 
                   
                   ; 
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0039]    b) with frequency-phase controlled NCO (NCO with frequency and phase control) (switch S in position 2 in  FIG. 2 ) 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               ϕ 
                               i 
                               LF 
                             
                             = 
                             
                               
                                 α 
                                 LF 
                               
                               · 
                               
                                  
                                 i 
                                 d 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               f 
                               i 
                               γ 
                             
                             = 
                             
                               
                                 f 
                                 
                                   i 
                                   - 
                                   1 
                                 
                                 γ 
                               
                               + 
                               
                                 
                                   γ 
                                   LF 
                                 
                                 · 
                                 
                                    
                                   i 
                                   d 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               f 
                               i 
                               β 
                             
                             = 
                             
                               
                                 f 
                                 
                                   i 
                                   - 
                                   1 
                                 
                                 β 
                               
                               + 
                               
                                 f 
                                 i 
                                 γ 
                               
                               + 
                               
                                 
                                   β 
                                   LF 
                                 
                                 · 
                                 
                                    
                                   i 
                                   d 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               f 
                               i 
                               LF 
                             
                             = 
                             
                               f 
                               i 
                               β 
                             
                           
                         
                       
                     
                     } 
                   
                   . 
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0040]    Digital phase samples φ i   LF  are fed to the NCO phase control input and abruptly change its phase by the corresponding value Δφ i   NCO =φ i   LF ·Δ φ   NCO , where Δ φ   NCO  is the phase step size in the NCO. Samples f i   LF  (frequency codes) are delivered to the NCO frequency input and determine its frequency f i   NCO =f i   LF ·Δ f   NCO , where Δ f   NCO  is the frequency step size in the NCO. Since NCO frequency is constant over the entire interval T c , NCO phase changes linearly on intervals T c . 
         [0041]      FIG. 3  shows a functional block-diagram to calculate full phase of NCO. The operation of the block is described by the following recurrent equations: 
         [0042]    a) for the case of frequency-controlled NCO (switch S in position 1 in  FIG. 2 ) 
         [0000]      φ i   NCO =φ i-1   NCO   +f   i-1   LF ·Δ f   NCO   ·T   c  [cycles].  (8)
 
         [0043]    b) for the case of frequency-phase-controlled NCO (switch S in position 2 in  FIG. 2 ) 
         [0000]      φ i   NCO =φ i-1   NCO +φ i   LF ·Δ φ   NCO   +f   i-1   LF ·Δ f   NCO   ·T   c  [cycles].  (9)
 
         [0044]    A block of primary estimates of input signal phase operates in accordance with the following recurrent equation: 
         [0000]      φ i   z   =z   i   d +φ i-1   NCO +0.5 ·f   i-1   LF ·Δ f   NCO   ·T   c .  (10)
 
         [0045]    The primary estimates of input signal phase (equation 10) are formed as the sum of three factors: z i   d  which is the output of the phase discriminator at a discrete time moment i (see equation (5)); φ i-1   NCO  which is the full phase of the filter, calculated at the previous discrete time moment i−1; and ½ of the product of three elements—the frequency output f i-1   LF  of the loop filter at the previous moment i−1, a discrete frequency step size Δ f   NCO  of the NCO [Hz] and the time period T c  of the PLL. 
         [0046]    Samples φ i   z  are fed to the input of the adaptive filter with variable transfer gains generated by an adaptation block ( FIG. 5 ). 
         [0047]    A third-order adaptive filter functions according to the recurrent equations: 
         [0048]    a variable at the output of the subtracting unit (SU in  FIG. 5 ) is equal to 
         [0000]        z   i   AF =φ i   z −( a   i-1   +b   i-1 +0.5 ·g   i-1 );  (11)
 
         [0049]    where auxiliary variables a i , b i  and g i  are 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               a 
                               i 
                             
                             = 
                             
                               
                                 a 
                                 
                                   i 
                                   - 
                                   1 
                                 
                               
                               + 
                               
                                 b 
                                 
                                   i 
                                   - 
                                   1 
                                 
                               
                               + 
                               
                                 0.5 
                                 · 
                                 
                                   g 
                                   
                                     i 
                                     - 
                                     1 
                                   
                                 
                               
                               + 
                               
                                 
                                   α 
                                   i 
                                 
                                 · 
                                 
                                    
                                   i 
                                   AF 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               b 
                               i 
                             
                             = 
                             
                               
                                 b 
                                 
                                   i 
                                   - 
                                   1 
                                 
                               
                               + 
                               
                                 g 
                                 
                                   i 
                                   - 
                                   1 
                                 
                               
                               + 
                               
                                 
                                   β 
                                   i 
                                 
                                 · 
                                 
                                    
                                   i 
                                   AF 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               g 
                               i 
                             
                             = 
                             
                               
                                 g 
                                 
                                   i 
                                   - 
                                   1 
                                 
                               
                               + 
                               
                                 
                                   γ 
                                   i 
                                 
                                 · 
                                 
                                    
                                   i 
                                   AF 
                                 
                               
                             
                           
                         
                       
                     
                     } 
                   
                   ; 
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
         [0050]    where α i , β i  and γ i  are the transfer coefficients defined by the adaptation block (AB); hence the estimated parameters are 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 ϕ 
                                 ^ 
                               
                               i 
                               c 
                             
                             = 
                             
                               
                                 a 
                                 i 
                               
                               + 
                               
                                 
                                   b 
                                   i 
                                 
                                 / 
                                 2 
                               
                               + 
                               
                                 
                                   g 
                                   i 
                                 
                                 / 
                                 12 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 f 
                                 ^ 
                               
                               i 
                               c 
                             
                             = 
                             
                               
                                 ( 
                                 
                                   
                                     b 
                                     i 
                                   
                                   + 
                                   
                                     
                                       g 
                                       i 
                                     
                                     / 
                                     2 
                                   
                                 
                                 ) 
                               
                               / 
                               
                                 T 
                                 c 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 
                                   f 
                                   . 
                                 
                                 ^ 
                               
                               i 
                               c 
                             
                             = 
                             
                               
                                 g 
                                 i 
                               
                               / 
                               
                                 T 
                                 C 
                                 2 
                               
                             
                           
                         
                       
                     
                     } 
                   
                   , 
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where
       {circumflex over (φ)} i   c  is the estimate of phase of the input signal,   {circumflex over (f)} i   c  the estimate of frequency of the input signal,   {dot over ({circumflex over (f)} i   c  is the estimate of changing rate of frequency of the input signal.       
 
         [0054]    At γ i =0 the order of the filter will be second, and if β i =0 as well, AF will be a first-order filter. 
         [0055]    At the beginning of operation the order of the adaptive filter is set considering a priori information about a movement pattern. 
         [0056]    By analyzing z i   AF  in the adaptive filter at the output of the subtracting unit and estimated parameters the adaptation block controls bandwidth and the order of the adaptive filter by changing transfer coefficients. 
         [0057]    The adaptation block changes the bandwidth of the adaptive filter by varying auxiliary variable k i  (k min ≦k i ≦k max ) that is used for calculation of AF transfer coefficients based on the following equations: 
         [0058]    in a first-order adaptive filter k min =1 
         [0000]      α i =1/( k   i +1),  (14)
 
         [0059]    in a second-order adaptive filter k min =2 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               α 
                               i 
                             
                             = 
                             
                               
                                 6 
                                 
                                   ( 
                                   
                                     
                                       k 
                                       i 
                                     
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                               - 
                               
                                 2 
                                 
                                   k 
                                   i 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               β 
                               i 
                             
                             = 
                             
                               6 
                               
                                 
                                   k 
                                   i 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       k 
                                       i 
                                     
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     } 
                   
                   , 
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
         [0060]    in a third-order adaptive filter k min =3 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 α 
                                 i 
                               
                               = 
                               
                                 
                                   ( 
                                   
                                     
                                       9 
                                       · 
                                       
                                         k 
                                         i 
                                         2 
                                       
                                     
                                     - 
                                     
                                       9 
                                       · 
                                       
                                         k 
                                         i 
                                       
                                     
                                     + 
                                     6 
                                   
                                   ) 
                                 
                                 / 
                                 D 
                               
                             
                           
                         
                         
                           
                             
                               
                                 β 
                                 i 
                               
                               = 
                               
                                 
                                   ( 
                                   
                                     
                                       36 
                                       · 
                                       
                                         k 
                                         i 
                                       
                                     
                                     - 
                                     18 
                                   
                                   ) 
                                 
                                 / 
                                 D 
                               
                             
                           
                         
                         
                           
                             
                               
                                 γ 
                                 i 
                               
                               = 
                               
                                 60 
                                 / 
                                 D 
                               
                             
                           
                         
                       
                       } 
                     
                     ; 
                   
                    
                   
                     
 
                   
                    
                   where 
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
             
               
                 
                   D 
                   = 
                   
                     
                       k 
                       i 
                       3 
                     
                     + 
                     
                       3 
                       · 
                       
                         k 
                         i 
                         2 
                       
                     
                     + 
                     
                       2 
                       · 
                       
                         
                           k 
                           i 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
         [0000]    From equations (14)-(17) it follows that as variable k i  increases, AF transfer coefficients decreases, and hence the bandwidth reduces as well. And otherwise, as variable k i  decreases, AF bandwidth increases. In order to minimize the transition process the adaptation block starts to operate at value k 1 =k s , at which the adaptive filter bandwidth is approximately equal to the PLL bandwidth. 
         [0061]    If |z i   AF | at the output of the subtracting unit does not exceed the preset threshold z thr   AF &gt;0, the adaptation block reduces AF bandwidth by increasing variable k i  by Δ k , and thereby reducing fluctuation errors of estimates for the signal parameters, i.e.: 
         [0000]      if | z   i   AF   |≦z   thr   AF , then  k   i   =k   i-1 +Δ k , where Δ k &gt;0;  (18)
 
         [0000]      if the obtained value  k   i   &gt;k   max , then  k   i   =k   max ;  (19)
 
         [0062]    The threshold z thr   AF  is selected based on compromise considerations: too high a threshold means the adaptation process will be long, and will have errors in the estimate during rapid changes in the input, while too low a value will lead to a worse estimate during operation that is close to steady state. 
         [0063]    If value |z i   AF | at the output of the subtracting unit exceeds the preset threshold z thr   AF , and the order of the adaptive filter N AF  is less than maximum preset value N AF   MAX , the adaptation block increases by 1 the order of the adaptive filter to reduce dynamic errors. The order of the adaptive filter is usually chosen as N AF ≦4. If value |z i   AF | at the output of the subtracting unit exceeds the preset threshold z thr   AF , and the order of the adaptive filter N AF  is equal to the maximum preset value N AF   MAX , the adaptation block increases AF bandwidth to reduce dynamic errors, i.e. 
         [0000]      if | z   i   AF   |&gt;z   thr   AF , then  k   i   =k   i-1   /r,  where  r&gt; 1;  (20)
 
         [0000]      if the obtained value  k   i   &lt;k   min , then  k   i   =k   min .  (21)
 
         [0064]    The higher the r, the higher the bandwidth of the adaptive filter during sharp changes in input. However, too high a value of r will lead to reduced accuracy. Typical values are 1&lt;r&lt;4). 
         [0065]    Further, obtained value k i  is used to calculate AF transfer coefficients according to the equations (14)-(17) corresponding to the filter order. 
         [0000]      FIG. 6  shows a block-diagram of the second embodiment of the invention. It differs from the first embodiment by absence of the block of primary estimates for signal phase, and by using a second-type adaptive filter instead of a first-type adaptive filter ( FIG. 6 ). Full NCO phase is fed to the input of the adaptive filter AF-2 ( FIG. 7 ) of the second embodiment of the invention, and a variable at the output of the subtracting unit is equal to 
         [0000]        z   i   AF =φ i   NCO −( a   i-1   +b   i-1 +0.5 ·g   i-1 ).  (22)
 
         [0066]    Auxiliary variables a i , b i  and g i  in the adaptive filter AF of the second embodiment of the invention are calculated based on the same recurrent equations (12), the same as in AF of the first embodiment of the invention. Signal phase estimate {circumflex over (φ)} i   c , signal frequency estimate {circumflex over (f)} i   c  and the estimate of frequency rate {dot over ({circumflex over (f)} i   c  for the second embodiment of the measuring system are presented by equations: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               
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                               c 
                             
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                                 f 
                                 ^ 
                               
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                               c 
                             
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                                 c 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 
                                   f 
                                   . 
                                 
                                 ^ 
                               
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                               c 
                             
                             = 
                             
                               
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                                 2 
                               
                             
                           
                         
                       
                     
                     } 
                   
                   , 
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
           
         
       
     
         [0067]    Comparison of (13) and (28) shows that signal phase estimates {circumflex over (φ)} i   c , signal frequency estimates {circumflex over (f)} i   c  for the second embodiment of the measuring system with a third-order AF should be computed in accordance with different equations. The closed loops of the filters of the first and second embodiments of the invention work in a similar manner, the difference is in equations (13) and (23), where the loop variables a i , b i  and g i  are used to form signal parameters {circumflex over (φ)} i   c , {circumflex over (f)} i   c  and {dot over ({circumflex over (f)} i   c . 
         [0068]    Having thus described a preferred embodiment, it should be apparent to those skilled in the art that certain advantages of the described method and apparatus have been achieved. 
         [0069]    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.