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.

Claims

1. 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 z.sub.i.sup.d between the input signal and reference signals from a Numerically Controlled Oscillator (NCO); and ii) a loop filter with a control period T.sub.c that generates a phase control signal .sub.i.sup.r for the NCO and a frequency control signal f.sub.i.sup.r for the NCO; and b) a block for calculation of full phase .sub.i.sup.NCO according to
.sub.i.sup.NCO=.sub.i1.sup.NCO+.sub.i.sup.r.Math..sub..sup.NCO+f.sub.i1.sup.r.Math..sub..sup.NCO.Math.T.sub.c, where .sub..sup.NCO is a phase step size in the NCO, and .sub..sup.NCO is a frequency step size in the NCO; c) a low-pass filter inputting the phase difference ,z.sub.i.sup.d and outputting z.sub.i.sup.A; d) a block that uses the full phase .sub.i.sup.NCO for generation of: a preliminary estimate {circumflex over ()}.sub.i.sup.c,E for a phase of the input signal, and a preliminary estimate {circumflex over ()}.sub.i.sup.c,E for a frequency of the input signal; e) a threshold unit outputting a true/false value J.sub.i based on the output z.sub.i.sup.A; and f) a block for jerk-corrections of the preliminary estimates that generates an estimate {circumflex over ()}.sub.i.sup.c for a phase of the input signal, and an estimate {circumflex over ()}.sub.i.sup.c for the frequency of the input signal, based on J.sub.i, z.sub.i.sup.A, {circumflex over ()}.sub.i.sup.c,E and {circumflex over ()}.sub.i.sup.c,E.

2. The system of claim 1, wherein the loop filter operates based on: $\begin{array}{c}{s}_i^{}=s_{i-1}^{}+.Math.z_i^d,\\ s_i^{}=s_{i-1}^{}+s_i^{}+.Math.z_i^d,\\ {}_i^r=\mathrm{round}\left(.Math.z_i^d/{}_{}^{\mathrm{NCO}}\right),\\ f_i^r=\mathrm{round}\left(s_i^{}/{}_{}^{\mathrm{NCO}}/T_c\right),\end{array}\},$ where , , are constants, s.sub.i.sup. corresponds to the frequency of the input signal, s.sub.i.sup. corresponds to a rate of change of the frequency of the input signal, and round (.Math.) is numerical rounding.

3. The system of claim 2, wherein the block in (d) that generates the preliminary estimate {circumflex over ()}.sub.i.sup.c,E and the preliminary estimate {circumflex over ()}.sub.i.sup.c,E also uses s.sub.i.sup..

4. The system of claim 3, wherein the block in (d) that uses .sub.i.sup.NCO and s.sub.i.sup. also generates a preliminary estimate {dot over ({circumflex over ()})}.sub.i.sup.c,E of a derivative of the frequency of the input signal.

5. The system of claim 4, wherein the block for jerk-corrections also generates an estimate {dot over ({circumflex over ()})}.sub.i.sup.c for the derivative of the frequency of the input signal based on J.sub.i, z.sub.i.sup.A, {circumflex over ()}.sub.i.sup.c,E, {circumflex over ()}.sub.i.sup.c,E and {dot over ({circumflex over ()})}.sub.i.sup.c,E.

6. The system of claim 5, wherein the preliminary estimates {circumflex over ()}.sub.i.sup.c,E, {circumflex over ()}.sub.i.sup.c,E, and {dot over ({circumflex over ()})}.sub.i.sup.c,E are generated according to
{circumflex over ()}.sub.i.sup.c,E=.sub.i.sup.NCO+s.sub.i.sup./K.sub.,
{circumflex over ()}.sub.i.sup.c,E=.sub..sup.NCO.Math.f.sub.i.sup.rs.sub.i.sup./(K.sub..Math.T.sub.c),
{dot over ({circumflex over ()})}.sub.i.sup.c,E=s.sub.i.sup./T.sub.c.sup.2; where K.sub. and K.sub. are constants.

7. The system of claim 6, wherein the block for jerk-corrections generates the estimates {circumflex over ()}.sub.i.sup.c, {circumflex over ()}.sub.i.sup.c and {dot over ({circumflex over ()})}.sub.i.sup.c according to: $\begin{array}{c}{\hat{}}_i^c={\hat{}}_i^{c,E}+z_i^A.Math.\left(K_0-/K_1+/K_2+/K_3\right)\\ {\hat{}}_i^c={\hat{}}_i^{c,E}+z_i^A.Math.\left(-/K_4-/K_5\right)/T_c\\ {\widehat{\stackrel{.}{}}}_i^c={\widehat{\stackrel{.}{}}}_i^{c,E}+z_i^A.Math./T_c^2\end{array}\}\mathrm{if}{J}_i=\mathrm{true},\begin{array}{c}{\hat{}}_i^c={\hat{}}_i^{c,E},\\ {\hat{}}_i^c={\hat{}}_i^{c,E}\\ {\widehat{\stackrel{.}{}}}_i^c={\widehat{\stackrel{.}{}}}_i^{c,E}\end{array}\}\mathrm{if}{J}_i=\mathrm{false},$ where K.sub.0, K.sub.1, K.sub.2, K.sub.3, K.sub.4, and K.sub.5 are constants.

8. The system of claim 7, further comprising a third order tracking filter (TFP) that operates based on: $\begin{array}{c}{\stackrel{\_}{}}_i^{c,T}={\hat{}}_{i-1}^{c,T}+{\hat{}}_{i-1}^{c,T}.Math.T_c+{\widehat{\stackrel{.}{}}}_{i-1}^{c,T}.Math.T_c^2/2\\ {\stackrel{\_}{}}_i^{c,T}={\hat{}}_{i-1}^{c,T}+{\widehat{\stackrel{.}{}}}_{i-1}^{c,T}.Math.T_c\\ {\stackrel{\_}{\stackrel{.}{}}}_i^{c,T}={\widehat{\stackrel{.}{}}}_{i-1}^{c,T}\end{array}\}{z}_i^T={}_i^{\mathrm{NCO}}-{\stackrel{\_}{}}_i^{c,T},\begin{array}{c}{\hat{}}_i^{c,T}={\stackrel{\_}{}}_i^{c,T}+{}^T.Math.z_i^T\\ {\hat{}}_i^{c,T}={\stackrel{\_}{}}_i^{c,T}+{}^T.Math.z_i^T/T_c\\ {\widehat{\stackrel{.}{}}}_i^{c,T}={\stackrel{\_}{\stackrel{.}{}}}_i^{c,T}+{}^T.Math.z_i^T/T_c^2\end{array}\},$ where .sup.T, .sup.T and .sup.T are constants, where .sub.i.sup.c,T, .sub.i.sup.c,T and {dot over ()}.sub.i.sup.c,T represent predictions of input signal phase, input signal frequency and input signal frequency derivative, respectively, from the TFP, and where z.sub.i.sup.T, is an instantaneous phase difference between NCO phase and input signal phase prediction, wherein the system outputs the estimates for input signal phase, input signal frequency and input signal frequency derivative {circumflex over ()}.sub.i.sup.c,T, {circumflex over ()}.sub.i.sup.c,T and {dot over ({circumflex over ()})}.sub.i.sup.c,T, respectively, from the TFP when there is no jerk and otherwise outputs the estimates for input signal phase, input signal frequency and input signal frequency derivative {circumflex over ()}.sub.i.sup.c,J, {circumflex over ()}.sub.i.sup.c,J and {dot over ({circumflex over ()})}.sub.i.sup.c,J, respectively, from the block for jerk-corrections, and where {circumflex over ()}.sub.i.sup.c,J, {circumflex over ()}.sub.i.sup.c,J and {dot over ({circumflex over ()})}.sub.i.sup.c,J are defined as $\begin{array}{c}{\hat{}}_i^{c,J}={\hat{}}_i^{c,E}+z_i^A.Math.C_{},\\ {\hat{}}_i^{c,J}={\hat{}}_i^{c,E}+z_i^A.Math.C_{}\\ {\widehat{\stackrel{.}{}}}_i^{c,J}={\widehat{\stackrel{.}{}}}_i^{c,E}+z_i^A.Math.C_{\stackrel{.}{}}\end{array}\}$ and C.sub., C.sub., C.sub.{dot over ()}are constants.

9. The system of claim 1, wherein the low-pass filter is based on equation
z.sub.i.sup.A=z.sub.i-1.sup.A+.sup.LPF.Math.(z.sub.i.sup.dz.sub.i-1.sup.A), where .sup.LPF is a constant transfer coefficient, 0<.sup.LPF<1.

10. A Global Navigation Satellite System (GNSS) receiver, comprising: a) an antenna for receiving signals from multiple GNSS satellites; b) a low noise amplifier for amplifying the received signals; c) an analog to digital converter converting the amplified signals into digital signals; d) a digital phase locked loop that includes: i) a phase discriminator that determines a phase difference z.sub.i .sup.d between the digital signals and reference signals from a Numerically Controlled Oscillator (NCO); and ii) a loop filter with a control period T.sub.c that generates a phase control signal .sub.i.sup.r for the NCO and a frequency control signal f.sub.i.sup.r for the NCO; and e) a block for calculation of full phase .sub.i.sup.NCO according to
.sub.i.sup.NCO=.sub.i1.sup.NCO+.sub.i.sup.r.Math..sub..sup.NCO+f.sub.i1.sup.r.Math..sub..sup.NCO.Math.T.sub.c, where .sub..sup.NCO is a phase step size, and .sub..sup.NCO is a frequency step size; f) a low-pass filter inputting the phase difference z.sub.i.sup.d and outputting z.sub.i.sup.A; g) a block that uses .sub.i.sup.NCO for generation of: a preliminary estimate {circumflex over ()}.sub.i.sup.c,E for a phase of the digital signals, and a preliminary estimate {circumflex over ()}.sub.i.sup.c,E for a frequency of the digital signals; h) a threshold unit outputting a true/false value J.sub.i based on z.sub.i.sup.A; and i) a block for jerk-corrections of the preliminary estimates that generates an estimate {circumflex over ()}.sub.i.sup.c for a phase of the digital signals, and an estimate {circumflex over ()}.sub.i.sup.c for the frequency of the digital signals, based on J.sub.i, z.sub.i.sup.A, {circumflex over ()}.sub.i.sup.c,E and {circumflex over ()}.sub.i.sup.c,E, j) wherein the receiver generates velocity and acceleration estimates based on {circumflex over ()}.sub.i.sup.c.

11. The receiver of claim 10, wherein the loop filter operates based on: $\begin{array}{c}{s}_i^{}=s_{i-1}^{}+.Math.z_i^d,\\ s_i^{}=s_{i-1}^{}+s_i^{}+.Math.z_i^d,\\ {}_i^r=\mathrm{round}\left(.Math.z_i^d/{}_{}^{\mathrm{NCO}}\right),\\ f_i^r=\mathrm{round}\left(s_i^{}/{}_{}^{\mathrm{NCO}}/T_c\right),\end{array}\},$ where , , are constants, s.sub.i.sup. corresponds to the frequency of the digital signals, s.sub.i.sup. corresponds to a rate of change of the frequency of the digital signals, and round (.) is numerical rounding.

12. The receiver of claim 11, wherein the block in (g) that generates {circumflex over ()}.sub.i.sup.c,E and {circumflex over ()}.sub.i.sup.c,E also uses s.sub.i.sup..

13. The receiver of claim 12, wherein the block in (d) that uses .sub.i.sup.NCO and s.sub.i.sup. also generates a preliminary estimate {dot over ({circumflex over ()})}.sub.i.sup.c,E of a derivative of the frequency of the digital signals.

14. The receiver of claim 13, wherein the block for jerk-corrections also generates an estimate {dot over ({circumflex over ()})}.sub.i.sup.c for a derivative of the frequency of the digital signals based on J.sub.i, z.sub.i.sup.A, {circumflex over ()}.sub.i.sup.c,E, {circumflex over ()}.sub.i.sup.c,E and {dot over ({circumflex over ()})}.sub.i.sup.c,E.

15. The receiver of claim 14, wherein the preliminary estimates {circumflex over ()}.sub.i.sup.c,E, {circumflex over ()}.sub.i.sup.c,E, and {dot over ({circumflex over ()})}.sub.i.sup.c,E are generated according to
{circumflex over ()}.sub.i.sup.c,E=.sub.i.sup.NCO+s.sub.i.sup./K.sub.,
{circumflex over ()}.sub.i.sup.c,E=.sub..sup.NCO.Math.f.sub.i.sup.rs.sub.i.sup./(K.sub..Math.T.sub.c),
{dot over ({circumflex over ()})}.sub.i.sup.c,E=s.sub.i.sup./T.sub.c.sup.2; where K.sub. and K.sub. are constants.

16. The receiver of claim 15, wherein the block for jerk-corrections generates the estimates {circumflex over ()}.sub.i.sup.c, {circumflex over ()}.sub.i.sup.c and {dot over ({circumflex over ()})}.sub.i.sup.c according to: $\begin{array}{c}{\hat{}}_i^c={\hat{}}_i^{c,E}+z_i^A.Math.\left(K_0-/K_1+/K_2+/K_3\right)\\ {\hat{}}_i^c={\hat{}}_i^{c,E}+z_i^A.Math.\left(-/K_4-/K_5\right)/T_c\\ {\widehat{\stackrel{.}{}}}_i^c={\widehat{\stackrel{.}{}}}_i^{c,E}+z_i^A.Math./T_c^2\end{array}\}\mathrm{if}{J}_i=\mathrm{true},\begin{array}{c}{\hat{}}_i^c={\hat{}}_i^{c,E},\\ {\hat{}}_i^c={\hat{}}_i^{c,E}\\ {\widehat{\stackrel{.}{}}}_i^c={\widehat{\stackrel{.}{}}}_i^{c,E}\end{array}\}\mathrm{if}{J}_i=\mathrm{false},$ where K.sub.0, K.sub.1, K.sub.2, K.sub.3, K.sub.4, and K.sub.5 are constants.

17. The receiver of claim 16, further comprising a third order tracking filter (TFP) that operates based on: $\begin{array}{c}{\stackrel{\_}{}}_i^{c,T}={\hat{}}_{i-1}^{c,T}+{\hat{}}_{i-1}^{c,T}.Math.T_c+{\widehat{\stackrel{.}{}}}_{i-1}^{c,T}.Math.T_c^2/2\\ {\stackrel{\_}{}}_i^{c,T}={\hat{}}_{i-1}^{c,T}+{\widehat{\stackrel{.}{}}}_{i-1}^{c,T}.Math.T_c\\ {\stackrel{\_}{\stackrel{.}{}}}_i^{c,T}={\widehat{\stackrel{.}{}}}_{i-1}^{c,T}\end{array}\}{z}_i^T={}_i^{\mathrm{NCO}}-{\stackrel{\_}{}}_i^{c,T},\begin{array}{c}{\hat{}}_i^{c,T}={\stackrel{\_}{}}_i^{c,T}+{}^T.Math.z_i^T\\ {\hat{}}_i^{c,T}={\stackrel{\_}{}}_i^{c,T}+{}^T.Math.z_i^T/T_c\\ {\widehat{\stackrel{.}{}}}_i^{c,T}={\stackrel{\_}{\stackrel{.}{}}}_i^{c,T}+{}^T.Math.z_i^T/T_c^2\end{array}\},$ where .sup.T, .sup.T and .sup.T are constants; where .sub.i.sup.c,T, .sub.i.sup.c,T and {dot over ()}.sub.i.sup.c,T represent predictions of input signal phase, input signal frequency and input signal frequency derivative, respectively, from the TFP, and where z.sub.1.sup.T, is an instantaneous phase difference between NCO phase and input signal phase prediction, wherein the system outputs the estimates for input signal phase, input signal frequency and input signal frequency derivative {circumflex over ()}.sub.i.sup.c,T, {circumflex over ()}.sub.i.sup.c,T and {dot over ({circumflex over ()})}.sub.i.sup.c,T, respectively , from the TFP when there is no jerk and otherwise outputs the estimates for input signal phase, input signal frequency and input signal frequency derivative {circumflex over ()}.sub.i.sup.c,J, {circumflex over ()}.sub.i.sup.c,J and {dot over ({circumflex over ()})}.sub.i.sup.c,J, respectively, from the block for jerk-corrections, and where {circumflex over ()}.sub.i.sup.c,J, {circumflex over ()}.sub.i.sup.c,J and {dot over ({circumflex over ()})}.sub.i.sup.c,J are defined as $\begin{array}{c}{\hat{}}_i^{c,J}={\hat{}}_i^{c,E}+z_i^A.Math.C_{},\\ {\hat{}}_i^{c,J}={\hat{}}_i^{c,E}+z_i^A.Math.C_{}\\ {\widehat{\stackrel{.}{}}}_i^{c,J}={\widehat{\stackrel{.}{}}}_i^{c,E}+z_i^A.Math.C_{\stackrel{.}{}}\end{array}\}$ and C.sub., C.sub., C.sub.{dot over ()} are constants.

18. The receiver of claim 10, wherein the low-pass filter is based on equation
z.sub.i.sup.A=z.sub.i1.sup.A+.sup.LPF.Math.(z.sub.i.sup.dz.sub.i1.sup.A), where .sup.LPF is a constant transfer coefficient, 0<.sup.LPF<1.

19. A system for estimating parameters of an input signal, the system comprising: a) a phase discriminator that determines a phase difference between the input signal and reference signals from a Numerically Controlled Oscillator (NCO); b) a loop filter with a period T.sub.c that generates a phase control signal .sub.i.sup.r for the NCO and a frequency control signal f.sub.i.sup.r for the NCO; c) a block for calculation of full phase .sub.i.sup.NCO according to
.sub.i.sup.NCO=.sub.i1.sup.NCO+.sub.i.sup.r.Math..sub..sup.NCO+f.sub.i1.sup.r.Math..sub..sup.NCO.Math.T.sub.c, where .sub..sup.NCO is a phase step size in the NCO, and .sub..sup.NCO is a frequency step size in the NCO; d) a low-pass filter inputting the phase difference and outputting z.sub.i.sup.A; e) a block that uses the full phase .sub.i.sup.NCO for generation of: a preliminary estimate {circumflex over ()}.sub.i.sup.c,E for a phase of the input signal, and a preliminary estimate {circumflex over ()}.sub.i.sup.c,E for a frequency of the input signal; f) a threshold unit outputting a signal J.sub.i based on the output z.sub.i.sup.A; and g) a block for jerk-corrections that generates an estimate {circumflex over ()}.sub.i.sup.c for a phase of the input signal, and an estimate {circumflex over ()}.sub.i.sup.c for the frequency of the input signal, based on J.sub.i, z.sub.i.sup.A, {circumflex over ()}.sub.i.sup.c,E and {circumflex over ()}.sub.i.sup.c,E.

Description

BRIEF DESCRIPTION OF THE ATTACHED FIGURES

(1) 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.

(2) In the drawings:

(3) FIG. 1 is a block diagram for a first embodiment of the invention.

(4) FIG. 2 is an example of an arctangent-type phase discriminator (PD).

(5) FIG. 3 is a block diagram for a second embodiment of the invention.

(6) FIG. 4 illustrates a jerk as a function of time.

(7) FIG. 5 shows an exemplary implementation of the full phase calculation block.

(8) FIG. 6 shows an exemplary implementation of the low pass filter.

(9) FIG. 7 shows an exemplary implementation of the PESP block.

(10) FIG. 8 shows an exemplary implementation of the block for jerk-corrections of preliminary estimates (JCPE).

(11) FIG. 9 shows an exemplary implementation of the block for tracking of filter phase.

(12) FIG. 10 shows an exemplary implementation of the GPS receiver where the components described herein can be used.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

(13) Reference will now be made in detail to the preferred embodiments of the present invention, examples of which are illustrated in the accompanying drawings.

(14) In embodiments of the present invention, adaptation to the nature of the movement of the receiver (see exemplary receiver in FIG. 10) is made not by changing the parameters of PLL, 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.

(15) 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 U.sub.n.sup.mix of an analog process U.sup.mix(t) at a sampling frequency f.sub.s are fed to the discriminator input. An analog process U.sup.mix(t)=U.sup.c(t)+U.sup.n(t) representing an additive mixture of quasi-harmonic signal U.sup.c(t) and Gaussian noise U.sup.n(t). Desired signal U.sup.c(t) is equal to U.sup.c(t)=A.sup.c.Math.cos [.sup.c(t)],

(16) where A.sup.c is the amplitude of the signal, .sup.c(t)=.sup.c(t).Math.dt+.sub.0 is the signal phase [in radians], .sup.c(t) is the signal frequency [in radian/s], .sub.0 is the initial signal phase [in radian].

(17) Signal phase .sup.c(t), signal frequency .sup.c(t) and frequency derivative {dot over ()}.sup.c(t) should be estimated (measured).

(18) A loop filter (LF) operates with a control period T.sub.c on the basis of recurrence equations:

(19) $\begin{array}{c}{}_i^{\mathrm{LF}}={}^{\mathrm{LF}}.Math.z_i^d,\\ s_i^{}=s_{i-1}^{}+{}^{\mathrm{LF}}.Math.z_i^d,\\ s_i^{}=s_{i-1}^{}+s_i^{}+{}^{\mathrm{LF}}.Math.z_i^d,\\ {}_i^r=\mathrm{round}\left({}^{\mathrm{LF}}/{}_{}^{\mathrm{NCO}}\right),\\ f_i^r=\mathrm{round}\left(s_i^{}/{}_{}^{\mathrm{NCO}}/T_c\right),\end{array}\},$
where .sup.LF, .sup.LF, .sup.LF are constant transfer coefficients, z.sub.i.sup.d is the PD output; .sub.i.sup.r is the phase code for NCO, f.sub.i.sup.r is the frequency code for NCO, .sub..sup.NCO is the phase step size (radian) in the NCO, .sub..sup.NCO is the frequency step size (radian/s) in the NCO, round ( ) is the operation of a numerical rounding.

(20) A numerically controlled oscillator (NCO) (104) has frequency and phase control. The phase input of the NCO is connected to the phase output .sub.i.sup.r of the loop filter (LF) and the frequency input of the NCO is connected to the frequency output f.sub.i.sup.r of the LF (103); wherein a complex output of a NCO connected to a reference input of a PD (102).

(21) FIG. 2 shows an example of PD. Input samples U.sub.n.sup.mix are multiplied by quadrature samples (I.sub.n.sup.ref, Q.sub.n.sup.ref) from the NCO,

(22) $\begin{array}{c}{I}_n^{\mathrm{ref}}=A^{\mathrm{NCO}}.Math.\cos \left({}_n^{w,\mathrm{NCO}}\right)\\ Q_n^{\mathrm{ref}}=A^{\mathrm{NCO}}.Math.\sin \left({}_n^{w,\mathrm{NCO}}\right)\end{array}\},$
where A.sup.NCO is the sample amplitude, and .sub.n.sup.w,NCO is the wrapped phase (i.e., 0.sub.n.sup.w,NCO<+2) of NCO in radians. Multiplication results

(23) $\begin{array}{c}{I}_n^{\mathrm{mr}}=U_n^{\mathrm{mix}}.Math.I_n^{\mathrm{ref}}\\ Q_n^{\mathrm{mr}}=U_n^{\mathrm{mix}}.Math.Q_n^{\mathrm{ref}}\end{array}\}$
are fed to the input of low-pass filters, which are typically the reset accumulators with frequency F.sub.c<<f.sub.s. The reset frequency of the accumulators F.sub.c is the control frequency in the PLL, for example, F.sub.c=50 Hz . . . 1000 Hz; f.sub.s=10 MHz . . . 100 MHz. The outputs of the reset accumulators are

(24) $I_i=\underset{m=1}{\overset{m=N_s}{.Math.}}{I}_{m+\left(i-1\right).Math.N_s}^{\mathrm{mr}}\mathrm{and}{Q}_i=\underset{m=1}{\overset{m=N_s}{.Math.}}{Q}_{m+\left(i-1\right).Math.N_s.}^{\mathrm{mr}}$
The output of a phase discriminator is
z.sub.i.sup.d=arctan(Q.sub.i/I.sub.i) [in radians].

(25) Further, the signal z.sub.i.sup.d from the PD output is inputted to the loop filter (LF) (FIG. 2), which operates with a control period T.sub.c=N.sub.s/f.sub.s on the basis of recurrence equation:

(26) $\begin{array}{c}{}_i^{\mathrm{LF}}={}^{\mathrm{LF}}.Math.z_i^d,\\ s_i^{}=s_{i-1}^{}+{}^{\mathrm{LF}}.Math.z_i^d,\\ s_i^{}=s_{i-1}^{}+s_i^{}+{}^{\mathrm{LF}}.Math.z_i^d,\\ {}_i^r=\mathrm{round}\left({}^{\mathrm{LF}}/{}_{}^{\mathrm{NCO}}\right),\\ f_i^r=\mathrm{round}\left(s_i^{}/{}_{}^{\mathrm{NCO}}/T_c\right),\end{array}\},$
where .sup.LF, .sup.LF, .sup.LF are constant transfer coefficients, z.sub.i.sup.d is the PD output; .sub.i.sup.r is the phase code for the NCO, f.sub.i.sup.r is the frequency code for the NCO, .sub..sup.NCO is the phase step size (radian) in the NCO, .sub..sup.NCO is the frequency step size (radian/s) in the NCO, and round (.) is the operation of a numerical rounding.

(27) Digital phase samples .sub.i.sup.r are fed to the NCO phase control input and abruptly change its phase by the corresponding value .sub.i.sup.NCO=.sub.i.sup.r.Math..sub..sup.NCO, where .sub..sup.NCO is the phase step size. Samples f.sub.i.sup.r (frequency codes) are delivered to the NCO frequency input and determine its frequency .sub.i.sup.ref=f.sub.i.sup.r.Math..sub..sup.NCO, where .sub..sup.NCO is the frequency step size [radian/s] in the NCO.

(28) The measuring system (see FIG. 1) comprises also:

(29) block (105) for calculation of full phase (CFP) of NCO, coupled with the LF outputs, operates on the basis of equation
.sub.i.sup.NCO=.sub.i-1.sup.NCO+.sub.i.sup.r.Math..sub..sup.NCO+f.sub.i-1.sup.r.Math..sub..sup.NCO.Math.T.sub.c;

(30) block (106)a low-pass filter (LPF) coupled with an output z.sub.i.sup.d of a PD;

(31) block (107)a block for preliminary estimation of signal parameters (PESP) coupled by its inputs with: the phase output .sub.i.sup.NCO of a block for CFP of a NCO, the frequency output f.sub.i.sup.r of the loop filter, the output s.sub.i.sup. of the loop filter; where a block for PESP operates on the basis of equations:
{circumflex over ()}.sub.i.sup.c,E=.sub.i.sup.NCO+s.sub.i.sup./12,
{circumflex over ()}.sub.i.sup.c,E=2.Math.f.sub.i.sup.rs.sub.i.sup./(2.Math.T.sub.c),
{dot over ({circumflex over ()})}.sub.i.sup.c,E=s.sub.i.sup./T.sub.c.sup.2;
where {circumflex over ()}.sub.i.sup.c,E is the preliminary estimate for a signal phase [in radians], {circumflex over ()}.sub.i.sup.c,E is the preliminary estimate for a signal frequency [radian/s], {dot over ({circumflex over ()})}.sub.i.sup.c,E is the preliminary estimate for a signal frequency derivative [radian/s.sup.2];

(32) block (108) is a threshold unit (which, like other blocks, can be implemented in hardware, such as discrete transistors/components, as an ASIC or in software), coupled with an output z.sub.i.sup.A of a LPF; where an output J.sub.i of a threshold unit is given by the formula:
J.sub.i=true, if z.sub.i.sup.A>T.sub.A,
J.sub.i=false, if z.sub.i.sup.AT.sub.A,

(33) here T.sub.A is a threshold; the threshold value is set equal to (3 . . . 5).Math.RMS(z.sub.i.sup.A).

(34) block (109)a block for jerk-corrections of preliminary estimates (JCPE) coupled with an output z.sub.i.sup.A of a LPF and with an output J.sub.i of a threshold unit; where the block JCPE operates on the basis of equations:

(35) $\begin{array}{c}{\hat{}}_i^c={\hat{}}_i^{c,E}+z_i^A.Math.C_{}\\ {\hat{}}_i^c={\hat{}}_i^{c,E}+z_i^A.Math.C_{}\\ {\widehat{\stackrel{.}{}}}_i^c={\widehat{\stackrel{.}{}}}_i^{c,E}+z_i^A.Math.C_{\stackrel{.}{}}\end{array}\}\mathrm{if}{J}_i=\mathrm{true},\begin{array}{c}{\hat{}}_i^c={\hat{}}_i^{c,E},\\ {\hat{}}_i^c={\hat{}}_i^{c,E}\\ {\widehat{\stackrel{.}{}}}_i^c={\widehat{\stackrel{.}{}}}_i^{c,E}\end{array}\}\mathrm{if}{J}_i=\mathrm{false},$ where {circumflex over ()}.sub.i.sup.c is the estimate for a signal phase [in radians], {circumflex over ()}.sub.i.sup.c is the estimate for a signal frequency [in radian/s], {dot over ({circumflex over ()})}.sub.i.sup.c is the estimate for a signal frequency derivative [in radian/s.sup.2],
C.sub.=1.sup.LF/2+.sup.LF/12+.sup.LF/24,
C.sub.=(.sup.LF.sup.LF/2.sup.LF/6)/T.sub.c,
C.sub.{dot over ()}=.sup.LF/T.sub.c.sup.2.

(36) 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).

(37) Block (309) for jerk-corrections of preliminary estimates (JCPE) coupled with an output z.sub.i.sup.A of a LPF and operates on the basis of equations:

(38) $\begin{array}{c}{\hat{}}_i^{c,J}={\hat{}}_i^{c,E}+z_i^A.Math.C_{},\\ {\hat{}}_i^{c,J}={\hat{}}_i^{c,E}+z_i^A.Math.C_{}\\ {\widehat{\stackrel{.}{}}}_i^{c,J}={\widehat{\stackrel{.}{}}}_i^{c,E}+z_i^A.Math.C_{\stackrel{.}{}}\end{array}\},$
where {circumflex over ()}.sub.i.sup.c,J, {circumflex over ()}.sub.i.sup.c,J, {dot over ({circumflex over ()})}.sub.i.sup.c,J are, respectively, estimates with jerk-corrections for a phase [in radians], frequency [in radian/s] and frequency derivative [radian/s.sup.2] of a signal.

(39) 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 ()}.sub.i.sup.c,E of the PESP, operates on the basis of recurrence equations:

(40) 0$\begin{array}{c}{\stackrel{\_}{}}_i^{c,T}={\hat{}}_{i-1}^{c,T}+{\hat{}}_{i-1}^{c,T}.Math.T_c+{\widehat{\stackrel{.}{}}}_{i-1}^{c,T}.Math.T_c^2/2\\ {\stackrel{\_}{}}_i^{c,T}={\hat{}}_{i-1}^{c,T}+{\widehat{\stackrel{.}{}}}_{i-1}^{c,T}.Math.T_c\\ {\stackrel{\_}{\stackrel{.}{}}}_i^{c,T}={\widehat{\stackrel{.}{}}}_{i-1}^{c,T}\end{array}\}{z}_i^T={}_i^{\mathrm{NCO}}-{\stackrel{\_}{}}_i^{c,T},\begin{array}{c}{\hat{}}_i^{c,T}={\stackrel{\_}{}}_i^{c,T}+{}^T.Math.z_i^T\\ {\hat{}}_i^{c,T}={\stackrel{\_}{}}_i^{c,T}+{}^T.Math.z_i^T/T_c\\ {\widehat{\stackrel{.}{}}}_i^{c,T}={\stackrel{\_}{\stackrel{.}{}}}_i^{c,T}+{}^T.Math.z_i^T/T_c^2\end{array}\},$
where .sup.T, .sup.T, .sup.T are constant transfer coefficients of the TFP.

(41) 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.

(42) $\begin{array}{c}{\hat{}}_i^c={\hat{}}_i^{c,T}\\ {\hat{}}_i^c={\hat{}}_i^{c,T}\\ {\widehat{\stackrel{.}{}}}_i^c={\widehat{\stackrel{.}{}}}_i^{c,T}\end{array}\}\mathrm{if}{J}_i=\mathrm{false},\begin{array}{c}{\hat{}}_i^c={\hat{}}_i^{c,J}\\ {\hat{}}_i^c={\hat{}}_i^{c,J}\\ {\widehat{\stackrel{.}{}}}_i^c={\widehat{\stackrel{.}{}}}_i^{c,J}\end{array}\}\mathrm{if}{J}_i=\mathrm{true};$
where {circumflex over ()}.sub.i.sup.c is the estimate for a signal phase [in radians], {circumflex over ()}.sub.i.sup.c is the estimate for a signal frequency [in radian/s], {dot over ({circumflex over ()})}.sub.i.sup.c is the estimate for a signal frequency derivative [in radian/s.sup.2].

(43) FIG. 4 shows an example of motion with jerks. This jerking motion consists of: 0<tt.sub.1 and t>t.sub.4 are states without movement, t.sub.1<tt.sub.2 and t.sub.3<tt.sub.4 are states with jerks, when the acceleration varies linearly, t.sub.2<tt.sub.3 is the state with a constant acceleration.

(44) FIG. 5 shows an exemplary implementation of the full phase calculation block 105. FIG. 6 shows an exemplary implementation of the low pass filter 106. FIG. 7 shows an exemplary implementation of the PESP block 107. FIG. 8 shows an exemplary implementation of the block for jerk-corrections of preliminary estimates (JCPE) 309. FIG. 9 shows an exemplary implementation of the block for tracking of filter phase 310. FIG. 10 shows an exemplary implementation of the GNSS receiver, showing the components that are relevant to the invention discussed herein, i.e., the components relevant to estimation of non-energy parameters. These are then converted, using OLS (ordinary least squares) into parameters of movement of the receiver, i.e., velocity and acceleration in X, Y, Z coordinates.

(45) As will be appreciated by one of ordinary skill in the art, the various blocks shown in FIGS. 1-10 can be implemented as discrete hardware components, as an ASIC (or multiple ASICs) and/or as software running on a processor.

(46) 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.

(47) 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.