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 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 T.sub.c operating based on equations: $\begin{array}{c}{}_i^{\mathrm{LF}}={}^{\mathrm{LF}}.Math.z_i^d,\\ s_i^{}=s_{i-1}^{}+{}^{\mathrm{LF}}.Math.z_i^d,\\ s_i^{}=s_{i-1}^{}+s_i^{}+{}^{\mathrm{LF}}.Math.z_i^d,\\ {}_i^r=\mathrm{round}\left({}_i^{\mathrm{LF}}/{}_{}^{\mathrm{NCO}}\right),\\ f_i^r=\mathrm{round}\left(s_i^{}/{}_{}^{\mathrm{NCO}}/T_c\right),\end{array}\},$ where .sup.LF, .sup.LF, .sup.LF are constant transfer coefficients, z.sub.i.sup.d is a PD output; .sub.i.sup.r is a phase code for a Numerically Controlled Oscillator (NCO), f.sub.i.sup.r is a frequency code for the NCO, .sub..sup.NCO is a phase step size in the NCO, .sub..sup.NCO is a frequency step size in the NCO, s.sub.i.sup. is an output of the LF representing a signal that is proportional to a frequency of the input signal; s.sub.i.sup. is an output of the LF representing a signal that is proportional to a rate of change of the frequency of the input signal; .sub.i.sup.LF 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 .sub.i.sup.r and whose frequency input is connected to the frequency code f.sub.i.sup.r, 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 .sub.i.sup.r and f.sub.i.sup.r and operating based on equation
.sub.i.sup.NCO=.sub.i-1.sup.NCO+.sub.i.sup.r.Math..sub..sup.NCO+f.sub.i-1.Math..sub..sup.NCO.Math.T.sub.c; c) a low-pass filter (LPF) inputting the output z.sub.i.sup.d of the PD and outputting z.sub.i.sup.A; d) wherein the receiver is further configured to generate a preliminary estimation of signal parameters using: the full phase .sub.i.sup.NCO, the frequency code f.sub.i.sup.r, and the output s.sub.i.sup. t of the LF, wherein the preliminary estimation of signal parameters are based on:
{circumflex over ()}.sub.i.sup.c,E=.sub.i.sup.NCO+s.sub.i.sup./12,
{circumflex over ()}.sub.i.sup.c,E=f.sub.i.sup.r.Math..sub..sup.NCOs.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 a preliminary estimate for a signal phase, {circumflex over ()}.sub.i.sup.c,E is a preliminary estimate for a signal frequency, {dot over ({circumflex over ()})}.sub.i.sup.c,E is a preliminary estimate for a signal frequency derivative; e) wherein the receiver is further configured to generate an output J.sub.i based on the output z.sub.i.sup.A of the LPF as follows
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, where T.sub.A is a threshold; f) wherein the receiver is further configured to jerk-correct the preliminary estimates by using the output z.sub.i.sup.A of the LPF and the output J.sub.i according to: $\begin{array}{c}{\hat{}}_i^c={\hat{}}_i^{c,E}+z_i^A.Math.C_{}\\ {\hat{}}_i^c={\hat{}}_i^{c,E}+z_i^A.Math.C_{}\\ {\widehat{\stackrel{.}{}}}_i^c={\widehat{\stackrel{.}{}}}_i^{c,E}+z_i^A.Math.C_{\stackrel{.}{}}\end{array}\}\mathrm{if}{J}_i=\mathrm{true},\begin{array}{c}{\hat{}}_i^c={\hat{}}_i^{c,E},\\ {\hat{}}_i^c={\hat{}}_i^{c,E}\\ {\widehat{\stackrel{.}{}}}_i^c={\widehat{\stackrel{.}{}}}_i^{c,E}\end{array}\}$ $\mathrm{if}{J}_i=\mathrm{false},$ where {circumflex over ()}.sub.i.sup.c is an estimate for a signal phase, {circumflex over ()}.sub.i.sup.c is an estimate for a signal frequency, {dot over ({circumflex over ()})}.sub.i.sup.c is an estimate for a signal frequency derivative,
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.sup.2.

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

3. The system of claim 1, wherein the LPF operates based on
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 0<.sup.LPF<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 T.sub.c based on equations: $\begin{array}{c}{}_i^{\mathrm{LF}}={}^{\mathrm{LF}}.Math.z_i^d,\\ s_i^{}=s_{i-1}^{}+{}^{\mathrm{LF}}.Math.z_i^d,\\ s_i^{}=s_{i-1}^{}+s_i^{}+{}^{\mathrm{LF}}.Math.z_i^d,\\ {}_i^r=\mathrm{round}\left({}_i^{\mathrm{LF}}/{}_{}^{\mathrm{NCO}}\right),\\ f_i^r=\mathrm{round}\left(s_i^{}/{}_{}^{\mathrm{NCO}}/T_c\right),\end{array}\},$ where .sup.LF, .sup.LF, .sup.LF are constant transfer coefficients, z.sub.i.sup.d is a PD output; .sub.i.sup.r is a phase code for a numerically controlled oscillator (NCO), f.sub.i.sup.r is a frequency code for the NCO, .sub..sup.NCO is a phase step size in the NCO, .sub..sup.NCO is a frequency step size in the NCO, s.sub.i.sup. is an output of the LF representing a signal that is proportional to a frequency of the input signal; s.sub.i.sup. is an output of the LF representing a signal that is proportional to a rate of change of the frequency of the input signal; .sub.i.sup.LF 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 .sub.i.sup.r and a frequency input is connected to the frequency code f.sub.i.sup.r, 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 .sub.i.sup.r and f.sub.i.sup.r, and operating based on 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; c) a low-pass filter (LPF) inputting the output z.sub.i.sup.d from the PD and outputting z.sub.i.sup.A; d) wherein the receiver is configured to generate preliminary estimates of signal parameters based on the full phase output .sub.i.sup.NCO, the frequency code f.sub.i.sup.r, and the output s.sub.i.sup. according to equations: $\begin{array}{c}{\hat{}}_i^{c,E}={}_i^{\mathrm{NCO}}+s_i^{}/12\\ {\hat{}}_i^{c,E}=f_i^r.Math.{}_{}^{\mathrm{NCO}}-s_i^{}/\left(2.Math.T_c\right)\\ {\widehat{\stackrel{.}{}}}_i^{c,E}=s_i^{}/T_c^2\end{array}\}$ where {circumflex over ()}.sub.i.sup.c,E is a preliminary estimate for a signal phase, {circumflex over ()}.sub.i.sup.c,E is a preliminary estimate for a signal frequency, {dot over ({circumflex over ()})}.sub.i.sup.c,E is a preliminary estimate for a signal frequency derivative; e) wherein the receiver is further configured to generate an output J.sub.i based on the output z.sub.i.sup.A of the LPF as follows:
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, where T.sub.A is a threshold; f) wherein the receiver is further configured to perform jerk-corrections of the preliminary estimates based on equations: $\begin{array}{c}{\hat{}}_i^{c,J}={\hat{}}_i^{c,E}+z_i^A.Math.C_{},\\ {\hat{}}_i^{c,J}={\hat{}}_i^{c,E}+z_i^A.Math.C_{}\\ {\widehat{\stackrel{.}{}}}_i^{c,J}={\widehat{\stackrel{.}{}}}_i^{c,E}+z_i^A.Math.C_{\stackrel{.}{}}\end{array}\}$ 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, frequency and frequency derivative of the input signal,
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; g) a third order tracking filter of phase (TFP) which operates based on equations: $\begin{array}{c}{\stackrel{\_}{}}_i^{c,T}={\hat{}}_{i-1}^{c,T}+{\hat{}}_{i-1}^{c,T}.Math.T_c+{\widehat{\stackrel{.}{}}}_{i-1}^{c,T}.Math.T_c^2/2\\ {\stackrel{\_}{}}_i^{c,T}={\hat{}}_{i-1}^{c,T}+{\widehat{\stackrel{.}{}}}_{i-1}^{c,T}.Math.T_c\\ {\stackrel{\_}{\stackrel{.}{}}}_i^c={\widehat{\stackrel{.}{}}}_{i-1}^{c,T}\end{array}\}$
z.sub.i.sup.T=.sub.i.sup.NCO.sub.i.sup.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; 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 $\begin{array}{c}{\hat{}}_i^c={\hat{}}_i^{c,T}\\ {\hat{}}_i^c={\hat{}}_i^{c,T}\\ {\widehat{\stackrel{.}{}}}_i^c={\widehat{\stackrel{.}{}}}_i^{c,T}\end{array}\}\mathrm{if}{J}_i=\mathrm{false},\begin{array}{c}{\hat{}}_i^c={\hat{}}_i^{c,J}\\ {\hat{}}_i^c={\hat{}}_i^{c,J}\\ {\widehat{\stackrel{.}{}}}_i^c={\widehat{\stackrel{.}{}}}_i^{c,J}\end{array}\}$ $\mathrm{if}{J}_i=\mathrm{true};$ where {circumflex over ()}.sub.i.sup.c is an estimate for a signal phase, {circumflex over ()}.sub.i.sup.c is an estimate for a signal frequency, and {dot over ({circumflex over ()})}.sub.i.sup.c 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=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.

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 T.sub.c operating based on: $\begin{array}{c}{}_i^{\mathrm{LF}}={}^{\mathrm{LF}}.Math.z_i^d,\\ s_i^{}=s_{i-1}^{}+{}^{\mathrm{LF}}.Math.z_i^d,\\ s_i^{}=s_{i-1}^{}+s_i^{}+{}^{\mathrm{LF}}.Math.z_i^d,\\ {}_i^r=\mathrm{round}\left({}_i^{\mathrm{LF}}/{}_{}^{\mathrm{NCO}}\right),\\ f_i^r=\mathrm{round}\left(s_i^{}/{}_{}^{\mathrm{NCO}}/T_c\right),\end{array}\},$ where .sup.LF, .sup.LF, .sup.LF are constants, z.sub.i.sup.d is a PD output; .sub.i.sup.r is a phase code for a Numerically Controlled Oscillator (NCO), f.sub.i.sup.r is a frequency code for the NCO, .sub..sup.NCO is a phase step size in the NCO, .sub..sup.NCO is a frequency step size in the NCO, s.sub.i.sup. is an output of the LF representing a signal that is proportional to a frequency of the input signal; s.sub.i.sup. is an output of the LF representing a signal that is proportional to a rate of change of the frequency of the input signal; .sub.i.sup.LF 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 .sub.i.sup.r and f.sub.i.sup.r, 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 .sub.i.sup.r and f.sub.i.sup.r from the LF and based on
.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; (c) a low-pass filter (LPF) inputting z.sub.i.sup.d and outputting z.sub.i.sup.A; (d) wherein the receiver is further configured to generate a preliminary estimate for a signal phase {circumflex over ()}.sub.i.sup.c,E and a preliminary estimate for a signal frequency {circumflex over ()}.sub.i.sup.c,E based on:
{circumflex over ()}.sub.i.sup.c,E=.sub.i.sup.NCO+s.sub.i.sup./12,
{circumflex over ()}.sub.i.sup.c,E=f.sub.i.sup.r.Math..sub..sup.NCOs.sub.i.sup./(2.Math.T.sub.c); (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 ()}.sub.i.sup.c and an estimate for a signal frequency {circumflex over ()}.sub.i.sup.c based on: $\begin{array}{c}{\hat{}}_i^c={\hat{}}_i^{c,E}+z_i^A.Math.C_{}\\ {\hat{}}_i^c={\hat{}}_i^{c,E}+z_i^A.Math.C_{}\end{array}\}\mathrm{if}{z}_i^A>T_A,\begin{array}{c}{\hat{}}_i^c={\hat{}}_i^{c,E},\\ {\hat{}}_i^c={\hat{}}_i^{c,E}\end{array}\}$ $\mathrm{if}$ $z_i^A{T}_A,$ where
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, and T.sub.A 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 ()})}.sub.i.sup.c as follows: the receiver is configured to generate a preliminary estimate for a signal frequency derivative {dot over ({circumflex over ()})}.sub.i.sup.c,E=s.sub.i.sup./T.sub.c.sup.2; and the receiver is configured to output
{dot over ({circumflex over ()})}.sub.i.sup.c={dot over ({circumflex over ()})}.sub.i.sup.c,E+z.sub.i.sup.A.Math.C.sub.{dot over ()}, if z.sub.i.sup.A>T.sub.A,
{dot over ({circumflex over ()})}.sub.i.sup.c={dot over ({circumflex over ()})}.sub.i.sup.C,E, if z.sub.i.sup.AT.sub.A,
where C.sub.{dot over ()}=.sub.LF/T.sub.c.sup.2.

10. The system of claim 6, where .sup.LF, .sup.LF, .sup.LF 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 z.sub.i.sup.d between the input signal and reference signals from a Numerically Controlled Oscillator (NCO); ii) a loop filter (LF) with a control period T.sub.c based on equations: $\begin{array}{c}{s}_i^{}=s_{i-1}^{}+.Math.z_i^d,\\ s_i^{}=s_{i-1}^{}+s_i^{}+.Math.z_i^d,\\ {}_i^r=\mathrm{round}\left(.Math.z_i^d/{}_{}^{\mathrm{NCO}}\right),\\ f_i^r=\mathrm{round}\left(s_i^{}/{}_{}^{\mathrm{NCO}}/T_c\right),\end{array}\},$ where , , are constants, .sub.i.sup.r is a phase control signal for the NCO, f.sub.i.sup.r is a frequency control signal for the NCO, .sub..sup.NCO is a phase step size in the NCO, .sub..sup.NCO is a frequency step size in the NCO, s.sub.i.sup. corresponds to a frequency of the input signal; s.sub.i.sup. corresponds to a rate of change of the frequency of the input signal; and round(.) is numerical rounding; and iii) the NCO inputting the .sub.i.sup.r and f.sub.i.sup.r 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 .sub.i.sup.NCO based on
.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; c) a low-pass filter (LPF) inputting the phase difference z.sub.i.sup.d and outputting z.sub.i.sup.A; d) wherein the receiver generates a preliminary estimation of signal parameters based on:
{circumflex over ()}.sub.i.sup.c,E=.sub.i.sup.NCO+s.sub.i.sup./K.sub.,
{circumflex over ()}.sub.1.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 {circumflex over ()}.sub.i.sup.c,E is a preliminary estimate for the phase of the input signal, {circumflex over ()}.sub.i.sup.c,E is a preliminary estimate for the frequency of the input signal, {dot over ({circumflex over ()})}.sub.i.sup.c,E is a preliminary estimate for a derivative of the frequency of the input signal, and K.sub. and K.sub. are constants; e) wherein the receiver is further configured to generate an output J.sub.i based on
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, where T.sub.A is a threshold; and f) wherein the receiver is further configured to perform jerk-corrections of the preliminary estimates based on: $\begin{array}{c}{\hat{}}_i^c={\hat{}}_i^{c,E}+z_i^A.Math.\left(K_0-/K_1+/K_2+/K_3\right)\\ {\hat{}}_i^c={\hat{}}_i^{c,E}+z_i^A.Math.\left(-/K_4-/K_5\right)/T_c\\ {\widehat{\stackrel{.}{}}}_i^c={\widehat{\stackrel{.}{}}}_i^{c,E}+z_i^A.Math./T_c^2\end{array}\}\mathrm{if}{J}_i=\mathrm{true},\begin{array}{c}{\hat{}}_i^c={\hat{}}_i^{c,E},\\ {\hat{}}_i^c={\hat{}}_i^{c,E}\\ {\widehat{\stackrel{.}{}}}_i^c={\widehat{\stackrel{.}{}}}_i^{c,E}\end{array}\}\mathrm{if}{J}_i=\mathrm{false},$ where {circumflex over ()}.sub.i.sup.c is an estimate for the phase of the input signal, {circumflex over ()}.sub.i.sup.c is an estimate for the frequency of the input signal, {dot over ({circumflex over ()})}.sub.i.sup.c is an estimate for the derivative of the frequency of the input signal, and K.sub.0, K.sub.1, K.sub.2, K.sub.3, K.sub.4, and K.sub.5 are constants.

12. The system of claim 11, where K.sub.0=1, K.sub.1=2, K.sub.2=12, K.sub.3=24, K.sub.4=2 and K.sub.5=6.

13. The system of claim 11, where K.sub.=12 and K.sub.=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 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 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, .sub..sup.NCO is a phase step size in the NCO, .sub..sup.NCO is a frequency step size in the NCO, s.sub.i.sup. corresponds to a frequency of the input signal, s.sub.i.sup. 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 .sub.i.sup.NCO according to
.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; c) a low-pass filter (LPF) inputting the phase difference z.sub.i.sup.d and outputting z.sub.i.sup.A; d) wherein the receiver uses .sub.i.sup.NCO and s.sub.i.sup. 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) wherein the receiver is configured to output a true/false value J.sub.i based on z.sub.i.sup.A; and f) wherein the receiver is configured to perform jerk-corrections of the preliminary estimates and to generate 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.

15. The system of claim 14, wherein the receiver is also configured to generate a preliminary estimate {circumflex over ()}.sub.i.sup.c,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 ()})}.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.

17. The system of claim 16, 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.

18. The system of claim 17, wherein the receiver is also configured to generate 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.

19. The system of claim 18, further comprising g) a third order tracking filter (TFP) that operates based on equations: $\begin{array}{c}{\stackrel{\_}{{}_i}}^{c,T}={\hat{}}_{i-1}^{c,T}+{\hat{}}_{i-1}^{c,T}.Math.T_c+{\widehat{\stackrel{.}{}}}_{i-1}^{c,T}.Math.T_c^2/2\\ {\stackrel{\_}{{}_i}}^{c,T}={\hat{}}_{i-1}^{c,T}+{\widehat{\stackrel{.}{}}}_{i-1}^{c,T}.Math.T_c\\ {\stackrel{\_}{{\stackrel{.}{}}_i}}^c={\widehat{\stackrel{.}{}}}_{i-1}^{c,T}\end{array}\}{z}_i^T={}_i^{\mathrm{NCO}}-{\stackrel{\_}{}}_i^{c,T},\begin{array}{c}{\hat{}}_i^{c,T}={\stackrel{\_}{{}_i}}^{c,T}+{}^T.Math.z_i^T\\ {\hat{}}_i^{c,T}={\stackrel{\_}{{}_i}}^{c,T}+{}^T.Math.z_i^T/T_c\end{array}\},$ where .sup.T, .sup.T are constants; wherein the receiver is also configured to output the estimates {circumflex over ()}.sub.i.sup.c,T and {circumflex over ()}.sub.i.sup.c,T from the TFP when there is no jerk and to output the estimates {circumflex over ()}.sub.i.sup.c and {circumflex over ()}.sub.i.sup.c otherwise.

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 arc tangent-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.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

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

(8) 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.

(9) 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)],

(10) 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].

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

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

(13) $\begin{array}{c}{}_i^{\mathrm{LF}}={}^{\mathrm{LF}}.Math.z_i^d,\\ s_i^{}=s_{i-1}^{}+{}^{\mathrm{LF}}.Math.z_i^d,\\ s_i^{}=s_{i-1}^{}+s_i^{}+{}^{\mathrm{LF}}.Math.z_i^d,\\ {}_i^r=\mathrm{round}\left({}^{\mathrm{LF}}/{}_{}^{\mathrm{NCO}}\right),\\ f_i^r=\mathrm{round}\left(s_i^{}/{}_{}^{\mathrm{NCO}}/T_c\right),\end{array}\},$

(14) where .sup.LF, .sup.LF, .sup.LF are constant transfer coefficients,

(15) z.sub.i.sup.d is the PD output;

(16) .sub.i.sup.r is the phase code for NCO,

(17) f.sub.i.sup.r is the frequency code for NCO,

(18) .sub..sup.NCO is the phase step size (radian) in the NCO,

(19) .sub..sup.NCO is the frequency step size (radian/s) in the NCO,

(20) round( ) is the operation of a numerical rounding.

(21) 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).

(22) 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,

(23) $\begin{array}{c}{I}_n^{\mathrm{ref}}=A^{\mathrm{NCO}}.Math.\cos \left({}_n^{w,\mathrm{NCO}}\right)\\ Q_n^{\mathrm{ref}}=A^{\mathrm{NCO}}.Math.\sin \left({}_n^{w,\mathrm{NCO}}\right)\end{array}\},$

(24) 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

(25) $\begin{array}{c}{I}_n^{\mathrm{mr}}=U_n^{\mathrm{mix}}.Math.I_n^{\mathrm{ref}}\\ Q_n^{\mathrm{mr}}=U_n^{\mathrm{mix}}.Math.Q_n^{\mathrm{ref}}\end{array}\}$

(26) 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

(27) $I_i=\underset{m=1}{\overset{m=N_s}{.Math.}}{I}_{m+\left(i-1\right).Math.N_s}^{\mathrm{mr}}\mathrm{and}{Q}_i=\underset{m=1}{\overset{m=N_s}{.Math.}}{Q}_{m+\left(i-1\right).Math.N_s}^{\mathrm{mr}}.$

(28) The output of a phase discriminator is
z.sub.i.sup.d=arctan(Q.sub.i/I.sub.i) [in radians].

(29) 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:

(30) $\begin{array}{c}{}_i^{\mathrm{LF}}={}^{\mathrm{LF}}.Math.z_i^d,\\ s_i^{}=s_{i-1}^{}+{}^{\mathrm{LF}}.Math.z_i^d,\\ s_i^{}=s_{i-1}^{}+s_i^{}+{}^{\mathrm{LF}}.Math.z_i^d,\\ {}_i^r=\mathrm{round}\left({}^{\mathrm{LF}}/{}_{}^{\mathrm{NCO}}\right),\\ f_i^r=\mathrm{round}\left(s_i^{}/{}_{}^{\mathrm{NCO}}/T_c\right),\end{array}\},$

(31) where .sup.LF, .sup.LF, .sup.LF are constant transfer coefficients,

(32) z.sub.i.sup.d is the PD output;

(33) .sub.i.sup.r is the phase code for the NCO,

(34) f.sub.i.sup.r is the frequency code for the NCO,

(35) .sub..sup.NCO is the phase step size (radian) in the NCO,

(36) .sub..sup.NCO is the frequency step size (radian/s) in the NCO, and

(37) round(.) is the operation of a numerical rounding.

(38) 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.

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

(40) 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;

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

(42) block (107)a block for preliminary estimation of signal parameters (PESP) coupled by its inputs with:

(43) the phase output .sub.i.sup.NCO of a block for CFP of a NCO,

(44) the frequency output f.sub.i.sup.r of the loop filter,

(45) the output s.sub.i.sup. of the loop filter;

(46) 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;

(47) 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];

(48) block (108) is a threshold unit 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,

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

(50) 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:

(51) $\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.

(52) 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).

(53) 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:

(54) $\begin{array}{c}{\hat{}}_i^{c,J}={\hat{}}_i^{c,E}+z_i^A.Math.C_{},\\ {\hat{}}_i^{c,J}={\hat{}}_i^{c,E}+z_i^A.Math.C_{}\\ {\widehat{\stackrel{.}{}}}_i^{c,J}={\widehat{\stackrel{.}{}}}_i^{c,E}+z_i^A.Math.C_{\stackrel{.}{}}\end{array}\},$

(55) 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.

(56) 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:

(57) 0$\begin{array}{c}{\stackrel{\_}{}}_i^{c,T}={\hat{}}_{i-1}^{c,T}+{\hat{}}_{i-1}^{c,T}.Math.T_c+{\widehat{\stackrel{.}{}}}_{i-1}^{c,T}.Math.T_c^2/2\\ {\stackrel{\_}{}}_i^{c,T}={\hat{}}_{i-1}^{c,T}+{\widehat{\stackrel{.}{}}}_{i-1}^{c,T}.Math.T_c\\ {\stackrel{\_}{\stackrel{.}{}}}_i^c={\widehat{\stackrel{.}{}}}_{i-1}^{c,T}\end{array}\}$
z.sub.i.sup.T=.sub.i.sup.NCO.sub.i.sup.c,T,

(58) $\begin{array}{c}{\hat{}}_i^{c,T}={\stackrel{\_}{}}_i^{c,T}+{}^T.Math.z_i^T\\ {\hat{}}_i^{c,T}={\stackrel{\_}{}}_i^{c,T}+{}^T.Math.z_i^T/T_c\\ {\widehat{\stackrel{.}{}}}_i^{c,T}={\stackrel{\_}{\stackrel{.}{}}}_i^{c,T}+{}^T.Math.z_i^T/T_c^2\end{array}\},$

(59) where .sup.T, .sup.T, .sup.T are constant transfer coefficients of the TFP.

(60) 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.

(61) $\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};$

(62) where

(63) {circumflex over ()}.sub.i.sup.c is the estimate for a signal phase [in radians],

(64) {circumflex over ()}.sub.i.sup.c is the estimate for a signal frequency [in radian/s],

(65) {dot over ({circumflex over ()})}.sub.i.sup.c is the estimate for a signal frequency derivative [in radian/s.sup.2].

(66) 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.

(67) 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.

(68) 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.