Kalman predictor for providing a relatively noise free indication of the phase of a carrier laden with noise

• US 5,062,123 A
• Filed: 08/16/1989
• Issued: 10/29/1991
• Est. Priority Date: 08/16/1989
• Status: Expired due to Fees

• Current Assignee: L-3 Communications Cincinnati Electronics Corporation (L3Harris Technologies, Inc.)
• Original Assignee: L-3 Communications Cincinnati Electronics Corporation (L3Harris Technologies, Inc.)
• Inventors: Kavanaugh, Patrick J., Geile, Michael J., Hill, Terrance J.
• Primary Examiner(s): Safourek, Benedict V.
• Application Number:
  US07/394,330
• Time in Patent Office: 804 Days
• Field of Search: 331/1 A, 331/17, 331/25, 329/307, 329/310, 329/358, 329/308, 328/133, 328/155, 328/165, 328/167, 375/15, 375/81, 375/96, 375/97, 364/724.01, 364/724.18, 364/724.19
• US Class Current: 375/327
• CPC Class Codes: H04L 2027/0032 at baseband and passband
• CPC Class Codes: H04L 2027/0048 Frequency multiplication
• CPC Class Codes: H04L 2027/0057 quadrature phase
• CPC Class Codes: H04L 27/2332 using a non-coherent carrier

Abstract

A receiver responsive to a noise laden phase modulated signal on a carrier hard limits the signal to derive a constant amplitude phase modulated r.f. signal. The constant amplitude phase modulated r.f. signal is supplied to processing circuitry to derive a digital signal having a value representing the phase of the noise laden carrier. A phase locked loop, including a minimum variance Kalman predictor filter, responds to the noise laden carrier to derive a relatively noise free indication of carrier phase. The noise laden indication of phase and the relatively noise free indication of carrier phase are combined to indicate the phase of the phase modulated signal to which the receiver is responsive.

Claims

1. A method of deriving a relatively noise free indication of an estimate of the phase of a noise laden signal replica comprising the step of supplying an indication of the phase of the noise laden signal replica to a Kalman filter that derives the relatively noise free indication of the signal replica phase.

2. A method of deriving a relatively noise free indication of an estimate of the phase of a noise laden signal replica comprising deriving an indication of the instantaneous phase of the noise laden signal replica, responding to a previous indication of a function of the relatively noise free indication of the signal replica phase to derive an indication of an estimate of the instantaneous phase of the signal replica, deriving an indication of the error between the indication of the instantaneous phase and the indication of the estimate of the instantaneous phase of the signal replica, modifying the error indication by a time-varying factor, and combining the modified error with a prior indication of the relatively noise free indication of the signal replica phase to derive the relatively noise free indication.

3. The method of claim 2 wherein the factor decreases in amplitude as a function of time.

4. The method of claim 2 wherein the factor is determined by the signal replica expected noise.

5. The method of claim 2 wherein the error indication is modified by first and second different time-varying factors to derive first and second different time-varying modified error indications, the combining step including:

combining the first time-varying modified error indication with a function of the prior relatively noise free indication and of a previous indication of the second time-varying modified error indication.

6. A method of deriving a relatively noise free indication of the phase of a noise laden carrier comprising deriving an indication of the instantaneous phase of the noise laden carrier, responding to a previous indication of a function of the relatively noise free indication of the estimate of carrier phase to derive an indication of an estimate of the instantaneous phase of the carrier, deriving an indication of the error between the indication of the instantaneous phase and the indication of the estimate of the instantaneous phase of the carrier, modifying the error indication by first and second different time-varying factors to derive first and second different time-varying modified error indications, deriving an indication of a prior estimate of the phase of the carrier, combining and delaying the indications of the relatively noise free estimate of the phase of the carrier and the prior estimate of the phase of the carrier to derive indications of first and second different delayed functions, combining the indication of the first delayed function with the first time-varying modified error indication to derive the relatively noise free indication of the estimate of the phase of the carrier, and combining the indication of the second delayed function with the second time-varying modified error indication to derive the indication of the prior estimate of the phase of the carrier.

7. The method of claim 6 wherein the function of the relatively noise free indication of the estimate of the carrier phase is said first delayed function.

8. The method of claim 7 wherein the first and second delayed functions are respectively:

space="preserve" listing-type="equation">φ

(k)+[φ

(k)-φ

(k-1)] and φ

(k),

where φ

(k) is the relatively noise free indication of the estimate of the phase, and φ

(k-1) is the indication of the prior estimate of the phase.

9. The method of claim 6 wherein the first and second delayed functions are respectively:

space="preserve" listing-type="equation">φ

(k)+[φ

(k)-φ

(k-1)] and φ

(k),

where φ

(k) is the relatively noise free indication of the estimate of the phase, and φ

(k-1) is the indication of the prior estimate of the phase.

10. A phase locked loop responsive to a carrier subject to noise for deriving a substantially noise free indication of the phase of the carrier comprising a signal controlled local oscillator for deriving an output signal, means responsive to the carrier and the local oscillator for deriving a signal having a value indicative of an error function between the phase of the first output signal and the instantaneous phase of the carrier, and a Kalman filter responsive to the error function indicating second output signal for deriving the substantially noise free indication of the carrier phase and a control signal for the frequency of the oscillator, the control signal being applied to the oscillator to control the frequency thereof,

the Kalman filter including means for deriving an indication of the error between the instantaneous phase of the carrier relative to a delayed function of the noise free indication of the phase of the carrier,

time-varying gain means for modifying the error indication,

means for combining an output signal of the time-varying gain means, an indication of the value of the control signal for the frequency of the first output signal and a delayed function of the noise free indication of the phase of the carrier, and

means responsive to (a) the time-varying gain means, (b) an indication of the value of the control signal for the oscillator, and (c) first and second delayed functions of the noise free indication of the phase of the carrier for deriving the substantially noise free indication of the phase of the carrier and an indication of a prior value of the phase of the carrier, and means for combining the substantially noise free indication of the phase of the carrier and the indication of the prior value of the phase of carrier to derive the control signal for the frequency of the oscillator.

11. The phase locked loop of claim 10 wherein the time-varying gain means includes means for modifying the error indication by first and second different time-varying functions to derive first and second output signals having values respectively indicative of the error indication as modified by the first and second time-varying functions, the means for deriving substantially noise free indication of the phase of the carrier and an indication of a prior value of the phase of the carrier including means for combining the first output signal with a first delayed function of the noise free indication of the phase of the carrier and an indication of the value of the control signal to derive the noise free indication of the phase of the carrier and for combining the second output signal with a second delayed function of both the noise free indication of the phase of the carrier and a prior indication of the phases of the carrier to derive the indication of the prior value of the phase of the carrier.

12. A receiver responsive to a replica of a phase modulated signal subject to being degraded with noise comprising means responsive to the signal for hard limiting the signal to derive a constant amplitude phase modulated r.f. signal, means responsive to the constant amplitude phase modulated r.f. signal for deriving a carrier subject to noise, means responsive to the carrier for deriving a relatively noise free indication of the phase of the carrier, said last named means including a Kalman filter, and means responsive to the constant amplitude phase modulated r.f. signal and the relatively noise free indication of the phase of the carrier for indicating the phase of the phase modulated signal to which the receiver is responsive, the Kalman predictor including means for deriving an indication of the error between the instantaneous phase of the carrier relative to a delayed function of the noise free indication of the phase of the carrier,

time-varying gain means for modifying the error indication,

means for combining an output signal of the time-varying gain means, and a delayed function of the noise free indication of the phase of the carrier, and

means responsive to (a) the time-varying gain means, and (b) first and second delayed functions of the noise free indication of the phase of the carrier for deriving the substantially noise free indication of the phase of the carrier and an indication of a prior value of the phase of the carrier, and means for combining the substantially noise free indication of the phase of the carrier and the indication of the prior value of the phase of carrier to derive the control signal for the frequency of the oscillator.

13. The receiver of claim 12 wherein the time-varying gain means includes means for modifying the error indication by first and second different time-varying functions to derive first and second output signals having values respectively indicative of the error indication as modified by the first and second time-varying functions, the means for deriving substantially noise free indication of the phase of the carrier and an indication of a prior value of the phase of the carrier, including means for combining the first output signal with a first delayed function of the noise free indication of the phase of the carrier and an indication of the value of the control signal to derive the noise free indication of the phase of the carrier and for combining the second output signal with a second delayed function of both the noise free indication of the phase of the carrier and a prior indication of the phases of the carrier to derive the indication of the prior value of the phase of the carrier.

14. Apparatus for deriving a relatively noise free indication of an estimate of the phase of a replica of a signal having substantial noise comprising means for deriving an indication of the instantaneous phase of the signal replica, means responsive to a previous indication of a function of the relatively noise free indication of the signal replica phase for deriving an indication of an estimate of the instantaneous phase of the signal replica, means for deriving an indication of the error between the indication of the instantaneous phase and the indication of the estimate of the instantaneous phase of the signal replica, means for modifying the error indication by a time-varying factor, and means for combining the modified error with a prior indication of the relatively noise free indication of the signal replica phase to derive the relatively noise free indication.

15. The apparatus of claim 14 wherein the factor decreases in amplitude as a function of time.

16. The apparatus of claim 14 wherein the means for modifying includes means for modifying the error indication by first and second different time-varying factors to derive first and second different time-varying modified error indications, the means for combining including:

means for combining the first time-varying modified error indication with a function of the prior relatively noise free indication and of a previous indication of the second time-varying modified error indication.

17. Apparatus for deriving a relatively noise free indication of the phase of a carrier subject to substantial noise comprising means for deriving an indication of the instantaneous phase of the carrier, means responsive to a previous indication of a function of the relatively noise free indication of the estimate of carrier phase to derive an indication of an estimate of the instantaneous phase of the carrier, means for deriving an indication of the error between the indication of the instantaneous phase and the indication of the estimate of the instantaneous phase of the carrier, means for modifying the error indication by first and second different time-varying factors to derive first and second different time-varying modified error indications, means for deriving an indication of a prior estimate of the phase of the carrier, means for combining and delaying the indications of the relatively noise free estimate of the phase of the carrier and the prior estimate of the phase of the carrier to derive indications of first and second different delayed functions, means for combining the indication of the first delayed function with the first time-varying modified error indication to derive the relatively noise free indication of the estimate of the phase of the carrier, and means for combining the indication of the second delayed function with the second time-varying modified error indication to derive the indication of the prior estimate of the phase of the carrier.

18. The apparatus of claim 17 wherein the function of the relatively noise free indication of the estimate of the carrier phase is said first delayed function.

19. The apparatus of claim 18 wherein the first and second delayed functions are respectively:

space="preserve" listing-type="equation">φ

(k)+[φ

(k)-φ

(k-1)] and φ

(k),

where φ

(k) is the relatively noise free indication of the estimate of the phase, and φ

(k-1) is the indication of the prior estimate of the phase.

20. The apparatus of claim 17 wherein the first and second delayed functions are respectively:

space="preserve" listing-type="equation">φ

(k)+[φ

(k)-φ

(k-1)] and φ

(k),

where φ

(k) is the relatively noise free indication of the estimate of the phase, and φ

(k-1) is the indication of the prior estimate of the phase.