perf T&F re perf T&F re

A6-1PPS8 bits of the tuning word. The coarse tune DAC is then set to providethe final tuning voltage. During all subsequent tuning, only the finetune DAC is used over its 16 bit range. If the range is exceeded, thenormalisation procedure is repeated.A state machine provides control of locking. After reset the lastvalue of the frequency control register, which has been stored inEEPROM on a regular basis, is restored. This will retune the controlledoscillator to very nearly the correct frequency. The Kalman update isdisabled and the software waits for the following all to occur (state0):a) Rubidium reference warm up input to go low or OCXO supplycurrent to drop below a threshold showing the Rubidium/OCXO haswarmed upb) A 1PPS input capture has occuredThe sofware then requests a reset of the internal clock (state 1). Thiswill normally occur on the next 1PPS to be received.Once a clock reset has occured, the Kalman filter trackingis started, however frequency corrections are not made to thecontrolled oscillator. (state 2) Each capture must be within 50us ofthe first capture, otherwise the reset state is reentered. After 100successful captures, state3 is entered provided the performancemonitor, MEANFREQERROR is below a threshold.falls below a second threshold. At this point the lock indicator isswitched off. (state 4)The following parameters set up the Kalman filter to match thecontrolled oscillator:a) Oscillator noise parameters:S1 variance of random walk FM noiseS2 variance of white FM noiseS3 variance of white phase noiseOC1OC2oscillator tuning constant in fractional frequency/voltmaximum oscillator tuning voltage in volts, assuming 0Vminimumb) 1PPS noise root variance (a function of the GPS receiver used)R measurement noise root variance in secondsThese parameters are programmed over the RS232 interface, and arestored in non volatile memory.The oscillator noise parameters may be obtained from a measuredAllen variance curve using a MathCad modelling program.18The performance monitor, MEANFREQERROR is calculated as follows:The mean of the Kalman frequency offset estimate is calculatedby means of a 5th order exponential filter. ( In the pre lock statethe mean may not be near zero, ie there may be a constant offsetbetween the controlled oscillator and GPS time)After each iteration of the Kalman filter, the current deviation iscalculated by subtracting the current frequency offset estimate fromthe running mean. This value is squared, and divided by the predictedvariance from the error covariance matrix that is maintained by thefilter. This normalises the actual deviation that is seen by the predicteddeviation from the filter. (The predicted deviation only depends uponthe system and measurement noise parameters NOT on the actualbehaviour of the system.)The normalised deviation in then filtered in a 4th order exponentialfilter. During warmup the performance measure will be high, indicatingthat the controlled oscillator is still drifting fast, relative to its predictedsteady state performance. When the controlled oscillator is stable, andthe Kalman filter has settled, the performance measure will drop belowa threshold. At this point frequency corrections will be started. (state 3)In state 3 corrections are made to the controlled oscillator. The filterand oscillator will continue to settle, until the performance monitorTel +44 (0)1803 862062Fax +44 (0)1803 86796218Technical featureFig. 1: Noise model of oscillatorto predict, and the state vectorwould contain the phase offset,frequency offset, and frequencydrift variables. The „state transitionmatrix“ defines the differentialrelationship that existsbetween the state variables overone time increment. The conceptof a system driven by noiseprocesses is important here. Ifour Rb had absolutely constantdrift, its output phase would beknown for all time once the initialdrift, frequency offset andphase offset had been determined.Data gathered a yearago would have as much validityas data an hour old. If theKalman filter is given this modelof the Rb, the results are identicalto the least squares fit of allthe data. Of course the quadraticleast squares fit assumesthat the Rb can be modelledby three constants.A more realistic physical modelwould allow the drift to vary. Ifthis varied in a deterministic way,we should add a further term towith white phase noise, whiteFM noise, and random walkFM noise due to the single anddouble integration in the model.This is shown in figure 2.The measurements are also assumedto be contaminated withgaussian white noise. In our casewe only have one measurement,that is phase offset. We do notknow that the main contributerto measurement noise, the GPSreceiver, is either white or gaussian.However this is a limitationof the simple Kalman filterthat we intend to use. If weare sure of the characteristics ofthe measurement noise, we caninclude this knowledge by addingmore terms to the state vector.We are then essentially includingthe known aspects ofthe measurement in the systemmodel.Email sales@quartzlock.comthe Rb , the filter will ignore thecorrection, and no extra settlingwww.quartzlock.comtime will be required. In effectAs well as the state vector, theKalman filter maintains a matrixthat gives the current variances(mean square error) ofrepresents the complete historyof the data), and less to the currentmeasurement. The measurementvariance, which we haveto tell the filter, also affects the„bandwidth“. If we tell the filterthat the measurement is noisy, itreduces the bandwidth.So far we have considered theKalman filter as a device foranalysing the incoming data inan optimum way. However weneed to control the Rb oscillator,and reduce the frequency offsetto zero. An elementary methodwould be to write periodic correctionsto the Rb control DAC,and wait for the Kalman filterto track out the resulting discontinuityin the measurements.However there is a much betterway. If we adjust the frequencyoffset term in the state vector atthe same time that we correctwe are defining the model of theRb to have a frequency disconovershootttrick that cknow thatment disconot knowexample wsignal disapWhen satellthere couldtinuity betwand the locnal clock. Atell the filterection of thcan tell it tmate of phareliable. Welarge numbterm of thetrix. The fiimum weigments to requickly as pit thinks itscurate, it doweight to thphase measuquency covThe Kalmaahead if meIn this caseand the errowill be updaestimated vdate the frematically. Frcan be madThe error cto reflect thin the prediWhen meathe filter wcover and twill start tois always aity of the fan unknowpected on rurements, t