ALFA Receiver Temperature Polynomial Fit
A. Deshpande (30 Sept. 2004)

Note: These models for T-receiver are based on measurements for all of the 14 pipelines.

download Trx polynomial fit parameters

The first line of this file consists of entries defining

• the default value as a substitude for the model when the later is not applicable,

• any additional offset to be addded as a correction not incorporated in the model (e.g. the contribution to receiver temperature from beyond the pre-amplifier stages),

• any additional scaling relevant when a variant of the modeled parameter is to be returned based on the data from this file (e.g. the ratio of low_cal to high_cal, in case this file has model for high-cal temperatures),

  • as in the present case, the first line reads 9.0,2.0,1.0 and would suggest 9 as the default estimate (say, for frequencies beyond the measured span), 2 would be addded to that suggested by the model, and no scaling is applied to estimate an additional parameter (meaning it would be redundant).

The rest of the above entries (from line 2 and onward) corresponding to each model fit refer to the following (in that sequence).

• beam no. (0 to 6 for ALFA),

• polarization channel no. (1 or 2 corresponding pol A or B, respectively),

• start and stop frequencies (MHz) for the model validity,

• reference frequency and the half-span in MHz (to be used to scale the frequency variable to -1 to +1 range before using it as an argument in the polynomial/harmonic functions fitted, e.g. the scaled frequency X = [frequency - reference_frequency]/half-span),

• No. of coefficients, n_poly, associated with the polymonial part of the fit (includes that for the 0th order; so the polymonial order is less by one), For example, the polymonial part of the model for this number as 4 would amount to c0 + c1*X + c2*X**2 + c3*X**3

• No. of coefficient pairs, n_harm, associated with the harmonic (Cos & Sin) part of the fit (where the final fit is a simple sum of the two parts)....,

  • For example, the harmonic part of the model would be (assuming n_poly = 4 in the above example),
    

    	c4*cos(pi*X/2)	+	c5*sin(pi*X/2)
    +	c6*cos(pi*X)	+	c7*sin(pi*X)
    +	c8*cos(3*pi*X/2)	+	c9*sin(3*pi*X/2)	...

    
    such that, in general, jth pair of basis functions would correspond to
    cos(j*pi*X/2) & sin(j*pi*X/2),
    with coeficient tags c#, c$ where # = (n_poly - j*2 - 2); $ = # + 1.

• the total number of coefficients to follow, say, N (= n_poly + 2*n_harm),

• the N best-fit coefficients, first those associated with the polynomial part and then the pairs associated with the harmonic part. (The model-fitting involves an iterative procedure to indentify and exclude out-liers from the data-set to be fitted, leading to hopefully somewhat robust estimation, particularly in the presence of RFI).

• the rms deviations of the data from the fit

• the degrees of freedom that the fit has benefited from

• a reference tag to relate to the plot-files showing the data & the best-fit

Note that the order in which the various model sets are listed above is not important, though useful. Results of more than one set of measurements can be listed above, and the subsequent interpreting code should be able to combine them suitably to obtain improved estimates of the relevant parameter ( 1/[rms**2] weighting is recommended). An example of such a code is fetch_from_best_fit_model.f made available for your use.

Any cribs about this blah blah may be directed to desh@naic.edu