The leading edge estimator (LEE) of a pulse signal is defined as the instant at which a filtered version of the received noisy signal passes a preset threshold. A rigorous analysis for a rectangular pulse model of the signal results in an exact probability density function for the LEE, valid within the time interval of the leading edge of the filtered pulse. Possible occurrence of the threshold crossing outside of this interval is considered to be an anomalous estimate, since it leads to a gross error in comparison with the regular cases. It is found that the density function of the LEE error is asymmetrical and therefore biased, that the probability PA of anomalous estimation increases with the filter bandwidth, thus setting a well definable limit to the latter and that, for prespecified PA, the minimum bias and variance are proportional, respectively, to R-1 and R-2, minima being obtained by allowing for the largest bandwidth compatible with PA. On the other hand, for given bandwidth the variance decreases only as R-1. Here R is the signal-to-noise energy ratio. Results are presented in form of parameterized graphs.
[1]
Jacob Ziv,et al.
Improved Lower Bounds on Signal Parameter Estimation
,
1975,
IEEE Trans. Inf. Theory.
[2]
Jacob Ziv,et al.
On the threshold effect in radar range estimation (Corresp.)
,
1969,
IEEE Trans. Inf. Theory.
[3]
Israel Bar-David,et al.
Passages and Maxima for a Particular Gaussian Process
,
1975
.
[4]
Israel Bar-David.
A sample path property of matched-filter outputs with applications to detection and estimation
,
1976,
IEEE Trans. Inf. Theory.
[5]
Don J. Torrieri.
The Uncertainty of Pulse Position Due to Noise
,
1972,
IEEE Transactions on Aerospace and Electronic Systems.
[6]
L. Seidman.
Performance limitations and error calculations for parameter estimation
,
1970
.
[7]
Don J. Torrieri.
Arrival Time Estimation by Adaptive Thresholding
,
1974,
IEEE Transactions on Aerospace and Electronic Systems.