Thesis - Leigh Moody.pdf - Bad Request - Cranfield University

Chapter 3 / Sensors / Radar Altimeter
_ _
Taking ground slopes every 100 m over an along-track distance of,
hG
g
3.7-4
( 1 − 2 g )
∆ P : = 3000 ⋅ ⋅
RMS
Equation 3.7-7
The random deviation (σM1) over flat ground was found to be 2 m to 3 m
increasing with rms ground slope,
σ
M1
: = 3 + 23.
5 ⋅ g
RMS
Equation 3.7-8
The vertically correlated noise (σM2) variation with rms ground slope,
RMS
MV
( 273.
8 − 6465 ⋅ gRMS
) gRMS
g < 0.
02 ⇒ σ : =
⋅
g > 0.
02 ⇒ σ : = 2.
6 − 15.
2 ⋅ g
RMS
MV
RMS
Equation 3.7-9
Equation 3.7-10
The rms horizontal map shifts (σM3) were 13.7 m to 25.7 m. The results
also showed that the nature of map-errors change from a 1 st to a 2 nd order
Gauss-Markov process for ground slopes in excess of 10%.
3.7.3 Measured Height Above the Ground
The injection of errors is controlled by the bit pattern of MS_RA_ER. The
reference height is corrupted at the reference rate by a time delay, height
rate limit and 1 st order dynamics,
D
P ~
ZG
f , m
: =
ϕ
D1L
ZG
( ϕ ( ϕ ( P ) ) )
RL
TD
f , m
Equation 3.7-11
A time delay of 0.01 s is followed by a height rate limit of 300 m/s and a 1 st
order lag with a bandwidth of 50 Hz. For sea-skimming missiles the low
pass filter bandwidth should be greater than twice the sea-wave encounter
frequency for sea-state estimation for missile height keeping. Constant bias,
random noise and a random walk are then superimposed.
A
ZG
f , m
SF
D ZG ( P + ϕ + ϕ + )
P : = ϕ
ϕ
f , m
CB
RN
MB1
Equation 3.7-12
The constant bias is small in solid state devices and is initialised using a
Gaussian distribution with a deviation of 2 m. The Gaussian noise has a
PSD of 0.45 m 2 /Hz at the reference frequency, equivalent to 3 m at 20 Hz.
The random walk deviation is 5 m with a correlation time of 500 s without