Body motion compensation filter

A filter for use in determining the vertical displacement of a body travelling through water relative to a datum, the body having an accelerometer with a predetermined accelerometer gain that produces a signal indicative of the vertical acceleration of the body, the body having a pressure transducer with a predetermined pressure transducer gain that produces a position signal, corrupted by pressure transducer noise, indicative of the vertical displacement of the body with respect to the datum, the filter comprising:

• (a) a first filter portion, connectable to the pressure transducer to produce a filtered position signal, the first filter portion having a transfer function which is substantially the product of a predetermined gain divided by the pressure transducer gain and a first real rational polynomial function of the form P.sub.1 (s)/Q(s);
• (b) a second filter portion, connectable to the accelerometer to produce a filtered acceleration signal, the second filter portion having a transfer function which is substantially the product of the predetermined gain divided by the accelerometer gain and a second real rational polynomial function of the form sP.sub.2 (s)/Q(s);
• and,
• (c) a first summer connected to the first and second filter portions to produce a signal proportional to the sum of the first and second filter portion signals, where:
• P.sub.1 (s), P.sub.2 (s) and Q(s) are predetermined real polynomial functions in the complex variable s;
• p2 the degree of Q(s) is an integer n greater than 2, and the degree of each of P.sub.1 (s) and P.sub.2 (s) is less than n;
• the magnitude of P.sub.1 (s)/Q(s) is less than 1 for s=jw when w is any radial frequency within the frequency range of the pressure transducer noise;
• and
• P.sub.1 (s) and P.sub.2 (s) satisfy the relationship P.sub.1 (s)+S.sup.3 P.sub.2 (s)=Q(s).